EBMC Resources - emPowerED Maths - Sample Booklet Year 8 : simplebooklet.com

was constructed by two experienced Mathematics specialists who combined have over 25 years of teaching experience in N.Z. Intermediate schools. Their mission was to gain back work/life balance by collaborating and sharing the load of plan-ning for Maths lessons. As time went by, it was evident that they had created a well-structured program that was differentiated, enjoyable and easy to teach and learn, and resulted in increased student confidence and ability in Mathematics. A measure on how effective the program was depended on how new staff and relievers were able to adopt it. It proved to be quick and easy to pick up and met the expectations of the year level. Knowing they had created a program that could help their colleagues all across N.Z., the duo formed EBMC Resources with the mission of gifting back time and energy to hard-working teachers by lessening their stress and planning time. The program also provides educators with the tools to lead lessons confidently and have a work/life balance. For four years, EBMC Resources has trialled and refined this program and are now keen to share it with other schools in the hope that their colleagues will have the same (if not better) Mathematical outcomes for their students. To get the most out of this program, it is important to understand that there are four elements to each concept: 1. Teacher introduction: Examples and ‘Our Turn’ align exactly with the teaching presentations accessed through a subscription to our website 2. Independent time: ‘Your Turn’ allows students to give it a go, plus extension ques-tions and a puzzle are included 3. Differentiation: Consists of different levelled workbook pages that offer support, on-level and extension material 4. Fun puzzles: Codebreakers, maze runners and more involve some calculated fun to finish Please note that once a workbook page is completed and marked, it can be decided whether a student begins the next level (increased challenge) or moves onto the puzzle page. This allows for a differentiated approach catered to the student. At the end of the unit there is a test. This can be used as revision or an assessment task. We have put this program into practice in our classrooms and are proud to share this resource with you. We trust you will find success and ease with it too. Happy teaching! From the team at EBMC Resources. Introducing our cartoon characters! Hi, I’m Sevi. Hey, I’m Teila. Kia ora, I’m Katie. Hello, I’m Tama.

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3. Year 8 emPowerED Maths ©2021 . com  Add, subtract, multiply and divide large numbers  Contextual word problems  Practice tests  Place value up to the millions  Rounding whole and decimal numbers to 3dp  Multiples, Factors and Prime numbers  Square & Square roots.  Add, subtract, multiply and divide large decimal numbers  Practice tests  Add, subtract, multiply and divide integers  Solve a range of operations using BEDMAS  Combined integers and BEDMAS equations  Contextual word problems  Practice tests  Mean, median, mode and range  Draw a bar graph of given data  Draw histogram graphs of given data  Construct a stem & leaf graph  Plan a Statistics Investigation using the P.P.D.A.C. enquiry model  Practice tests  Count to one hundred  Classroom objects  Colours  A range of shapes  Basic facts tests  Find a fraction and a % of a given value  Add, subtract and multiply fractions  Convert between fractional numbers  Equivalent and simplifying fractions  Converting improper to mixed fractions  Writing fractions and decimals in expanded form  Practice tests  Collecting like terms  Simplify indices and multiply expressions  Find and write an algebraic formula  Substitution  Calculate algebraic equations  Solve life situations involving algebra  Practice tests  Convert between units of length, weight and volume  Identify 2D shapes and list their properties  Area of rectangles, triangles, parallelograms, and trapeziums  Area of compound shapes  Volume of basic prisms  Contextual word problems  Time and word problems  Practice tests  Measuring and constructing angles around a point  Angle and triangle properties  Reflection, rotation, translation, lines of symmetry and tessellations  Construct and draw nets of 3D shapes  Plot and indicate co-ordinates

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4. Year 8 emPowerED Maths ©2021 . com Step 2: Just like in short division, begin dividing. • How many times does the number outside the bus stop (the divisor) go into the first digit inside the bus stop (the dividend)? • Write the number of times above the first digit (see purple). • Instead of carrying the left over amount, multiply the purple digit by the outside number then subtract from the inside digit to get a new digit (see green). • Bring down the next digit of the inside number (see dark orange). 0 32 5 5 2 0 - 0 5 5 Step 3: Repeat Step 2 until you have divided the last digit inside the bus stop. If necessary, add a decimal point and up to three zeros (see pink). Round to two decimal places (d.p). 0 1 7 2.5 32 5 5 2 0.000 - 0 5 5 - 3 2 2 3 2 - 2 2 4 8 0 - 6 4 1 6 0 - 1 6 0 0 1. 282 ÷ 12 2. 962 ÷ 22 WHOLE NUMBERS Division Wehewehenga Learning Intention:  We are learning how to calculate quotients of whole numbers. Complete the following short divisions. Explain the steps you took in your short division to a classmate. What steps did you take? First I ..._________________________________ ___________________________________ Then I ... ____________________________ ___________________________________ Finally I ... ___________________________________ ___________________________________ For long division, we must use the same steps as short division along with showing your working. Long Division — Long division is similar to the process of short division. Use this method when dividing by larger numbers. Divide 5520 by 32. Step 1: Write using a “bus stop”. • The FIRST number goes “inside” the bus stop. 32 5 5 2 0 3 7 6 4 1 6 5 1 3 6 0 8 5 5 4 42 25 8 5 5 4 2 5 - 4 0 2 5 - 2 5 0 12 2 8 2

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5. Year 8 emPowerED Maths ©2021 . com Did you meet your Success Criteria? Yes / No What did you do well in Maths class today? ___________________________________ ___________________________________ ___________________________________ What can you do to improve your learning tomorrow? ___________________________________ ___________________________________ WHOLE NUMBERS Division Wehewehenga Complete the following by showing all your working. 1. 894 ÷ 6 2. 973 ÷ 7 3. 836 ÷ 4 4. 648 ÷ 9 5. 9102 ÷ 12 6. 3927 ÷ 12 Success Criteria:  I can use long division to divide numbers by two-digits.  I can show all working using long division. 6 8 9 4 Extension: Find the following quotients. “Quotient” means “answer to a division problem”. Round to 2 d.p. 1. Find the quotient of 950 ÷ 53. 2. Find the quotient of 898 ÷ 26. Puzzle: Solve the following magic squares. All rows, columns and diagonals must equal the given sum. The sum is 74 The sum is 154 46 41 40 38 42 44 45 31 13 23 15 18 17 24 25 11 7 9 7 3

