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CONCISE CURRICULUM Georgia s K 12 Mathematics Standards Learn It See It Explain It with Constructed Response Literacy Across the Curriculum 4th grade Student Text

FOURTH GRADE STANDARDS 4 MP Display perseverance and patience in problem solving Demonstrate skills and strategies needed to succeed in mathematics including critical thinking reasoning and effective collaboration and expression Seek help and apply feedback Set and monitor goals 4 NR 1 Recognize patterns withing the base ten place value system with quantities presented in real life situations to compare and round multi digit whole numbers through the hundred thousands place 4 NR 2 Using part whole strategies solve problems involving addition and subtraction through the hundred thousands place as well as multiplication and division of multi digit whole numbers presented in real life mathematical situations 4 PAR 3 Generate and analyze patterns including those involving shapes input output diagrams factors multiples prime numbers and composite numbers 4 NR 4 Solve real life problems involving addition subtraction equivalence and comparison of fractions with denominators of 2 3 4 5 6 8 10 12 and 100 using part whole strategies and visual models 4 NR 5 Solve real life problems involving addition equivalence comparison of fractions with denominators of 10 and 100 and comparison of decimal numbers as tenths and hundredths using part whole strategies and visual models 4 MDR 6 Measure time and objects that exist in the world to solve real life mathematical problems and analyze graphical displays of data to answer relevant questions 4 GSR 7 Investigate the concepts of angles and angle measurement to estimate and measure angles 4 GSR 8 Identify and draw geometric objects classify polygons based on properties and solve problems involving area and perimeter of rectangular figures 2 Copyright 2023 by Concise Curriculum Do not duplicate

Table of Contents Numerical Reasoning place value rounding comparisons with multi digit numbers addition and subtraction multiplicative comparisons multiplication and division involving whole numbers 4 NR 1 CHECK IN page 6 4 NR 1 1 pages 7 17 4 NR 1 2 pages 18 21 4 NR 1 3 pages 22 29 4 NR 1 4 pages 30 45 CHECK OUT page 46 4 NR 2 CHECK IN page 48 4 NR 2 1 pages 49 73 4 NR 2 2 pages 74 85 4 NR 2 3 pages 86 110 4 NR 2 4 pages 111 133 4 NR 2 5 pages 134 145 CHECK OUT page 146 Patterning and Algebraic Reasoning patterns input output tables factors multiples composite numbers prime numbers 4 PAR 3 CHECK IN page 148 4 PAR 3 1 pages 149 160 4 PAR 3 2 pages 161 163 4 PAR 3 3 pages 164 171 4 PAR 3 4 pages 172 177 CHECK OUT page 178 3 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 CHECK IN pages 180 181 4 NR 4 1 pages 182 186 4 NR 4 5 pages 182 192 4 NR 4 1 4 2 4 3 pages 193 220 4 NR 4 4 pages 221 226 4 NR 4 6 pages 227 270 CHECK OUT pages 271 272 4 NR 5 CHECK IN page 274 4 NR 5 1 pages 275 280 4 NR 5 2 pages 282 288 4 NR 5 3 pages 289 296 CHECK OUT page 297 Measurement and Data Reasoning time metric measurements distance elapsed time liquid volume mass and length 4 MDR 6 pages 300 329 Geometric and Spatial Reasoning 4 GSR 7 pages 331 341 4 GSR 8 pages 344 393 4 Copyright 2023 by Concise Curriculum Do not duplicate

Numerical Reasoning place value rounding comparisons with multi digit numbers addition and subtraction multiplicative comparisons multiplication and division involving whole numbers 4 NR 1 Recognize patterns within the base ten place value system with quantities presented in real life situations to compare and round multidigit whole numbers through the hundredthousands place 4 NR 1 1 Read and write multi digit whole numbers to the hundred thousands place using base ten numerals and expanded form 4 NR 1 2 Recognize and show that a digit in one place has a value ten times greater than what it represents in the place to its right and extend this understanding to determine the value of a digit when it is shifted to the left or right based on the relationship between multiplication and division 4 NR 1 3 Use place value reasoning to represent compare and order multi digit numbers using and symbols to record the results of comparisons 4 NR 1 4 Use place value understanding to round multidigit whole numbers 5 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK IN 4 NR 1 4 NR 1 1 1 What is 8 123 written in expanded form A 8 000 100 20 3 B 8 000 20 3 C 800 100 20 3 D 8 000 100 23 2 What is the correct standard form of 700 000 5 000 90 A 75 590 B 705 090 C 700 509 D 7 590 4 NR 1 2 3 Tammy has ten times the amount of money that her brother Sam has Sam has 70 dollars How much money does Tammy have A 70 B 7 000 C 700 D 70 000 4 The value of the 5 in the hundreds place in the number 96 585 is worth ______ times the value of the 5 in the ones place A 10 B 100 C 1000 D 10 000 4 NR 1 3 Use

4 NR 1 1 Read and Write Multi Digit Whole Numbers Expectations Read and write multi digit whole numbers to the hundred thousands place using base ten standard numerals and expanded form Learn About It A whole number is a number that does not contain any decimal numbers There are three different ways that whole numbers can be written base ten standard form expanded form and word form In fourth grade we will focus on base ten standard form and expanded form See It See the ways that whole numbers can be written Standard form base ten Expanded form Word form Base Ten Standard Form 23 897 Expanded Form 20 000 3 000 800 90 7 7 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 1 Read and Write Multi Digit Whole Numbers Expanded Form add the values of each digit See It Let s look at the number 954 This number is a three digit number made up of hundreds tens and ones How many hundreds are there in 954 9 9 hundreds look like this 900 How many tens are there in 954 5 5 tens look like this 50 How many ones are there in 954 4 4 ones look like this 4 So to write the expanded form of 954 add each value 900 50 4 Look at this method Another way 7 321 7 321 7 000 300 7 321 7 321 20 1 8 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 1 Read and Write Multi Digit Whole Numbers Learn About It A place value chart can also help you read and write whole numbers The place value of a number is the name of the position where the number is located The place value position of the number will help you determine the value or worth of the number Place Value Use a place value chart to help you determine the position of a number The position will also help you determine the value or what the number is worth See It Look at the place value chart below Hundred Tens Thousands Thousands Thousands 6 7 2 Hundreds Tens Ones 4 8 9 What is the place value position of the digit 7 Ten Thousands What is the place value position of the digit 4 Hundreds Your Turn Circle each correct answer below What is the place value position of the digit 8 ones tens hundreds What is the place value position of the digit 6 hundred thousands ones tens What is the place value position of the digit 9 ones tens hundreds 9 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 1 Read and Write Multi Digit Whole Numbers Let s Try Another One A Fill in the place value chart according to the directions given 1 Place a 5 in the ten thousands position 2 Place a 4 in the hundreds position 3 Place a 2 in the hundred thousands position 4 Place a 6 in the tens position 5 Place a 9 in the thousands position 6 Place a 7 in the ones position Hundred Tens Thousands Thousands Thousands Hundreds Tens Ones B Write the number you made above in standard form __________________________________________________ C Write the number you made above in expanded form ____________________________________________________ ____________________________________________________ ____________________________________________________ 10 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 1 Read and Write Multi Digit Whole Numbers See It Missing place values Sometimes there are missing place values This is when a 0 falls into that place value Oftentimes we want to skip that place value All that will do is make our answer incorrect Example 7 000 30 6 Look at the first numeral 7 000 How many digits are in the numeral 7 000 4 So our answer will have 4 digits Even if you only see 3 numerals that we are adding together we still need 4 digits because the number with the GREATEST place value is a 4 digit number We still have four place value positions to fill ___7_____ ___0_____ __3____ __6___ thousands hundreds tens ones In which place value did you place a 0 to hold that place value spot ________________ You Try It 6 000 80 9 Your number MUST have 4 digits since the highest place value has 4 digits ______ _____ ____ ____ 11 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 1 Read and Write Multi Digit Whole Numbers Practice It A Write each whole number below in expanded form 1 23 567 2 607 345 _______________________ ______________________ 3 4 546 119 421 088 ________________________ _______________________ 5 6 423 112 ________________________ 78 379 ______________________ B Write each expanded form numeral into standard form 7 3 000 400 20 7 _________________________ 8 40 000 3 000 70 8 ______________________ 9 423 112 ________________________ 10 78 379 ______________________ C Read each sentence below and follow the directions 11 There are 812 students enrolled in Coweta Elementary Write the number 812 in expanded form __________ 12 The Atlanta Stadium holds sixty four thousand twenty five seats Write that number in standard form _________ 13 Write the standard form for two hundred seventy five _________________________________________________ 14 Write the expanded form for the number 798 132 _________________________________________________ 12 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 1 Read and Write Multi Digit Whole Numbers D Read each question below and choose the best answer 1 40 000 5 000 700 50 is the expanded form of what number below A 4 575 B 40 575 C 45 750 D 45 705 2 What is the standard form of 200 000 5 000 70 A 200 570 B 205 007 C 250 700 D 205 070 3 What is the expanded form 4 500 000 20 000 500 of twenty eight thousand 60 9 is the expanded forty form of what number A 20 000 8 000 40 B 20 000 800 40 C 28 40 D 28 000 4 A 502 569 B 52 569 C 520 569 D 522 569 5 How do you write the expanded form of the number 607 899 6 How do you write the expanded form of the number 509 821 7 4 000 20 3 _____ 8 50 000 800 9 _____ A B C D 423 4000203 4 023 4 203 A 50 809 B 589 C 508009 D 5 809 13 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 1 Read and Write Multi Digit Whole Numbers Real World and Relevant with Constructed Response A Read About It Allison s geography class was assigned a project on the mountains of North America Her group was assigned these five mountain ranges Mount Rainier Mount McKinley Denali Mount Saint Elias Mount Blackburn and Mount Antero Their task was to find the elevations of the five mountain ranges and list them Allison s group discovered that Mount Rainier s elevation is 14 411 feet Mount McKinley s Denali elevation is 20 320 feet Mount Saint Elias is 18 009 feet Mount Blackburn is 16 390 feet and Mount Antero s elevation is 14 276 feet 1 Write the elevation of Mount Rainier in expanded form ____ ____________________________________________________ 2 Write the elevation of Mount Saint Elias in standard form __ ____________________________________________________ 3 Write the elevation of Mount Antero in standard form ____ ____________________________________________________ 4 Which mountain has an elevation of 10 000 6 000 300 90 when written in expanded form ____________________ 5 Which mountain range has an elevation of twenty thousand three hundred twenty feet when written in word form ____________________________________________________ 14 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 1 Read and Write Multi Digit Whole Numbers B Reading for Meaning 6 What is the main idea of the paragraph A Allison loves geography B The elevation of Mount Rainier is 14 411 feet C Allison s group had to find the elevations of five mountains D The Internet is a great tool for research projects 7 Who was doing a research project _______________ _______________________________________________ 8 What was the topic of the research project _________ _______________________________________________ C Vocabulary Acquisition 9 Write a bold faced word that means the same as a b c d e found heights given natural features of land collections D Write About It Opinion Writing Give your opinion if you think it is important to read numbers in standard and expanded form What could happen if someone wasn t able to read numbers in both forms Give examples to support your paragraph 15 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 1 Read and Write Multi Digit Whole Numbers Learn About It Knowing the place value of a number will help you determine the value of a number The value is what a number is worth You can use the position of the number to help you determine the number s value See It Start by finding the place value of the number Finding the place value will determine the value of the number Hundred Tens Thousands Thousands Thousands 4 6 9 Hundreds Tens Ones 2 5 7 Find the value of the 6 in the number 469 257 Look at the place value chart above to help you 1 What place is the 6 in The 6 is in the ten thousands place 2 Since the 6 is in the ten thousands place the value of the 6 is 6 ten thousands or 6 x 10 000 3 6 x 10 000 60 000 4 So the value of the 6 in the number 469 257 is 60 000 16 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 1 Read and Write Multi Digit Whole Numbers A Use the chart to help determine the value of each number Hundred Tens Thousands Thousands Thousands 1 0 3 Hundreds Tens Ones 5 8 2 1 What is the value of the 3 ________________ 2 What is the value of the 5 ________________ 3 What is the value of the 8 ________________ 4 What is the value of the 1 ________________ 5 What is the value of the 2 ________________ 6 What is the value of the 0 ________________ B Write the value of each bold faced digit below 7 56 798 ______________ 8 322 451 ____________ 9 112 980 ____________ 10 478 498 ____________ 11 506 321 ___________ 12 225 401 ____________ C Explain It Explain how to find the value of the bold faced 8 13 488 312 ________________________________________ ____________________________________________________ ____________________________________________________ 17 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 2 Recognize and Show Values of a Digit Expectations Recognize and show that a digit in one place has a value ten times greater than what it represents in the place to its right and extend this understanding to determine the value of a digit when it is shifted to the left or right based on the relationship between multiplication and division Learn About It Each place in the chart is worth 10 times the amount of the place beside it A 7 in the tens place is worth 10 times what a 7 in the ones place is worth See It Hundred Ten Thousands Thousands Thousands 2 5 6 Hundreds Tens Ones 6 4 9 The value of the 6 in the thousands place equals 6 000 The value of the 6 in the hundreds place equals 600 The 6 in the thousands place is worth 10 times what the 6 is worth in the hundreds place 600 X 10 6 000 Hundred Ten Thousands Thousands Thousands 7 2 7 Hundreds Tens Ones 1 4 9 The value of the 7 in the hundred thousands place is 700 000 The value of the 7 in the thousands place is 7 The 7 in the hundred thousands place is worth 100 times 10 x 10 the 7 in the thousands place 18 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 2 Recognize and Show Values of a Digit You Try It Tell if the value of the bold faced digit on the left is 10 times 100 times or 1 000 times the value of the bold faced digit on its right Circle the correct answer 10 times 100 times 1 000 times 1 565 10 times 100 times 1 000 times 2 443 3 92 793 10 times 100 times 1 000 times 4 17 218 10 times 100 times 1 000 times 5 25 523 10 times 100 times 1 000 times 19 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 2 Recognize and Show Values of a Digit Real World and Relevant with Constructed Response Comparing the Value of Numbers A Read each prompt below and answer with a constructed response Look at the number below 13 532 Frederick said that the 3 in the thousands place is worth ten times the value of the 3 in the tens place Gabriel said that the 3 in the thousands place is worth one hundred times the value of the 3 in the tens place 1 Who is correct Frederick or Gabriel _______________ 2 Explain how you know who is correct ______________ _______________________________________________ _______________________________________________ _______________________________________________ 3 Show It Show how you found your answer 13 532 20 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 2 Recognize and Show Values of a Digit Constructed Response Comparing the Value of Numbers B Explain how the bold faced digits below compare to each other Example 227 029 The 2 in the hundred thousands place is worth 10 times the 2 in the ten thousands place and is worth 10 000 times the 2 in the tens place The 2 in the ten thousands place is worth 1 000 times more than the 2 in the tens place 1 713 727 ____________________________________________________ ____________________________________________________ 2 828 895 ____________________________________________________ ____________________________________________________ 3 130 151 ____________________________________________________ ____________________________________________________ 21 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 3 Represent Compare and Order Numbers Expectations Use place value reasoning to represent compare and order multi digit numbers using and symbols to record the results of comparisons Learn About It We compare whole numbers to see which number is larger smaller or equal to To compare whole numbers we start in the greatest place The greatest place is the number furthest left If the digits are the same they are equal to If the first number is larger than the second it is greater than If the first number is smaller than the second it is less than

4 NR 1 3 Represent Compare and Order Numbers Let s Try Some More 1 Put the whole numbers in order from least to greatest Rewrite the numbers in the chart to help you compare 563 254 562 543 564 652 2 Put the whole numbers in order from least to greatest Rewrite the numbers in the chart to help you compare 213 276 231 267 213 267 3 Put the whole numbers in order from greatest to least Rewrite the numbers in the chart to help you compare 563 254 562 543 564 652 23 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 3 Represent Compare and Order Numbers A Place the numbers in order from greatest to least 1 115 678 115 768 115 687 ________________________ 2 234 678 243 678 234 687 ________________________ B Look at each set of numbers below Circle the GREATEST number Put a box around the SMALLEST number 3 56 798 56 987 56 897 65 789 56 879 4 16 293 16 923 16 239 16 932 19 632 C Put the set of numbers below in order from least to greatest 5 39 024 39 204 39 042 34 092 34 902 Least _______________ _______________ _______________ _______________ Greatest _______________ C Follow the directions for each problem below 9 10 Write a number that falls between the two whole numbers 546 213 and 546 321 _________________________ Which number sentence below is TRUE A 345 678 B 675 561 C 123 778 D 767 455 356 998 675 565 233 123 778 980 24 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 3 Represent Compare and Order Numbers Real World and Relevant Constructed Response A Answer each prompt with a constructed response Kyla s test on ordering whole numbers was a complete surprise All of the numbers were written in expanded form In order to place the numbers in order she would need to write them in base ten standard form first Here is Kyla s test Place the numbers in order from LEAST to GREATEST 1 2 3 4 900 20 1 900 8 10 9 1 000 900 Rewrite the numbers in standard form from LEAST to GREATEST __________ __________ __________ __________ Explain It Explain how you ordered the numbers above from least to greatest _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ 25 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 3 Represent Compare and Order Numbers Constructed Response B Answer each prompt with a constructed response 1 Which number is GREATER _______________ 10 000 7000 OR 1 000 700 Work It Explain how you found your answer ___________________________ _______________________________________________ _______________________________________________ _______________________________________________ 2 Which number is SMALLER _______________ 80 000 5 OR 80 000 50 Explain how you found your answer Work It ____________________________ _______________________________________________ _______________________________________________ _______________________________________________ 26 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 3 Represent Compare and Order Numbers Real World and Relevant with Constructed Response A Read About It Susan s class was studying populations of cities in the state of Georgia Susan was required to do a research report The teacher gave two specific criteria for the research report Susan had to research at least five cities in the state Susan also had to use the Internet to do her research Susan found a website that listed the populations of cities in Georgia for the year 2010 In 2010 the city of Atlanta had a population of 420 003 She also found that the city of Athens had a population of 115 452 Savannah is a city located along the coast of Georgia Savannah s population was 136 286 in 2010 The city of Columbus is located in the valley region of Georgia The population of Columbus was 189 885 in 2010 The other city Susan looked up was Augusta The population of Augusta was 195 844 1 Which city has the largest population _________________ 2 Which city has the smallest population _______________ 3 Order the populations from smallest to largest City Work It Population Line up the whole numbers to compare 27 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 3 Represent Compare and Order Numbers B Explain It 1 How did you find the smallest and largest populations ___ ____________________________________________________ ____________________________________________________ 2 Explain how you ordered the populations from smallest to largest ____________________________________________________ ____________________________________________________ 3 Explain the process you used to solve the problem ________ ____________________________________________________ ____________________________________________________ ____________________________________________________ C Reading for Meaning 4 What is the main idea of the paragraph A B C D Susan likes to use the computer Susan had to do a research project on city populations The population of Atlanta is 420 003 The Internet is a great tool for research projects 5 Who was doing a research project ________________ 6 What were the two requirements for the research project 1 ______________________________ 2 ______________________________ 28 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 3 Represent Compare and Order Numbers D Vocabulary Acquisition 7 Write a bold faced word that means the same as a b c d e investigation exact inhabitants standards shoreline E Write About It Write a personal narrative a time when you had to do a research project Did you use the Internet or did you read a book How did you organize your information What specific math skills did you use _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ 29 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers Expectations Use place value understanding to round multi digit whole numbers Learn About It Rounding tells us when a number is closest or closer to another numbers We can use rounding for many different types of things We may use rounding at the grocery store to see if we have enough money to buy the items that we need When rounding whole numbers the number to the right of the place to which you are rounding will tell you how to round UP or STAY the SAME If the digit to the right is 5 6 7 8 or 9 then round up If the digit to the right is 4 3 2 1 or 0 stay the same Hint 5 or more RAISE the score 4 or less let it REST See It Round 157 to the nearest ten Underline the digit in the tens place 157 Look to the digit to the right of the tens place 157 Does the 7 that is next to the tens place follow the rule of 5 or more RAISE the score or 4 or less let it REST 5 or more RAISE the score 4 or less let it REST 5 6 7 8 or 9 will RAISE the 4 3 2 1 or 0 will let the underlined digit up to the next underlined digit REST number The 7 in the number 157 follows the rule 5 or more RAISE the score So the 5 is raised up to a 6 and the 7 changes to a zero All of the numbers to the left of the place you are rounding to stay the same The 1 next to the tens place stays the same 157 160 30 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers Rounding Whole Numbers Learn About It Round the number 1 345 to the nearest thousands place Steps 1 Underline the digit in the thousands place 1 345 2 Look next door to the place where you are rounding and highlight or circle it 1 345 3 Does the 3 follow the rule 5 or more raise the score or 4 or less let it rest 4 Since the 3 follows the rule 4 or less let it rest the 1 in the thousands place will rest or stay the same 5 The 1 in the thousands place stays the same and the other numbers all change to zeros Answer It 1 345 rounds to 1 000 to the nearest thousand You Try It Round each number below to the nearest thousand 1 3 456 ______ 2 6 789 ______ 3 4 789 ______ 4 1 256 ______ 5 2 134 ______ 6 8 129 _______ 31 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers Practice It Use rounding rules to round each number below to the indicated place Hint Underline the place to which you are rounding and highlight or circle the number to the right of that place If the number highlighted or circled is 5 or more you RAISE the score of the underlined digit If it is 4 or less let it REST Everything to the right of the underlined digit becomes a zero Everything to the left of the underlined digit stays the same 1 Round each number below to the tens place 147 672 581 345 119 150 _____ ______ ______ _____ 2 Round each number below to the hundreds place 348 15 132 8 989 _____ ______ ______ 341 4 761 ______ ______ 3 Round each number below to the tens place 129 _____ 612 827 782 912 _____ ______ ______ _____ 4 Round each number below to the hundreds place 389 14 532 8 431 398 1 792 _____ _____ ______ ______ _____ 32 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers Practice It Use rounding rules to round each number below to the indicated place Hint Underline the place to which you are rounding and highlight or circle the number to the right of that place If the number highlighted or circled is 5 or more you RAISE the score of the underlined digit If it is 4 or less let it REST Everything to the right of the underlined digit becomes a zero Everything to the left of the underlined digit stays the same 1 Round each number below to the tens place 147 612 889 345 150 _____ ______ ______ 112 _____ 2 Round each number below to the hundreds place 548 16 172 8 235 320 _____ _____ ______ ______ 4 551 _____ 3 Round each number below to the tens place 246 342 186 331 139 _____ _____ _____ _____ _____ 4 Round each number below to the hundreds place 148 5 482 2 629 _____ ______ ______ 541 ______ 761 _____ 33 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers Practice It Use rounding rules to round each number below to the indicated place Hint Underline the place to which you are rounding and highlight or circle the number to the right of that place If the number highlighted or circled is 5 or more you RAISE the score of the underlined digit If it is 4 or less let it REST Everything to the right of the underlined digit becomes a zero Everything to the left of the underlined digit stays the same 1 Explain how to round 12 999 to the nearest thousand ____________________________________________________ ____________________________________________________ ____________________________________________________ 2 Explain how to round 999 to the nearest hundred ____________________________________________________ ____________________________________________________ ____________________________________________________ 3 Explain how to round 17 399 to the nearest thousand ____________________________________________________ ____________________________________________________ ____________________________________________________ 4 Explain how to round 1 999 to the nearest hundred ____________________________________________________ ____________________________________________________ ____________________________________________________ 34 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers Other methods to use when rounding 1 Use a number line to round Learn About It When a number falls halfway or more between two larger numbers then you would round to the higher number When a number falls less than halfway you would round to the lower number See It Would the number 46 round to 40 or 50 This is halfway Is 46 half way or higher or does it fall less than halfway 46 is greater than halfway so it would round up to 50 2 Use a roller coaster Learn About It The top of the roller coaster represents the halfway point of two numbers If the number being rounded is on the top or over then it will round to the higher number If the number does not go to the top then it will roll back down to the lower number 715 Does the number 712 round to 710 or 720 The number 712 will roll back down the hill to 710 714 713 712 711 710 716 717 718 719 720 35 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers More With Number Lines We can use number lines to help us decide if a number rounds up or stays closer to the ten hundred thousand ten thousand or hundred thousand Let s Try It Which thousand is 6 790 CLOSEST to Look on a number line We can put the mid point on the number line to help us with our answer Which TWO thousands would 6 790 be CLOSEST to 6 000 and 7 000 6000 6500 7000 Think about which side 6 790 would fall on Would 6 790 fall BETWEEN 6000 and 6500 or would 6790 fall BETWEEN 6500 and 7000 The number 6 790 would fall between 6500 and 7000 so the number 6 790 would round UP to 7 000 Answer It 6 790 rounds up to 7 000 36 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers Think About the number 120 789 What TWO hundred thousands is 120 789 BETWEEN 120 789 would fall between 100 000 and 200 000 100 000 150 000 200 000 Where would the number 120 789 FALL on the number line Would it fall between 100 000 and 150 000 or 150 000 and 200 000 The number 120 789 would fall between 100 000 and 150 000 so the closest hundred thousand is 100 000 You Try It Think about the number 189 567 100 000 150 000 200 000 189 567 rounds to the number __________________ 37 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers Practice It Place an X on the side where each number would fall on the number line Then round the number to the correct ten thousand 1 59 341 rounds to ___________ 50 000 55 000 60 000 2 19 461 rounds to ___________ 10 000 15 000 20 000 3 24 289 rounds to ___________ 20 000 25 000 30 000 4 32 781 rounds to ___________ 30 000 35 000 40 000 38 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers Place an X on the side where each number would fall on the number line Then round the number to the correct ten thousand 5 179 360 rounds to ___________ 170 000 175 000 180 000 6 343 391 rounds to ___________ 340 000 345 000 350 000 7 561 289 rounds to ___________ 560 000 565 000 570 000 8 429 744 rounds to ___________ 420 000 425 000 430 000 39 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers Rounding a number to the nearest 1 000 10 000 and 100 000 places Place an X on the side where the number falls This shows how to round Here s the number we will round to all three places 543 789 1 Round 543 789 to the nearest hundred thousand __________________ 500 000 550 000 600 000 2 Round 543 789 to the nearest ten thousand __________________ 540 000 545 000 550 000 3 Round 543 789 to the nearest thousand __________________ 543 000 543 500 544 000 40 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers You Try It 1 Round the number 478 721 to the nearest Hundred thousand ___________________ Ten thousand ______________ Thousand _________________ 2 Round the number 123 768 to the nearest Hundred thousand ___________________ Ten thousand ______________ Thousand _________________ 3 Round the number 532 901 to the nearest Hundred thousand ___________________ Ten thousand ______________ Thousand _________________ 4 Round the number 238 629 to the nearest Hundred thousand ___________________ Ten thousand ______________ Thousand _________________ 41 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers Practice It A Read each problem below and find the correct answer 1 Which number rounds to 40 2 Which number rounds to 20 when rounded to the when rounded to the nearest ten nearest ten A B C D 32 45 34 41 A B C D 3 Which number rounds to 120 when rounded to the nearest ten A B C D 132 125 124 149 A B C D 52 45 54 56 4 Which number rounds to 40 when rounded to the nearest ten A B C D 5 Which number does NOT round to the number 50 when rounded to the nearest ten 12 15 29 25 32 45 44 49 6 Which number does NOT round to the number 80 when rounded to the nearest ten A B C D 82 85 84 79 42 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers A Round each number below to the underlined place Show a strategy for rounding number line roller coaster etc 1 45 634 rounds to ____________ Strategy 2 75 124 rounds to ___________ Strategy 3 15 689 rounds to ___________ Strategy 4 25 036 rounds to ___________ Strategy 5 35 284 rounds to ___________ Strategy 43 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers Real Life and Relevant with Constructed Response A Read About It Jensyn Jaidyn and Jilleyn volunteered to collect cans for a food pantry Their job was to tally the can count from different schools The girls were to count the exact number of cans and then check their answers by estimating or rounding Westside Elementary School collected 12 578 cans Eastside Elementary School collected 16 235 cans and Newnan Elementary School collected 21 567 cans All of the girls were excited that each school had collected so many cans 1 Which school collected about 10 000 cans __________ _______________________________________________ 2 Which two schools collected about 20 000 cans each _________________ Work It and ________________ Strategy Make a chart round each answer to the greatest place Westside Elementary Eastside Elementary Newnan Elementary 44 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 1 4 Rounding Multi Digit Whole Numbers B Explain It 3 Explain how you estimated the can total for each school _______________________________________________ _______________________________________________ _______________________________________________ 4 Is it fair to say that the two schools who collected about 20 000 cans apiece tied in the can collection Explain _______________________________________________ _______________________________________________ _______________________________________________ C Vocabulary Acquisition 5 Which word means to count _____________________ 6 Which word means approximating ________________ 7 Which word means to gather ____________________ 8 Which word means worked for free _______________ 9 Which word means precise _____________________ 10 Which word means a storeroom _________________ 45 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK OUT 4 NR 1 4 NR 1 1 1 What is 6 723 written in expanded form A 600 70 23 B 6 000 700 20 3 B 6 000 700 2 D 6 000 70 23 2 What is the correct standard form of 200 000 500 70 8 A 20 578 B 200 758 C 200 578 D 2 578 4 NR 1 2 3 Tim has ten times the amount of money that his brother Terrell has Terrell has 50 dollars How much money does Tim have A 50 B 5 000 C 500 D 500 000 4 The value of the 5 in the ten thousands place in the number 56 583 is worth ______ times the value of the 5 in the hundreds place A 10 B 100 C 1000 D 10 000 4 NR 1 3 Use

Using part whole strategies solve problems involving addition and subtraction through the hundred thousands place as well as multiplication and division of multi digit whole numbers presented in real life mathematical situations 4 NR 2 1 Fluently add and subtract multi digit numbers to solve practical mathematical problems using place value understanding properties of operations and relationships between operations 4 NR 2 2 Interpret model and solve problems involving multiplicative comparison 4 NR 2 3 Solve relevant problems involving multiplication of a number with up to four digits by a 1digit whole number or involving multiplication of two twodigit numbers using strategies based on place values and the properties of operations Illustrate and explain the calculation equations rectangular arrays and or area models 4 NR 2 4 Solve authentic division problems involving up to 4 digit dividends and 1 digit divisors including whole number quotients with remainders using strategies based on place value understanding properties of operations and the relationships between operations 4 NR 2 5 Solve multi step problems using addition subtraction multiplication and division involving whole numbers Use mental computation and estimation strategies to justify the reasonableness of solutions 47 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK IN 4 NR 2 4 NR 2 1 A Rewrite and solve each problem below 1 16 299 8 645 ______ 3 1 567 934 ______ 2 782 323 ______ 4 885 430 ______ 4 NR 2 2 5 Andrea has 32 toy yoyos The toy store holds ten times the number of toy yoyos Andrea has How many toy yoyos does the store have ________ 4 NR 2 3 6 Toy cars cost 15 dollars apiece at the toy store Eleven toy cars would cost how much A 165 B 15 C 155 D 26 4 NR 2 4 7 Hadley is evenly dividing 65 lemons into five bowls How many lemons will she put in each bowl ________ 4 NR 2 5 8 Damien is buying four shirts that cost 18 dollars apiece His mom gave him 80 dollars to spend How much does Damien pay for the four shirts ______ How much money does he have left over _____ 48 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Expectations Fluently add and subtract multi digit numbers to solve practical mathematical problems using place value understanding properties of operations and relationships between operations Learn About It Addition properties can help you when you are adding numbers There are three addition properties the commutative property of addition the associative property of addition and the identity property of addition The commutative property of addition this property says that even when you change the order of the addends the sum is still the same Addends are the numbers that are added together to find a sum See It 32 16 16 32 BOTH models show the same SUM because of the commutative property You Try It 1 42 13 ___ 42 2 155 67 ____ 155 3 101 ___ 37 101 4 78 24 24 ___ 49 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Learn About It The associative property of addition this property says that even when you group addends differently the sum is still the same Always add the numbers in parentheses first See It Parentheses first 14 15 3 14 15 3 29 3 14 18 32 32 This is TRUE Learn About It The identity property of addition this property says that the sum of any number addend and zero is that same number addend See It 23 0 23 Any number plus zero equals that SAME number You Try It 1 49 0 ___ 2 7 0 ___ 3 0 4 ___ 4 ___ 72 72 5 28 ___ 28 6 6 0 ___ 50 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Practice It A Write commutative associative or identity property below for each problem One will be used twice 1 54 39 39 54 _________________ 3 19 0 19 ____________________ 2 61 7 8 61 7 8 ___________________ 4 617 244 244 617 ______________________ B Fill in each blank below with the correct number 5 61 73 _____ 61 6 394 0 _____ 7 83 42 42 _____ 8 709 ____ 709 C Explain It Explain which property is used to make each number sentence below true 11 41 50 7 41 50 7 _____________________________________________ _____________________________________________ 12 42 59 59 42 _____________________________________________ ___________________________________________________ 51 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Adding Using the Place Value Method Learn About It A place value algorithm is one method you can use to add whole numbers This method using the places ones tens hundreds and thousands to help you add It is a great way to organize addition See It Place Value Algorithm 732 213 First rewrite the problem horizontally 732 213 Start adding in the ones column 732 213 5 40 900 945 Start in the ones column Then move to the tens column Next move to the hundreds column Now add all of the columns Place a zero in each column to hold the place before moving to the next place value Answer It 945 52 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Let s Try Another One Sometimes there will be a two digit number answer when adding using the place value algorithm method 634 128 12 Start in the ones column 50 Then move to the tens column 700 Next move to the hundreds 762 Answer It 762 Practice It Use the place value algorithm 1 531 169 2 742 108 3 685 291 4 342 109 5 380 332 6 461 425 53 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Adding in the Hundreds Tens and Ones Columns Learn About It You can also take a three digit number and add in the hundreds tens and ones columns Write the three digit number in expanded form and then add all of the expanded forms together to find the answer The answer will be the same as the answer you get when you add the columns in regular addition See It Take each three digit number and write it in expanded form Now add all three columns to find the answer for the three digit addition A 245 532 ____ B 371 124 ____ 245 200 40 5 532 500 30 2 371 300 70 1 124 100 20 4 700 70 7 400 90 5 Answer It 777 Answer It 495 Let s Try Another One 121 546 _____ 121 100 20 1 546 500 40 6 600 60 7 Answer It 667 54 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Practice It Hundreds Tens 1 355 143 _______ 2 430 202 _______ 3 512 128 _______ 4 490 216 _______ 5 345 163 _______ 6 435 208 _______ 7 117 162 _______ 8 331 259 _______ 55 Copyright 2023 by Concise Curriculum Do not duplicate Ones

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Learn About It Traditional Algorithms Adding whole numbers to find a sum is easy You must line up the places first before you begin It is very important to line up the place values when adding whole numbers Clue words for addition are total sum total amount added together plus in all altogether etc Always rewrite the problem VERTICALLY What not to do Don t start at the highest place value 1 235 325 1 235 325 You will get the wrong answer What to do Line up the numbers starting with the ones column 1 235 325 1 235 325 Answer It Try It _____ 1 467 356 Rewrite It Answer It _________ 56 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Practice It A Find the sum of each problem below Remember to rewrite and line up the place values 1 1 125 175 Answer _____ 4 4 399 7 645 Answer _____ 2 876 13 Answer _____ 5 3 Answer _____ 788 3 234 Answer _____ 1 977 892 6 987 1 222 Answer _____ B Read each story problem below and solve 7 A stadium in Columbus GA holds 1 345 people Another stadium in Macon GA holds 2 678 people Work It How many people will both stadiums hold Answer _____________ 8 Kayla traveled 2 521 miles last summer to see her cousin in a foreign country This year Kayla traveled 6 549 miles to see her cousin How many miles did Kayla travel in all Answer _____________ Work It 57 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Practice It A Find the sum of each problem below Remember to rewrite and line up the place values 1 525 1 465 Answer _____ 4 1 745 399 Answer _____ 2 8 913 176 3 Answer _____ 5 1 288 39 Answer _____ 60 892 9 132 Answer _____ 6 50 637 8 242 Answer _____ B Read each real world problem below solve 7 A theater in Macon GA holds 1 247 people Another theater in Kennesaw GA holds 3 608 people Work It How many people will both theaters hold Answer _____________ 8 Kim traveled 598 miles last summer Work It to summer camp This year Kim traveled 409 miles to summer camp How many miles did Kim travel in all Answer _____________ 58 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Real World and Relevant with Constructed Response A Read About It A new amusement park opened up in Jack and Ben s town The boys were ecstatic that they were finally going to ride a real roller coaster The first week the park was open there were 1 678 people who bought admission tickets During the second week the park was open 2 456 people bought admission tickets By the third week there were 2 980 people who bought tickets to the park Many of those people were famished and bought hot dogs The first week 478 people bought hot dogs The second week 872 people bought hot dogs and the third week 902 people bought hot dogs 1 How many people in ALL bought admission tickets to the park during the first three weeks Work It ___________________________________ 2 How many people in ALL bought hot dogs during the first three weeks Work It ____________________________________ B Explain It 3 Explain how you worked out problems 1 and 2 ____________________________________________________ _____________________________________________________ 59 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers C Vocabulary Acquisition 4 Write the bold faced word from the passage that means the same as a b c d hungry very happy fun or leisure entrance fee D Reading for Meaning 5 Cause and Effect The cause is the why and the effect is the result Reread the real world story problem on the previous page and determine the cause and effect CAUSE _____________________________________________ EFFECT Jack and Ben were finally going to ride a roller coaster 6 Main Idea The main idea is what the story is MOSTLY about What is the main idea of this story A B C D The boys spent money on food at the amusement park Jack and Ben spent 5 25 on a drink Someone wanted a hot dog A new amusement park opened up in Jack and Ben s town 60 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Expectations Fluently subtract multi digit numbers to solve practical mathematical problems using place value understanding properties of operations and relationships between operations Learn About It Traditional Algorithms Subtracting whole numbers is EASY It s just like adding whole numbers when you LINE UP the place values The subtraction rules apply for regrouping and borrowing Always rewrite the problem VERTICALLY Key words for subtraction difference more than how many more subtract etc See It Find the difference 15 678 3 942 Remember LINE up the place values 4 16 Rewrite the problem vertically 15 678 Remember to BORROW 3 942 11 736 Let s Do Some More Find each difference Remember to LINE UP the place values 1 61 542 8 678 2 45 246 9 578 ________________ ________________ 61 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Subtract in the Hundreds Tens and Ones Columns Learn About It You can also take a three digit number and higher and subtract in the hundreds tens and ones columns Write the three digit number in expanded form and then subtract all of the expanded forms to find the answer The answer will be the same as the answer when you subtract the columns in regular subtraction See It Take each three digit number and write it in expanded form Now subtract all three columns to find the answer for the three digit subtraction A 565 132 ____ B 879 124 ____ 565 500 60 5 132 100 30 2 879 800 70 9 124 100 20 4 400 30 3 700 50 5 Answer It 433 Answer It 755 We subtract each column and then add to find the answer 62 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Practice It Use the place value method Hundreds Tens 1 755 143 _______ 2 436 202 _______ 3 579 128 _______ 4 495 213 _______ 5 398 163 _______ 6 472 241 _______ 7 787 162 _______ 8 439 209 _______ 63 Copyright 2023 by Concise Curriculum Do not duplicate Ones