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6. Year 8 emPowerED Maths ©2021 . com TUATAHI: How to calculate quotients of whole numbers. Me pehea te tatau i nga wahanga tau katoa ma te whakamahi wehenga poto. Worked Examples: Example of short division: Calculate the quotient of 875 ÷ 6. Example of long division: Calculate the quotient of 496 ÷ 8. Find the quotient. Round to 2 decimal places. 1. 8. 15. Find the quotient: 307 ÷ 5 2. 9. 16. Find the quotient: 275 ÷ 3 3. 10. 17. Find the quotient: 734 ÷ 4 4. 11. 18. Find the quotient: 556 ÷ 3 5. 12. 6. 13. Step it up! 19. Sevi has 128 marbles and wants to share them among his 8 mates. How many marbles will they each receive? 7. 597 ÷ 8 14. 849 ÷ 6 1 4 5 8 3 6 8 7 5 0 0 6 2 8 4 9 6 - 4 8 1 6 - 1 6 0 2 3 5 2 No numbers left? Then start adding zero to the remainders. ALL the working is displayed underneath 4 5 6 9 3 4 5 6 5 7 8 6 7 9 5 9 6 8 5 2 9 4 7 7 8 7 4 8 4 6 9 3 7 9 1 8 3 5 2 9 6 9 2 0 9 5 5 8 5 3 0 7 3 2 7 5 Number Correct: __ / 19 How strong is your understanding? Number and algebra Level 3: Use a range of division strategies with whole numbers & know your basic division facts. What is your tip of the day? All remainders go to the top left of the next digit. The dividend has a decimal point and zero added to it to get a decimal answer. Every whole number has an invisible decimal point at the end.

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7. Year 8 emPowerED Maths ©2021 . com TUARUA: How to calculate quotients of whole numbers. Me pehea te tatau i nga wahanga tau katoa ma te whakamahi wehenga poto. Worked Examples: Example of short division: Calculate the quotient of 8754 ÷ 4. Example of long division: Calculate the quotient of 274 ÷ 11. Find the quotient. Round to 2 decimal places. 1. 2. 15. Find the quotient: 4087 ÷ 9. 3. 4. 16. Find the quotient: 6205 ÷ 6. 5. 6. 17. Find the quotient: 3317 ÷ 11. 7. 8. 18. Find the quotient: 9422 ÷ 12. 9. 10. 11. 12. Next Level! 19. Kiwifruit is N.Z’s national fruit. They produce 5581 thousand metric tonnes per year. This is exported to 32 countries around the world. If there is an equal amount sent to each country, how much kiwifruit would go to each country? 13. 14. 2 1 8 8 5 4 8 7 5 4 0 0 2 4 9 1 1 2 7 4 0 - 2 2 5 4 - 4 4 1 0 0 - 9 9 1 3 3 2 No numbers left? Then start adding a zero under each remaining number. All the working is displayed underneath. 5 6 8 2 6 5 8 7 3 4 4 8 2 1 1 3 7 9 4 1 2 4 8 6 1 1 2 1 0 9 6 9 4 7 8 3 1 1 1 2 5 9 1 2 1 3 2 6 1 1 7 6 8 3 8 5 8 0 3 1 2 1 6 3 3 1 1 6 3 8 1 Number Correct: __ / 19 How strong is your understanding? Number and algebra Level 3/4: Use a range of division strategies with whole numbers & know your basic division facts. What is your tip of the day? Double digit remainders are ok when dividing by a double digit. Add zeros after the decimal point. 7 9 3 7 For two digit divisors, the process is the same.

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8. Year 8 emPowerED Maths ©2021 . com TUATORU: How to calculate quotients of whole numbers. Me pehea te tatau i nga wahanga tau katoa ma te whakamahi wehenga poto. Worked Examples: Find the quotient of 2719 ÷ 3. Find the quotient of 4307 ÷ 11. Final answer: 391.55 (2 d.p.) Find the quotient. Round to 2 decimal places. 1. 2. 15. Find the quotient: 63756 ÷ 30. 3. 4. 16. Find the quotient: 77253 ÷ 25. 5. 6. 17. Find the quotient: 80035 ÷ 35. 7. 8. 18. Find the quotient: 24087 ÷ 22. 9. 10. Extension! 11. 12. 19. A large crowd of 8194 Aucklanders are waiting for a bus. How many buses are needed to transport them if each bus holds 54 passengers and a driver? 13. 14. When the divisor does not fit into the dividend, place a zero in the answer. 9 0 6 3 3 3 3 2 7 1 9 0 0 0 1 1 1 1 3 9 1 5 4 5 1 4 3 0 7 0 1 0 0 10 1 6 5 6 You can have two digit remainders with double digit divisors. Number Correct: __ / 19 How strong is your understanding? Number and algebra Level 3/4: Use a range of division strategies with whole numbers & know your basic division facts. What is your tip of the day? Round all your answers to 2 decimal places. Add zeros after the decimal point. What, there are two digit dividends in division? 6 3 6 3 7 4 3 2 2 9 5 3 5 1 9 1 1 4 3 8 5 1 3 7 4 5 5 1 5 5 9 6 6 1 2 6 4 3 3 1 4 9 0 5 6 2 5 7 9 0 4 1 7 4 0 6 3 1 2 2 0 1 9 1 3 6 0 7 0 1 9 7 7 0 3 8 7 2 5