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Practice It A Rewrite each problem vertically and find the difference 1 7 178 6 154 2 4 5 132 1 678 5 1 255 576 1 367 708 3 3 470 889 6 344 235 B Read the real world problem below and solve 7 Marissa needs at least 15 678 to buy a new car She has saved 4 399 Work It Make a math problem How much more money does Marissa need to buy a new car __________ 64 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Practice It A Rewrite each problem vertically and find the difference 1 63 103 12 158 2 1 255 476 3 3 970 589 4 56 132 15 672 5 6 1 344 735 81 367 508 B Read each real world problem below and solve 7 Maurice needs at least 25 678 to buy a new boat He has saved 14 379 Work It Make a math problem How much more does Maurice need to buy a new boat ___________________________ 65 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Real World and Relevant with Constructed Response A Read About It Matt wanted to go on vacation to relax He didn t want to do anything but have fun and rest He found a resort that offered many leisure activities like snorkeling and water skiing Last year Matt went on vacation for a week and spent 1 256 This year because of the leisure activities Matt wanted to participate in he spent 1 876 1 How much more did Matt spend on vacation this year compared to what he spent last year ______________ 2 How much did Matt spend both years on vacation ____________________________________________ Work It Make a math problem B Explain It 3 Explain how you solved problem 1 ________________ _______________________________________________ 4 Explain how you solved problem 2 ________________ _________________________________________________ C Vocabulary Acquisition 5 Write the bold faced word from the story that means a relaxation b take part in c to unwind d presented 66 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers D Reading for Meaning 6 Reread the story and determine the cause or effect CAUSE _____________________________________________ EFFECT Matt spent more money this year on vacation 7 Why did Matt want to go on vacation ______________ _______________________________________________ 8 How much did Matt spend on vacation the first year __ _______________________________________________ 9 How much did Matt spend on vacation the second year _______________________________________________ E Real World Write About It Write a personal narrative about a vacation you would like to take Pretend you have a budget of 2 000 you can spend How would this budget affect your choices of what you would do on your vacation ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ 67 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Learn About It Estimate means to round numbers to a certain place value The exact answer is not needed when you estimate Estimating gives you an answer that is close to the exact answer When you estimate you do not have to give the exact answer Sums are estimated when you are adding and differences are estimated when you are subtracting The directions will tell you to what place you are estimating the answer See It Estimating a Sum Round each number below to the nearest hundred then add 431 329 329 rounds to 300 431 rounds to 400 Now add your new numbers Answer It 400 300 700 is your estimated answer Check It Check the exact answer against the estimated answer Your answer should make sense or be reasonable Exact answer Estimated answer 1 431 329 760 These answers are close They are reasonable 400 300 700 68 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers You Try One Find the estimated difference of 78 52 Round each number to the nearest 10 and subtract 78 rounds to ______ 52 rounds to ______ ____ ____ ______ This is your new estimated answer Check It Check your exact answer against the estimated answer to see if the answer is reasonable 78 52 This is your exact answer Let s Try Some More Find the estimated difference of 45 12 Round each number to the nearest 10 and subtract 45 rounds to ______ 12 rounds to ______ ____ ____ ______ Check It This is your new estimated answer 45 12 ____ 69 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Practice It Estimate each real world problem below and then compare the exact answer to the estimated answer 1 There were 23 456 people that visited the theater in October and 31 567 people who visited the theater in November About how many people visited the theater both months Estimated Answer Exact Answer 2 The Ice Cream Shoppe made 12 266 during the month of June 13 899 the month of July and 11 344 during the month of August About how much money did the Shoppe make during those three months Estimated Answer Exact Answer 3 Hayden scored 6 789 points on her computer game and her sister scored 4 321 points on the same game About how many more points did Hayden score on the game than her sister Estimated Answer Exact Answer 70 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Practice It 4 Nancy s family was taking a trip across the country They traveled 567 miles the first week 827 miles the second week and 399 miles the third week About how many miles did the family travel those three weeks Estimated Answer Exact Answer 5 The Pizza Parlor sold 4 589 pizzas in January 5 234 pizzas in February and 7 231 pizzas in March About how many pizzas did the Pizza Parlor sell during those three months Estimated Answer Exact Answer 6 There were 7 344 people that attended the theater in September and 5 890 people that attended in October About how many more people attended in September than October Estimated Answer Exact Answer 71 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers Real World and Relevant with Constructed Response A Read About It Marilyn and Eva were trying to estimate the cost of a vacation they are planning for the summer The plane tickets will cost 1 567 for the two friends The cost to stay at a resort that includes food sightseeing and hotel will be 6 495 for both of them Marilyn and Eva have a budget of 8 000 This amount is the most Marilyn and Eva would be able to spend When Marilyn estimated the cost she said the vacation would cost 9 000 Eva disagreed and said the estimated cost was 8 000 Here are their two estimates A Estimated cost 1 567 6 495 2 000 6 000 B Estimated cost 1 567 6 495 2 000 7 000 1 Which one of these estimates belongs to Eva _______ 2 Which one of these estimates belongs to Marilyn ____ 3 Which one is the CORRECT estimate to the nearest thousand _____ Work It Make a math problem below to show the correct estimate The correct estimate is ___________ 72 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 1 Fluently Add and Subtract Multi Digit Numbers B Explain It 4 Explain how you decided which estimate belonged to Eva and which estimate belonged to Marilyn _______________________________________________ _______________________________________________ C Vocabulary Acquisition Use context clues to determine the meaning of the bold faced words 5 Which word means did not agree _________________ 6 Which word means total _______________________ 7 Which word means contains ____________________ 8 Which word means approximation ________________ 9 Which word means a money plan ________________ D Real World Write About It Think about a time when it would be necessary to estimate correctly when using money What could happen if you did not estimate correctly Write an informational paragraph _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ 73 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 2 Multiplicative Comparison Problems Expectations Interpret model and solve problems involving multiplicative comparison Let s Review Multiplication First Learn About It Multiplication is the same as repeated addition Sometimes it is easier to multiply than it is to use addition Multiplication will show equal groups Factors are multiplied together to get a product 6x3 See It Factors 6 3 18 Product 18 Various ways to show multiplication 1 Repeated addition 3 3 3 3 3 3 18 2 A picture of 6 groups of 3 3 An array XXXXXX XXXXXX XXXXXX 4 Skip counting on a number line 3 3 3 3 3 3 18 74 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 2 Multiplicative Comparison Problems You Try It 4 x 7 28 Factors 4 7 Product 28 There are several ways to show this multiplication sentence 1 Repeated addition 7 7 7 7 28 2 A picture of 4 groups of 7 3 An array XXXX XXXX XXXX XXXX XXXX XXXX XXXX 4 Skip counting on a number line 7 7 7 7 28 75 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 2 Multiplicative Comparison Problems Multiplying by 0 and 1 Learn About It When any number is multiplied by 0 the answer will be zero When any number is multiplied by the number 1 the answer will be the same number See It 0X6 0 0 X 356 0 1X6 6 1 X 789 789 When there are zero groups of 6 the answer is zero When there are zero groups of 356 the answer is zero When there is one group of 6 the answer is 6 When there is one group of 789 the answer is 789 You Try It 1 0 X 9 _______ 6 35 X 0 _______ 2 1 X 7 _______ 7 234 X 1 _______ 3 0 X 8 _______ 8 3 231 X 0 ______ 4 1 X 45 ______ 9 1 X 589 _______ 5 634 X 1 ______ 10 0 X 21 _______ 76 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 2 Multiplicative Comparison Problems Multiplying by 2 and 3 Learn About It When any number is multiplied by 2 the number is doubled When any number is multiplied by 3 the number is tripled See It 2 X 6 12 2 X 8 16 3 X 6 18 3 X 7 21 When there are two groups of any number the number is doubled Think of doubles when you are multiplying by 2 When there are three groups of any number the number is tripled You Try It 1 2 X 9 _______ 6 3 X 1 _______ 2 2 X 7 _______ 7 3 X 9 _______ 3 2 X 8 _______ 8 3 X 7 _______ 4 3 X 4 _______ 9 3 X 5 _______ 5 8 X 3 _______ 10 2 X 6 _______ 77 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 2 Multiplicative Comparison Problems Multiplying by 4 and 5 Learn About It When any number is multiplied by 4 the answer is four times the number you started with When any number is multiplied by the number 5 the answer is five times the number you started with See It 4 X 6 24 4 X 3 12 When you multiply by four you can double the number and then double that answer 4X6 6 6 12 12 12 24 5 X 6 30 5 X 3 15 An easy way to multiply by five is to count by fives 5 10 15 20 25 30 35 etc You Try It 1 4 X 9 _______ 6 5 X 2 _______ 2 5 X 7 _______ 7 4 X 4 _______ 3 4 X 8 _______ 8 4 X 2 _______ 4 5 X 4 _______ 9 5 X 9 _______ 5 5 X 3 _______ 10 3 X 3 _______ 78 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 2 Multiplicative Comparison Problems Multiplying by 6 7 8 and 9 Learn About It Use strategies such as making a number line drawing a picture and repeated addition when multiplying by 6 7 8 and 9 See It Draw a number line Use repeated addition Draw a picture You Try It 1 6 X 9 _______ 6 7 X 3 _______ 2 8 X 7 _______ 7 8 X 5 _______ 3 9 X 8 _______ 8 9 X 4 _______ 4 6 X 5 _______ 9 6 X 8 _______ 5 7 X 4 _______ 10 8 X 8 _______ 79 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 2 Multiplicative Comparison Problems Practice It A Use a strategy to solve each multiplication problem 1 8 X 2 _____ 2 7 X 6 _____ 3 9 X 5 _____ 4 7 X 8 _____ 5 9 X 9 _____ 6 6 X 7 _____ 7 9 X 4 _____ 8 8 X 3 _____ 9 7 X 5 _____ 10 9 X 2 _____ 11 Which is greater The answer to 8 X 7 or the answer to 9 X 6 ___________ Explain ______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ 80 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 2 Multiplicative Comparison Problems Multiplying by 10 and 11 Learn About It When any number is multiplied by 10 the answer will be a multiple of ten When any number is multiplied by the number 11 the answer will be the double of that number See It 10 X 6 60 10 X 5 50 11 X 6 66 11 X 7 77 When multiplying by 10 multiply the basic fact and then add a zero 10 X 7 1 X 7 7 7 add a 0 70 When multiplying by 11 you can double the number you are multiplying by to find the product You Try It 1 11 X 9 _______ 6 10 X 5 _______ 2 11 X 7 _______ 7 11 X 3 _______ 3 10 X 8 _______ 8 10 X 2 _______ 4 11 X 4 _______ 9 11 X 6 _______ 5 11 X 5 _______ 10 4 X 10 _______ 81 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 2 Multiplicative Comparison Problems Multiplicative Comparison and Additive Comparison Learn About It It is important for us to know the difference between multiplicative comparison problems and additive comparison problems Multiplicative Comparison focuses on comparing two quantities by showing that one quantity is a specific number of times larger than another quantity Additive comparisons focus on the difference between 2 quantities See It Multiplicative Comparison or Additive Comparison Kayla ran four miles during track practice Kylie ran 2 more miles than Kayla How many miles did Kylie run during track practice Answer It Kayla Kylie This is an ADDITIVE COMPARISON problem Kylie ran 6 miles We are COMPARING how many miles Kylie ran to how many miles Kayla ran ANSWER IT Kylie ran 6 miles during track practice 82 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 2 Multiplicative Comparison Problems Let s Try Another One Additive Comparisons Using a Number Line Quan sold 15 candy bars to support the school fundraiser Quincy sold 6 candy bars less than Quan sold How many candy bars did Quincy sell to support the school fundraiser ________ In this problem we are still comparing two quantities This time we are going backwards on the number line Quan sold 15 candy bars Quincy sold 6 candy bars LESS than Quan When we count back 6 we land on the number nine Answer It __________ Additive Comparison Bar Model Anissa runs 2 miles out of the 10 the track team is running for the week Amelia runs 3 more miles than Anissa ran that day How many miles did Amelia run ______ miles 2 miles 3 miles 5 miles Anissa and Amelia Track Team 10 miles Answer It ________ 83 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 2 Multiplicative Comparison Problems Multiplicative Comparison Problems Learn About It Multiplicative Comparison problems focus on comparing two quantities or amounts by showing that one is a specific number of times larger than the other See It Brenna brought 4 cases of bread to the Food Drive Her teacher brought two times the number of cases of bread that Brenna did to the Food Drive How many cases of bread did Brenna s teacher bring to the Food Drive FIRST QUANTITY 4 cases of bread SECOND QUANTITY two times the 1st quantity What type of problem is this This is a MULTIPLICATIVE COMPARISON problem The word times is letting us know that we are comparing a larger amount to the first quantity 4 cases of bread times 2 8 cases of bread Answer It ________ 84 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 2 Multiplicative Comparison Problems More Multiplicative Comparison Problems 1 Jamaal has six soccer balls His teammate brought two times the number of soccer balls that Jamaal has to practice How many soccer balls does Jamaal s teammate have Answer It ___________ 2 Bailey has ten balloons to bring to decorate for the Homecoming Game Bailey s classmates bring three times the number of balloons that Bailey has to decorate for the game How many balloons do Bailey s classmates have to decorate for the Homecoming Game Answer It ___________ 3 Gerald brings five batteries to school to donate to the science club Maria brings two times the number of batteries that Gerald brings to school to donate to the science club How many batteries does Maria bring to school to donate Answer It ___________ 4 Jane has 8 oranges Bev has 100 times that amount How many oranges does Bev have Answer It ___________ 85 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 Expectations Solve relevant problems involving multiplication of a number with up to four digits by a 1 digit whole number or involving multiplication of two 2 digit numbers Learn About It When multiplying whole numbers the numbers that are multiplied together are called the factors and the answer is called the product It is important to know basic multiplication facts in order to multiply greater numbers You can also use an area model to count the number of squares in each row to find the product See It Use basic facts to find the product 26 x 4 2 26 Factor X 4 Factor 104 Product See It Count the squares in each row of an area model Area Model You can count the rows and columns to find the product 1 2 3 4 There are 4 rows Count the squares in each row There are 26 So 26 26 26 26 104 86 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 Practice It A Multiply in the ones place first then the tens place 1 53 X 8 5 62 X 4 9 43 X 8 2 67 X 2 6 55 X 9 10 27 X 6 3 32 X 4 4 67 X 7 7 31 X 7 8 92 X 2 11 39 X 4 12 63 X 4 13 67 X 2 14 52 X 5 15 33 X 3 16 94 X 5 17 64 X 6 18 51 X 9 19 37 X 2 20 14 X 8 87 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 B Multiply in the ones then tens then hundreds place 1 567 X 4 2 678 X 5 3 324 X 3 4 607 X 8 7 671 X 3 8 932 X 2 5 567 X 9 6 582 X 4 9 521 X 8 10 153 X 8 11 326 X 7 12 607 X 5 11 547 X 8 12 172 X 4 13 382 X 8 14 127 X 4 15 243 X 8 16 147 X 4 17 322 X 6 18 116 X 4 88 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 B Multiply in the ones then tens then hundreds place 1 5 351 X 4 2 6 258 X 5 3 3 431 X 3 5 6 164 X 9 6 5 852 X 4 7 2 715 X 3 9 5 131 X 8 10 1 253 X 8 11 3 926 X 7 13 3 824 X 8 14 1 627 X 4 15 2 243 X 8 4 6 722 X 8 8 1 932 X 2 12 6 507 X 5 16 1 947 X 4 89 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 Learn About It Partial Products Expanded Algorithm You can use partial products to multiply whole numbers This is another method that breaks apart the factors into smaller numbers It is easy to break apart numbers into multiples of tens Example 28 would break apart into 20 2 X 10 plus 8 See It Find the product of 43 x 17 1 Break apart 43 into 40 3 2 Then break apart 17 into 10 7 3 Make a window to display the partial products 40 3 10 7 4 Now multiply each factor and place the answer in the corresponding window 10 7 Solve It 40 400 280 3 30 21 400 30 280 21 731 Add all of the partial products together 731 The answer for the problem 43 X 17 731 90 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 You Try It Area Models Partial Products Expanded Algorithm Multiply the whole numbers using the partial product window method 1 98 X 90 2 Add all of the partial products 8 2 Answer _________ 2 48 X 40 4 Add all of the partial products 8 4 Answer _________ 3 18 10 X 9 Add all of the partial products 8 9 Answer _________ 91 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 Let s Try Some More Area Models Partial Products Expanded Algorithm Multiply the whole numbers using the partial product window method 4 53 X 3 50 Add all of the partial products 3 3 Answer _________ 5 72 X 70 6 Add all of the partial products 2 6 Answer _________ 6 88 80 X 5 Add all of the partial products 8 5 Answer _________ 92 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 You Try It Partial Products Expanded Algorithm Multiply the whole numbers using the partial product window method 1 56 X 14 50 Add the partial products 6 10 4 Answer __________ 2 23 X 20 58 Add the partial products 3 50 8 Answer __________ 3 47 40 X 35 Add the partial products 7 30 5 Answer __________ 93 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 Let s Try Some More Partial Products Expanded Algorithm Multiply the whole numbers using the partial product window method 4 46 X 23 40 Add the partial products 6 20 3 Answer _________ 5 45 X 40 18 Add the partial products 5 10 8 Answer _________ 6 71 X 70 43 Add the partial products 1 40 3 Answer _________ 94 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 Learn About It Traditional Algorithm When multiplying whole numbers the numbers that are multiplied together are called the factors and the answer is called the product See It 56 x 17 56 Factor x17 Factor Product Next multiply in the tens place The 1 is in the tens place so you are really multiplying by 10 Multiply in the ones place first 4 56 x 17 392 560 56 x 17 392 Then add both products together 1 392 560 952 56 x 7 56 x 10 95 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 You Can Write an Equation when Multiplying Learn About It Write an Equation You can write an equation when multiplying whole numbers When you write an equation to solve a word problem you will use a variable to represent the unknown value See It There were 59 people that attended a carnival in May The next time there was a carnival there were 8 times the number of people there than at the first carnival 1 How many people attended the second carnival 2 The number of people that attended the 2nd carnival variable 3 Let p stand for the number of people variable that attended the second carnival 4 Write an equation 59 first concert x 8 p second carnival 5 Write a multiplication problem 59 x 8 6 How many people attended the second concert _________ 96 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 Practice It A Find each product below Remember to show your work 1 27 x 8 ______ 2 83 x 9 _______ Work It Work It 3 4 22 x 3 _______ Work It 76 x 9 _______ Work It B Read and solve the word problem below Circle the key words 5 The Civic Center has 256 rows of seats Each row contains 8 seats Work It How many seats are there in all in the Civic Center __________ 97 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 Real World and Relevant with Constructed Response A Read About It Alexis and Karcin made a wager to see which of their preferred restaurants sold the most food each year If Alexis won Karcin would do her chore of doing dishes for a month If Karcin won Alexis would do her chore of mowing the lawn for a month Neither one wanted to do the other s chores for the month Alexis thought the Hamburger Hangout sold more food each year but Karcin bet the Hotdog Heaven did They went to each restaurant to discover the truth The Hamburger Hangout sells 32 hamburgers a week Hotdog Heaven sells 100 hotdogs a month Work It Make a math problem for each restaurant Hamburger Hangout amount per year Hotdog Heaven amount per year Hint 52 weeks are in a year use for hamburgers 12 months are in a year use for hotdogs 1 Who won the bet ____________________ 2 Hamburger Hangout sells ___________ hamburgers a year 3 Hotdog Heaven sells ____________ hotdogs a year 98 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 B Explain It 4 Explain how you found your answer _______________ _____________________________________________________ C Vocabulary Acquisition 5 Match the vocabulary word with the correct definition a wager _____ b preferred _____ c chores _____ 1 jobs 2 liked the best 3 a bet D Reading for Meaning 6 CAUSE and EFFECT Determine the cause or effect CAUSE Alexis and Karcin made a bet to see who would win the contest EFFECT ____________________________________________ 7 What chore would Alexis do if Karcin won the bet ____ _______________________________________________ _______________________________________________ 8 What chore would Karcin do if Alexis won the bet ____ _______________________________________________ 9 Are Alexis and Karcin related Explain your answer _______________________________________________ _____________________________________________________ 99 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 Learn About It There are several properties rules that can help us with multiplication We will explore all of these properties to help us learn more about multiplication 1 Multiplicative Identity Property of One 2 Associative Property of Multiplication 3 Commutative Property of Multiplication 4 Distributive Property of Multiplication See It 1 Multiplicative Identity Property of One The Multiplicative Identity Property of One says that any number multiplied by the number one will equal that same number 456 X 1 456 You Try It Fill in each blank with the correct answer 1 567 x ___ 567 3 13 456 x 1 ______ 5 1 x ___ 78 7 1 x 23 899 _______ 9 _____ x 398 398 11 955 x 1 _____ 2 4 6 8 10 12 354 x 1 ______ 12 x 1 ______ _____ x 880 880 90 x 1 ______ ____ x 4 672 4 672 1 x 10 000 _____ 100 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 2 Associative Property of Multiplication The Associative Property of Multiplication says that factors in a multiplication problem can be grouped in different ways and the product will be the same no matter how the numbers are grouped See It 45 x 2 x 30 45 x 2 x 30 90 x 30 45 x 60 2 700 2 700 You Try It 1 32 x 2 x 40 ____ x 40 ______ 2 x 15 x 3 x 20 ____ 20 ______ 32 x 2 x 40 32 x ____ ______ 15 x 3 x 20 15 x ____ ______ 101 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 3 Commutative Property of Multiplication The Commutative Property of Multiplication says that factors can be multiplied in any order and the product is the same See It You Try It 6 X 7 42 so 7 X 6 42 53 X 2 106 so 2 X 53 106 4 X 5 20 so 5 X 4 20 Fill in each blank with the correct answer 1 If 5 x 6 ____ then 6 x 5 30 2 If 4 x 9 36 then 9 x 4 ____ 3 If 40 x 3 ____ then 3 x 40 120 4 If 20 x 3 60 then 3 x 20 ____ 5 If 5 x 7 ____ then 7 x 5 35 6 If 9 x 7 63 then ____ x 9 63 7 If 30 x 3 90 then ____ x 30 90 8 If 4 x 20 80 then ____ x 4 80 102 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 4 The Distributive Property Learn About It When you use the distributive property you are distributing one of the factors of the multiplication problem into two numbers See It Find the product of 23 x 56 Rewrite the 2nd factor 56 in expanded form 50 6 Then multiply each of the addends by the first factor 23 Rewrite the problem 23 x 56 50 6 23 x 50 23 x 6 1 150 Solve It 138 Add all of the products together 1 150 138 1 288 Answer It You Try It Find the product of 34 x 29 Rewrite the 2nd factor in expanded form ____ ____ Rewrite the problem 34 x ____ 34 x ____ Add the products together _____ _____ _____ Answer ________ 103 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 Practice It A Use one of the multiplication properties to solve each problem below 1 Thomas has 1 group of 94 345 toy cars Property Used __________________________ Answer ________ ______________________ 2 94 X 34 ___ 94 Property Used __________________________ Answer ________ ____________________ 3 7 X 8 X 12 7 X __ X 12 Property Used _______________________ Answer ________ 4 89 X 13 Answer ________ ____________________ Property Used _______________________ ____________________ B Find the answer to each problem Use the properties of multiplication to help you 5 78 X 89 ____ X 78 6 24 X 5 X 8 24 X ___ X 8 7 789 X 1 ______ 8 34 X 13 ______ 104 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 Estimating Products Learn About It Estimate means to round numbers to a certain place value Estimating gives you an answer that is close to the exact answer When you estimate you do not have to give the exact answer Products are estimated when the problem involves multiplication Follow the directions when rounding to a certain place Sometimes using compatible numbers will help you when estimating Be sure to check your estimated answer with the exact answer See It Estimating a Product Round each number to the nearest 10 then multiply 43 X 32 43 rounds to 40 32 rounds to 30 Now multiply your new numbers Answer It Check It 43 X 32 186 1290 1 376 40 X 30 1 200 is your estimated answer Is your exact answer of 1 376 close to your estimated answer of 1 200 Yes Your estimated answer is a reasonable answer 105 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 You Try One Find the estimated product of 6 X 71 Round the two digit number to the nearest 10 and multiply 6 keep the 6 71 rounds to ____ 6 X ____ _____ Check It Find the exact answer and check it to see if it is close to your estimated answer 71 X 6 This is your new estimated answer Compatible Numbers Learn About It Sometimes compatible numbers can be used to estimate an answer Compatible numbers are numbers that are easy to multiply and divide See It Alexis has 37 baskets Each basket holds about 7 pieces of fruit About how many pieces of fruit does Alexis have Think About It Think of numbers that can be multiplied easily 37 is close to 40 and 7 is close to 10 So 40 X 10 400 Answer It Alexis has 400 pieces of fruit 106 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 Practice It A Estimate your answer by rounding to the greatest place Compare your estimate to the exact answer 1 Kara Joy has to pay 145 dollars a month for 6 months for her new scooter About how much will she pay for her scooter ______ Estimated price ______ Price of scooter _______ 2 Claire is paying 56 dollars a month for her gym membership About how much will Claire pay a year for her gym membership ______ Estimated price _____ Gym membership _____ 3 Mrs Nickelson s class collected 112 cans for 9 months for the food drive About how many cans did Mrs Nickelson s class collect _______ Estimated amount ____ Cans collected ________ 107 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 Practice It 4 Mr Green buys 1 431 flowers a month for his Flower Shop About how many flowers does Mr Green buy in 8 months ______ Estimated flowers _____ Exact answer _______ 5 Molly pays 189 dollars a month for dog food for her pet sitting business About how much does Molly spend in 7 months ______ Estimated amount______ Exact answer _______ 6 Mandy has 52 jars with 95 jelly beans in each jar About how many jelly beans does she have in all of the jars ______ Estimated amount_____ Exact answer ________ 108 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 Real World and Relevant and Constructed Response A Read About It Haley was assigned math homework by her teacher Mrs Johnson She was instructed to work out four math problems and use one of the multiplication properties the class studied that week to assist her Here is Haley s homework 1 457 299 x 1 ______ 2 75 x 23 ______ B Explain It Explain the properties Haley will use for problems 1 4 1 _________________________________________________ ____________________________________________________ 2 _________________________________________________ ____________________________________________________ 3 _________________________________________________ ____________________________________________________ 4 _________________________________________________ ____________________________________________________ 109 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 3 Solve Relevant X Problems 4 by 1 and 2 by 2 C Vocabulary Acquisition 5 Match the vocabulary word with the correct definition a b c d assigned _____ instructed _____ properties _____ assist _____ 1 2 3 4 a set of rules aid or help given to trained D Reading for Meaning 6 Who gave Haley math homework ________________ 7 How many properties did Haley s math class learn about ____ _______________________________________________ 8 The main idea is what the story is MOSTLY about What is the main idea of this story A B C D Haley is in fourth grade Mrs Johnson is a great teacher Fourth grade math is difficult Haley used the multiplication properties when she did her homework E Write About It Write an opinion piece on homework Do you think doing homework is valuable Why or Why not Give examples of why you think homework is valuable or is not valuable 110 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Learn About It Division is the opposite of multiplication Division and multiplication are inverse operations When you divide to show equal groups you can use multiplication to check your answer There are three parts to a division sentence the dividend the divisor and the quotient Here are some ways to show division 1 related multiplication facts 2 repeated subtraction 3 use a number line 4 draw an array 1 Relate Multiplication Facts to Division Learn About It You can relate multiplication facts to division facts They are inverse operations If you know a related multiplication fact you can answer a division problem See It 63 9 Think About It Do you know any multiplication facts with 63 and 9 Yes So 9 X something 63 9 X 7 63 Answer It 63 9 7 111 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors How to Check Division with Multiplication When you have finished a division problem you can check your answer with multiplication You multiply the quotient answer by the divisor the number you are dividing by If there is a remainder then you add the remainder to your answer If your answer is correct you will get the dividend the number you started with See It 2 3 or 4 digit dividend problems 2 88 8 08 4 4 44 Check with multiplication 44 X2 88 Let s Try Another One HTO 3 936 9 03 06 6 0 3 1 312 x 3 936 2 312 112 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Repeated Subtraction Learn About It You can use repeated subtraction to find answers to division problems Start with the dividend and subtract the divisor until you end up with the number zero The number of times you subtract the divisor is the quotient See It 24 3 ____ Start with the dividend 24 and subtract the divisor 3 until you have zero 24 3 21 21 3 18 18 3 15 15 3 12 12 3 9 9 3 6 6 3 3 3 3 0 How many subtraction problems did you make ______ There are 8 subtraction problems so 24 3 _____ 3 Use a Number Line to Show Repeated Subtraction See It 24 3 ____ Start at 24 and subtract 3 on the number line until you reach 0 How many jumps did you make ______ So 24 3 ____ 113 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Draw an Array to Show Division Learn About It You can draw an array to help show division The dividend is the total number in the division problem You take the dividend and put it into an array with rows that represent the dividend The number of pieces in each group in the array represents your quotient See It 27 3 ____ Total pieces in the array 27 number of rows in the array 3 Draw an array that contains a total of 27 pieces divided into 3 rows The number of pieces in each row represents your quotient XXXXXXXXX XXXXXXXXX XXXXXXXXX Count the number of Xs in each row There should be an equal number in each row There are 9 Xs in each row Answer It So 27 3 9 There are 9 pieces in each row 114 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Practice It A Use a strategy to answer each division problem 1 45 9 ____ 2 40 5 ____ 3 14 7 ____ 4 42 7 ____ 5 48 8 ____ 6 32 8 ____ 7 45 5 ____ 8 40 8 ____ 9 44 11 ____ 10 72 8 ____ 11 16 8 ____ 12 63 7 ____ B Read each word problem and use a division strategy 13 Dana has 45 pencils to divide evenly among 9 classmates How many pencils will each classmate receive _____ 14 Ali loves to bake cookies Ali brings 25 cookies to school She wants to give them to 5 friends at lunch How many cookies will each friend get ______ 15 Dwayne has 60 trucks to divide between 6 friends How many trucks will each friend receive ______ 115 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Division Facts A Use a strategy and show each division problem 1 Kendall has 45 pencils She wants to put an even amount into five jars How many pencils will she put into each jar _______ 2 There are thirty cars at the car lot The owner needs to load all of the cars onto 5 trucks How many cars will go onto each truck ______ 3 There are seven storage bins at the grocery store The stocker must put 49 boxes evenly into the seven storage bins How many boxes will go in each bin _______ 4 How can Kyle put thirty two mushrooms onto four pizzas evenly ________ 116 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Real World and Relevant with Constructed Response A Read About It Jeffery Matthew Jose and Miguel were all going to the movies When they went to the ticket booth the attendant told them that for all four of them to attend the movie it would cost a total of 36 00 dollars After they purchased their tickets they went to the concession stand At the concession stand they spent a total of 40 00 for popcorn and drinks They spent an equal amount on popcorn as they did on drinks 1 How much did each person spend on their ticket _____ _______________________________________________ 2 How much did each person spend on popcorn _______ _______________________________________________ 3 How much did each person spend on a drink ________ _______________________________________________ Work It Strategy Make a chart Ticket Popcorn Drink 117 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors B Explain It 4 Explain how you found the answers to problems 1 3 _______________________________________________ _______________________________________________ _______________________________________________ C Vocabulary Acquisition 5 Match the vocabulary word with the correct definition a b c d booth _____ attendant _____ attend _____ concession ____ 1 2 3 4 stall be present there assistant drinks and snacks D Reading for Meaning 6 Who went to the movies _______________________ _______________________________________________ 7 How much did they ALL spend on tickets ___________ _______________________________________________ 8 How much did they ALL spend at the concession stand _______________________________________________ _______________________________________________ 118 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Learn About It Place Value Division See It Kiera has a box of 243 building blocks She wants to put the blocks into 8 groups How can we see how many blocks are in each group Let s write the number 243 in expanded form 240 3 How many times will 8 go into 24 3 Using what we know about zeros how many 8 will go into 240 30 What s left The number 3 is left Will 8 go into 3 No so 3 is the remainder Answer It So 243 divided by 8 30 remainder 3 Let s Try Another One Marcus has 455 letters to send to pen pals for his class project He is going to divide the letters into 5 boxes What is 455 5 Step 1 Write 455 in EXPANDED FORM 400 50 5 Step 2 ____ X 5 400 80 X 5 400 Step 3 ____ X 5 50 10 X 5 50 Step 4 ____ X 5 5 1X5 5 Answer It 80 10 1 91 So 455 5 91 119 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Place Value Algorithm Learn About It We can divide using place value division We will use our knowledge of place values to divide Think About It Think about multiplying with zeros How many times will 5 go into 1500 Division 5 1525 1500 25 25 0 CHECK IT 305 X 5 300 5 305 2 305 X 5 1525 120 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Practice It A Solve each division problem below using place value division Check your work with multiplication Write the dividend in expanded form 1 3 39 30 30 9 3 ___ 9 3 ___ Add the quotients together ___ ___ ____ Answer It 39 3 _____ 2 5 95 3 4 84 4 6 36 121 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors B Solve each problem below using place value division strategies 5 5 55 6 2 86 7 3 93 8 2 42 122 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Practice It A Solve each division problem Check your work with multiplication 1 3 393 2 5 955 3 4 896 4 6 336 123 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors 5 5 3 150 6 2 8 362 7 8 8 4 086 2 4 223 124 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Word Problems 1 Jane has 7 689 apples to put into 9 crates How many apples will go in each crate _____ Are there any apples left over _____ Work It 2 Jan has 1 689 oranges to put into 3 crates How many oranges will go in each crate _____ Are there any oranges left over _____ Work It 3 Amy has 885 flowers to put into 5 vases How many flowers will go in each vase _____ Are there any flowers left over _____ Work It 125 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Learn About It When multiplying by 10 100 or 1 000 you will ADD the same number of zeros as in the 10 100 or 1 000 Dividing by a multiple of 10 100 or 1 000 is just the opposite Instead of adding zeros you would TAKE AWAY zeros Remember when DIVIDING by a multiple of 10 100 or 1 000 your answer is going to be smaller than the number you started with 40 10 See It Take 1 zero away from the 40 There is 1 zero in the number 10 40 10 4 Answer It Let s Try Another One 40 10 4 500 10 ___ How many zeros are in 10 1 Take 1 zero away from 500 500 10 500 When you take 1 zero away from 500 you get 50 Answer It 500 10 50 Any 0 in the divisor cancels out a 0 in the dividend 126 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Practice It A Use the patterns to divide Problem of zeros to subtract Answer 430 10 4 300 10 43 000 10 4 300 100 43 000 100 43 000 1 000 430 000 1 000 B Read the problems and solve with division 1 There are 6 000 oranges delivered every week to the market The oranges are divided evenly into 100 crates How many oranges are in each crate _____ 2 The post office has 45 000 letters to deliver this week There are 100 trucks that will take the letters How many letters will each truck deliver _____ 127 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Practice It A Find each quotient below 1 780 10 _____ 2 30 10 _____ 3 600 100 _____ 4 500 10 _____ 5 70 10 _____ 6 200 100 _____ 7 900 10 _____ 8 90 10 _____ 9 1 700 100 _____ 10 4 000 100 _____ 11 700 10 _____ 12 2 000 1 000 _____ 13 900 10 _____ 14 90 10 _____ 15 2 700 10 _____ 16 8 000 10 _____ 17 200 10 _____ 18 9 000 10 _____ 128 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Real World and Relevant with Constructed Response B Read the story problem and solve Jane s homework in math was to divide 2 400 by the number 100 Jane worked the problem and got an answer of 240 When Jane s teacher checked her problem the next day she marked Jane s answer as incorrect Jane s response was one of astonishment Jane was surprised she did not get the right answer 1 Who had math homework ______________________ 2 Why was Jane surprised the next day _____________ _______________________________________________ _______________________________________________ C Explain It 3 Explain what Jane did INCORRECTLY on her homework __ ____________________________________________________ ____________________________________________________ 4 Explain what the correct answer is to the homework ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ 129 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Estimating Quotients Learn About It Estimate means to round numbers to a certain place value Estimating gives you an answer that is close to the exact answer When you estimate you do not have to give the exact answer When you are dividing you are estimating the quotient The directions will tell you to what place you are estimating the answer Sometimes using compatible numbers will help you when estimating Be sure to check your estimated answer with the exact answer See It Estimating a Quotient 179 9 179 9 179 rounds to 180 9 rounds to 10 Now divide 180 10 18 Answer It 18 is your estimated answer Check It 179 9 9 179 171 8 Answer It 19 19 remainder 8 130 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors You Try One Find the estimated quotient of 123 5 Round the first number to the nearest hundred and then divide 123 rounds to ____ Check It Find the exact answer and check it to see if it is close to your estimated answer 5 stays the same 5 123 _____ 5 _____ Exact Answer _______ Estimated Answer ______ Is your answer reasonable ______ Let s Try Some More Round to the greatest place 1 345 3 ____ 2 35 4 ____ 3 567 6 ____ 4 67 7 ____ 5 912 9 ____ 6 91 9 ____ 7 756 8 ____ 8 17 5 ____ 9 231 2 ____ 10 23 4 ____ 11 456 2 ____ 12 89 4 ____ 13 781 4 ____ 14 167 5 ____ 131 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Practice It A Round to the nearest hundred or use compatible Numbers then compare to the exact answer 1 Joy paid a total of 898 dollars over 9 months for a new couch About how much did Joy pay a month for the new couch ______ Estimated answer _____ Exact answer ______ 2 Carol has 4 buckets with 319 apples in the buckets altogether About how many apples are in each bucket _______ Estimated answer _____ Exact answer _______ 3 Mrs Zern s class collected a total of 421 cans during 6 months for the food drive About how many cans did Mrs Zern s class collect each month _______ Estimated answer _____ Exact answer ________ 132 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 4 Division with 4 Digit Dividends 1 Digit Divisors Practice It 4 Mr Grant has 559 flowers to plant an equal amount in eight flower beds About how many flowers will go in each bed _______ Estimated answer ____ Exact answer ______ 5 The movie theater seated a total number of 933 people during the three matinee shows If each show had the same number of people then how many people attended each show _______ Estimated answer ____ Exact answer ________ 6 Brandi has 719 doughnuts to place in 9 doughnut trays About how many doughnuts will go in each tray ______ Estimated amount ____ Exact answer ________ 133 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 5 Solve Multi Step Problems Learn About It Interpreting remainders Sometimes there will be remainders or leftovers in a division problem It is important to know how to interpret the remainder See It Michaela s class is going on a field trip The teacher will have the students sit together at tables in groups of 5 There are 34 students in the class How many tables will be needed to seat all of the students in Michaela s class ________ Solve It You will divide the 34 students by the 5 groups Answer It 6 r 4 5 34 6 30 4 Can the answer be 6 NO because there is a remainder of 4 You must ADD an extra table so everyone will have a seat Answer It The answer is 7 because 6 1 7 You Try It Miguel went on a field trip to an amusement park There are 47 students that want to ride on a roller coaster The seats on the roller coaster hold 6 students How many seats are needed to give all of the students a seat _______ Work It Answer It 134 Copyright 2023 by Concise Curriculum Do not duplicate ________

4 NR 2 5 Solve Multi Step Problems Practice It A Solve each division problem below and interpret the remainder 1 The soccer van holds 7 people How many vans will the team need if there are 23 players on the team ______ vans are needed 2 Each class in fourth grade can hold 21 students How many classes are needed if there are 95 students in fourth grade ______ classes are needed 3 Each bike rack at school can hold 10 bikes How many bike racks are needed if 55 bikes need to be locked at the rack ______ bike racks are needed 4 Six students can sit at each lunch table in the cafeteria How many lunch tables are needed if Ms Hall has 20 students in her class ______ lunch tables are needed 135 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 5 Solve Multi Step Problems B Solve each division problem below and interpret the remainder 1 The most popular ride at the amusement park can hold seven people How many times will the ride need to run if twenty four people want to ride The ride will need to run ______ times 2 Meryl can put six flowers in a basket at the flower shop How many baskets will Meryl use if she has thirty four flowers ______ baskets will be used 3 Each box can hold nine cookies How many boxes will Dana need if she makes twenty five cookies ______ boxes are needed 4 Eight students can sit at each lunch table in the cafeteria How many lunch tables are needed if Ms Smith has twentyseven students in her class ______ tables are needed 136 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 5 Solve Multi Step Problems Real World and Relevant with Constructed Response A Read About It Brandi wants her parents to purchase a new computer for her to use for her schoolwork Brandi s parents decide not to buy her a computer They want to teach Brandi responsibility by letting her earn the money herself To earn the money Brandi decides to sell magazine subscriptions Brandi s goal is to sell 2 544 magazine subscriptions over the course of six months If Brandi wants to achieve her goal how many subscriptions will Brandi need to sell each month 1 How many subscriptions will Brandi need to sell each month to meet her goal ______ Work It B Vocabulary Acquisition Context Clues 2 Write the word from the story that means the SAME as a b c d attain buy objective duty C Reading for Meaning 3 Who decides to teach Brandi responsibility ________ _______________________________________________ 4 CAUSE and EFFECT The cause is the why and the effect is what happened CAUSE _____________________________________________ EFFECT Brandi needs to sell 2 544 subscriptions in 6 months 137 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 5 Solve Multi Step Problems 5 Why does Brandi want a new computer ____________ _______________________________________________ 6 What is the MAIN IDEA of the story A Brandi likes computers B Brandi s parents are strict C Brandi is learning responsibility D Magazines are fun to read D Write About It Do you think Brandi s parents should have given her the money or made her learn some responsibility Write an opinion paragraph telling why you think Brandi should learn responsibility and earn the money or if you think her parents should have given her the money _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ 138 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 5 Solve Multi Step Problems Real World and Relevant with Constructed Response A Read About It Leah and Bailey both wanted to join the soccer club Both of the girls enjoyed being outdoors and playing a sport Of course playing soccer is great exercise The flyer that the soccer club sent out offered a significant discount if you signed up within the first week Leah and her mom went to sign up for the soccer club the first week of sign ups Leah s mom would have to pay 149 00 a month for three months The fee included a uniform a pair of cleats and registration Bailey and her mom forgot to sign up during the first week so Bailey s fee was higher than Leah s fee Bailey s mom would have to pay 159 00 dollars a month for three months 1 Round to the nearest hundred a Bailey s mom paid ____ b Leah s mom paid ____ 2 Round to the nearest ten a Bailey s mom paid ____ Work It b Leah s mom paid ____ Make a chart and a math problem Bailey s mom Leah s mom 139 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 5 Solve Multi Step Problems B Explain It 3 Explain which answer is nearest the exact answer rounding to the nearest hundred or rounding to the nearest ten Why _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ C Vocabulary Acquisition Use context clues to determine the meaning of the bold faced words 4 Which word means a large amount _______________ 5 Which word means to come with _________________ 6 Which word means liked _______________________ 7 Which word means act of signing up ______________ 8 Which word means an organization ______________ D Write About It Write in your math journal Think about a time when you wanted to join an activity or play a sport Why would it be necessary for your parents to know the costs of the activity or sport before you joined Write a narrative paragraph describing an experience you ve had playing a sport 140 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 5 Solve Multi Step Problems More Multi Step Word Problems 1 Dan is buying 15 cupcakes that cost 2 dollars apiece How much does Dan pay for the cupcakes _________ Dan takes the cupcakes to school and divides the 15 cupcakes evenly among 3 friends How many cupcakes will each friend receive ______ 2 Alice bakes seventy two pumpkin muffins She sells the muffins at the school bake sale for 3 dollars apiece How much money will Alice make at the bake sale Alice made _________ dollars at the bake sale Alice owes her mother for the ingredients she bought Alice owes her mother 21 dollars for the ingredients How much money is left after Alice pays her mother for the ingredients Alice has _________ dollars left after paying her mom 3 Monty has 50 dollars to spend at the store on shirts for school He buys three shirts that cost 14 dollars apiece How much does Monty spend on shirts ________ How much money does Monty have leftover ________ 4 Cooper wants to buy a new motor scooter Cooper can spend as much as 800 00 The payments on the scooter he wants to buy are 139 00 for six months Can Cooper afford the new motor scooter YES or NO Explain Your Answer ___________________________ _____________________________________________ 141 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 5 Solve Multi Step Problems Real World and Relevant with Constructed Response A Read About It Grace and Ali got summer jobs toiling in a fashion warehouse Both of them were to assist the clothing manager in sorting the shoes and clothes to be delivered to stores around the country Every Monday they would receive a list of the items that needed to be shipped to the different stores Grace and Ali would have to use their math skills and estimate how many items would go into each box They decided to round the larger numbers to the nearest ten Here is the list they received on Monday shoes 422 pairs to go into 7 boxes shirts 539 to go into 6 boxes pants 241 to go into 6 boxes dresses 719 to go into 8 boxes Help Grace and Ali estimate how many items will go into each box 1 shoes ___________ 2 shirts ____________ 3 pants ___________ 4 dresses ____________ Work It shoes Make a math problem for each item shirts pants dresses Round the larger numbers to the nearest ten before estimating 142 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 5 Solve Multi Step Problems B Explain It 5 Explain how to estimate a quotient Give an original example _______________________________________________ _______________________________________________ _______________________________________________ Example _______________________________________ C Vocabulary Acquisition 6 Write the bold faced word that means the same as a b c d working transported organizing help D Reading for Meaning 7 Cause and Effect The cause is the why and the effect is the result Reread the story problem and determine the cause and effect CAUSE Every Monday Grace and Ali would receive a list EFFECT ____________________________________________ 143 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 5 Solve Multi Step Problems A Read About It Daniel Preston Carson and Sammy were going on a camping trip The local sporting goods store was offering discounts in its outdoor department All the boys went together to purchase their equipment Everyone needed a flashlight a water bottle a hat and a pair of gloves The flashlights were on sale for five dollars apiece The water bottles were on sale for three dollars apiece The hats were regular price and they were seven dollars apiece Two pair of gloves cost six dollars 1 How much did each boy spend on camping equipment _____ ____________________________________________________ 2 How much did the boys spend altogether on their equipment _______________________________________ ____________________________________________________ Work It Strategy Make a chart Daniel Preston Carson Sammy 144 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 2 5 Solve Multi Step Problems B Explain It 3 Explain how you found how much each boy spent on equipment ____________________________________________________ ____________________________________________________ 4 One of the items the boys needed to buy was two pairs for six dollars How did you find out the cost of a pair of gloves for one boy Explain how you found your answer _____________________________________________________ _____________________________________________________ C Reading for Meaning 5 Who was going on a camping trip ________________ _______________________________________________ D Vocabulary Acquisition 6 Write a bold faced word that means the same as a reductions b buy c gear or tools d residential e outside 145 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK OUT 4 NR 2 4 NR 2 1 A Rewrite and solve each problem below 1 4 399 7 645 ______ 3 567 134 ______ 2 788 3 234 ______ 4 981 477 ______ 4 NR 2 2 5 Deandre has three toy cars His brother Derrick has four times the number of toy cars Deandre has How many toy cars does Derrick have ________ 4 NR 2 3 6 Toy cars cost 12 dollars apiece at the toy store Seven toy cars would cost how much A 19 B 84 C 72 D 12 4 NR 2 4 7 Harold is evenly dividing 95 gold fish in five ponds How many goldfish will he put into each pond ________ 4 NR 2 5 8 Damien is buying three shirts that cost 15 dollars apiece His mom gave him 55 dollars to spend How much does Damien pay for the three shirts ______ How much money does he have left over _____ 146 Copyright 2023 by Concise Curriculum Do not duplicate

Patterning and Algebraic Reasoning patterns input output tables factors multiples composite numbers prime numbers 4 PAR 3 Generate and analyze patterns including those involving shapes input output diagrams factors multiples prime numbers and composite numbers 4 PAR 3 1 Generate both number and shape patterns that follow a provided rule 4 PAR 3 2 Use input output rules tables and charts to represent and describe patterns find relationships and solve problems 4 PAR 3 3 Find factor pairs in the range 1 100 and find multiples of single digit numbers up to 100 4 PAR 3 4 Identify composite numbers and prime numbers and explain the relationship with the factor pairs 147 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK IN 4 PAR 3 4 PAR 3 1 A Circle the pattern that matches each rule below 1 Add 8 a 4 12 20 28 2 Subtract 5 a 4 6 12 18 b b 5 10 15 20 25 20 15 10 B Draw the next 3 shapes in the pattern below 3 4 PAR 3 2 C Draw the shapes for Stage 3 below 4 Stage 1 Stage 2 Stage 3 4 PAR 3 3 D Circle the correct MULTIPLE below 5 Which is a MULTIPLE of 8 a 18 b 16 4 PAR 3 4 E Circle each COMPOSITE number below Make a box around each PRIME number below 148 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 1 Generate Both Number and Shape Patterns Expectations Generate both number and shape patterns that follow a provided rule Learn About It When a series of numbers follows a rule we call that a pattern Once you find the rule of the pattern you will know how to find the next number or term in the pattern PATTERNS Ask yourself if the numbers are the numbers increasing getting larger or decreasing getting smaller INCREASING DECREASING If the numbers in the pattern are getting larger then you are using addition or multiplication If the numbers in the pattern are getting smaller then you are using subtraction or division Example Pattern 2 7 12 17 Ask yourself Are the numbers in this pattern increasing or decreasing INCREASING The numbers in this pattern are increasing Look at each number in the pattern Can you multiply the first number times another number to get to the next number or can you add a number to the next number to get the next number Addition Multiplication You can add each time to get to the next number in the pattern You cannot multiply each time to get to the next number in the pattern Think What can you add to each number 2 __ 7 7 __ 12 12 __ 17 You can add 5 to each number RULE Add 5 149 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 1 Generate Both Number and Shape Patterns Practice It A Find the rule for each pattern Ask yourself these questions Is the pattern increasing If yes you are adding or multiplying Is the pattern decreasing If yes you are subtracting or dividing Pattern Rule 1 14 12 10 8 6 4 2 2 30 25 20 15 10 5 0 3 3 6 12 24 48 96 4 4 8 12 16 20 24 28 B Find the missing numbers in each pattern RULE 1 32 29 ___ 23 20 ___ ________ 2 6 12 ___ 24 30 36 ___ ________ 3 20 18 16 ___ 12 ___ 8 ________ 4 5 10 ___ 20 25 ___ 35 ________ 150 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 1 Generate Both Number and Shape Patterns Practice It A Match each pattern with the correct rule 1 Add 8 2 Add 10 _______ _______ a 15 25 35 45 55 b 3 11 19 27 35 3 Multiply by 4 _______ c 0 20 40 60 80 4 Divide by 2 _______ d 1 4 16 64 256 5 Add 20 _______ e 80 40 20 10 5 B Find the missing terms in each pattern below Rule 6 5 12 _____ 26 33 _____ __________ 7 42 35 28 _____ 14 _____ __________ 8 25 21 _____ 13 9 _____ __________ 9 2 5 _____ 11 14 _____ __________ 10 40 35 30 _____ 20 _____ __________ 11 20 21 _____ 23 24 _____ __________ 151 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 1 Generate Both Number and Shape Patterns Practice It C Writing Patterns Use each rule given below and write a pattern with at least five terms that follows each rule 1 Multiply by 6 Pattern ______________________________________ 2 Add 14 Pattern _____________________________________ 3 Subtract 11 Pattern ______________________________________ 4 Divide by 2 Pattern ______________________________________ 5 Add 9 Pattern ______________________________________ 6 Multiply by 3 Pattern ______________________________________ 7 Multiply by 5 Pattern ______________________________________ 152 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 1 Generate Both Number and Shape Patterns Real World and Relevant with Constructed Response A Answer each prompt with a constructed response When Mrs Kelley was making a math quiz for her students on patterns she decided to make the quiz more challenging than the previous quiz she had given She wanted her students to find errors in the patterns that would be on the quiz This way she would really know if her student s understood patterns and the rules for finding patterns Here is the quiz Mrs Kelley gave her students 1 Rule Multiply by 3 Pattern 5 15 45 135 575 2 Rule Subtract 30 Pattern 150 120 90 50 30 3 Rule Divide by 2 Pattern 4 400 200 100 40 25 Rule Add 15 Pattern 10 25 30 55 70 153 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 1 Generate Both Number and Shape Patterns Constructed Response B Help Mrs Kelley s students with their math test 1 Rule Multiply by 3 Pattern 5 15 45 135 575 What is the error ________________________________________ Explain how to correct the error ____________________________ ______________________________________________________ 2 Rule Subtract 30 Pattern 150 120 90 50 30 What is the error ________________________________________ Explain how to correct the error ____________________________ ______________________________________________________ 3 Rule Divide by 2 Pattern 400 200 100 40 25 What is the error ________________________________________ Explain how to correct the error ____________________________ ______________________________________________________ 4 Rule Add 15 Pattern 10 25 30 55 70 What is the error _______________________________________ Explain how to correct the error ____________________________ ______________________________________________________ 154 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 1 Generate Both Number and Shape Patterns Learn About It Patterns with Figures and Shapes There are also patterns with figures or shapes You can look at the figures and find the rule See It 1 What is the rule for this pattern 1 circle 1 oval 1 triangle and 1 square 2 What is the 14th figure in this pattern An oval There are 12 figures in the pattern Count two more figures to find the 14th figure Let s Try Another One 1 What is the rule for this pattern __________________ 2 What is the 12th figure in this pattern _____________ 3 Explain how you found the 12th figure for the pattern _______________________________________________ _______________________________________________ _______________________________________________ 155 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 1 Generate Both Number and Shape Patterns More Shape Patterns Draw the next four figures in each pattern below 1 5 2 6 3 7 4 8 156 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 1 Generate Both Number and Shape Patterns More Shape Patterns Draw the 10th figure in each pattern below 1 5 2 6 3 7 4 8 157 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 1 Generate Both Number and Shape Patterns Practice It 1 What is the next number in the pattern below 2 What is the rule for the pattern below 20 15 10 5 ___ A B C D 5 0 10 15 1 2 4 8 16 A B C D 3 What is the missing number in the pattern below 4 What is the rule for the pattern below 7 10 13 ___ 19 A 16 B 3 C 22 D 4 11 16 21 26 31 A B C D 5 What is the 10th figure in this pattern add 4 add 2 multiply by 2 multiply by 4 add 11 add 5 multiply by 2 multiply by 4 6 Which pattern below has the rule of add 5 A B C D triangle star circle oval 7 What is the missing number in the pattern below 4 8 12 ___ 20 A B C D 8 20 16 4 A B C D 6 8 10 12 5 8 11 14 25 20 15 10 2 7 12 17 8 What is the rule for the pattern below 1 3 9 27 A B C D multiply by 3 add 2 multiply by 2 multiply by 4 158 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 1 Generate Both Number and Shape Patterns Real World and Relevant with Constructed Response A Read About It Rebecca was selling magazine subscriptions for her girls club The club was having a contest to see who could sell the most subscriptions to raise money As Rebecca was walking through the neighborhood she noticed the numbers of the houses on the curb The first house number was the number 40 The next house number was 37 By the time Rebecca got to the third house she speculated that there was a pattern to the house numbers on the curb The third house was numbered 34 That confirmed Rebecca s theory She was right There was a pattern to the house numbers 1 Rebecca saw a pattern of 40 37 and 34 on the curb Write the next 3 numbers in the pattern _____ _____ _____ 2 What is the rule for the pattern __________________ Work It Show your work B Explain It 3 Explain how you found the rule for the pattern _______ _______________________________________________ _______________________________________________ 159 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 1 Generate Both Number and Shape Patterns C Reading for Meaning 4 The cause is why something happened and the effect is the result Reread the paragraph and find the cause CAUSE ________________________________________ EFFECT Rebecca was selling magazine subscriptions D Vocabulary Acquisition Match the vocabulary word with the correct definition a b c d e f subscriptions _____ contest _____ noticed _____ speculated _____ confirmed _____ theory _____ 1 2 3 4 5 6 a challenge between people guessed at an outcome established or solidified observed or detected an idea or a notion recurring payments for a good E Think About It Think of your own number pattern Write the first 5 numbers in the pattern Make sure that it follows a rule Let a friend try to figure out the next three numbers in the pattern and determine the rule Pattern ____ ____ ____ ____ ____ Next Three Numbers ____ ____ ____ Rule __________ 160 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 2 Use Input Output Rules Tables and Charts Expectations Use input output rules tables and charts to represent and describe patterns find relationships and solve problems Analyzing Patterns Learn About It You can analyze study carefully patterns We can look at patterns and see what is coming next and show that information in an input output table See It Look at the pattern below Stage 1 Stage 2 Stage 3 Stage 1 2 3 Hexagon Diamonds Total 1 2 3 1 4 5 1 6 7 161 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 2 Use Input Output Rules Tables and Charts Analyzing More Patterns 1 Stage 1 Stage 2 Stage 1 2 3 2 Stage 3 Shaded White 1 3 1 1 Total 4 Stage 1 Stage 1 2 3 Stage 2 Shaded White Stage 3 Total 162 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 2 Use Input Output Rules Tables and Charts Analyzing More Patterns Draw Stage 4 1 Stage 1 Stage 2 Stage 3 Stage 4 Explain It Explain how you were able to draw Stage 4 ______________________________________________ ______________________________________________ 2 Stage 1 Stage 2 Stage 3 Stage 4 Explain It Explain how you were able to draw Stage 4 ______________________________________________ ______________________________________________ 163 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 3 Find Factor Pairs and Multiples Expectations Find factor pairs in the range 1 100 and find multiples of single digit numbers up to 100 Learn About It Factors Factors are the numbers you multiply together to get the product answer of a multiplication problem Example What are the factors of 14 Think What are the numbers that I can multiply together to get 14 1 x 14 14 2 x 7 14 Think Is there anything else that I can multiply to get 14 No So the factors of 14 are 1 2 7 14 See It Write out the multiplication facts to find all of the factors Fill in each blank in the chart Number Multiplication Facts 25 1 x 25 25 5 x 5 25 Factors 1 5 25 18 1 __ 3 6 __ 18 1 x __ 18 2 x __ 18 3 x 6 __ 32 35 14 1 Which numbers have the greatest number of factors ______ 2 Which number has the least number of factors _______ 164 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 3 Find Factor Pairs and Multiples Learn About It Multiples Multiples are the product of a multiplication problem Multiples are always equal to the number or higher Multiples can NEVER be lower than your starting number Multiples of 5 5 10 15 20 25 30 35 40 45 50 5 x 1 5 x 2 5 x 3 5 x 4 5 x 5 5 x 6 5 x 7 5 x 8 5 x 9 5 x 10 Multiples of 7 7 14 21 28 35 42 49 56 63 70 7 x 1 7 x 2 7 x 3 7 x 4 7 x 5 7 x 6 7 x 7 You Try It 7 x 8 7 x 9 7 x 10 Fill in each blank with the correct multiple 1 Multiples of 4 4 8 __ 16 __ 24 28 __ 36 40 Start with the answer to 4 x 1 then 4 x 2 4 x 3 and so on 2 Multiples of 3 3 6 9 __ 15 18 __ 24 27 __ Start with the answer to 3 x 1 then 3 x 2 3 x 3 and so on 3 Multiples of 9 __ __ 27 36 __ 54 __ 72 __ 90 Start with the answer to 9 x 1 then 9 x 2 9 x 3 and so on 4 Multiples of 2 __ __ ___ ___ ___ ___ ___ ___ ___ Start with the answer to 2 x 1 then 2 x 2 2 x 3 and so on 165 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 3 Find Factor Pairs and Multiples Practice It A List ALL the factors of each number below 1 10 _________________ 2 30 ___________________ 3 49 ________________ 4 15 ___________________ 5 32 _________________ 6 50 ____________________ 7 42 ________________ 8 11 ___________________ 9 36 _________________ 10 55 ___________________ B List the first ten multiples of each number below 11 6 ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ 12 8 ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ 13 9 ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ 14 2 ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ 15 7 ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ 166 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 3 Find Factor Pairs and Multiples Practice It C Circle the correct answer for each problem below 16 Which answer correctly 17 Which answer lists the lists ALL factors of 24 first 6 multiples of 7 A B C D 1 2 12 24 1 2 3 8 12 24 1 2 3 4 6 8 12 24 1 2 3 4 5 6 7 8 12 24 18 Which answer correctly lists ALL factors of 15 A B C D 1 3 15 1 2 3 5 15 30 1 3 5 15 15 30 45 60 75 20 Which number below has the MOST factors A B C D 20 45 49 24 Show It A B C D 19 Which answer lists the first 6 multiples of 8 A B C D 1 8 16 24 28 48 8 16 21 28 32 40 8 16 24 32 40 48 0 8 16 24 32 40 21 Which number has the least number of factors A B C D Show your work for 20 1 7 14 23 28 35 7 14 21 28 35 42 7 14 22 27 34 41 0 7 14 21 28 35 20 45 49 24 Show It Show your work for 21 167 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 3 Find Factor Pairs and Multiples Real World and Relevant with Constructed Response A There are 21 students in the school Glee Club How many different ways can the director arrange the 21 students in groups so they can practice with different people Show It Explain It Explain Your Answer _______________________________________________ _______________________________________________ _______________________________________________ B There are 42 kids coming to Marissa s birthday party How many different seating arrangements can Marissa s mother make for the kids at the party Show It Explain It Explain Your Answer _______________________________________________ _______________________________________________ _______________________________________________ 168 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 3 Find Factor Pairs and Multiples Real World and Relevant with Constructed Response C There are 50 students in line for a concert at school Every fifth student will get a FREE ticket to the concert How many students will receive a FREE ticket to the concert Show It Explain It Explain Your Answer _______________________________________________ _______________________________________________ _______________________________________________ D Mrs Roberts has 24 students in her classroom Mrs Roberts is giving every fourth student in line a pass to the library How many students will get a pass to the library Show It Explain It Explain Your Answer _______________________________________________ _______________________________________________ _______________________________________________ 169 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 3 Find Factor Pairs and Multiples Real World and Relevant with Constructed Response A Read About It Mark and Jeff were both working on the same math problem They were trying to discover all the factors of the number 40 Both boys were working diligently to find the answer The person who got the correct answer first would get a reward of a free ice cream at lunch that day When they were finished with their work both boys had a different answer Mark said that there were six factors of the number 40 and Jeff said that there were eight factors of the number 40 1 Who was right Mark or Jeff ____________________ 2 List all the factors of 40 ________________________ Work It Strategy Find ALL factors of 40 to see who was right B Explain It 3 Explain how you determined who was right Mark or Jeff ____________________________________________________ ____________________________________________________ ____________________________________________________ 170 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 3 Find Factor Pairs and Multiples C Vocabulary Acquisition Context clues help determine the meanings of words 4 Which word from the paragraph means the same as thoroughly A correct B diligently C reward D discover 5 Reread the story to determine the cause or effect CAUSE ________________________________________ EFFECT Mark and Jeff were working hard to answer their math problem correctly 6 Who was working on the same math problem _______ _______________________________________________ 7 How would the winner be rewarded ______________ _______________________________________________ 8 Who said there were six factors of 40 ___________ 9 Who said there were eight factors of 40 __________ D Write About It Write in your math journal Write a personal narrative about a time when you had to work diligently to accomplish something or complete something 171 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 4 Identify Prime and Composite Numbers Expectations Identify prime numbers and composite numbers and explain the relationship with the factor pairs Learn About It Now that you ve learned about factors let s go one step further A prime number is a number that only has 2 factors the number itself and the number one A composite number is a number that has more than two factors A composite number would have factors of the number one itself and also other additional factors See It Steps to finding prime and composite numbers 1 List ALL the factors of the number 2 A prime number will only have itself and 1 as factors 3 A composite number will have more factors than 1 and itself Is 36 prime or composite _____________ Factors of 36 1 36 6 6 2 18 4 9 3 12 172 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 4 Identify Prime and Composite Numbers Practice It A List the factors of each number below Circle prime or composite 1 16 _______________________ prime or composite 2 63 ________________________ prime or composite 3 80 ________________________ prime or composite 4 11 ________________________ prime or composite 5 21 ________________________ prime or composite 6 19 ________________________ prime or composite B Decide if the following numbers are prime or composite Then write the number in the correct box 27 45 81 2 19 37 42 57 35 18 11 64 PRIME COMPOSITE 173 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 4 Identify Prime and Composite Numbers Practice It Circle each correct answer below 1 Which number below is PRIME A B C D 24 43 45 56 A B C D 3 Which composite number has LESS than four factors A B C D 15 9 60 75 25 67 45 15 4 Which number below is NOT composite 6 Which is COMPOSITE A B C D 7 List 3 composite numbers below _____ 1 3 4 7 A 8 B 15 C 17 D 21 5 Which number is PRIME A B C D 2 Which number below is COMPOSITE _____ _____ 23 44 11 5 8 List 3 PRIME numbers below _____ _____ 174 Copyright 2023 by Concise Curriculum Do not duplicate _____

4 PAR 3 4 Identify Prime and Composite Numbers Constructed Response A Answer each prompt with a constructed response 1 List all of the PRIME numbers between 1 and 20 _______________________________________________ Explain how you found your answer _________________ _______________________________________________ _______________________________________________ 2 List all of the COMPOSITE numbers between 20 and 40 _______________________________________________ Explain how you found your answer __________________ _______________________________________________ _______________________________________________ 3 Find the ERROR in the list of composite numbers Composite Numbers 25 32 44 56 91 100 Explain how you found the ERROR __________________ _______________________________________________ _______________________________________________ 175 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 4 Identify Prime and Composite Numbers Real World and Relevant with Constructed Response A Read About It Jason and Kyle were assigned a math project about prime and composite numbers They were given the task of sorting numbers into two categories prime and composite The numbers they were assigned were 11 56 89 90 17 45 2 100 5 and 47 Kyle sorted the numbers like this Prime 11 17 2 and 5 Composite 56 89 90 45 100 and 47 Jason sorted the numbers like this Prime 11 17 89 2 5 and 47 Composite 56 90 45 and 100 1 Who sorted the numbers correctly Jason or Kyle ___ ____________________________________________________ B Explain It 2 Explain how you know who is correct _______________ ____________________________________________________ ____________________________________________________ ____________________________________________________ 176 Copyright 2023 by Concise Curriculum Do not duplicate

4 PAR 3 4 Identify Prime and Composite Numbers 3 Explain the difference in prime and composite numbers ____________________________________________________ ____________________________________________________ C Vocabulary Acquisition 4 Write the bold faced word that means the same as a b c d job given arranging groups D Reading for Meaning 5 Who was given a math assignment _______________ 6 What was their assignment _____________________ _______________________________________________ D Write About It Write in your math journal Write a personal narrative about a time when you had to do a project with a partner What was this like Was it a good experience Is there anything you would do differently next time Be sure to have a clear beginning middle and ending _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ 177 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK OUT 4 PAR 3 4 PAR 3 1 A Circle the pattern that matches each rule below 1 Add 5 a 4 12 20 28 b 5 10 15 20 2 Multiply by 3 a 3 9 27 81 b 3 6 9 12 B Draw the next 3 shapes in the pattern below 3 4 PAR 3 2 C Draw the shapes for Stage 3 below 4 Stage 1 Stage 2 Stage 3 4 PAR 3 3 D Circle the correct MULTIPLE of the number below 5 Which is a MULTIPLE of 7 a 49 b 17 4 PAR 3 4 E Circle each COMPOSITE number below Make a box around each PRIME number below 178 Copyright 2023 by Concise Curriculum Do not duplicate