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9. Year 8 emPowerED Maths ©2021 . com Place 3 Problem: 847.5 ÷ 15 427.44 ÷ 13 854.4 ÷ 12 2420.8 ÷ 34 1029.16 ÷ 22 563.97 ÷ 11 Working Space: Letter: Problem: 259 ÷ 7 1228.5 ÷ 7 1053 ÷ 6 853.2 ÷ 9 498.4 ÷ 7 3942.9 ÷ 9 561.36 ÷ 12 461.43 ÷ 9 863.94 ÷ 11 Place 2 Working Space: 0 3 7 7 2 25 49 Letter: A Problem: 114 ÷ 6 568.8 ÷ 6 1516 ÷ 8 585.64 ÷ 11 421.02 ÷ 9 314.16 ÷ 4 395.5 ÷ 7 Place 1 Working Space: 0 1 9 6 1 11 54 Letter: B Unscramble the letters below to find the name of three places in the world. Place 1: B ___ ___ ___ ___ ___ ___ Place 2: A ___ ___ ___ ___ ___ ___ ___ ___ Place 3: L ___ ___ ___ ___ ___ ___ A B C D E F G H I J K L M N O P Q R S T U V W Y 71.2 19 32.5 20.25 945 17.5 78.54 46.93 46.78 44 319.7 56.5 53.24 175.5 31.5 21.99 65.5 438.1 23.2 51.27 189.5 32.88 16.5 87.5 Code INSTRUCTIONS:  Work out the division problems in the second row. There may be some decimal answers.  Find your answer in the code and write the letter in the 3rd row.  Unscramble the letters to find three names of places around the world. LEARNING INTENTION:  We are learning how to calculate the quotient of whole numbers. Kei te ako tatou ki te tatau i nga haurua tau katoa, ma te whakamahi wehenga poto. WHOLE NUMBERS - DIVISION Find three names of places around the world.

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10. Year 8 emPowerED Maths ©2021 . com We can see that when the digit next to the place value we are rounding to is 5 or greater, it will be closest to the larger number. A digit of 4 or less will be closer to the smaller number. We round numbers to a specific place value. This means that every digit after that place becomes a zero. Here is a rhyme to remember the steps for rounding and an example in the speech bubble: Underline the place value Look at the digit next door 5 or greater we add one more 4 or less we do nothing and rest. Why do we round up when a digit is 5? ___________________________________ ___________________________________ Why do we round down when a digit is 4 or less? ___________________________________ ___________________________________ Would the Swedish rounding system still work now that 5 cent coins are no longer used in New Zealand? ___________________________________ ___________________________________ SPECIAL NUMBERS Rounding Whakaawhiwhi Learning Intention:  We are learning how to round whole numbers up to billions place and three decimal places. From 1990 to 2006, New Zealand supermarkets applied a process called Swedish rounding to calculate a customer’s total bill. Swedish rounding involves rounding your money to the nearest 5 cents. For example: $3.78 rounds up to $3.80 $51.71 rounds down to $51.70 Do you think $47.52 rounds up or down to the nearest 5 cents? Why? ___________________________________ Do you think $199.93 rounds up or down to the nearest 5 cents? Why? ___________________________________ Why do you think NZ supermarkets used this system? ___________________________________ ___________________________________ Rounding numbers is useful when estimating. When we round, we look at which value a certain number is closest to on the number line. For example: When rounding 1,084,738 to the nearest ten thousand, we see that it is closer to 1,080,000 rather than 1,090,000. When rounding 4.501 to the nearest one, or unit, we see that it is closer to 5 rather than 4 1,090,000 1,080,000 1,084,738 5 4 4.501 Round 936.926 to the nearest hundredth. 936.926 936.926 936.926 Answer: 936.93 This is greater than 5 so we round up. NOTE: Add commas when a number is over 1 million. This reduces mistakes! (For example: 9,704,231,893.832)

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11. Year 8 emPowerED Maths ©2021 . com SPECIAL NUMBERS Rounding Whakaawhiwhi 1. Round to the nearest whole number. 435.4390 = 2. Round to the nearest tenth. 398.984 = 3. Round to the nearest thousandth. 983.48953 = 4. Round to the nearest hundred thousand. 3129478984 = 5. Round to the nearest ten thousand. 3904999 = 6. Round to the nearest hundred. 972099999.9239 = Did you meet your Success Criteria? Yes / No What did you do well in Maths class today? ___________________________________ ___________________________________ ___________________________________ What can you do to improve your learning tomorrow? ___________________________________ ___________________________________ Extension: Number Guess Who Read the speech bubble hints Teila is giving to you. Match these to the spaces below. Success Criteria:  I can round numbers to a given place value.  I can round decimal numbers to a given decimal place. 1. Round to the nearest tenth. 384.584 = 2. Round to the nearest hundred. 27364892 = 3. Round to the nearest hundredth. 89.9834 = 4. Round to the nearest ten thousand. 97853889.09 = 5. Round to the nearest million. 9584576205 = 6. Round to the nearest hundred. 1293999999.83 = What number am I? ____ ____ ____ ____ ____ ____ . ____ ____ I am a number with 6 digits in front of the decimal point and 2 digits after. My thousands and hundreds digit are 4 less than the tens and hundredths digit, respectively. None of my digits repeat. I do not contain the digits 3 or 8. When rounded to the tenths place, I round up and the tenths digit becomes a 5. When rounding to the hundreds place, the hundreds digit rounds up to become a 2. When rounded to the ten thousands place, I round down and my value is 970000.

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12. Year 8 emPowerED Maths ©2021 . com TUATAHI: How to round whole numbers up to billions place and three decimal places. Me pēhea te whakatata i ngā tau katoa tae atu ki te nuinga o nga wāhi me ngā wāhi ira e toru. Worked Examples: Round this number to the nearest hundredth. Round to the nearest tenth. Answer: 58.16 Answer: 5.8 Round the number on the left to the nearest tenth and hundredth. Dice roll. Find the sum of the dice rolled and then round the number to the nearest tens place value. The first one is done for you. 1. 2. 3. 4. Tick the correct rounded number that matches the purple number. 5. 6. eg. + = 14 + 15 29 30 7. 8. 18. + = 9. 10. 19. + = 11. 12. 20. + = 13. 14. 21. + = Round the following number up or down to the place value given. Step it up! Round the following number up or down to the place value given. 15. Round to the nearest whole number. 16. Round to the nearest tenth. 22. Round to the nearest whole number. 17. Round to the nearest hundredth. 23. Round to the nearest tenth. 5 9 1 3 2 9 6 3 2 8 4 1 Number Correct: __ / 23 How strong is your understanding? Number and algebra Level 3/4: Apply multiplicative strategies flexibly to whole numbers. What is your tip of the day? Round a digit up when the digit that follows is above 5. Keep the digit the same when the digit that follows is below 5. Number Round to tenths Round to hundredths 45.197 194.725 638.697 19574.829 14 31 19 23 15 28 6 5 4 3 2 1 1 5 2 6 3 5 5 6 4 5 Look at the place holder that comes after the one you are to round. 5 8 1 5 7 5 8 1 5 7  2.5 2.593  2.59  3.92 3.936  3.94  1.09 1.094  1.08  0.2 0.255  0.26  0.95 0.925  0.93  1.94 1.935  1.93  7.11 7.112  7.12  3.16 3.106  3.12  3.89 3.388  3.90  2.51 2.508  2.50