Numerical Reasoning fraction equivalence comparison of fractions and addition and subtraction of fractions with like denominators 4 NR 4 Solve real life problems involving addition subtraction equivalence and comparison of fractions with denominators of 2 3 4 5 6 8 10 12 and 100 using part whole strategies and visual models 4 NR 4 1 Using concrete materials drawings and number lines demonstrate and explain the relationship between equivalent fractions including fractions greater than one and explain the identity property of multiplication as it relates to equivalent fractions Generate equivalent fractions using these relationships 4 NR 4 2 Compare two fractions with the same numerator or the same denominator by reasoning about their size and recognize that comparisons are valid only when the two fractions refer to the same whole 4 NR 4 3 Compare two fractions with different numerators and or different denominators by flexibly using a variety of tools and strategies and recognize that comparisons are valid only when the two fractions refer to the same whole 4 NR 4 4 Represent whole numbers and fractions as the sum of unit fractions 4 NR 4 5 Represent a fraction as a sum of fractions with the same denominator in more than one way recording with an equation 4 NR 4 6 Add and subtract fractions and mixed numbers with like denominators using a variety of tools 179 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK IN 4 NR 4 4 NR 4 1 A Write the correct fraction next to each fraction model 1 one third five eighths two fifths one whole 2 Is the fraction closer to one half or one whole Explain your answer _____________________________ ______________________________________________ 4 NR 4 2 4 NR 4 3 B Label each number line below to help you find equivalent fractions ________ Write an equivalent fraction for ________ 3 Write an equivalent fraction for 4 180 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK IN 4 NR 4 5 Marilee has two thirds of a cup of lemonade Her friend Yan has four fifths of a cup of lemonade Who has the most lemonade _________ Draw It 4 NR 4 4 C Write an addition sentence to show unit fractions 6 ______ ______ ______ unit fraction ______ 4 NR 4 5 D Write the addition sentences shown by each model 7 _____ _____ _____ ______ 8 _____ _____ 4 NR 4 6 E Complete the addition sentence shown below 9 _____ ______ 181 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 Use Materials Drawings and Number Lines Expectations Use concrete materials drawings and number lines to demonstrate the relationship between equivalent fractions Learn About It Benchmark fractions are common fractions you can use as a guide when working fraction problems to help you decide if the answers to the problem are REASONABLE or if they make sense Common benchmark fractions are Match each picture to the correct benchmark fraction 182 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 Use Materials Drawings and Number Lines Learn About It You can use fraction strips to show benchmark fractions Line up the fraction strips against the benchmark fraction strip to compare the fractions See It Which benchmark fraction is each fraction closer to 1 0 Use the benchmark fractions to order the 3 fractions above LEAST to GREATEST _______ _______ _______ 183 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 Use Materials Drawings and Number Lines A Draw a fraction strip and circle the closest benchmark fraction for each fraction below Fraction 1 Fraction Strip Benchmark Fraction 0 1 2 0 1 3 0 1 4 0 1 5 1 0 6 1 0 B Explain It closer to one half or one whole Is the fraction Explain your answer _____________________________________________________ _____________________________________________________ _____________________________________________________ 184 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 Use Materials Drawings and Number Lines Learn About It Drawing a fraction strip of each fraction will help you place the fractions in order from LEAST to GREATEST or GREATEST to LEAST Comparing the fractions to one whole will help See It one whole two fifths five sevenths one third Here are the fractions listed from LEAST to GREATEST Here are the fractions in order from GREATEST to LEAST 185 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 Use Materials Drawings and Number Lines A Draw fraction strips to help you order each set of fractions below 1 Order the fractions from LEAST to GREATEST _______ _______ _______ 2 Order the fractions from GREATEST to LEAST _______ _______ _______ B Explain how to order fractions using fraction strips _____________________________________________________ _____________________________________________________ 186 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 5 Represent a Fraction as a Sum of Fractions Expectations Represent a fraction as a sum of fractions with the same denominator in more than one way Learn About It You can multiply a WHOLE number by a fraction When you are multiplying a WHOLE number by a fraction you will need to make the WHOLE number look like a fraction by rewriting the whole number as a fraction over the number 1 Multiplying a fraction by a whole number is the SAME as repeated addition See It See how each whole number is changed to a fraction before starting multiplication 3 groups of 2 groups of 3 groups of 187 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 5 Represent a Fraction as a Sum of Fractions Learn About It Sometimes when you multiply a fraction by a whole number your answer will be an improper fraction When that happens you must change the improper fraction to a mixed number See It 6 groups of 1 whole 1 out of 5 1 You Try It 5 groups of Shade in fraction square below to show 5 188 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 5 Represent a Fraction as a Sum of Fractions Practice It A Rewrite and solve each multiplication problem B Circle the fractions that can be reduced or simplified Show how you simplified the fractions from above C Write the fractions that can be changed into a mixed number Show how you changed the fractions from above into a mixed number 189 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 5 Represent a Fraction as a Sum of Fractions Real World and Relevant with Constructed Response A Read About It A Destiny is making a costume for her school play For her costume she needs 12 yards of fabric She is also making a costume for her little sister For her sister s costume she only needs onethird of the amount of the fabric she needed for her own costume Work It How much fabric is needed for her sister s costume __________ B Todd usually runs 5 miles every day On Tuesday he ran only one fourth as long as he normally runs Work It How many miles did Todd run on Tuesday _______ C Savannah rides her horse for 4 miles each day Savannah s sister only rides one half of the 4 miles Work It How many miles does Savannah s sister ride each day ________ 190 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 5 Represent a Fraction as a Sum of Fractions Constructed Response A Read About It Suzanne has 5 cups of flour in her pantry She is baking a cake and the recipe only requires her to use of that amount for her cake She also has 2 cups of sugar available The recipe calls for of that amount Suzanne is undecided if she wants to make a chocolate cake or a vanilla cake If she decides to make a chocolate cake she will need to add cocoa to her mix Suzanne s pantry contains 4 cups of cocoa The recipe calls for only of that amount 1 How many cups of flour will be used to make the cake ______________ 2 How much sugar will Suzanne use ________________ 3 How much cocoa will she need __________________ Work It Find the amount of flour sugar and cocoa need to make the cake flour sugar cocoa 191 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 5 Represent a Fraction as a Sum of Fractions B Explain It 4 Explain how you found the amount of flour sugar and cocoa Suzanne needed to bake her cake _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ C Vocabulary Acquisition 5 Use context clues to determine the meaning of each word Give the word that means the same as a needs c attainable b quantity d unsure D Reading for Meaning 6 Cause and Effect The cause is why and the effect is what happens as a result CAUSE Suzanne decided to add cocoa to her cake EFFECT _____________________________________________ 192 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Learn About It A fraction is part of a whole It can also be a part of a group The numerator is the number on the top of the fraction bar The numerator names the parts of the whole or group The denominator is the number on the bottom of the fraction bar The denominator names the total number of the parts in the whole or the group See It There are 4 parts of this whole The number of total parts is 4 so it is the denominator One part is shaded so 1 is the numerator Equivalent Fractions Equivalent fractions are fractions that name the same part of the whole but they have different names There are 8 parts of this whole The 8 is the denominator Four parts are shaded so 4 is the numerator The second figure is the same as the first just divided differently This figure is divided into 2 parts and 1 part is shaded 193 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Ways to find equivalent fractions a number line simplify or reduce multiplication fraction strips 1 Use a number line 0 1 0 1 Look at the first number line Look at the fraction Now look at the 2nd number line The fraction that is the same distance from the 0 is the fraction So and are equivalent fractions You Try It Use the number line to name an equivalent fraction ____ ____ Let s Try Another One 0 1 0 1 ________ Write an equivalent fraction for ________ A Write an equivalent fraction for B 194 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions 2 Using multiplication to find an equivalent fraction Learn About It Equivalent fractions can also be found by multiplying the numerator and denominator by the same number The number 2 is an easy number to use but as long as you multiply the top and the bottom by the SAME number you will find an equivalent fraction See It so You Try It so Multiplying only part of the fraction You may also be given part of an equivalent fraction It is up to you to determine what number was used to find the fraction See It Look at these two fractions 4 x 4 16 In the second fraction the numerator is missing Use the denominators to determine what number was used to multiply the first denominator by to get the second denominator so 195 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Practice It A Use multiplication to find an equivalent fraction 1 2 3 4 5 6 7 8 B Use multiplication and find the equivalent fraction 9 10 11 12 196 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions 3 Simplify fractions to find an equivalent fraction Learn About It Simplify Fractions Find the GCF To simplify or reduce a fraction you will find the greatest common factor or GCF The GCF is the largest factor that both numbers have in common That will allow you to divide and change the fraction to its lowest terms See It This fraction is NOT in lowest terms To simplify this fraction you need to find the GCF of the numbers 12 and 15 To find the GCF write out the factors of 12 and 15 The GCF of these numbers is 3 Divide the numerator and 12 1 2 3 4 6 12 denominator by 3 to find an 15 1 3 5 15 equivalent fraction Answer It You Try It Simplify this fraction 1 List the factors of 10 and 16 10 ______________________ 16 ______________________ 2 Circle the GCF 3 Now divide by the GCF 4 Write your new fraction 10 16 197 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions 4 Use fraction strips Learn About It Fraction strips can also show equivalent fractions Line up both sets of fraction strips that show the denominator of the two fractions you are comparing Line up the fraction strips to find an equivalent fraction See It What fraction is equal to Steps 1 Go to the end of the section that shows one fourth 2 Draw a line up to the other fraction strip 3 Count the fractions that match the fraction one fourth You Try It 1 What fraction is equal to 2 What fraction is equal to 3 What fraction is equal to 198 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions A Practice It Use a strategy to find an equivalent fraction 1 Find the equivalent fraction 2 Find the equivalent fraction ____ ____ 3 Simplify the fraction below 4 Simplify the fraction below simplified fraction ______ simplified fraction ______ 5 Use multiplication to find an equivalent fraction for 7 Two thirds is equal to 0 1 ___ 6 Use multiplication to find an equivalent fraction for 8 Two sixths is equal to 0 1 0 1 ___ 199 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions B Practice It Find each equivalent fraction below Show your work Work It 1 Which fraction below is equivalent to A B C D 2 Which fraction below is equivalent to A B C D B C D 4 Which fraction is NOT equivalent to A B C D 3 What is the simplest form of A 5 Write an equivalent fraction _____ 6 Explain It Explain how you would simplify the fraction _____________________________________________________ _____________________________________________________ _____________________________________________________ 200 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Constructed Response A Show three ways to find an equivalent fraction for the fraction five tenths 1 Number line Show It Explain It ____________________________________________________ ____________________________________________________ 2 Fraction strips Show It Explain It ____________________________________________________ ____________________________________________________ 3 Divide by GCF Show It Explain It ____________________________________________________ ____________________________________________________ 201 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Constructed Response A Show three ways to find an equivalent fraction for three ninths 1 Number line Show It Explain It ____________________________________________________ ____________________________________________________ 2 Fraction strips Show It Explain It ____________________________________________________ ____________________________________________________ 3 Divide by GCF Show It Explain It ____________________________________________________ ____________________________________________________ 202 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Real World and Relevant with Constructed Response A Read About It Abby is making a batch of cookies Here is part of the recipe flour cup milk cup white sugar cup brown sugar cup Abby looked for a measuring cup and could only find one that had measurements in eighths and tenths Abby went and complained to her mom about not having the right measuring cup Abby s mom asked Abby if her class had studied equivalent fractions When Abby said yes her mom told her to calm down As long as Abby knew how to find equivalent fractions then she could use the measuring cup that measured in eights and tenths Abby s mom knew that if Abby had studied equivalent fractions then her cookies would not be ruined 1 What part should Abby use to measure the flour and the milk eighths or tenths _________ 2 What part should Abby use to measure the white and brown sugar eighths or tenths ________ 3 Find the equivalent fractions using eighths and tenths Work It flour milk brown sugar white sugar 203 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions B Explain It 4 Explain how Abby can use a measuring cup with different measures and still have the same amount of her ingredients Explain how you know her cookies will NOT be ruined _____________________________________________________ _____________________________________________________ C Vocabulary Acquisition 5 a Which bold faced word means grumbled ___________ b Which bold faced word means a set of ___________ D Reading for Meaning 6 Cause and Effect The cause is the why something happened and the effect is the result CAUSE ____________________________________________ EFFECT Abby was upset E Write About It Write in your math journal Write an informational piece about the importance of finding equivalent fractions when using a recipe or making food ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ 204 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Expectations Compare two fractions with different numerators and or different denominators by flexibly using a variety of tools and strategies and recognize that comparisons are valid only when the two fractions refer to the same whole Learn About It There are several ways you can compare fractions Fractions cannot be compared unless you are comparing the same whole You will use greater than less than

4 NR 4 1 4 2 4 3 Comparing Fractions 2 Use fraction strips to compare fractions Learn About It You can use fraction strips to compare fractions Line up the fraction strips of the fractions that you are comparing The fraction farthest to the right is the greater fraction and the fraction closer to the left is the lesser fraction See It Use greater than less than or equal to Compare the fractions Answer It So is less than Compare the shaded in parts of each fraction The fraction shaded farthest to the right is the larger fraction You Try It Use greater than less than or equal to Compare the fractions 206 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions 3 Compare fractions using cross multiplication Learn About It You can also compare fractions by using the method of cross multiplication With cross multiplication you would multiply the denominator of 1 fraction with the numerator of the other fraction Then you would multiply the denominator of the other fraction with the numerator of the remaining fraction See It 21 25 Multiply 7 x 3 Multiply 5 x 5 The number above each fraction tells you which one is larger Since 25 is larger than 21 then five sevenths is larger than three fifths You Try It Compare these fractions by using cross multiplication Use the symbols A B C 207 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions 4 Compare fractions using common denominators Learn About It Equivalent fractions can also be found by finding a common denominator You can find a common denominator by finding the least common multiple and Compare these two fractions Look at the denominators 3 and 5 Think about the multiples of 3 and 5 What multiples do they have in common Write out the multiples of 3 and 5 Multiples of 3 3 6 9 12 15 18 21 24 27 30 Multiples of 5 5 10 15 20 25 30 35 40 45 What multiples do they have in common 15 and 30 So you would multiply since you multiply 3 by 5 to get to the least common multiple Then you would multiply since you would multiply 5 by 3 to get the answer 15 which is the least common multiple Now you can compare these fractions since they have the SAME denominator Since the numerator 10 is smaller than the numerator 12 then ten fifteenths is smaller than twelve fifteenths Answer It 208 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions 5 Compare common numerators Learn About It You can use common numerators to compare fractions When comparing fractions you can find a common numerator by using multiplication The fraction that has the SMALLER denominator of the two fractions will be the LARGER fraction The smaller denominator means that the pieces of that fraction are larger than pieces of the other fraction See It 1 Compare these fractions 2 Find a common numerator and 3 Now you can compare the fractions Since 3 is the larger numerator you will try to make the other numerator a 3 So 1 times what number equals the number 3 and 4 Since the denominator of the first fraction is SMALLER the pieces of that fraction are LARGER 5 So When the numerators are the SAME the fraction with the smaller denominator is the LARGER fraction 209 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Practice It Compare the fractions and use the symbols A Find a common numerator to compare fractions Show your work B Find a common denominator to compare fractions Show your work C Use cross multiplication to compare fractions Show your work 210 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Practice It 1 Circle each fraction greater than Work It Work It Work It 5 Circle each fraction less than 6 Circle each fraction greater than Work It 4 Circle each fraction less than 3 Circle each fraction less than Work It 2 Circle each fraction greater than Work It 211 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions 7 Circle each fraction greater than 8 Circle each fraction greater than Work It 9 Circle each fraction less than Work It 10 Circle each fraction more than Work It 11 Circle each fraction less than Work It 12 Circle each fraction greater than Work It 212 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Real World and Relevant with Constructed Response A Read About It The fourth grade classes at Coweta Elementary School were having a contest to see which class could recycle the most aluminum cans in a month The winner would receive a pizza party For every five cans recycled the students would hang a paper tree out in the hallway Each class had different colors of paper trees so that it would be easy to tell which class was in the lead The principal challenged each class to see if they could hang their paper trees all the way down the hall to reach the cafeteria At the end of two weeks the contest was over Read the results to see how each class did This chart shows how far each class made it down the hall Mrs Cheatham s class Mrs Trudeau s class Mrs Mulkey s class Mrs Johnson s class 1 Which class won the contest ____________________ which class had the largest fraction 2 Which class came in last place ___________________ which class had the smallest fraction Work It Use a strategy to compare the fractions 213 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions B Explain It Explain the strategy you used in problems 1 2 _______________________________________________ _______________________________________________ C Vocabulary Acquisition Match the vocabulary word with the correct definition a b c d e f recycle _____ aluminum _____ lead _____ challenged _____ cafeteria _____ results _____ 1 2 3 4 5 6 position ahead of end product metallic element reuse place to eat lunch contested D Reading for Meaning 1 What was the contest about _____________________ _______________________________________________ 2 What would the winning class receive _____________ _______________________________________________ 3 Who challenged each class to bring in cans _________ _______________________________________________ 4 How many cans would equal one paper tree ________ _______________________________________________ 214 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Learn About It You can use fraction strips to order fractions and you can also find a common denominator along with fraction strips to order fractions See It Find a common denominator before ordering the fractions from LEAST to GREATEST Use the strategy of finding the least common multiple to find a common denominator Order these fractions Find a common denominator by finding the LCM List the multiples of each denominator until you find the LCM 3 3 6 9 12 12 12 24 36 48 4 4 8 12 16 The least common multiple LCM for 3 12 and 4 is 12 Now find the new numerator for each of these fractions 215 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Ordering Fractions by Finding a Common Denominator The LCM for 3 12 and 4 is 12 Think to yourself What number times 3 equals 12 Multiply the numerator by the same number Do the same for each fraction See It Look at the new fractions with the same denominator Now it is very easy to compare fractions with the same denominator Order the fractions from LEAST to GREATEST ___ ___ ___ Order the fractions from GREATEST to LEAST ___ ___ ___ 216 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Practice It Find a common denominator for each set of fractions A Order each set of fractions from LEAST to GREATEST 1 ___ ___ ___ 2 ___ ___ ___ 3 ___ ___ ___ B Order each set of fractions from GREATEST to LEAST 1 ___ ___ ___ ___ ___ ___ 2 217 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Practice It Find a common denominator for each set of fractions A Order each set of fractions from LEAST to GREATEST 1 ___ ___ ___ ___ ___ ___ 2 3 ___ ___ ___ B Order each set of fractions from GREATEST to LEAST 1 ___ ___ ___ ___ ___ ___ 2 218 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Practice It Find a common denominator to compare each set of fractions A Compare each set of fractions with or 1 Show It 2 Show It 3 Show It 4 Show It 219 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 1 4 2 4 3 Comparing Fractions Real World and Relevant with Constructed Response A Read each prompt and answer with a constructed response 1 Marilee has two thirds of a cup of lemonade Her friend Yan has four fifths of a cup of lemonade Who has the most lemonade _______________________ Explain how you found your answer _________________ _______________________________________________ _______________________________________________ _______________________________________________ 2 Rayvon wants one half of a pizza His brother Markeith gives him four eighths of a pizza and Rayvon gets upset because his brother didn t give him what he wanted Should Rayvon be upset __________________________ Explain why Rayvon SHOULD or SHOULD NOT be upset __ _______________________________________________ _______________________________________________ _______________________________________________ 220 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 4 Represent Whole Numbers Fractions Unit Fractions Expectations Represent whole numbers and fractions as the sum of unit fractions Learn About It Fractions that have a numerator greater than 1 are just a part of a larger fraction When we break these fractions apart we are decomposing them and finding their unit fraction There are three ways to decompose and find unit fractions 1 addition 2 multiplication 3 models See It Let s look at the fraction Four fifths is composed of the unit fraction of fifths Look at the denominator when determining the unit fraction How many units of fifths does it take to make the fraction Look at the numerator The numerator is 4 so it will take 4 unit fractions of fifths to make the fraction four fifths 1 Addition Let s Try Another One Look at the fraction What is the unit fraction How many units will it take to make the fraction Answer It It will take 3 units 221 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 4 Represent Whole Numbers Fractions Unit Fractions 2 Multiplication Learn About It You can use multiplication to find unit fractions Find the unit fraction by looking at the denominator You will use the numerator to find out how many times to multiply by the unit fraction See It Look at the fraction What is the unit fraction How many units will it take to make the fraction 5 units Show It Show the unit fraction using multiplication 5 units X or 5 X A number line can also be used to show multiplication This number line shows sixths One sixth times 5 equals five sixths Answer It 5 X This shows the multiplication of five sixths on the number line 222 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 4 Represent Whole Numbers Fractions Unit Fractions 3 Models Learn About It You can use models of unit fractions Unit fractions always have a numerator of one Unit fractions are a part of a larger fraction that has been decomposed Unit fractions are compared to one whole See It Look at the fraction What is the unit fraction How many units will it take to make the fraction It will take 2 units to make the fraction two thirds Show It Show the unit fraction using a model 2 units of or 1 whole 223 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 4 Represent Whole Numbers Fractions Unit Fractions Practice It A Use addition to decompose and find the unit fraction 1 2 ______________ unit fraction ___________ 3 ______________ unit fraction ___________ 5 ______________ unit fraction ___________ ______________ unit fraction ___________ 4 ______________ unit fraction ___________ 6 ______________ unit fraction ___________ Explain It B Explain how to decompose and find the unit fraction for five eights _____________________________________________________ _____________________________________________________ _____________________________________________________ 224 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 4 Represent Whole Numbers Fractions Unit Fractions Practice It A Use multiplication to decompose and find the unit fraction 1 2 ______________ ______________ unit fraction ___________ 3 unit fraction ___________ 4 ______________ ______________ unit fraction ___________ 5 unit fraction ___________ 6 ______________ ______________ unit fraction ___________ unit fraction ___________ Explain It B Explain how to decompose and find the unit fraction for the fraction nine elevenths _____________________________________________________ _____________________________________________________ 225 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 4 Represent Whole Numbers Fractions Unit Fractions Practice It A Draw a model to decompose and find the unit fraction 1 Fraction Model Number Line unit Fraction ____________ 2 Fraction Model Number Line unit Fraction ____________ 3 Fraction Model Number Line unit Fraction ____________ B Can you decompose and find the unit fraction for the fraction one half _____ Explain It _______________________________________________ _______________________________________________ _______________________________________________ 226 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Learn About It Mixed numbers are basically whole numbers combined with a fraction Improper fractions are another way to represent a mixed number An improper fraction has a larger number as the numerator The denominator is smaller than the numerator See It Mixed numbers and improper fractions are basically the same way to represent the same number or Each rectangle is divided into 4 parts and seven parts are shaded 1 whole The denominator is not the total number of pieces in both figures It is the number of pieces that each one of the figures is divided into You Try It If the mixed number for this figure is that means you would shade in 1 WHOLE figure and 2 out of 3 pieces of the next figure The mixed number is Now write the improper fraction _____ 227 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers See It 1 Use a model to find improper fractions To find an improper fraction using a model you would count the number of shaded pieces or parts to find the numerator To find the denominator you would count the number of equal parts in each figure There are 7 shaded parts in the numerator Each figure is divided into 6 pieces for the denominator How do you find the mixed number from an improper fraction 1 1 whole 1 out of 6 Count the figures that are shaded in completely The figure s shaded completely is your whole number 1 whole Next count the number of parts shaded in the figure that is not shaded in completely 1 out of 6 That number represents your fraction You Try It Find the improper fraction and mixed number using the model below improper fraction ______ mixed number _______ 228 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers 2 Use a number line Learn About It You can use a number line to show improper fractions and mixed numbers See It Find the mixed number shown on the number line The place marked on the number line is after the whole number 1 and before the whole number 2 It is half way between so the mixed number is 1 If you count over from the 0 the place marked is on the third half mark So the improper fraction is You Try It Find the mixed number and the improper fraction of the number that is marked on the number line 1 mixed number ____ 2 improper fraction ____ Count over from 0 to find the numerator of the improper fraction There are four equal spaces between each whole number That means that the number line is divided into fourths so the denominator is 4 229 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It A Write the improper fraction and the mixed number 1 improper fraction _____ mixed number _____ Explain It Explain how this model shows an improper fraction and a mixed number ___________________________________________________ ___________________________________________________ ___________________________________________________ 2 improper fraction _____ mixed number _____ Explain It Explain how this model shows an improper fraction and a mixed number ___________________________________________________ ___________________________________________________ ___________________________________________________ 230 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It B Write the improper fraction and the mixed number 1 improper fraction _____ mixed number _____ Explain It Explain how this model shows an improper fraction and a mixed number ___________________________________________________ ___________________________________________________ ___________________________________________________ 2 improper fraction _____ mixed number _____ Explain It Explain how this model shows an improper fraction and a mixed number ___________________________________________________ ___________________________________________________ ___________________________________________________ 231 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It A Shade in the correct parts on each model to show each improper fraction Write the mixed number next to each improper fraction 1 2 3 4 5 6 7 8 232 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It B Shade in the correct parts to show each improper fraction Write the mixed number next to each improper fraction 1 2 3 4 5 6 7 8 233 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Learn About It Changing improper fractions to mixed numbers To change an improper fraction to a mixed number you will divide the denominator into the numerator See It The quotient becomes your whole number the remainder becomes the numerator and the divisor becomes the denominator The whole number is 1 and the fraction is So the mixed number is 1 Changing mixed numbers to improper fractions When changing a mixed number to an improper fraction you will multiply the denominator times the whole number and then add the numerator to the answer See It 4 4 the whole number x 5 the denominator 20 Then add the answer 20 to the numerator 20 3 23 23 is your new numerator The number 5 is still the denominator So the improper fraction is 234 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It A Change each mixed number below to an improper fraction 1 1 ___ 5 ___ 6 ___ 2 ___ ___ 3 ___ 3 ___ 3 ___ 2 7 3 7 ___ 3 ___ 5 ___ 3 ___ B Change each improper fraction below to a mixed number 4 ___ ___ ___ ___ 5 ___ ___ ___ ___ 6 ___ ___ ___ ___ 7 ___ ___ ___ ___ 235 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers C Explain It 8 Taylor s fourth grade class is learning about changing improper fractions to mixed numbers Taylor has been asked by her teacher to explain this process to a new student How can Taylor explain this to the new student _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ D Show It 9 Show an example Taylor could use to help explain how to change an improper fraction to a mixed number 236 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Real World and Relevant with Constructed Response A Read each prompt and answer with a constructed response Bailey was having difficulty changing mixed numbers to improper fractions especially when the mixed number was written in word form Explain to Bailey how to write the mixed number and the improper fraction of a number 1 one and five sixths __________ __________ Explain It _______________________________________________ _______________________________________________ 2 two and four fifths __________ __________ Explain It _____________________________________________________ _____________________________________________________ 3 four and three fourths _________ __________ Explain It _____________________________________________________ _____________________________________________________ 237 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Constructed Response B Find and CORRECT the ERROR in each problem below 1 1 Correct Answer Explain It _____________________________________________________ _____________________________________________________ 2 2 Correct Answer Explain It _____________________________________________________ _____________________________________________________ 3 1 Correct Answer Explain It _____________________________________________________ _____________________________________________________ 238 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Real World and Relevant with Constructed Response A Read About It Steve had math homework to work on last night Steve s math homework was to convert a mixed number to an improper fraction When Steve exchanged papers the next day with Jason Jason told him his homework was incorrect Jason and Steve got into an argument about the homework Jason argued that Steve did his homework incorrectly Steve argued that his homework was correct This is what Steve s homework looked like 1 Is Steve s homework correct or incorrect ___________ _______________________________________________ Work It B Explain It 2 Explain how you found your answer correct or incorrect _______________________________________________ _____________________________________________________ 239 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers 3 Explain how to change a mixed number to an improper fraction ____________________________________________________ ____________________________________________________ ____________________________________________________ Show It 4 Give an example of how to change a mixed number to an improper fraction C Vocabulary Acquisition 5 Write the bold faced word that means a not correct __________ c disagreement b traded _____________ _________ d change ______________ D Reading for Meaning 6 Cause and Effect The cause is the why something happened and the effect is the result CAUSE ____________________________________________ EFFECT Jason and Steve got into an argument 240 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Expectations Add and subtract fractions and mixed numbers with like denominators using a variety of tools Learn About It FRACTIONS WITH LIKE DENOMINATORS Fractions can only be added if they have the SAME denominator When fractions have the same denominator the numerators are added together and the denominator stays the same See It Fractions With Like Denominators Add the numerators straight across 1 2 3 The denominator stays the same 4 stays a 4 See It Again Add the numerators straight across 2 1 3 The denominator stays the same 5 stays a 5 You Try It Add each set of fractions below A B C D 241 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Adding fractions using fraction strips Learn About It You can use fraction strips to add fractions Count the shaded pieces in the first fraction strip and add it to the shaded pieces in the second fraction strip Your denominator stays the same See It The denominator stays the SAME You Try It Add the SHADED parts of each fraction 1 2 _____ 3 _____ 4 _____ _____ 242 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Adding fractions then finding simplest form Learn About It Many times when you add fractions the answers are NOT in simplest form If the answer is an IMPROPER FRACTION then you will need to change it to a MIXED NUMBER If the answer is NOT in simplest form then you will need to find the GCF and divide to simplify the fraction See It This answer is an IMPROPER FRACTION Change this to a MIXED NUMBER Method 1 Divide the denominator into the numerator 1 6 7 6 1 The mixed number is Method 2 Draw a picture There are 7 pieces out of 6 Pretend there is a jar that holds only 6 marbles You have 7 marbles to place in the jar You can only place 6 in the jar and the leftovers would be turned into a fraction This jar only holds as much as the denominator of the fraction The mixed number is 1 whole jar 1 out of 6 marbles left 243 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It A Adding Fractions with LIKE denominators Row 1 ____ ____ ____ Row 2 ____ ____ ____ ____ ____ ____ Row 3 Row 4 ____ ____ ____ Row 5 ____ ____ ____ B Circle and simplify the fractions above that are NOT simplified Show your work 244 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Constructed Response A Read About It Story A Hannah was baking cookies for her after school club Hannah wanted to make sure her cookies tasted delicious so she bought a recipe book Hannah needed one fourth of a cup of white flour and one fourth of a cup of wheat flour The recipe also called for one third of a cup of sugar and one third of a cup of milk 1 How much of both types of flour did she need altogether __________ 2 How much sugar and milk did she use altogether _________ Work It 3 Explain It Explain how you solved the problem ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ 245 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Story B The art school where Tammy worked was having a contest Each artist was going to paint their art studio and see whose studio looked the best Tammy was painting her art studio purple She painted two walls on Monday with purple paint and used of a gallon of paint On Tuesday she painted the other two walls and used of a gallon of the purple paint 1 How much paint did she use altogether ____________ _______________________________________________ Explain It 2 Did Tammy use a WHOLE gallon of paint How do you know _______________________________________________ _______________________________________________ Inference 3 From this story we can infer that Tammy is a a small child b a salesman c a teacher d an artist 4 Cause and Effect The cause is why something happened and the effect is the result CAUSE Tammy s art studio was having a contest EFFECT ___________________________________________ 246 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Learn About It Subtracting fractions with like denominators is super EASY You subtract the numerators straight across The denominator stays the same Make sure you simplify the answer You can simplify your answer by finding the greatest common factor Once you find the greatest common factor you will divide the numerator and the denominator by that number to reduce or simplify your answer See It Use fraction strips to show subtraction Five out of the six strips are shaded To show subtraction you would cross out two of the strips The number of strips leftover 3 is your answer Simplest form The answer is NOT in simplest form Use the GREATEST COMMON FACTOR of 3 and 6 to simplify the fraction The GCF of 3 and 6 is 3 Answer It is the answer simplified or in lowest terms 247 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It A Subtract and simplify each fraction problem below ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ B Read the word problem below and solve of the box out for her friend Tammy Trina then pours out another of the box Trina has of a box of trail mix She pours out for her friend Maxine How much trail mix is left in Trina s box ______________ _______________________________________________ Work It Show your answer in lowest terms 248 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Constructed Response A Read About It Mike s little sister spilled paint on the carpet in the living room Now he needed to replace that piece of carpet For his project Mike purchased a piece of carpet that was of a yard long Mike didn t need as much carpet as he thought when he fixed the spot He had yard of carpet leftover after he finished the repairs 1 How long was the piece of carpet Mike bought ______ 2 How long was the piece of carpet Mike used ________ Work It Make a math problem to show the length of the piece of carpet that Mike used B Explain It 3 Write an explanation of how you found the answer _______________________________________________ _______________________________________________ _______________________________________________ C Reading for Meaning 4 Why did Mike need to replace a piece of carpet at his house _______________________________________________ 249 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers 5 Did Mike use all of the carpet he bought ___________ 6 CAUSE and EFFECT The cause is the why and the effect is what happened CAUSE Mike s little sister spilled paint on the carpet EFFECT ________________________________________ D Vocabulary Acquisition Reread the story and determine the answer 7 Which vocabulary word means bought _____________ 8 Which vocabulary word means dribbled on __________ 9 Which vocabulary word means switched out _________ E Write About It Write in your math journal Write a real world problem that you would use your knowledge of subtracting fractions Write down the problem and explain how to solve it Draw a picture to help show how you solved the problem ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ 250 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Learn About It Adding mixed numbers is ALMOST the same as adding fractions You just separate the whole number side and the fraction side Add the whole numbers first and then move to the fraction part When adding the fraction part remember to add the numerators and leave the denominator the SAME See It 2 1 Rewrite It 2 1 3 3 or 3 Let s Try Another One 2 1 3 How can you rename Answer It 3 The fraction 1 whole 3 1 4 251 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Adding Mixed Numbers Let s Try Some More Count the whole numbers first then the fractions 2 1 3 2 1 3 or 4 wholes You Try It Count the whole numbers first then the fractions 1 2 3 Explain It Explain how to add mixed numbers _______________________________________________ _______________________________________________ _______________________________________________ 252 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It A Use each model below to add mixed numbers 2 1 2 1 1 2 Explain your answer _____ Explain your answer _____ _________________________ _________________________ _________________________ _________________________ 3 1 Explain your answer _____ 1 3 4 Explain your answer _____ _________________________ ________________________ _________________________ ________________________ 253 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It B Draw models to match each addition problem below 1 Model 2 1 2 Model 3 Model 2 2 254 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It A Add each set of mixed numbers Simplify as needed 5 2 ____ 6 3 ____ 2 2 ____ 5 2 ____ 4 1 ____ 8 5 ____ 1 2 ____ 8 3 ____ 1 5 ____ 5 1 ____ 1 1 ____ 3 1 ____ B Write the addition problem shown by each model 1 ______ ______ _____ 2 ______ _____ _____ 255 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Real World and Relevant with Constructed Response Answer each prompt with a constructed response Mari was reading a recipe that used mixed numbers for measuring the ingredients She was not very good yet with adding mixed numbers so her mother suggested she draw models to help One part of the recipe called for three and two sixths cups of milk for the cake part and the icing part called for one and three sixths cups of milk Mari wanted to make sure she added correctly so she could ask her mom to buy the correct amount of milk at the store 1 How much milk does Mari need for her recipe _______ 2 How do you know what she needs _______________ _______________________________________________ Show It 3 If Mari s mother buys four cups of milk will that be enough _______________________________________________ _______________________________________________ 256 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Learn About It Subtracting mixed numbers is ALMOST the same as subtracting fractions You just separate the whole number side and the fraction side Subtract the whole numbers first and then move to the fraction part When subtracting the fraction part remember to subtract the numerators and leave the denominator the SAME 2 1 See It Rewrite the second fraction under the first fraction See It 2 1 1 Start with 1 whole 1 whole Answer 2 and cross out 1 Since this is subtraction cross out the second fraction Count what is leftover to find the answer 257 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Let s Try Another One Subtract the whole numbers first then the fractions Only draw the models for the first number in the subtraction problem Cross out the models of the numbers you are subtracting 2 1 1 Cross out 1 on the 2 1 1 Cross out1 on the model model Count the pieces that are left Count the pieces that are left Explain It Explain how to subtract mixed numbers _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ 258 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It A Use the models below to subtract mixed numbers 1 2 2 1 2 1 Cross out the number you are subtracting on the model Cross out the number you are subtracting on the model Your answer _________ Your answer _________ 3 4 2 1 3 2 Cross out the number you are subtracting on the model Cross out the number you are subtracting on the model Your answer _________ Your answer _________ 259 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It B Draw models to match the subtraction problems 1 Model 4 1 Hint Model the first number and cross out the number you are subtracting 2 Model 5 1 3 Model 2 2 260 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It A Write the subtraction problem shown by each model 1 Explain It Explain how you found the answer to the problem _____________________________________________________ _____________________________________________________ 2 Explain It Explain how you found the answer to the problem _____________________________________________________ _____________________________________________________ 261 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Real World and Relevant with Constructed Response Read each prompt and answer with a constructed response Leena was working on her Science Fair Project She was watering plants and measuring their growth She started out the week with five and four fifths cups of water At the end of the week she had three and one fifth cups of water leftover Leena needed to write down how much water she used during the week for her project Leena needs to make a math problem to find out how much water she used 1 How much water did Leena use for her project ______ _______________________________________________ 2 Draw a model of the amount of water Leena used Model 3 Explain how you found your answer _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ 262 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Constructed Response A Read About It Megan s girls club was having a pie baking contest Megan knew how to win She would persuade her mom to bake an apple pie for her Her mom s apple pie was the best Megan knew that her mom s apple pie would secure her the first place prize When Megan asked her mom to bake the pie she was shocked by mom s answer Mom told Megan she would give her the recipe but that she would not cheat and bake the pie for her Here is Mom s apple pie recipe 2 cups of red apples 1 cups of green apples 1 cups of brown sugar 1 cups of white sugar 2 cups of white flour 1 cups of wheat flour How many cups IN ALL did Megan use of 1 red and green apples ______________ 2 brown and white sugar _____________ 3 white and wheat flour _____________ Work It Make a math problem red and green apples brown and white sugar white and wheat flour 263 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers B Explain It 4 How did Megan found the total of ALL sugar in the recipe _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ C Reading for Meaning 5 Why did Megan want her mom s apple pie recipe ____ _______________________________________________ 6 Explain why Mom wouldn t bake the pie for Megan ___ _______________________________________________ _______________________________________________ D Vocabulary Acquisition Context Clues Use context clues to determine word meanings 7 Write the bold faced word that means the same as a guarantee b stunned c convince 264 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Learn About It You can add and subtract fractions and mixed numbers on a number line When you are adding you will be moving to the RIGHT on the number line When you are subtracting you will be moving to the LEFT on the number line See It The number line will be partitioned into the same number of pieces as the denominator of the fractions in your problem Start at five sixths Since you are subtracting four sixths you will move four times to represent four sixths on the number line Starting point ______ Ending point ______ 265 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It Let s Try Another One _____ 1 Start on the fraction three fourths 2 To subtract one fourth move one space to the left Starting point ______ Ending point ______ Let s Try Another One _____ Label the number line correctly to show sevenths Show the subtraction problem on the number line Starting point ______ Ending point ______ 266 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Add and Subtract Fractions on a Number Line Learn About It Mixed numbers are different than fractions When adding or subtracting mixed numbers you will move the distance of the whole number and the fraction on the number line See It 2 1 2 2 3 3 Start at the whole number two When you add you will move to the right one whole and one third Remember You are moving one whole Not one space To move one whole number you will move three spaces You will land on the whole number three Start at three and then move one third Starting point ______ Ending point ______ 267 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Practice It A Draw a number line to represent each problem 1 Number line _____ 2 Number line 1 _____ 3 Number line _____ 4 Number line _____ 5 Number line _____ 268 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Constructed Response A Write the problem that each number line represents 1 1 1 Problem ______________ Explain It Explain how you found your answer ___________________________________________________ ___________________________________________________ 2 Problem ______________ Explain It Explain how you found your answer ___________________________________________________ ___________________________________________________ 269 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 4 6 Add and Subtract Fractions and Mixed Numbers Real World and Relevant with Constructed Response A Answer each prompt with a constructed response Yolanda had four and three fourths feet of rope Her little brother Scott needed some rope for an outdoor project he was working on Scott took Yolanda s rope and cut two and one fourth feet of the rope Yolanda needs at least two and one half feet of rope for her school project After Scott cut his piece of rope Yolanda complained to their mother that she didn t have enough rope left 1 How much rope does Yolanda have left ____________ 2 Does she have enough for her school project _______ Explain It Explain your answer _______________________________________________ _______________________________________________ Show It 270 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK OUT 4 NR 4 4 NR 4 1 A Write the correct name next to each fraction model 1 one third five eighths two fifths one whole 2 Is the fraction closer to one half or one whole ____ Explain your answer _____________________________ ______________________________________________ 4 NR 4 2 4 NR 4 3 B Label each number line below to help you find equivalent fractions 3 Write an equivalent fraction for ________ 4 Write an equivalent fraction for ________ 271 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK OUT 4 NR 4 5 Maurice has three fifths of a cup of milk His brother Steven has one half of a cup of milk Who has the most milk ________ Draw It 4 NR 4 4 C Write an addition sentence to show unit fractions 6 ________________ unit fraction ________ 4 NR 4 5 D Write the addition sentence shown by each model 7 _____ _____ _____ _____ ______ 8 _____ _____ _____ _____ _____ _____ ______ 4 NR 4 6 E Complete the addition sentence shown below 9 272 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 Solve real life problems involving addition equivalence comparison of fractions with denominators of 10 and 100 and comparison of decimal numbers as tenths and hundredths using part whole strategies and visual models 4 NR 5 1 Demonstrate and explain the concept of equivalent fractions with denominators of 10 and 100 using concrete materials and visual models Add two fractions with denominators of 10 and 100 4 NR 5 2 Represent read and write fractions with denominators of 10 or 100 using decimal notation and decimal numbers to the hundredths place as fractions using concrete materials and drawings 4 NR 5 3 Compare two decimal numbers to the hundredths place by reasoning about their size Record the results of comparisons with the symbols or

CHECK IN 4 NR 5 4 NR 5 1 A Write the decimal for each model below 1 2 3 ______ ______ ______ 4 NR 5 2 B Write each decimal number as a fraction 4 0 24 _____ 5 0 09 _____ 6 0 76 _____ 7 0 3 _____ 4 NR 5 3 C Compare each set of decimals below Use or 0 03 0 30 9 0 13 1 30 10 0 12 0 21 11 0 56 0 60 8 274 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 1 Equivalent Fractions with Denominators 10 100 Expectations Demonstrate and explain equivalent fractions with denominators of 10 and 100 Learn About It Decimals are parts of a whole The decimal point separates the whole number side from the partial number side See It This block represents one whole Tenths When one whole is broken into ten pieces the whole is divided into tenths Shade in one of the blocks to show a tenth Hundredths When one whole is broken into onehundred pieces the whole is divided into hundredths Shade in one of the blocks to show a hundredth If the square is a whole then the blocks represent a decimal part 1 How many tenths would make up a whole _______ 2 How many hundredths would make up a whole ______ 275 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 1 Equivalent Fractions with Denominators 10 100 Finding the value of decimal numbers Learn About It Here s how to find the value of each digit in a decimal number The place value helps you determine the value of a number We already know how to find the value of whole numbers Whole numbers are the numbers to the left of the decimal place Now let s learn how to find the value of decimal numbers See It Look at this decimal number Tens Ones 3 5 Tenths 2 Hundredths 7 The standard form of this number is 35 27 Tenths The value of the 2 is written as 0 2 This shows that the 2 in the tenths place is right next to the decimal Hundredths The value of the 7 is written as 0 07 This shows that the 7 in the hundredths place is next to the tenths place not right next to the decimal The word form of this number is thirty five and twenty seven hundredths the last number of the decimal names the place 276 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 1 Equivalent Fractions with Denominators 10 100 How to name decimal models Learn About It You can name decimal models in standard form and in word form Decimals in tenths and hundredths can also be equal to each other Some numbers can have whole numbers and decimals at the same time equivalent decimals There are 4 tenths shaded in this figure Standard form 0 4 Word form four tenths There are 40 hundredths shaded in this figure Standard form 0 40 Word form forty hundredths Decimals with whole numbers Some decimals also have whole numbers Standard form A 2 56 Word form two and fifty six hundredths B Standard form 1 40 Word form one and fortyhundredths 277 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 1 Equivalent Fractions with Denominators 10 100 Practice It A Write the decimal number for each model below 1 2 3 ____ ____ ____ ____ ____ ____ ____ ____ ____ B Shade in each model below to show the decimal 0 56 0 17 0 08 0 75 0 25 0 39 278 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 1 Equivalent Fractions with Denominators 10 100 Real World and Relevant with Constructed Response A Answer each prompt with a constructed response 1 Shade in the decimal model correctly to show 1 07 Lana shaded in her decimal model Then she wrote the decimal number in word form Lana wrote one and seven tenths Explain why one and seven tenths is CORRECT or INCORRECT _____________________________________________________ _____________________________________________________ 2 Shade in the model to show one and twenty six hundredths 1 26 Explain how to shade in the decimal model correctly _______________________________________________ _______________________________________________ 279 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 1 Equivalent Fractions with Denominators 10 100 Constructed Response A Read each prompt and write a constructed response 1 Shade in the model below to show 1 45 Explain It Explain how to shade in the model to show 1 45 _______ _______________________________________________ _______________________________________________ Write 1 45 in word form __________________________ _______________________________________________ 2 What is the difference in 0 90 and 0 09 ____________ ______________________________________________ Explain It Explain your answer _____________________________________________________ _____________________________________________________ _____________________________________________________ 280 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 2 Represent Read and Write Fractions Expectations Represent read and write fractions with denominators of 10 or 100 using decimal notation Learn About It Decimals can also be written as fractions You can break apart a decimal number and write each digit as a fraction See It The standard form of this decimal is written as 0 22 The word form of this decimal is written as twenty two hundredths How to write 0 22 as a fraction Look at the word form of the decimal twenty two hundredths This means the fraction would be the number 22 over the number 100 It is written like this Now write it as a sum of two fractions You cannot add tenths and hundredths so change two tenths to an equivalent fraction Now you can show the fraction as a sum of two fractions 281 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 2 Represent Read and Write Fractions Decimals as Fractions Let s Try Some More Write the decimal 0 57 as a fraction fifty seven hundredths 57 is the numerator and 100 is the denominator Write the fraction Explain It The number behind the decimal is the number that is your numerator Name the place of the last digit in your number and that will name the denominator One More Write the number 1 3 as a fraction one and three tenths 1 is a whole number 3 is the numerator and 10 is the denominator Write the number 1 Explain It The number behind the decimal is the number that is your numerator Name the place of the last digit in your number and that will name the denominator In this number you have a whole number at the beginning before the decimal The whole number goes in front of the fraction 282 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 2 Represent Read and Write Fractions Practice It A Write each decimal in word form and as a fraction Decimal number Word Form Fraction 0 56 0 78 2 45 1 2 0 12 7 8 B Write the decimal and fraction form of each number 1 eighty nine hundredths ________________________ _______________________________________________ 2 seventeen hundredths _________________________ _______________________________________________ 3 six tenths ___________________________________ _____________________________________________________ 283 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 2 Represent Read and Write Fractions Practice It A Write each decimal as a fraction Show each fraction as a sum Fraction _____ Sum _______ Fraction _____ Sum _______ Fraction _____ Sum _______ Fraction _____ Sum _______ Fraction _____ Sum _______ Fraction _____ Sum _______ Fraction _____ Sum _______ Fraction _____ Sum _______ B Shade in the model below to show the decimal 0 78 Now write the decimal as a fraction and show it as a sum of two fractions Fraction _______ Sum _______ 284 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 2 Represent Read and Write Fractions Learn About It Decimals can also be shown on a number line Since decimals are not whole numbers they will be found in between the whole numbers There will be 10 equal parts or partitions between each whole number See It A B Point A 1 4 Point B 1 8 1 Write each decimal as a fraction Point A 1 Point B 1 2 Name a decimal 1 BETWEEN Point A and Point B _________ 2 BEFORE Point A on the number line ________ 3 AFTER Point B on the number line _________ 285 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 2 Represent Read and Write Fractions Decimals on a number line You Try It Write in the decimals between the whole numbers Then name each point labeled on the number line C D 3 0 1 Point C _____ 4 0 Point D _____ 2 Write each decimal as a fraction Point C _____ Point D _____ 3 Name a decimal BETWEEN Point C and Point D ____________ BEFORE Point C on the number line ________ AFTER Point D on the number line _________ 4 Write the name of that decimal as a fraction ________ 5 Write the name of that decimal as a fraction ________ 286 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 2 Represent Read and Write Fractions Decimals to the hundredths place on a number line Learn About It Decimals numbers on a number line can be partitioned into tenths and also into hundredths Between each whole number are ten spaces tenths and between each tenth are ten spaces hundredths 4 0 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 5 0 Let s break down 4 4 and 4 5 into hundredths E F 4 40 4 50 1 Point E _____ 2 Write each decimal as a fraction mixed number Point E _____ Point F _____ Point F _____ 287 Copyright 2023 by Concise Curriculum Do not duplicate 4 60

4 NR 5 2 Represent Read and Write Fractions Constructed Response A Answer each prompt with a constructed response 1 Start the number line with the whole number 5 End the number line with the whole number 6 Label the decimals in between 5 and 6 Explain It Explain how you labeled the number line correctly _____________________________________________________ _____________________________________________________ _____________________________________________________ 2 Label 5 2 as Point A Write 5 2 as a fraction mixed number _______ 3 Label 5 9 as Point B Write 5 9 as a fraction mixed number _______ 288 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 3 Compare Two Decimal Numbers Expectations Compare two decimal numbers to the hundredths place by reasoning about their size Record the results of comparisons with the symbols or If the first number is smaller than the second it is less than

4 NR 5 3 Compare Two Decimal Numbers You Try One 1 0 79 Compare each set of decimals below 0 78 0 87 Tenths Hundredths 2 0 21 0 12 0 23 Tenths Hundredths Put the decimals in order from least to greatest ___ ___ ___ greatest to least ___ ___ ___ Put the decimals in order from least to greatest ___ ___ ___ greatest to least ___ ___ ___ Comparing decimals using hundredths models Learn About It You can also compare decimals using hundredths models Count the blocks shaded on the models to see which decimal is smaller or larger See It Count the shaded blocks to compare the decimals ____ ____ ____ ____ 290 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 3 Compare Two Decimal Numbers Practice It A Place the decimals in order from greatest to least 1 0 68 2 1 32 0 76 1 34 0 67 0 86 ________________________ 1 43 1 33 _________________________ B Use the symbol that makes each number sentence true 0 56 0 89 0 89 0 87 0 33 0 34 0 67 0 23 291 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 3 Compare Two Decimal Numbers Constructed Response A Answer the prompt with a constructed response Kyra s test on ordering decimals was a complete surprise All of the numbers were written in word form In order to place the decimals in order she would need to write them in standard form first Below is Kyra s test Place the decimal numbers below in order from LEAST to GREATEST 1 2 3 4 nine and nine and nineteen nineteen two hundredths two tenths and two hundredths hundredths Show your work Rewrite each decimal in standard form from LEAST to GREATEST __________ ___________ __________ __________ Explain It Explain how you ordered the decimals from least to greatest _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ 292 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 3 Compare Two Decimal Numbers Constructed Response B Answer each prompt with a constructed response 1 Which decimal is GREATER _______________ seven hundredths OR seven tenths Explain how you found your answer Work It ___________________________ _______________________________________________ _______________________________________________ 2 Which decimal is SMALLER _______________ five hundredths OR five tenths Explain how you found your answer Work It ____________________________ _______________________________________________ _____________________________________________________ 293 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 3 Compare Two Decimal Numbers Constructed Response A Decimal Numbers Look at each set of decimal numbers below Circle equal or not equal and explain why the two numbers are EQUAL or why the two numbers are NOT EQUAL 1 0 23 and 0 230 Equal Not Equal Explain It _______________________________________________ _______________________________________________ 2 1 23 and 10 23 Equal Not Equal Explain It _______________________________________________ _______________________________________________ 3 0 12 and 0 012 Equal Not Equal Explain It ____________________________________________ _______________________________________________ 4 4 56 and 4 506 Equal Not Equal Explain It _______________________________________________ _______________________________________________ 294 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 3 Compare Two Decimal Numbers Constructed Response A Read About It Hayden Sydney and Bethany trained all year for the state track competition All three girls wanted to qualify for the regional meet In order to qualify for the regional meet a runner had to have the fastest time in that event The girls competed in two different events the 1 mile run and 2 mile run Their times in minutes are below 1 mile run 2 mile run Hayden 9 27 19 31 Sydney 9 36 18 43 Bethany 9 19 19 34 1 Who had the fastest time on the 1 mile run ____________ 2 Who had the slowest time on the 1 mile run ____________ 3 Who had the fastest time on the 2 mile run _____________ 4 Who had the slowest time on the 2 mile run ___________ Work It Making a chart would be a great idea 1 mile run 2 mile run Hayden Sydney Bethanny 295 Copyright 2023 by Concise Curriculum Do not duplicate

4 NR 5 3 Compare Two Decimal Numbers 5 Order the 1 mile run from the fastest runner to the slowest ____________ ____________ ___________ 6 Order the 2 mile run from the fastest runner to the slowest ___________ ____________ ___________ B Explain It 7 How did you find the fastest and slowest times ______ _______________________________________________ _______________________________________________ 8 Explain the process you used to solve the problem _______________________________________________ _______________________________________________ C Vocabulary Acquisition Context Clues Use context clues to determine word meanings 9 Write a vocabulary word that means the same as a b c d e f rivalry district participated in practiced meet requirements happenings 296 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK OUT 4 NR 5 4 NR 5 1 A Write the decimal for each model below 1 2 3 ______ ______ ______ 4 NR 5 2 B Write each decimal number as a fraction 4 0 14 _____ 5 0 25 _____ 6 0 89 _____ 7 0 7 _____ 4 NR 5 3 C Compare each set of decimals below Use or 8 0 14 10 0 18 0 9 0 21 9 0 50 11 0 63 0 5 0 69 297 Copyright 2023 by Concise Curriculum Do not duplicate