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13. Year 8 emPowerED Maths ©2021 . com TUARUA: How to round whole numbers up to billions place and three decimal places. Me pēhea te whakatata i ngā tau katoa tae atu ki te nuinga o nga wāhi me ngā wāhi ira e toru. Worked Examples: Round this number to the nearest hundredth. Round this number to the nearest tenth. Answer: 3.63 Answer: 7.0 Round the number on the left to the nearest tenth and hundredth. Dice roll. Find the sum of the dice rolled and then round the number to the place value given. The first one is done for you. 1. 2. 3. 4. Tick the correct rounded number that matches the front large number. 5. 6. eg. + = 6.09 + 30.98 37.07 37.1 1dp 7. 8. 18. + = 1dp 9. 10. 19. + = 1dp 11. 12. 20. + = 1dp 13. 14. 21. + = 1dp Round the following number up or down to the place value given. Next level! Round the following number up or down to the place value given. 15. Round to the nearest whole number. 16. Round to the nearest tenth. 22. Round to the nearest whole number. 17. Round to the nearest hundredth. 23. Round to the nearest tenth. 7 7 4 5 6 3 7 2 3 1 5 8 Do you know your tenths and hundredths? Number Correct: __ / 23 How strong is your understanding? Number and algebra Level 3/4: Apply multiplicative strategies flexibly to whole numbers. What is your tip of the day? Round a digit up when the digit that follows is above 5. Keep the digit the same when the digit that follows is below 5. Number Round to tenths Round to hundredths 89.250 513.255 903.719 2713.074 6.09 29 31.24 43 30.98 53.81 6 5 4 3 2 1 1 5 2 6 3 5 5 6 4 5 3 6 2 9 1 7 0 4 9 1  11.18 11.1083  11.11  10.04 10.0361  10.03  9.18 9.1934  9.19  4.42 4.4073  4.41  6.11 6.109  6.01  0.92 0.9271  0.93  0.01 0.0095  0.10  1.01 1.0051  1.00  2.01 2.0139  2.40  2.10 2.0901  2.9

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14. Year 8 emPowerED Maths ©2021 . com Number Correct: __ / 23 How strong is your understanding? Number and algebra Level 3/4: Apply multiplicative strategies flexibly to whole numbers. What is your tip of the day? Round a digit up when the digit that follows is above 5. Keep the digit the same when the digit that follows is below 5. TUATORU: How to round whole numbers up to billions place and three decimal places. Me pēhea te whakatata i ngā tau katoa tae atu ki te nuinga o nga wāhi me ngā wāhi ira e toru. Worked Examples: Round to the nearest tenth. Round this number to the nearest hundredth. Answer: 161.1 Answer: 49.33 Round the number on the left to the nearest tenth and hundredth. Dice roll. Find the sum of the dice rolled and then round the number to the place value given. The first one is done for you. 1. 2. 3. 4. Tick the correct rounded number to 2 decimal places so it matches the front large number. 5. 6. eg. + = 6.09 + 10.695 16.785 16.8 1dp 7. 8. 18. + = 2dp 9. 10. 19. + = 2dp 11. 12. 20. + = 1dp 13. 14. 21. + = 1dp Round the following number up or down to the place value given. Extension! Round the following number up or down to the place value given. 15. Round to the nearest whole number. 16. Round to the nearest tenth. 22. Round to the nearest whole number. 17. Round to the nearest hundredth. 23. Round to the nearest tenth. 1 0 9 5 6 8 8 3 7 2 5 5 Number Round to tenths Round to hundredths 175.355 3.8467 193.319 52.175 6.09 36.058 31.245 30.981 10.695 53.781 6 5 4 3 2 1 1 5 2 6 3 5 5 6 4 5 1 6 1 0 8 4 9 3 2 5 9 There is no difference in rounding to a whole and a decimal number.  10.38 10.376  10.37  2.01 2.003  2.00  1.03 1.029  1.02  42.40 42.398  42.39  2.24 2.243  2.20  9.93 9.9371  9.94  3.36 3.3526  3.35  0.71 0.707  0.77  9.0 9.007  9.01  26.90 26.920  26.92

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15. Year 8 emPowerED Maths ©2021 . com “Why did the two 4’s not want any lunch?” Unscramble the letters below to find the answer to “Why did the two 4’s not want any lunch?” ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___! INSTRUCTIONS:  Write the answer to the problem in the second row.  Find your answer in the code and write the letter in the 3rd row.  Unscramble the letters to find the answer to the joke. SPECIAL NUMBERS - ROUNDING Round: 87594873 [round to millions] 3000495.555 [round to thousands] 87.112 [round to tens] 18003.795 [round to tens] 89009.999 [round to 2 d.p.] What digit is in the hundreds place when 59775.34 is rounded to the hundreds? Answer: Letter: Write the number here: LEARNING INTENTION:  We are learning how to round whole numbers up to billions place and three decimal places. Kai te ako mātau me pēhea te whakatata i ngā tau katoa tae atu ki te nuinga o nga wāhi me nga wāhi ira e toru. A B C D E H L R S T U Y 18000 98480 9837.53 88000000 90 4389.4 89280 89010.00 543.9 9000.390 8732 3000000 Code Round: 4389.438 [round to 1 d.p.] 2875389.3 [round to millions] 94.38 [round to tens] 9000.3895 [round to 3 d.p.] 89275.98 [round to tens] 18029.5 [round to hundreds] Answer: Letter: - Round: 98475 [round to tens] 8732.4 [round to ones] 92.3 [round to tens] 543.89 [round to 1 d.p.] 85.834 [round to tens] 9837.534 [round to 2 d.p.] 18487.534 [round to thousands] Answer: 98480 Letter: B