Measurement and Data Reasoning time metric measurements distance elapsed time liquid volume mass and length 4 MDR 6 Measure time and objects that exist in the world to solve real life mathematical problems and analyze graphical displays of data to answer 4 MDR 6 1 Use the four operations to solve problems involving elapsed time to the nearest minute intervals of time metric measurements of liquid volumes lengths distances and masses of objects including problems involving fractions with like denominators and also problems that require expressing measurements given in a larger unit in terms of a smaller unit and expressing a smaller unit in terms of a larger unit based on the idea of equivalence 4 MDR 6 2 Ask questions and answer them based on gathered information observations and appropriate graphical displays to solve problems relevant to everyday life 4 MDR 6 3 Create dot plots to display a distribution of numerical quantities quantitative measurement data 298 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK IN 4 MDR 6 4 MDR 6 1 A Read and solve each problem below 1 Todd worked in the yard from 3 35 P M until 4 55 P M How long did Todd work in the yard Find the elapsed time ELAPSED TIME _______ 2 A box of coins weighs 5 000 grams How many kilograms does the box of coins weigh 5 000 grams _______ kilograms 3 Matthew has 2 liters of lemonade How many milliliters of lemonade does he have 2 liters ______ milliliters 4 MDR 6 2 4 MDR 6 3 Use the dot plot to answer the questions below The students in Mrs Doyal s class grew cabbage plants Growth of cabbage plants in centimeters X X X X X X X 0 1 of a centimeter _______ How many plants grew of a centimeter ______ 1 How many plants grew 2 299 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Expectations Use the four operations to solve problems involving elapsed time to the nearest minute and intervals of time Learn About It Everyone should be able to tell time on a clock by the hour and minute hand by now Now we will learn about elapsed time Elapsed time is the amount of time that has passed between the beginning and the end A M is the time from midnight until noon and P M is the time from noon until midnight Other Units of Time 1 hour 60 minutes 1 minute 60 seconds 1 day 24 hours 1 week 7 days 1 year 12 months See It Todd worked in the yard from 3 30 P M until 4 45 P M How long did Todd work in the yard Find the elapsed time Todd started at 3 30 P M Todd ended at 4 45 P M Steps to finding elapsed time 1 Find the difference in the hours the first hour is 3 and the second hour is 4 Difference 1 hour 2 Find the difference in the minutes the first minutes is 30 and the second minutes is 45 Difference 15 minutes Answer It Elapsed Time 1 hour and 15 minutes 300 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Learn About It Other Units of Time When converting other units of time you will either go from a larger unit to a smaller unit or a smaller unit to a larger unit Other Units of Time 1 hour 60 minutes 1 minute 60 seconds 1 day 24 hours 1 week 7 days 1 year 12 months Important A larger unit will make a smaller unit bigger so you will use multiplication to convert the units A smaller unit will make a larger unit smaller so you will use division to convert the units See It Gary goes camping for 2 days How many hours is Gary gone camping _______ How many hours are in 1 day 24 So to convert you will multiply 2 x 24 Convert 2 days ___ hours Larger unit to a smaller unit multiply Answer It 2 x 24 48 so Gary was camping for 48 hours You Try It Solve each problem Be sure to show your work 1 Susan went on vacation for 2 weeks How many days was Susan on vacation ___________ 2 Todd can jump rope for 3 minutes How many seconds can Todd jump rope __________ 3 Kelsey s dance class is 2 hours long How many minutes long is her dance class _________ 301 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Practice It Solve each problem below Show your work 1 Kendall rode her bike for 2 hours How many minutes did she ride her bike _____ Work It 2 Lee read a book from 9 30 A M until 10 15 A M How many minutes did Lee read her book ____ Work It 3 Destiny went on a camping trip for 3 days How many hours did Destiny go camping _____ Work It 4 Brad swam laps in the pool for 5 minutes How many seconds did Brad swim laps ______ Work It 5 Suzanna went to summer camp for 3 weeks How many days did Suzanna go to camp ______ Work It 6 Yisel spent 55 minutes cleaning her room She started at 6 25 P M What time did Yisel finish _____ Work It 7 Jenny worked on her art project for 1 hour and 20 minutes Jenny finished at 6 00 P M so when did she start _____ Work It 302 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Units of Time Number Line Learn About It You can also use a number line to help show units of time Divide a number line into 4 partitions or parts to show 15 minutes of each hour Each of these partitions is one fourth of an hour See It Each mark on the number line represents 15 minutes or Minutes 0 15 30 45 of an hour 1 Fraction of an hour You Try It Use the number line above to answer the following questions 1 Susan spent 45 minutes working on her book report What fraction of an hour did Susan spend on her report _____ 2 Kaitlyn spent of an hour cleaning her room How many minutes did Kaitlyn spend cleaning her room _______ 3 Destiny and LaKendra walked for of an hour on Tuesday and of an hour on Wednesday How many minutes did they walk altogether on both days ______ 303 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Multiplication with Time Learn About It You can use multiplication to find units of time Usually you will see the word of in the multiplication problem For example one fourth of the two hours was spent blowing bubbles You would multiply one fourth times 2 hours See It Marla takes a three hour bus ride to Grandma s house Marla spends of the time reading a book Question How long did Marla read her book _______ Multiply the length of the bus ride times the time she spent reading 3 Marla spent of an hour reading Use the chart on previous page to show fractions and minutes How many minutes did Marla spend reading Question How long did Marla read her book _______ Answer It Marla spent 45 minutes of her bus ride reading 304 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems You Try It Use multiplication to solve each word problem 1 Gavin has 2 hours to clean up the yard before his mom comes home He spent one fourth of the time raking leaves He spent another one fourth of the time trimming bushes Cutting grass took him the longest amount of time and he spent two fourths of the time cutting the grass How many minutes did Gavin spend on each task Work It raking leaves trimming bushes cutting grass 2 Gary has 4 hours to do all of his homework and chores before he can play baseball Gary spends half of his time doing his chores He spends one fourth of his time doing his math homework and one fourth of his time doing his social studies homework How many minutes did Gary spend on each task Work It chores math homework social studies homework 305 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Real World and Relevant with Constructed Response A Answer each prompt with a constructed response Tamara spends eight hours a day in school Three fourths of her day is spent attending her academic classes science math reading language arts and social studies The other fourth of her day is spent at P E and lunch Tamara complained to her mother that she spent seven hours a day in her academic classes Tamara was INCORRECT about the amount of time that she spent in her academic classes 1 Does Tamara spend seven hours a day in her academic classes Circle YES or NO 2 How much time does she spend in her academic classes _______________________________________________ Explain It Explain how you found your answer _______________________________________________ _______________________________________________ _______________________________________________ 3 How much time does she spend at P E lunch ______ Explain It _______________________________________________ _______________________________________________ _______________________________________________ 306 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Real World and Relevant Constructed Response B Answer each prompt with a constructed response Chad was excited about attending a sports camp during the summer For six hours every day Chad was going to play his favorite sports One third of his time would be spent playing basketball One third of his time would be spent playing soccer and the last third of his time would be spent swimming Chad told his mother that he would be playing basketball for an hour each day playing soccer for two hours each day and swimming for three hours each day 1 Is Chad correct about his schedule ________________ _______________________________________________ Explain It Explain how you found your answer _______________________________________________ _______________________________________________ 2 How much time will Chad spend on each sport every day basketball ___________ Work It soccer ______________ swimming ____________ 307 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Real World and Relevant with Constructed Response A Read About It Coach Young was planning Field Day for Westside Elementary School The events were scheduled to start at 8 00 A M The day would not end until 3 15 P M Coach planned the events the week before but misplaced his schedule There was time between each event for the students to have a break and drink water He tried to recreate his chart but couldn t remember everything correctly Help Coach Young fill in the chart for the Field Day events Events sack race Starting Time Elapsed Time 8 00 A M 50 minutes kick ball 9 15 A M egg toss 10 25 A M disc throw 11 00 A M relay race 11 45 A M 55 minutes picnic lunch 1 05 P M 25 minutes softball toss 1 45 P M tug of war 2 20 P M broad jump 2 50 P M End Time 10 05 A M 20 minutes 11 35 A M 2 10 P M 25 minutes 3 15 P M Work It Show your work to find the missing elapsed times or end times 308 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems B Vocabulary Acquisition Match the vocabulary word to the correct definition a b c d e events ____ scheduled ____ planned ____ misplaced ____ recreate ____ 1 2 3 4 5 list of planned activities arranged create again designed lost temporarily C Reading for Meaning Locate the answers in the story 1 Why does Coach need help with his schedule _______ ____________________________________________ ____________________________________________ 2 What time does field day start and end _______ and _______ 3 CAUSE and EFFECT The cause is why something happened the effect is the result CAUSE Coach lost his schedule EFFECT _____________________________________ D Write About It Write in your math journal Write a schedule of five activities with start and end times Have a partner find the elapsed times and write an explanation about how they found the elapsed time 309 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Mass Metric System Learn About It In the metric system the measure of how much matter an object has is called mass Mass can be measured in milligrams mg grams g kilograms kg and metric tons t The mass of an object never changes Units of Mass in the Metric System 1 gram 1 000 milligrams 1 kilogram 1 000 grams 1 metric ton 1 000 kilograms See It GRAM A gram is VERY LIGHT A pinch of salt could weigh a gram KILOGRAM It takes 1 000 grams to make 1 kilogram 7 apples could weigh a kilogram You Try It Tell whether each object below could weigh a gram or a kilogram 1 a dollar bill _________ 2 bag of rice ___________ 3 a penny _________ 4 a cantaloupe ___________ 5 a button _________ 6 a business card _________ 7 small paper clip ________ 8 a large dictionary _______ 310 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Practice It A Read each problem and convert each unit 1 Lauren s new puppy weighs 2 kilograms How many grams does the puppy weigh ______ grams 2 Ted has 4 kilograms of flour How many grams of flour does Ted have ______ grams 4 Kaylee s backpack weighs 5 kilograms How many grams does Kaylee s backpack weigh ______ grams 5 A box of coins weighs 5 000 grams How many kilograms does the box of coins weigh Work It Work It Work It Work It ______ kilograms B Compare the units Circle the correct answer 6 Which is larger 2 grams or 1 000 milligrams 7 Which is larger 1 ton or 1 kilogram 8 Which is larger 5 000 grams or 8 kilograms 311 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Use a number line to show weight Learn About It You can show weight on a number line See It Tamiya bought 2 kilograms of rice at the grocery store Where would this amount fall on a number line It would fall between the numbers 1 and 4 Make a black dot to show the correct amount on the number line You Try It Tim bought 3 kilograms of vegetables for dinner Where would this fraction fall on a number line It would fall between the whole numbers ___ and ___ Show the amount on the number line Label the number line above with the correct amounts 312 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Repeated addition or multiplication See It Graham bought 2 boxes of popcorn at the movie theater Each box weighed 1 kilograms How much did both boxes of popcorn weigh_______ 1 Use repeated addition 1 1 2 2 Simplify your answer 1 whole 3 Add 1 whole to the whole number 2 to equal 3 whole numbers 1 Use multiplication 1 2 2 Change both numbers to fractions 3 Simplify 3 Answer It The boxes of popcorn weighed 3 kilograms You Try It Greg bought 3 boxes of doughnuts Each box weighed 2 kilograms How much did all the boxes of doughnuts weigh Use repeated addition or multiplication Work It Answer It The boxes of doughnuts weighed ________ kilograms 313 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Capacity Metric System Learn About It Capacity is the measure of how much something will hold In the metric system we measure capacity with milliliters mL and liters L Units of Capacity in the Metric System 1 liter 1 000 milliliters Things we measure in liters fuel oil milk laundry detergent shampoo juice soda dish detergent conditioner lotion Things we measure in milliliters soup medicine honey perfume mouthwash syrup toothpaste liquid make up 314 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Method 2 Using multiplication and division Convert SMALLER units to LARGER units you will DIVIDE Convert LARGER units to SMALLER units you will MULTIPLY See It Matthew has 2 liters of lemonade How many milliliters of lemonade does he have ______ Convert L to mL larger to a smaller unit 1 liter 1 000 mL multiply 2 liters ___ mL 2 liters x 1 000 mL 2 000mL Answer It Matthew has 2 000 mL of lemonade Another Method Make a Table liters milliliters 1 1 000 2 Multiply 2 times the number of milliliters in a liter How many milliliters are in 2 liters _________ 315 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Practice It A Fill in each chart below to convert the units 1 Miss Connie is making biscuits for breakfast at school She will need 5 liters of milk How many milliliters of milk will Miss Connie use for her biscuits liters milliliters 1 liter 1 000 2 liters 3 liters 4 liters 5 liters Answer It Miss Connie will use _______ milliliters of milk 2 Madelyne has 6 liters of liquid to use for her science fair project How many milliliters does Madelyne have liters milliliters 1 liter 1 000 2 liters 3 liters 4 liters 5 liters 6 liters Answer It Madelyne has _______ milliliters of liquid 316 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems 3 Courtney has 7 000 milliliters of melted butter to pour into the popcorn machine at school How many liters of melted butter does Courtney have liters 1 liter milliliters 1 000 mL Answer It Courtney has _____ liters of melted butter 4 Shawn buys 3 liters of soda for his after school club party How many milliliters of soda does Shawn have liters 1 liter 2 liters 3 liters milliliters 1 000 mL Answer It Shawn buys _____ milliliters of soda 317 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Learn About It There are metric units of measurement that we use to measure how tall or long something is The units of measure for length are millimeters mm centimeters cm meters m kilometers km Metric System 1 centimeter 10 millimeters 1 meter 100 centimeter 1 kilometer 1 000 meters Think About It Think about how you would convert units when converting a larger unit to a smaller unit you will multiply and when converting a smaller unit to a larger unit you will divide You can also compare the units to see what the new measurement will be Maurice measured the pink eraser that he used in math class every day The eraser measured 20 millimeters How many centimeters would his eraser measure 1 centimeter 10 millimeters ___ centimeters 20 millimeters If 1 centimeter equals 10 millimeters so 2 centimeters equals 20 millimeters 318 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems You Try It 1 Jilleyn practices swimming three kilometers each day How many meters does Jilleyn swim each day ________ Work It 1 kilometer 1 000 meters 2 Sam is on the track team and runs after school each day Each day Sam runs 2 kilometers How many meters does Sam run each day _________ Work It 1 kilometer 1 000 meters 3 Aaliyah was measuring the length of her desk Her desk measured 15 centimeters How many millimeters is the length of her desk ________ Work It 1 centimeter 10 millimeters 4 Kayla and Kyleigh walk 12 meters to the bus stop each morning How many centimeters do they walk each morning _______ Work It 1 centimeter 10 millimeters 319 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Show Length on a Number Line Learn About It You can also show length on a number line See It Jason walks 1 2 kilometers to his friend Todd s house The boys then walk another 0 6 kilometers to Steve s house How many kilometers did the boys walk in all _________ Start 1 2 on 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 Answer It __________ You Try It Jason and Todd walked 1 1 kilometers to another friend s house Then the boys walked 0 3 kilometers to the convenience store for a soda How many miles did the boys walk in all ____________ 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 Answer It __________ 320 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems Constructed Response A Answer each prompt with a constructed response Dan got a job as a math tutor Before he could start tutoring on his own he had to pass a test on converting measurements in the metric system Some of the answers on his test were CORRECT and some of them were INCORRECT In order to pass the test Dan had to decide which conversions were correct and which were incorrect Help Dan figure out which problems are CORRECT and which ones are INCORRECT Circle CORRECT or INCORRECT If the answer is INCORRECT explain how to make the corrections 1 3 centimeters 40 millimeters CORRECT or INCORRECT ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ 2 5 000 meters 5 kilometers CORRECT or INCORRECT ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ 321 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 1 Solving Measurement Problems B Jenna Julia and Jessica were competing in a charity run with their Girls Club The winner of the run would earn money to donate to charity Jenna ran 4 kilometers Julia ran 6 000 meters and Jessica ran 5 kilometers Work It Step 1 Convert the 6 000 meters to kilometers Step 2 Compare all of the lengths in kilometers Show each length on a number line Lengths in kilometers 1 Who ran the farthest __________________________ 2 Who ran the shortest distance ___________________ 3 Place the runners in order from greatest distance to shortest distance ________________ _______________ ________________ 322 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 2 6 3 Ask and Answer Questions Learn About It A line plot is another way of graphing and organizing data The number line on the bottom shows what you are measuring or graphing and above the number line you would use an x or a dot to show the measurement for that category See It This line plot shows the amount of time spent doing homework Time Spent Doing Homework There are 3 Xs There are 2 Xs X X X X X X X 0 1 1 How many students worked of an hour _____ Count the number of Xs above the mark on the number line 2 How many students worked of an hour _____ Count the number of Xs above the number line mark on the 3 How many students worked one half an hour or less ____ Count the number of Xs at the mark and less Add all of the Xs together to find the total 323 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 2 6 3 Ask and Answer Questions You Try It Amount of Peppermint in kilograms X X X X X X 0 1 Amy and Celeste went to the candy store with four of their friends The girls were able to scoop their own peppermint and put it into a bag The store then weighed the peppermint for each girl 1 How many girls bought of a kg of peppermint _____ 2 How many girls bought a kg of peppermint ______ 3 What was the total weight of peppermint the girls bought that weighed of a kilogram _________ 4 How many girls bought a peppermint ________ kilogram or more of 5 Explain It Explain how you found the answer for problem 4 _______ _____________________________________________________ _____________________________________________________ _____________________________________________________ 324 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 2 6 3 Ask and Answer Questions Practice It 1 Use the data from the dot plot to answer 1 5 2 Use the data from the dot plot to answer questions 6 9 This dot plot shows how high the cabbage plants that the students in Mrs Doyal s class grew in one month This dot plot shows the weight of meat sold at the deli in one day Growth of cabbage plants in centimeters X X X X X X X X X X X 0 1 1 How many plants grew centimeter _______ of a 2 How many plants grew centimeter ______ 3 How many plants grew centimeter _______ Weight of deli meat sold in kilograms XX XX XX X X X X 0 1 6 What is the total weight of meat sold that weighed kilogram _____ of a of a 4 Which two heights had an equal number of plants ______ and ______ 5 How many more plants grew of a centimeter than 1 cm ________ plants of a 7 How many packages of meat were sold that weigh of a kg _____ packages 8 Which size of meat was the most popular weight at the deli that day _____ 9 Put the weights of meat in order from most popular to the least popular ____ ____ ____ 325 Copyright 2023 by Concise Curriculum Do not duplicate ____

4 MDR 6 2 6 3 Ask and Answer Questions Constructed Response A Read About It Nancy and Lindsey were making goody bags for the class endof the year party They went to the store to buy all their supplies They bought 3 bags of milk chocolate that weighed one fourth of a pound each They also bought 4 bags of white chocolate that weighed three fourths of a pound each Dark chocolate was also on their list The store was out of dark chocolate that day Also to complete the goody bags they bought 5 bags of peanuts that weighed one half a pound each Make a line plot to show the number of goodies they bought Remember to place an x for each bag that was purchased 1 What was the total weight of milk chocolate purchased ____________________________________________ 2 What was the total weight of white chocolate purchased ___________________________________ 3 What was the total weight of peanuts purchased _____________________________________________ B Explain It 4 Explain how you found the total weight of peanuts purchased _____________________________________________________ 326 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 2 6 3 Ask and Answer Questions Student Generated Collect Data Make a Dot Plot Think of a question you can ask your classmates or family members Asking someone about something that could be their favorite is a great way to start Question ________________________________ ________________________________________ Data Make at least 5 different categories and record your data below _________ ________ _________ ________ _________ Now take your data and make a line plot below Place an x over each category for each person that answered in that category Write the names of your categories here _____ _____ _____ _____ _____ 327 Copyright 2023 by Concise Curriculum Do not duplicate

4 MDR 6 2 6 3 Ask and Answer Questions Student Generated Collect Data Make a Line Plot Think of a question you can ask your classmates or family members Asking someone about something that could be their favorite is a great way to start Question ________________________________ ________________________________________ Data Make at least 5 different categories and record your data below _________ ________ _________ ________ _________ Now take your data and make a line plot below Place an x over each category for each person that answered in that category Write the names of your categories here _____ _____ _____ _____ _____ 328 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK OUT 4 MDR 6 4 MDR 6 1 A Read and solve each problem below 1 Taj worked in the yard from 1 25 P M until 3 35 P M How long did Taj work in the yard Find the elapsed time ELAPSED TIME _______ 2 A box of coins weighs 4 000 grams How many kilograms does the box of coins weigh 4 000 grams _______ kilograms 3 Matteo has 3 liters of lemonade How many milliliters of lemonade does he have 3 liters ______ milliliters 4 MDR 6 2 4 MDR 6 3 Use the dot plot to answer the questions below The students in Mrs Doyal s class grew tomato plants X X X X X X X X Growth of tomato plants in centimeters 0 1 1 How many plants grew of a centimeter _______ 2 How many plants grew of a centimeter ______ 329 Copyright 2023 by Concise Curriculum Do not duplicate

Geometric and Spatial Reasoning polygons points lines line segments rays angles perpendicular lines area perimeter 4 GSR 7 Investigate the concepts of angles and angle measurement to estimate and measure angles 4 GSR 7 1 Recognize angles as geometric shapes formed when two rays share a common endpoint Draw right acute and obtuse angles based on the relationship of the angle measure to 90 degrees 4 GSR 7 2 Measure angles in a reference to a circle with the center at the common endpoint of two rays Determine an angle s measure in relation to the 360 degrees in a circle through division or as a missing factor problem 330 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK IN 4 GSR 7 4 GSR 7 1 A Write the correct name of each angle below acute 1 right 2 obtuse 3 _____ _____ _____ 4 GSR 7 2 B Find the measure of the rest of the angle 125 90 180 125 ___ 180 90 ___ C Find the angle measure using multiplication of 360 ___ This angle is one fourth of the circle What is one fourth of 360 ______ degrees 331 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 7 1 Recognize Angles as Geometric Shapes Expectations Recognize angles as geometric shapes formed when two rays share a common endpoint Draw right acute and obtuse angles based on the relationship of the angle measure to 90 degrees Learn About It When two rays meet an angle is formed The endpoint where they meet is called the vertex See It ray vertex ray Types of Angles A right angle has a measure of 90 An acute angle has a measure of less than 90 A circle has a measure of 360 An obtuse angle has a measure greater than 90 A straight line measures 180 This is half of a circle 332 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 7 1 Recognize Angles as Geometric Shapes See It Tell whether the hands on each clock form an acute angle a right angle or an obtuse angle The hands on the clock form an acute angle The hands on the clock form a right angle The hands on the clock form an obtuse angle You Try It Write the type of angle formed by the hands of each clock acute right or obtuse 1 2 3 _______ ________ 4 5 _______ ________ 6 ________ ________ 333 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 7 1 Recognize Angles as Geometric Shapes Practice It Circle each correct answer below 1 Label the right angle and the two acute angles in the triangle below 2 What type of angles are found in this square 3 What type of angle is shown by the clock hands below 4 What type of angle is shown by the clock hands below right or acute right or acute right or obtuse 334 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 7 1 Recognize Angles as Geometric Shapes Learn About It The center of the circle is called the vertex A degree is 1 out of 360 degrees of a full turn around the circle This equals 1 When a circle is divided into four equal pieces four right angles are formed Each of 360 of the circle is equal to 90 See It Multiply the fraction times 360 to find the measure of the angle 1 2 of 360 _____ _____ degrees 4 of 360 _____ _____ degrees 5 __ of 360 _____ _____ degrees __ of 360 _____ _____ degrees 3 of 360 _____ _____ degrees 6 __ of 360 _____ _____ degrees 335 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 7 1 Recognize Angles as Geometric Shapes How to measure angles with a protractor Learn About It A protractor measures angles A protractor is half the size of a circle so it measures up to 180 When an angle starts on 0 on the right side and is open up to the left side you will use the inside numbers on the protractor This angle measures 130 When an angle starts on 0 on the left side and is open up to the right side you will use the outside numbers on the protractor This angle measures 140 336 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 7 2 Determine an Angle s Measure Measuring angles with partial measures Learn About It Sometimes you will be given partial angle measures You can find the measurements of some angles when given a partial measurement of the angle See It This angle measures 120 degrees 55 Answer It To find the value of the X start with the total number of degrees and subtract the value of the known part of the angle 55 X 120 55 65 X 65 You Try It A straight line measures 180 Find the measure of the other part of the angle 165 90 Answer It 180 165 ___ Answer It 180 90 ___ 337 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 7 2 Determine an Angle s Measure Drawing an angle with a protractor Learn About It When given an angle measure you can use a protractor to draw the angle See It Draw an angle that measures 45 1 If your angle will open to the right side then you will use the zero on the right side of the protractor 2 Make a mark on the zero the 45 degree mark and the center circle 3 The center mark is the vertex of the angle 45 You Try It Draw each angle using a protractor 1 1200 2 1600 3 1450 4 900 338 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 7 2 Determine an Angle s Measure Practice It Which is MOST LIKELY the measurement of each angle 1 2 This angle measures 120 60 A B C D 45 degrees 60 degrees 130 degrees 180 degrees 3 A B C D A B C D 45 degrees 60 degrees 120 degrees 180 degrees 4 45 degrees 90 degrees 180 degrees 150 degrees A B C D 45 degrees 20 degrees 180 degrees 130 degrees 5 Bethanny is working on her homework measuring angles Angle T measures 75 One part of angle T measures 40 What is the measure of the other part of angle T 75 40 X x T 40 Answer It ___________ 339 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 7 2 Determine an Angle s Measure Constructed Response A Answer each prompt with a constructed response Look at the protractor below Keela was learning how to measure angles in her class For homework she had to measure an angle on her own When she measured the angle at home Keela said that the angle measure 120 degrees 1 Is Keela correct by saying that the angle measured 1200 _____________________________________________________ 2 What is the CORRECT angle measure ______________ Explain It 3 What mistake did Keela make when using the protractor _______________________________________________ _______________________________________________ _______________________________________________ 340 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 7 2 Determine an Angle s Measure Constructed Response B Answer each prompt with a constructed response Barbara is working on measuring angles for a home project She needs to make sure that the wood she cuts has the correct measure Angle S measures 80 degrees One part of angle S measures 45 degrees Barbara needs to find the measure of the smaller angle angle x x Angle S Barbara s answer 800 450 45 degrees 1 Is Barbara s answer CORRECT ___________________ 2 What MISTAKE did Barbara make _________________ _______________________________________________ Explain It 3 Explain how Barbara can correct her mistake ________ _______________________________________________ _____________________________________________________ _____________________________________________________ 341 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK OUT 4 GSR 7 4 GSR 7 1 A Write the correct name of each angle below acute 1 right obtuse 2 _____ 3 _____ _____ 4 GSR 7 2 B Find the measure of the unknown angle 165 110 180 165 ___ 180 110 ___ C Find the angle measure using multiplication of 360 ___ This angle is one half of the circle What is one half of 360 ______ degrees 342 Copyright 2023 by Concise Curriculum Do not duplicate

Geometric and Spatial Reasoning 4 GSR 8 Identify and draw geometric objects classify polygons based on properties and solve problems involving area and perimeter of rectangular figures 4 GSR 8 1 Explore investigate and draw points lines line segments rays angles right acute obtuse perpendicular lines parallel lines and lines of symmetry Identify these in twodimensional figures 4 GSR 8 2 Classify compare and contrast polygons based on lines of symmetry the presence or absence of parallel or perpendicular line segments or the presence or absence of angles of a specified size and based on side lengths 4 GSR 8 3 Solve problems involving area and perimeter of composite rectangles involving whole numbers with known side lengths 343 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK IN 4 GSR 8 4 GSR 8 1 A Draw the correct figures in each box below line segment line ray point 4 GSR 8 2 B Circle the figure that does NOT have a line of symmetry C Circle the correct name of the figure below A pentagon B triangle C hexagon D square 4 GSR 8 3 D Read the word problem below Elyse s mother made a birthday cake for her That had a perimeter of 32 inches The cake was in the shape of a square How long was each side of the cake ____ 344 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 1 Explore Two Dimensional Figures Expectations Explore investigate and draw points lines line segments rays angles right acute obtuse perpendicular lines parallel lines and lines of symmetry Identify these in twodimensional figures Learn About It There are many parts to lines and angles A line goes on and on in opposite directions without end A ray is part of a line It has one endpoint and then goes in one direction and does not end A line segment has two endpoints A line segment is part of a line A point names a specific place on a line or plane See It line This is line AB line segment This is line segment CD A B C ray This is ray EF E point D This is point G F Types of lines There are many types of lines parallel lines intersecting lines and perpendicular lines Parallel lines do not cross and are always the same distance apart Intersecting lines are lines that meet and cross at exactly one point Perpendicular lines are lines that intersect at one point and form four right angles parallel lines intersecting lines perpendicular lines 345 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 1 Explore Two Dimensional Figures Practice It Match each picture with the correct definition 1 a intersecting lines that form four right angles 2 b lines that never meet they go on and on without touching 3 c names a specific place on a line or plane 4 d has two endpoints 5 e part of a line that has one endpoint and goes on in the other direction 6 f goes on and on in opposite directions and does not end 7 g lines that meet and cross at exactly one point 346 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 1 Explore Two Dimensional Figures Constructed Response A Answer each prompt with a constructed response 1 Is there a difference in a line and a line segment _______ Show It Explain It _______________________________________________ _______________________________________________ 2 Is there a difference in a ray and a line _______ Show It Explain It _______________________________________________ _______________________________________________ 3 Are intersecting lines and perpendicular lines the SAME YES or NO _____ Show It Explain It _______________________________________________ _______________________________________________ 347 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 1 Explore Two Dimensional Figures Real World and Relevant Constructed Response B Answer each prompt with a constructed response 4 Are parallel lines and intersecting lines the SAME or are they DIFFERENT Parallel lines and intersecting lines are _______________ Show It Explain how they are ALIKE or how they are DIFFERENT Explain It _______________________________________________ _______________________________________________ 5 Which is TRUE A line is part of a ray OR A ray is part of a line Show It Explain It _______________________________________________ _______________________________________________ 348 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 1 Explore Two Dimensional Figures Learn About It There are three types of angles right obtuse and acute A right angle has a measure of exactly 90 An obtuse angle has a measure that is greater than 90 An acute angle has a measure that is greater than zero but less than 90 See It right angle A right angle is exactly 90 It is one fourth of a circle acute angle An acute angle is less than 90 and greater than 0 obtuse angle An obtuse angle is greater than 90 Fill in each blank with right obtuse or acute 1 An __________ angle measures greater than 90 degrees 2 An _________ angle measures less than 90 degrees 3 A __________ angle measures exactly 90 degrees 349 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 1 Explore Two Dimensional Figures Comparing Angles to Hands on a Clock Learn About It You can compare angles to the hands on a clock Hands on a clock can form all three types of angles right acute and obtuse angles The hour hand and the minute hand together will form an angle See It Tell whether the hands on each clock form an acute angle a right angle or an obtuse angle The hands on the clock clock form an acute angle The hands on the clock form a right angle The hands on the form an obtuse angle You Try It Write the type of angle formed by the hands of each clock 1 2 _______ 3 ________ ________ 350 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 1 Explore Two Dimensional Figures Practice It 1 What type of angle is found in this triangle ________ 2 What type of angle is found in this square _______ 3 What two types of angles are found in this triangle ________ and ________ 4 What type of angles are found in this quadrilateral _______ and _________ 5 What type of angle is shown by the clock hands below ____________ 6 What type of angle is shown by the clock hands below _____________ 351 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 1 Explore Two Dimensional Figures Constructed Response A Read About It Cameron s class was studying lines and angles in geometry All of the students in the class had to develop a project in which another classmate would complete Cameron was assigned the task of identifying lines and angles in everyday life Cameron made a decision He would draw a picture that included all of the things he had learned about lines and angles He would number each section of his picture His classmate would have to label that section correctly 1 Find the following lines and angles in the picture above Label each section of the picture with the correct letter a point b parallel lines d right angle e ray f perpendicular lines i line segment c intersecting lines g acute angle h obtuse angle j line 352 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons Expectations Classify compare and contrast polygons based on lines of symmetry the presence or absence of parallel or perpendicular line segments or the presence or absence of angles of a specified size and based on side lengths Learn About It A plane figure is a two dimensional figure this means that it is flat A closed plane figure with straight sides is a polygon We classify polygons by naming the number of sides angles and vertices that they have Each side is called a line segment Circle A circle is a plane figure with equal points that revolve around the center A regular polygon has all equal sides and all equal angles Count the sides and the angles of each figure triangle ___ sides ___ angles square ___ sides ___ angles pentagon ___ sides ___ angles hexagon ___ sides ___ angles octagon circle quadrilateral ___ sides ___angles ___ sides ___angles ___ sides ___ angles 353 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons Polygons Learn About It Polygons have straight sides Figures that do not have straight sides are NOT polygons See It Polygon Not a polygon This figure has straight sides This figure does not have straight sides You Try It Place an X on the figures that are NOT polygons A B D E C F 354 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons See It Fill out the information about each plane figure 1 2 This shape is called a ___________ It has ____ sides and ______ angles Describe the types of angles ____________ ___________________________________ Is this shape a polygon ________ This shape is called a _____________ It has _____ sides and ______ angles Describe the types of angles ____________ ___________________________________ Is this shape a polygon ________ 3 4 5 This shape is called a _____________ It has _____ sides and ______ angles Describe the types of angles ____________ __________________________________ Is this shape a polygon ________ This shape is called a _____________ It has _____ sides and ______ angles Describe the types of angles ___________ __________________________________ Is this shape a polygon ________ This shape is called a _____________ It has _____ sides and ______ angles Describe the types of angles ___________ __________________________________ Is this shape a polygon ________ 355 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons Practice It Circle the correct answer to each question 1 Which shape has 4 sides and 4 angles A B C D pentagon triangle hexagon square 3 Name the figure below 2 Which figure has 3 sides and 3 angles A B C D 4 Name the figure below A B C D pentagon triangle hexagon square 5 Is this figure a polygon _________ pentagon triangle hexagon square A B C D pentagon triangle hexagon square 6 Is this figure a polygon _________ 356 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons Learn About It A plane figure with 4 sides and 4 angles is called a quadrilateral There are many different kinds of quadrilaterals Quadrilaterals can be sorted into different groups Some quadrilaterals can be a part of several different groups Quadrilaterals See It Parallelograms This is a rhombus This is a parallelogram Opposite sides are All four sides have the parallel and have the same length Opposite same length angles have the same measure This is a rectangle Opposite sides are equal It has four right angles This is a square It is a rectangle and a rhombus It has four equal sides and four equal angles Other Quadrilaterals A trapezoid has 1 pair of parallel sides This is a kite It has two pair of connected sides of equal length 357 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons Practice It Read each statement and circle true or false 1 A trapezoid is also a parallelogram true or false Explain your answer _____________________________ _______________________________________________ 2 A rhombus can also be a kite true or false Explain your answer _____________________________ _______________________________________________ 3 A rectangle is also a parallelogram true or false Explain your answer _____________________________ _______________________________________________ 4 A kite is also a quadrilateral true or false Explain your answer _____________________________ _______________________________________________ 5 A rectangle can also be a square true or false Explain your answer _____________________________ _______________________________________________ 358 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons Constructed Response A Answer each prompt with a constructed response 1 Draw a figure that has only 1 pair of parallel sides Name It ___________ Draw It Explain It Explain how you drew the figure ____________________ _______________________________________________ _______________________________________________ 2 Draw a figure that has 2 pair of connected sides of equal length Name It ___________ Draw It Explain It Explain how you drew the figure ____________________ _______________________________________________ _______________________________________________ 359 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons Constructed Response B Answer each prompt with a constructed response Kymia and her 4th grade class started working on a project on quadrilaterals Kymia s part of the project was to explain to her classmates about the relationships of the figures that were classified as quadrilaterals Here are the topics Kymia will report on to her class 1 Explain why a parallelogram rhombus rectangle and square are all classified as PARALLELOGRAMS and a trapezoid and a kite are NOT classified as PARALLELOGRAMS Explain It _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ 2 Explain why a SQUARE is a RECTANGLE but a RECTANGLE is NOT a SQUARE Explain It _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ 360 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons Constructed Response C Read each prompt and answer with a constructed response Kymia and her 4th grade class started working on a project on quadrilaterals Kymia s part of the project was to explain to her classmates about the relationships of the figures that were classified as quadrilaterals Here are the topics Kymia will report on to her class 3 Explain why a RECTANGLE is ALSO a PARALLELOGRAM Explain It _______________________________________________ _______________________________________________ _______________________________________________ 4 Explain why a SQUARE is also a RECTANGLE and also a RHOMBUS Explain It _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ 361 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons Constructed Response A Read About It Kristen was taking a class in high school to help her learn more about teaching She was assigned to help the pre K class at a nearby elementary school The teacher gave Kristen the task of classifying the shapes that she was going to use for instruction the next day Kristen sorted these figures The first shape that Kristen picked up had five equal sides and five equal angles The second figure that Kristen picked up had six equal sides and six equal angles The third figure did not have any straight sides All of this figure s points were an equal distance from a point called the center The fourth figure had eight sides and eight angles All of the sides and angles of this figure were also equal 1 Name the figures that Kristen sorted for the Pre K class a first figure ___________ b second figure ___________ c third figure ___________ d fourth figure ____________ 2 Kristen sorted the figures into two categories List the shapes Kristen sorted in the correct category Polygons Not polygons 362 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons B Explain It 3 Explain how Kristen decided the name of each figure and how she sorted the shapes ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ 4 How can Kristen explain the way she sorted the figures to the Pre K class she is helping ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ _____________________________________________________ 363 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons Learn About It When a figure can be folded in half and both parts match that is called symmetry The line where you fold the figure is called the line of symmetry Some figures have a line of symmetry and some figures do not have a line of symmetry There are figures that do not have a line of symmetry at all Every regular polygon has the same number of lines of symmetry as it has sides See It Which figure below shows a line of symmetry Even though this is the same figure the line of symmetry cannot be drawn just anywhere Yes No You Try It Draw a line of symmetry on each figure below A B C 364 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons Practice It A Circle each figure that shows a line of symmetry B How many lines of symmetry can be drawn for each figure Draw each line of symmetry to show your work ____ ____ lines lines ____ lines ____ lines 365 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons Practice It 1 Circle the figure that does NOT have a line of symmetry 2 Circle the figure that has MORE than 1 line of symmetry 3 How many lines of symmetry will this figure have ____ 4 How many lines of symmetry will this figure have ____ 5 How many lines of symmetry 6 How many lines of symmetry will this figure have ____ will this figure have ____ 7 Draw ALL lines of symmetry 8 Draw ALL lines of symmetry 366 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons Constructed Response A Answer each prompt with a constructed response 1 Is a correct line of symmetry a vertical line up and down or a horizontal line side to side _________ Explain It _____________________________________________________ _____________________________________________________ _____________________________________________________ 2 Is a correct line of symmetry a vertical line up and down or a horizontal line side to side ___________ Explain It _____________________________________________________ _____________________________________________________ _____________________________________________________ 367 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 2 Classify Compare Contrast Polygons Constructed Response B Answer each prompt with a constructed response 3 Sammy says that this figure has a line of symmetry that ONLY runs horizontally side to side Is Sammy CORRECT ___________ Explain It _____________________________________________________ _____________________________________________________ 4 Draw a figure that DOES NOT have a line of SYMMETRY Draw It Explain It _____________________________________________________ _____________________________________________________ _____________________________________________________ 368 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Expectations Solve problems involving area and perimeter of composite rectangles involving whole numbers with known side lengths Learn About It The perimeter of a figure is the distance around the outside of the figure Compare perimeter to a fence A fence is a barrier around the outside of a yard You can add all sides of the figure to find the perimeter or you can use the formula for finding the perimeter of a rectangle or a square The formula for finding the perimeter of a rectangle is 2 X s 2 X s The formula for finding the perimeter of a square is 4 X s See It Find the perimeter of the rectangle 1 Use the formula 6 inches 3 in 3 in 2 X s 2 X s 2 X 6 2 X 3 12 6 18 inches 2 Add all of the sides Perimeter s s s s 6 3 6 3 18 inches 6 inches The perimeter is 18 inches See It Find the perimeter of the square 2 feet 1 Use the formula 2 ft 2 ft 2 feet The perimeter is 8 feet 4 X s 4 X 2 4 X 2 8 feet 2 Add all of the sides Perimeter s s s s 2 2 2 2 8 feet 369 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Practice It Find the perimeter of the figures below Use the formulas or just add ALL of the sides Work It 1 1 ft perimeter _________ 4 feet Work It 2 3 cm perimeter _________ 5 cm 3 Work It 5 inches perimeter _________ 4 Work It 4 cm 16 cm perimeter _________ Work It 5 2 cm perimeter _________ 7 cm 6 Work It 4 inches perimeter _________ 370 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Practice It Read each problem below and solve 1 Barney s dog pen has a perimeter of 20 feet If the dog pen is a square what is the length of each side ___________ Work It 2 The rug in Lauren s room is shaped like a rectangle The perimeter of the rug is 14 feet What could be the length of each side of the rug ____ ____ ____ ____ Work It 3 Ronald s mom has to buy a new refrigerator The length of one side is 5 feet and the width of one side is 3 feet Give the length and width of the remaining sides ______ and ______ What is the perimeter of the refrigerator _____ _____ _____ _____ ______ Work It 371 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter 4 Oreo is a guinea pig His cage has a perimeter of 36 inches If the cage is a rectangle what are the measures of the four sides _____ _____ _____ _____ ______ Work It 5 Marlon s new sandbox has a perimeter of 32 feet If the cage is a rectangle what are the measures of the four sides _____ _____ _____ _____ ______ Work It 6 Kyra s grandmother was making a quilt for a birthday present The quilt she made was 8 squares long and 6 squares wide What is the perimeter of Kyra s new quilt _______________ Work It 372 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Constructed Response Bandit s old dog pen had a perimeter of 20 feet There are many possibilities for the measurements of the sides of Bandit s dog pen A What would be the measurement of the four sides if the pen were shaped like a square _____ _____ _____ _____ B There would be several possible answers if Bandit s dog pen were a rectangle Give at least 3 different possibilities Explain It Explain why there is only one possibility of a measurement if the dog pen is a square and several possibilities when it s a rectangle _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ 373 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Constructed Response A Answer each prompt with a constructed response Josie got a silver jewelry box from her grandmother The jewelry box had a perimeter of 20 inches 1 What is the length and width of the jewelry box _____ 2 Is there more than one possibility ________________ Draw It Explain It Explain how you can find the length and width of an object when given the perimeter _____________________________________________________ _____________________________________________________ _____________________________________________________ 374 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Constructed Response B Answer each prompt with a constructed response Jenna s dad was building Jenna and her brother a new sandbox Jenna s dad told the kids to make drawings of what they wanted the sandbox to look like He told them that the perimeter of the sandbox would be 18 feet Dad also told the kids that before he built the box they had to show him the four possibilities of the dimensions of the sand box Draw the FOUR possibilities of the dimensions of the sandbox Explain It Explain how you can find the length and width of an object when given the perimeter _____________________________________________________ _____________________________________________________ ____________________________________________________ 375 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Constructed Response C Answer each prompt with a constructed response Jane was making a quilt for her grandmother Grandmother wanted the perimeter of the quilt to be 50 feet Jane asked four of her friends to help her with the design Each friend drew a design None of the measurements were alike All of them had a perimeter of 50 feet Draw FOUR possibilities of the dimensions of the quilt Explain It Explain how you can find the length and width of an object when given the perimeter _____________________________________________________ _____________________________________________________ _____________________________________________________ 376 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Constructed Response A Read About It Randy and Nick needed to build a new pen for their dog Bandit There were two reasons they needed to build Bandit a new pen Bandit s old pen was getting too small for him and the lock was broken They went to a scrap yard to look for material to build Bandit a new pen Randy found a piece of fencing that was 6 feet long Nick found a piece of fencing that was 7 feet long Both boys were ecstatic with the material they found Now all they needed to do was find two more pieces of fencing that matched the pieces they already found 1 What are the measurements of the two other pieces of fencing _________ and _________ 2 What will be the perimeter of Bandit s new dog pen __ ____________________________________________ 3 Draw a picture of Bandit s new dog pen Show all four sides of Bandit s new dog pen B Explain It 4 Explain how you found the lengths of Bandit s new dog pen _______________________________________________ _______________________________________________ 377 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter C Vocabulary Acquisition 5 Write a word that means the same as the vocabulary word a b c d thoughts piece happy substance D Reading for Meaning 6 Who was building a new dog pen _________________ _______________________________________________ 7 What were the two reasons for building the dog pen _ _______________________________________________ 8 Where did Randy and Nick go to look for the material for the new dog pen __________________________ ______________________________________________ 9 Cause and Effect Find the cause or effect Cause Bandit s dog pen was too small and the lock was broken Effect _________________________________________ E Write About It Write in your math journal Write about why it would be important to know how to find perimeter when you are working on a building project What could happen if you did not know how to find perimeter correctly 378 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Learn About It Area is what it takes to cover the surface or the inside of something We measure area in squares or square units For example if the measurement is in inches then it is called square inches See It Method 1 Count the squares Method 2 Use multiplication formula l x w 3 ft 5 ft AREA ______ AREA ________ You Try It Find the area 3 ft 8 ft area _________ area _________ 379 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Practice It Count the squares to find the area of each figure 1 2 Key Each Key Each 1 square inch 1 square inch Answer It _____ square inches Answer It _____ square inches 3 4 Key Each 1 square centimeter Answer It _____ square inches Key Each 1 square inch Answer It _____ square inches 380 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Practice It Find the area of each shaded figure Each square unit 1 area ___ sq units 3 area ___ sq units 5 area ___ sq units equals 1 2 area ___ sq units 4 area ___ sq units 6 area ___ sq units 381 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Practice It Read each problem and solve 1 Buddy s dog pen has an area of 30 feet What are two possible measurements of the dog pen ____ X ____ or ____ X ____ Work It 2 The rug in Kerri s room is shaped like a rectangle The area of the rug is 16 feet What are two possible measurements of the rug ____ X ____ or ____ X ____ Work It 3 Ronald s mom needs to buy a new refrigerator The length of one side is 5 feet and the width of one side is 3 feet What is the area of the refrigerator _______ Work It 382 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Constructed Response A Read About It Grammy wanted to install new tile in her kitchen When she went to the tile store to browse and look at different colors of tile she found several that she would like to try in her kitchen The worker at the store told her that she would need to measure the kitchen floor so that she would purchase the right quantity He told her to measure the length and the width of the kitchen floor When Grammy found the length and width then she would be able to find the area of the kitchen floor When Grammy measured the kitchen floor this is what she measured length 9 feet width 12 feet 1 Why did she need to find the length and width of the floor _______________________________________________ _______________________________________________ 2 What was the area of the kitchen floor __________ Work It Find the area of the kitchen floor Find the area Draw a model of the kitchen floor 383 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter B Explain It 3 Explain how you found the area of the kitchen floor __ _______________________________________________ _______________________________________________ C Vocabulary Acquisition 4 Match the vocabulary word to the correct definition a b c d e install ___ browse ___ several ___ purchase ___ quantity ___ 1 2 3 4 5 buy amount look around more than one put in D Reading for Meaning 5 Who wanted new kitchen tile ___________________ 6 Why was Grammy measuring the length and width of the kitchen ______________________________________________ ______________________________________________ ______________________________________________ E Think About It Write in your math journal Why would someone need to know how to find area when buying new carpet or tile for their house What would happen if someone did not know how to find area Could they purchase too much or too little Could they waste money Explain your answer 384 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Learn About It Area is what it takes to cover the surface or the inside of something We measure area in squares or square units For example if the measurement is in inches then it is called square inches To find the area of irregular shapes you must decompose the overlapping shapes and then add the areas of the smaller shapes together Perimeter is the distance AROUND a shape We can find the perimeter of irregular figures by counting the squares around the figure See It There are 3 shapes that come together to form one larger shape Find the area of each non overlapping shape then add the three areas together When you Shape 1 8 square units count around the figure the Shape 2 4 square units perimeter is 24 units Shape 3 8 square units Total AREA 8 4 8 20 square units 385 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Finding Area and Perimeter of Irregular Figures Let s Try Another One Shape 1 25 square units Shape 2 18 square units Total AREA 25 18 43 square units PERIMETER 32 units Explain It Explain how you found the area of the larger figure by adding the area of the two smaller figures together _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ 386 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Finding Area and Perimeter of Irregular Figures Partial Squares Some shapes will only cover half of a square Two halves added together will make one whole square Add two halves of squares to make one square See It Remember 2 half squares will equal one whole square 1 How many full squares are there inside the triangle _______ 2 How many partial half squares ______ 3 The partial squares add up to _______ whole squares 4 The triangle has an area of _______ square units 5 The triangle has a perimeter of _________ units Explain It Explain how you found the area of the triangle _______________________________________________ _______________________________________________ _______________________________________________ 387 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Finding the Area and Perimeter of Irregular Figures A Find the area and perimeter of each figure Remember it takes 2 half squares to equal one whole square 1 Area _________ Perimeter _______ 2 Area _________ Perimeter ________ 3 Area _________ Perimeter ________ 388 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Finding the Area of Irregular Figures Another Method Subtraction Learn About It You can also use subtraction to find the area of rectilinear figures With this method you will count a whole area of squares which should be easier to count and then subtract a partial area in order to find the area of the figure you are looking for See It 1 Make the triangle into a square to make counting easier 2 Count the whole squares in the square _____ 3 Count the pieces in the partial area _____ 4 Make a subtraction problem to find the area of the triangle Subtraction Problem Area _________ 389 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Real World and Relevant Constructed Response A Answer each prompt with a constructed response A Kerron was working on his math homework finding the area of irregular shapes Kerron added up the squares to find the area Here is his answer Area 15 square units What is wrong with Kerron s answer ______________________________ ______________________________ ______________________________ Show your work to find the CORRECT answer Explain It Explain how to find the area of figures with partial squares _____________________________________________________ _____________________________________________________ _____________________________________________________ 390 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Constructed Response B Answer each prompt with a constructed response B Here is a drawing of Mrs Doyle s kitchen floor The sink overflowed and ruined some of the tile She needs an accurate measure of the area that was ruined in order to buy the correct amount of new tile 1 How many feet of square tile will Mrs Doyle need to buy She will need to buy ____________ square feet Show two ways to find the AREA of the new kitchen floor Method 1 Method 2 391 Copyright 2023 by Concise Curriculum Do not duplicate

4 GSR 8 3 Solve Problems with Area and Perimeter Constructed Response C Answer each prompt with a constructed response C Stanley is making a mosaic for his art class He wants to paint the inside of the mosaic blue and the outside pieces green Help Stanley figure out how many tiles will be painted blue and how many will be painted green 1 How many tiles are inside the mosaic ________ 2 How many tiles are outside the mosaic ________ Explain It 3 How can you use SUBTRACTION to find the total number of tiles INSIDE the mosaic _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ ______________________________________________ 392 Copyright 2023 by Concise Curriculum Do not duplicate

CHECK OUT 4 GSR 8 4 GSR 8 1 A Draw the correct lines in each box below parallel lines intersecting lines perpendicular lines 4 GSR 8 2 B Circle the figure that does NOT have a line of symmetry C Circle the correct name of the figure below A pentagon B triangle C hexagon D square 4 GSR 8 3 D Find the area of each figure below area ____ sq units area ____ sq units 393 Copyright 2023 by Concise Curriculum Do not duplicate

GLOSSARY A A M also a m Ante meridiem Latin for before midday any time after midnight and before noon acute angle An angle that measures less than 90 O angle A geometric shape that is formed wherever two lines rays share a common endpoint called a vertex area The surface that a two dimensional or flat object takes up measured in square units associative property of multiplication A property of multiplication that states that the grouping of factors in different ways does not change the product of the factors Example 6 x 3 x 2 6 x 3 x 2 B base ten numeral A number written using the digits 0 9 from the decimal numbering system which is based on the number 10 also called standard form bill Paper currency used as money C cent The smallest money value in the United States equal to 1 100 or 01 of a dollar centimeter cm A unit of measurement of length in the metric system abbreviation is cm 1 100 of meter or 0 01 meter change The amount of money left over after a purchase coin Round metal currency common denominator a shared multiple of the denominators of two or more fractions commutative property of multiplication A property of multiplication that states that changing the order of factors does not change the product of the factors Example 6 x 3 3 x 6 compare To determine if a number is greater than less than or equal to another number 394 Copyright 2023 by Concise Curriculum Do not duplicate

compatible numbers Numbers that are easy to multiply and divide mentally composite number A number that has more than two factors Example The factors of 8 are 1 2 4 and 8 8 is a composite number convert To change from one form or unit to an equivalent amount in another form or unit counting up A strategy for finding totals of money or for counting change starting with a known amount of money and counting the coins or bills up to a certain amount of money cup c A customary unit of capacity equal to 8 ounces currency A system of money customary units Standard units used in the United States to measure length weight and capacity Examples inches feet yards miles ounces pounds tons ounces cups pints quarts gallons D day A period of time equal to about 24 hours the amount of time the Earth takes to complete one rotation on its axis decimal A part of a whole decimal fractions are fractions written as decimal numbers with one or more digits to the right of the decimal decimal point The symbol to the right of a whole number that separates the whole number from the decimal fraction a symbol that separates the ones from the tenths place the symbol between whole dollars and cents or parts of a dollar decreasing Becoming less in value or size denominator The number below the fraction bar that tells how many parts a whole number is divided into Example 2 4 4 is the denominator difference The amount left over after subtraction 395 Copyright 2023 by Concise Curriculum Do not duplicate

distributive property of multiplication A property of multiplication that states that multiplying a sum of two or more addends by a number is the same as multiplying each addend of the sum by the number and then adding the products together dividend The number that is divided by the divisor in a division problem Example 48 2 2 48 The dividend is 48 divisor The number that divides the dividend in a division problem Example 48 2 2 48 The divisor is 2 dollar A unit of currency equal to 100 cents E elapsed time The amount of time that has passed endpoint The point at which a ray begins the point at which a line segment begins or ends equal to Having the same value as another number represented by the symbol equation A mathematical statement math sentence that uses an equal sign to show that two expressions are of equal value equivalent fractions Fractions that name the same part of a whole but that have different numerators and denominators estimate 1verb Find a number that is close in value to an exact amount 2noun A number that is close in value to an exact amount expanded form A number written in a way that shows the value of each digit in the number so that the value of each digit is written and added together Example 745 700 40 5 F factor A whole number that is multiplied by another number to find a product feet ft The plural of foot which is the unit of length in the customary or standard system of measurement that is equal to 12 inches foot ft The unit of length or distance in the customary or standard system of measurement that is equal to 12 inches 396 Copyright 2023 by Concise Curriculum Do not duplicate

fraction Part of a whole or a part of a group a part of a whole written with a numerator and a denominator Example G gallon gal The customary unit of measurement used to measure capacity that is equal to 4 quarts gram g A metric unit for measuring weight or mass that is equal to 1 1000 of a kilogram greater than Having more value than another number represented by the symbol greatest common factor GCF The greatest factor two or more numbers share H hour A measure of time equal to 60 minutes one of the 24 hours in a day hundredths Two places to the right of the decimal represented by the fraction 1 100 I improper fraction A way to represent a mixed number a fraction in which the numerator is greater than the denominator Example 5 4 or 17 16 inch in The customary unit of measure used to measure length or distance that is equal to 1 12 of a foot 12 inches 1 foot increasing Growing larger in value or size intersecting lines Two or more lines in a plane that share one common point at which the lines cross inverse operations Operations that reverse or undo each other addition and subtraction are inverse operations multiplication and division are inverse operations K kilogram kg The metric unit of mass or weight that is equal to 1 000 grams 397 Copyright 2023 by Concise Curriculum Do not duplicate

kilometer km The metric unit of length or distance that is equal to 1 000 meters kite A quadrilateral that has two different pairs of connected sides of equal length L less than Having less or smaller value than another number represented by the symbol line A straight path through at least two points in a plane that goes on without end line of symmetry The line by which a figure can be divided into two exactly congruent mirror or reflective images line plot A way of graphing and organizing data using an x a dot or some other mark above a number line to show frequency line segment A section of a line that has two endpoints liter L The metric unit of measure of capacity that is equal to 1 000 milliliters lowest terms A fraction written so that the greatest common factor of the numerator and denominator is 1 M meter m The metric unit of length or distance that is equal to 100 centimeters 1 1 000 0 001 of a kilometer metric units Units of measure used in the metric system which is a decimal system of measurement that uses units of ten Example The metric units of measure for length are millimeters mm centimeters cm meters m kilometers km Mass can be measured in milligrams mg grams g kilograms kg and metric tons t Capacity is expressed as milliliters mL and liters L mile mi The customary unit of for measuring length or distance that is equal to 5 280 feet milliliter mL The metric unit of measurement for capacity that is equal to 1 1000 of a liter Example There are 1 000 milliliters in 1 liter 398 Copyright 2023 by Concise Curriculum Do not duplicate

millimeter mm The metric unit of length or distance that is equal to 0 001 or 1 1000 of a meter Example There are 1 000 millimeters in a meter minute A measure of time equal to 60 seconds mixed number Value written as both a whole number and a fraction Example 1 2 4 is a mixed number money Something usually coins and paper currency that can be exchanged for goods and services month The approximate amount of time the moon takes to orbit the earth usually 28 31 days or about 4 weeks Example The 12 months of the year are January February March April May June July August September October November and December multiples The products of a certain number by other whole numbers multiplication The operation of repeatedly adding a number to itself a number of times a way of finding the total quantity of items in a certain number of equal size sets or groups the inverse operation of division multiplicative identity property of one A property of multiplication that states that the product of multiplying a number times 1 will equal that number N number A quantity or amount represented by a numeral number name A way of writing a number using words instead of numerals also called word form Example 821 eight hundred twenty one numerator The number above the fraction bar that tells how many parts of a whole Example 2 4 2 is the numerator O obtuse angle An angle that measures greater than 90O and less than 180O 399 Copyright 2023 by Concise Curriculum Do not duplicate

ounce oz The customary unit of measurement used to measure weight that is equal to 1 16 pound Example There are 16 ounces in a pound P P M also p m post meridiem Latin for after midday any time after noon and before midnight parallel lines Two or more lines in a plane that always stay the same distance apart and never intersect parallelogram A quadrilateral whose opposite sides are parallel and of equal length and whose opposite angles are equal parts equal segments of a whole perimeter The measure of the distance around a closed plane figure perpendicular lines Lines in a plane that form right 90 O angles at the point at which they intersect or cross pint pt The customary unit of measurement used to measure capacity that is equal to 2 cups or 16 fluid ounces Example There are 8 fluid ounces in a cup and 16 fluid ounces in a pint place value The name or value of the position of a digit in a number point A specific place on a line or a plane pound lb The customary unit of measurement used to measure weight that is equal to 16 ounces Example There are 16 ounces in 1 pound prime number A number that has exactly two factors itself and 1 Example 3 5 7 11 13 and 17 are prime numbers product The result of multiplying two or more factors together the answer to a multiplication problem Example 12 x 10 120 120 is the product of 12 and 10 protractor A tool used to measure or draw angles Q quadrilateral A closed geometric figure or polygon with four sides quart qt The customary unit of measurement used to measure capacity that is equal to 2 pints 4 cups or 32 fluid ounces 400 Copyright 2023 by Concise Curriculum Do not duplicate

Example There are 8 fluid ounces in a cup and 32 fluid ounces in a quart quotient The answer to a division problem the number found after dividing a dividend by a divisor Example 48 2 24 The quotient is 24 R ray A part of a line that begins at one endpoint and continues forever in one direction rectangle A parallelogram that has four right angles reduce To simplify a fraction to its simplest form so that the greatest common factor of the numerator and denominator is 1 to divide a fraction s numerator and denominator by their greatest common factor remainder The number left over after dividing rhombus A parallelogram with four sides of equal length right angle An angle that measures exactly 90 O rounding Changing a number to another number similar in value telling about how much or about how many S second A measure of time equal to 1 60 of a minute 60 seconds are in a minute simplify To reduce a fraction to its simplest form so that the greatest common factor of the numerator and denominator is 1 to divide a fraction s numerator and denominator by their greatest common factor square A parallelogram that has four right angles and four congruent sides a quadrilateral that is both a rectangle and a rhombus subtraction The operation used to find what amount is left after removing a part from a whole sum The answer to an addition problem the amount found by adding together two or more addends 401 Copyright 2023 by Concise Curriculum Do not duplicate

symmetry Having an exact congruence in a reflective or mirror image on opposite sides of an imaginary divisive line T tenth One out of ten equal parts of a whole tenths The name of the place immediately to the right of the decimal time The continuum through which experiences pass through the future present and future a measure given by a clock total The complete amount or number trapezoid A quadrilateral with exactly one pair of parallel sides V value How much a number is worth variable An unknown number or numbers represented by a letter or symbol vertex The endpoint at which two or more rays meet in a solid figure the point at which three or more edges meet the top point of a cone singular of vertices vertices Plural of vertex more than one vertex W week A unit of team equal to 7 days Example There are 52 weeks in a year weight The measure of the pull of gravity on an object whole number One of the numbers 0 1 2 3 4 and so on a number without a fraction 402 Copyright 2023 by Concise Curriculum Do not duplicate