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16. Year 8 emPowerED Maths ©2021 . com Multiply 7.25 by 3.2 Step 1: Write as a vertical algorithm. • The number with the most digits goes on top. • In multiplication, we IGNORE the decimal points until after we have multiplied! Step 2: Multiply as if the numbers are whole numbers. • Multiply the top number by the ones digit. • After multiplying, place the ones digit in the answer and carry the tens digit to the next column. Step 3: Put your placeholder zero and multiply the top number by the tens digit. • After multiplying, place the ones digit in the answer and carry the tens digit to the next column. • Add the two rows togethers. Step 4: Place the decimal point in the answer. • Count the total number of digits behind the decimal in both of the numbers that were multiplied. 7.25 has 2 digits behind the decimal 3.2 has 1 digit behind the decimal Total number of digits behind decimal point: 3 • Place the decimal point so that there is the same total number of digits behind the decimal point of the answer. (answer) DECIMAL NUMBERS Multiplication Whakareatanga Learning Intention:  We are learning how to multiply decimal numbers, using algorithms. The coach of Team EBMC is ordering new jerseys for her bowling team. There are 4 players on the team. If jerseys are $31.24 each, how much money will the coach need to pay? See if you can find 2 different ways to solve for the cost. Now share your strategies with a classmate or the class. What have you learnt about decimal multiplication by looking at these different strategies? Multiplication is REPEATED ADDITION. To find 3.75 x 3, we can... add or multiply. Strategy 1: Strategy 2: Add: 3.75 3.75 + 3.75 11.25 Multiply: 3 . 7 5 x 3 1 1 . 2 5 Decimal stays put. Come in from the right the same number of digits. +1 7 . 2 5 x 3 . 2 1 4 5 0 V +1 7 . 2 5 x 3 . 2 1 4 5 0 + 2 1 745 0 2 3 2 0 0 V 2 3 2 0 0 = 2 3.2 1

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17. Year 8 emPowerED Maths ©2021 . com Did you meet your Success Criteria? Yes / No What is one big thing you learnt today? ___________________________________ ___________________________________ ___________________________________ Where can you use this knowledge again? ___________________________________ ___________________________________ DECIMAL NUMBERS Multiplication Whakareatanga 1. 38.7 x 0.032 2. 4.32 x 2.94 Complete the following by showing all working. 1. 4.83 x 3.9 2. 7.45 x 6.7 3. 0.382 x 17.2 3 8 7 x 0 0 3 2 + 4 8 3 x 3 9 + Extension: Use multiplication to find the product. Puzzle: Fill in the gaps in this grid by multiplying the top row by the left column number. Success Criteria:  I can multiply two decimal numbers (up to 2 decimal places).  I can correctly place the decimal point in the answer. 1. Find the product: 0.9327 x 13.28 2. Find the product: 10432.85 x 0.001542 x 1.2 0.5 3.2 2.6 0.3 4.7 2.8 2.6

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18. Year 8 emPowerED Maths ©2021 . com TUATAHI: How to multiply decimal numbers, using algorithms. Me pēhea te whakarea i ngā tau ā-ira, mā te whakamahi i ngā hātepe papatono. Worked Examples: Calculate the product: 63 x 1.3 Remove the decimal point at the start. Calculate these equations. Calculate these equations. 1. 14 x 0.7 6. Calculate the product: 3.5 x 0.6 2. 5.3 x 1.1 7. Calculate the product: 18.4 x 1.3 3. 32.7 x 3.6 8. Calculate the product: 6.13 x 2.7 4. 6.82 x 5.6 Step it up! 9. A bag of lollies costs $1.30. Teila buys 8 bags. How much will this cost her? 10. Each bag of lollies costs $4.93. Sevi buys 7.75 bags for his birthday party. How much did this cost? 5. 4.2 x 5 x It’s best to start with no decimals. Number Correct: __ / 10 How strong is your understanding? Number and algebra Level 3: Use a range of multiplicative strategies with decimal numbers. What is your tip of the day? Start multiplying, removing all decimal points. The number of decimal places in the answer depends on the number of digits behind the decimal point. x x 6 3 x 1 3 1 8 9 6 3 0 8 1 9 How many digits does the decimal point come in?

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19. Year 8 emPowerED Maths ©2021 . com TUARUA: How to multiply decimal numbers, using algorithms. Me pēhea te whakarea i ngā tau ā-ira, mā te whakamahi i ngā hātepe papatono. Worked Example: Find the product: 1.203 & 0.08 Calculate these equations. Calculate these equations. 1. 11.57 x 0.04 6. Calculate the product: 7.243 x 0.53 Look at the structure and solve these equations. 2. 213.8 x 0.26 7. Calculate the product: 34.90 x 0.14 3. 2.397 x 0.13 8. Calculate the product: 0.425 x 3.07 4. 0.243 x 3.24 Next Level! 9. A box of 20 pencils costs $7.80. Teila buys 0.4 of the box. How much will this cost her? 10. 2.000 x 0.03 5. 1.25 x 0.06 Number Correct: __ / 10 How strong is your understanding? Number and algebra Level 3/4: Use a range of multiplicative strategies with decimal numbers. What is your tip of the day? If there are zeros at the start of end, remove them when calculating. Set out the equations with no decimal point at the start. 1 1 5 7 x 4 1 2 0 3 x 8 0 0 9 6 2 4 3 + 2 = 5 Move from the right 5 decimal places How many digits come after the decimal point? Notice that you can quickly calculate these if you remove the 0’s.

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21. Year 8 emPowerED Maths ©2021 . com TUATORU: How to multiply decimal numbers, using algorithms. Me pēhea te whakarea i ngā tau ā-ira, mā te whakamahi i ngā hātepe papatono. Worked Examples: Calculate the product of 3.48 & 0.0065 Calculate these equations. Calculate these equations. 1. 554.8 x 9.56 2. 64.55 x 224.7 11. Calculate the product: 0.4281 x 9.200 3. 54.34 x 220.7 4. 234.1 x 60.45 12. Calculate the product: 0.0045 x 0.973 5. 33.05 x 2.803 6. 3.775 x 902.5 13. Calculate the product: 0.153 x 0.000635 7. 0.0386 x 128.5 8. 1.47 x 0.0305 Extension! 14. A crate full of sacks of potatoes cost $328.55. A supermarket purchases thirteen and a half crates. How much will this cost them? 9. 700.9 x 0.0320 10. 0.927 x 0.0037 Number Correct: __ / 14 How strong is your understanding? Number and algebra Level 4: Use multiplicative strategies to work with decimal numbers. What is your tip of the day? Remove any 0’s that are at the start of a number. Remove the decimal points until the calculations are finished and then return them. 3 4 8 x 6 5 1 7 4 0 2 0 8 8 0 2 2 6 2 0 0 2 4 Bring the decimal point in from the right 6 digits. Two things to remember: number of digits after the decimal pint & no decimal pints in the equation.

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22. Year 8 emPowerED Maths ©2021 . com Instead: Subtraction Example: Subtraction is the same process as addition but we subtract the numerators! Why do we need a common denominator when adding and subtracting fractions? In the problem above, can we subtract first? Why or why not? 1. 2. 3. 4. FRACTIONS Add and Subtract Tāpiri me te Ā-roto Learning Intention:  We are learning how to add and subtract fractions. 1/2 of our Maths class prefers chocolate ice cream. 1/3 prefers vanilla ice cream. The rest do not like ice cream. How would you figure out what fraction of the class likes ice cream? What fraction does not like ice cream? We can add the fraction that prefers chocolate ice cream to the fraction that prefers vanilla ice cream by finding a common denominator. We see here that: We also see that: When we have a common denominator, we can add the numerators and the denominator stays the same. We must have a common denominator to add! When we don’t, it doesn’t work out. 1 = 3 2 6 1 = 2 3 6 3 + 2 5 = 6 6 6 1 - 1 4 - 3 = 1 = 3 4 12 12 12 8 - 5 - 2 9 9 9 5 - 2 9 9 2 + 3 + = = = 5 4 6 - 3 = - = 7 8 11 + 8 = 15 9 7 - 5 = 9 12 + = = - 1 + 3 4 = 2 4 6 1 = 4 2 8 3 = 6 4 8 4 + 6 = 10 = 1 1 8 8 8 4 + = X X + =

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23. Year 8 emPowerED Maths ©2021 . com Did you meet your Success Criteria? Yes / No How would you rate your effort in Maths class today? (out of 10) ___________________________________ What is one big thing you learnt today? ___________________________________ ___________________________________ FRACTIONS Add and Subtract Tāpiri me te Ā-roto 5. 6. Success Criteria:  I can add a proper and mixed fraction.  I can subtract a proper and mixed fraction. Extension: Puzzle: The bottom two blocks, when applied to the rule, create the block above them. Find the top number and write the rule for the pattern. Rule: _______________ _______________ Rule: _______________ _______________ 5 5 - 4 = 3 6 7 4 5 + 1 = 2 8 20 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 2 + 4 = 7 7 3 + 4 = 5 5 1 + 3 = 4 8 2 + 8 = 3 9 5 + 2 = 6 5 3 + 5 = 7 8 3 - 2 = 4 3 6 - 2 = 7 3 11 - 5 = 12 9 5 - 7 = 2 10 4. 5. 2 3 - 1 1 = 8 5 3 5 - 1 11 = 7 12 1. 2. 3. 3 3 + 5 11 = 8 12 1 4 + 1 1 = 9 6 2 1 + 1 14 = 4 15 4 3 2 5 10 4 8 38 30 ? 4 3 8 5 15 17 29 62 80 ?

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24. Year 8 emPowerED Maths ©2021 . com TUATAHI: How to add and subtract fractions. Me pēhea te tāpiri me ngā hautanga ā-roto. Worked Examples: Add these fractions. Subtract these fractions. Find the sum of these fractions. Find the difference of these fractions. 1. 10. 2. 11. 3. 12. 4. 13. 5. 14. 6. 15. What is the difference between eight ninths and four fifths? Step it up! 7. 16. Two used pizzas, three fifths of one pizza and five sevenths of the other are pulled together. How much pizza is there altogether? 8. 17. When Teila arrived at a party there was one full cake and two ninths. When she left there was seven eighths left over. How much was eaten during her stay? 9. What is the sum of one fifth and two sevenths? Number Correct: __ / 17 How strong is your understanding? Number and Algebra Level 4: Calculate fractions. What is your tip of the day? Make the denominators are equal first. Make sure what you do to the denominator is the same as you do to the numerator. 3 + 4 = 21 + 40 = 61 10 7 70 70 70 5 - 2 = 25 - 12 = 13 6 5 30 30 30 2 + 1 = 3 2 - 3 = 7 3 + 2 = + = 5 3 1 3 + 2 2 = 7 7 6 + 1 = + = 7 3 2 + 5 = + = 9 6 3 + 1 = + = 7 4 3 + 2 = + = 7 9 3 + 2 = + = 9 3 7 - 2 = 9 9 4 - 1 = - = 10 7 6 - 2 = - = 11 8 11 - 3 = - = 12 10 Whatever you do to the denominator you must also do to the numerator.

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25. Year 8 emPowerED Maths ©2021 . com TUARUA: How to add and subtract fractions. Me pēhea te tāpiri me ngā hautanga ā-roto. Worked Examples: Add these fractions together. Subtract these fractions together. Find the sum of these fractions. Find the difference of these fractions. 1. 10. 2. 11. 3. 12. 4. 13. 5. 14. 15. Calculate the difference of two and two sevenths and ten ninths. 6. 7. Next Level! 16. Teila walks five eighths of a kilometre to school and Sevi walks seven ninths of a kilometre to school. How far do they walk altogether? 8. 9. Calculate the sum of two fifths and three eighths. 17. Mani ate three sevenths of a pizza and Marei ate four twelfths of a pizza. How much pizza is leftover altogether? Find the equivalent fraction for both fractions. Number Correct: __ / 17 How strong is your understanding? Number and Algebra Level 4: Calculate fractions. What is your tip of the day? Make the denominators are equal first. Make sure what you do to the denominator is the same as you do to the numerator. 3 + 4 = 7 2 - 9 = 8 3 + 1 = + = 7 6 1 3 + 2 1 = 4 5 1 3 + 4 = 21 + 40 = 61 1 10 7 70 70 70 2 + 3 = + = 5 4 1 + 5 = + = 3 6 7 + 2 = + = 8 3 3 + 2 = 8 9 6 + 4 = 8 5 9 - 2 = - = 10 7 13 - 2 = - = 15 9 4 - 14 = - = 2 7 9 3 1 - 1 4 = 6 5 1 - 4 = 35 - 24 = 11 1 6 5 30 30 30

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26. Year 8 emPowerED Maths ©2021 . com TUATORU: How to add and subtract fractions. Me pēhea te tāpiri me ngā hautanga ā-roto. Worked Examples: Add these fractions together. Subtract these fractions together. Find the sum of these fractions. Find the difference of these fractions. 1. 10. 2. 11. 3. 12. 4. 13. 5. 14. 6. 15. Calculate the difference between two and seven twelfths and fifteen sixths. 7. Extension! 16. Teila’s class recycled two and 7/8 boxes of paper in a week and Sevi’s class recycled three and 1/12 boxes of paper in a week. How much altogether did they recycle? 8. 9. Calculate the sum of three and four ninths and two and three fifths. 17. In Mani’s free time he spends 3/8 watching videos and 1/9 swimming. How much time does he still have left to read his book? 2 4 + 1 = 12 + 5 = 4 2 1 5 3 15 15 15 Number Correct: __ / 17 How strong is your understanding? Number and Algebra Level 4: Calculate fractions. What is your tip of the day? Make the denominators are equal first. Make sure what you do to the denominator is the same as you do to the numerator. Add all the whole numbers together first. 4 + 6 = 5 3 - 7 = 5 4 + 8 = 7 9 2 2 + 1 4 = 3 6 5 + 6 = 4 8 4 + 7 = 7 9 2 + 8 = 5 7 5 + 5 = 7 9 4 + 7 = 3 6 5 - 8 = 7 11 6 - 9 = 7 10 11 - 12 = 2 12 9 5 - 6 = 11 10 2 4 - 1 5 = 14 - 11 = 84 - 55 29 = 5 6 5 6 30 30 30

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27. Year 8 emPowerED Maths ©2021 . com LEARNING INTENTION:  We are learning how to add fractions with same and different denominators. E ako ana mātau me pēhea te tāpiri hautanga ki ngā tauira ōrite, rerekē hoki. FRACTIONS - ADDITION INSTRUCTIONS:  Add two fractions that are next to each other in the top row.  Write your simplified answer in the box beneath them and find the corresponding letter in the code.  Unscramble the letters to spell the answer to the joke below. Unscramble the letters below to find the answer to “Statistically, how many people have trouble with fractions?” A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 3 1 2 Code 1 6 3 4 3 12 1 3 1 2 7 6 5 12 5 4 5 7 2 6 7 4 8 9 5 2 4 6 18 34 14 3 7 12 4 3 7 4 11 12 5 6 8 11 13 12 1. 1 4 1 4 1 2 3 4 2 4 Letter: Letter: Letter: Letter: 3. 5 30 16 48 17 34 2 Letter: Letter: Letter: Letter: 2. Letter: Letter: Letter: 7 6 3 18 1 3 10 6 ___ ___ ___ ___ ___ ___ ___ O F ___ ___ ___ ___

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28. Year 8 emPowerED Maths ©2021 . com Some of these measuring instruments have scales. A scale is a series of small lines that indicate intervals. These intervals represent an amount. In other words, the small lines are each worth the same amount, and we can count the lines to figure out the measurement. Example 1: In the scale to the right, we see there is one small line between each larger line marked with a multiple of 10. Since there are two equal parts that make up 10 on this scale, we do 10 ÷ 2 = 5 so each small line will represent 5 ml. To find the measurement, we need to look at the liquid and record the line that it is on. Here we see the amount of liquid is 25 ml. Example 2: In the scale to the left, we see there are four small lines between each larger line marked with a multiple of 10. Since there are five equal parts that make up 10 on this scale, we do 10 ÷ 5 = 2 so each small line will represent 2 ml. Here we see that the liquid is between the 40 mark and 42 mark. We can do half of 2 = 1 then add 40 to see our final measurement: 41 ml. What would the intervals be worth on the following scales? What would the measurements be? 1. 2. 3. MEASUREMENT Reading a Range of Scales Tahuri Wae Learning Intention:  We are learning how to read a range of scales. What type of measuring instrument would you use to: • Weigh a watermelon? • Measure the height of a desk? • Tell the temperature? • Measure sugar for baking cookies? We use measuring instruments to help us measure length, weight and capacity (volume or liquid). To measure length, we can use a: • Ruler • Metre stick • Tape measure To measure weight, we can use a: • Scale • Balance • Digital scale To measure capacity, we can use a: • Teaspoon • Cup • Gallon • Test tube • Beaker ml 10 20 30 40 50 60 10 20 30 40 50 60 ml ˚C 15 6 3 9 12 0 -15 -12 -9 -6 -3 0 40 20 80 100 60 g

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29. Year 8 emPowerED Maths ©2021 . com Did you meet your Success Criteria? Yes / No How would you rate your effort in Maths class today? (out of 10) ___________________________________ What can you do to improve your Maths learning tomorrow? ___________________________________ ___________________________________ ___________________________________ MEASUREMENT Reading a Range of Scales Tahuri Wae Success Criteria:  I can read a range of scales accurately. Extension: Draw a scale on the beakers below that fit the criteria. 14 21 -2 5 12 2 4 11 1 10 19 7 9 18 22 -1 6 27 4 18 8 10 17 19 9 16 23 25 15 24 6 28 12 Puzzle: Solve the following magic squares. The sum of all rows, columns and diagonals are the same. 1. Interval: _________ Measurement: __________ 2. Interval: _________ Measurement: __________ 3. Interval: ________ Measurement: __________ 4. Interval: _________ Measurement: __________ ml 10 20 30 40 50 60 1. Interval: _________ Measurement: __________ 2. Interval: _________ Measurement: __________ 3. Interval: _________ Measurement: __________ ˚C 15 -15 -12 -9 -6 -3 0 3 6 9 12 ml 10 20 30 40 50 60 ml 10 20 30 40 50 60 0 4 2 8 10 6 kg 1. Draw a scale going up to 300 ml in intervals of 15 ml. Indicate multiples of 60 with larger lines. 2. Draw a scale going up to 175 ml in intervals of 7 ml. Indicate multiples of 35 with larger lines. ml ml

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30. Year 8 emPowerED Maths ©2021 . com TUATAHI: How to read a range of scales. Me pēhea te pānui i ngā awhe tauine. Worked Examples: What is the weight on this scale? = 68 grams How much fluid is in each flask? What do these temperatures read? 1. 2. 9. 10. 11. ml ml 3. 4. How much do these items weigh? (look carefully at the units). ml ml 12. 13. What are these weights? 5. g 14. 15. 6. g 7. Step it up! 16. Look at the scales below to determine the weight of each shape. g 8. g Always check what each mark on the scale represents. How much fluid is in this flask? 0 40 80 100 60 g 20 22 Shape Weight 11 15 Number Correct: __ / 16 How strong is your understanding? Measurement 3/4: Use appropriate scales, devices, and metric units. What is your tip of the day? Check what each mark on the scale represents. Look carefully at the units used on the devices. 15 ˚C -12 6 3 9 12 0 -3 -6 -9 -15 ˚C 15 ˚C -15 -12 -9 6 3 9 12 0 -6 -3 ˚C 15 6 3 9 12 0 -15 -12 -9 -6 -3 ˚C ml 25 ml 10 20 30 40 50 60 ml 10 20 30 40 50 60 ml 10 20 30 40 50 60 ml 200 300 600 400 500 100 ml 200 300 600 400 500 100 0 4 2 8 10 6 kg How heavy is this watermelon? 1.25 kg ˚C 0 4 2 8 10 6 kg 0 40 80 mg 100 60 20 0 4 2 8 10 6 kg g g g

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31. Year 8 emPowerED Maths ©2021 . com TUARUA: How to read a range of scales. Me pēhea te pānui i ngā awhe tauine. Worked Examples: How much fluid is in each flask? What do these scales read? 1. 2. 9. 10. 11. 12. 3. 4. How long are these colouring pencils? 13. How much do these items weigh? Answer: 14. 5. 6. Answer: 15. Answer: 7. 8. Next level! 16. Look at the scales below to determine the weight of each shape. Number Correct: __ / 16 How strong is your understanding? Measurement 3/4: Use appropriate scales, devices, and metric units. Don’t forget to apply the correct units to your answers. What is your tip of the day? Check what each mark on the scale represents. Look carefully at the units used on the devices. ml 10 20 30 40 50 60 ˚C 15 -15 -12 -9 -6 -3 0 3 6 9 12 -10˚C c) What is this temperature? a) What is this measurement? 40 ml b) What is this weight? 90 g 10 20 30 40 50 60 ml 10 20 30 ml 40 50 60 ml 100 200 300 400 500 600 ml 200 300 600 400 500 100 0 4 2 8 10 6 kg 0 400 200 800 1000 600 mg 0 4 2 8 10 6 kg 0 40 20 80 100 60 g 45 40 30 Shape Weight g g g cm cm cm

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32. Year 8 emPowerED Maths ©2021 . com Number Correct: __ / 16 How strong is your understanding? Measurement 3/4: Use appropriate scales, devices, and metric units. What is your tip of the day? Check what each mark on the scale represents. Look carefully at the units used on the devices. TUATORU: How to read a range of scales. Me pēhea te pānui i ngā awhe tauine. Worked Examples: How much fluid is in each flask? What do these scales read? 1. 2. 9. 10. 11. 12. 3. 4. How long are these colouring pencils? 13. How much do these items weigh? Answer: 14. 5. 6. Answer: 15. Answer: 7. 8. Extension! 16. Look at the scales below to determine the weight of each shape. These scales are more challenging. c) What is this temperature? ml 10 20 30 40 50 60 ˚C 15 -12 -9 -6 -3 0 3 6 9 12 -15 -13˚C a) What is this measurement? 32.5 ml b) What is this weight? 68 g 10 20 30 40 50 60 ml 10 20 30 ml 40 50 60 ml 400 500 600 0 4 2 8 10 6 kg 0 400 200 800 1000 600 mg 8 2.5 1.75 Shape Weight 300 ml 200 300 600 400 500 100 100 200 0 4 2 8 10 6 kg 0 40 20 80 100 60 g kg kg kg

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33. Year 8 emPowerED Maths ©2021 . com LEARNING INTENTION:  We are learning how to read a range of scales. E ako ana matou ki te panui i te whānuitanga o nga unahi. MEASUREMENT - READING SCALES INSTRUCTIONS:  Read the scales and find the correct measurement in the code below.  Write the letter in the space provided then unscramble the letters to reveal the answer to the joke. A B C E G H L M N O R T U V Y 3.6 3.25 8.7 7 9.2 10.8 11.8 8.8 5.25 11 1.5 11.5 9.5 -1.5 -14 Code “You know what’s odd?” Answer: Letter: Answer: Letter: Answer: Letter: Answer: Letter: Answer: Letter: Unscramble the letters below to find the answer to “You know what’s odd?” ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ! 0 4 2 8 10 6 kg ˚C 15 -12 -9 -6 -3 0 3 6 9 12 -15 Answer: Letter: Answer: Letter: Answer: Letter: Answer: Letter: Answer: Letter: Answer: Letter: Answer: Letter: Answer: Letter: Answer: Letter: Answer: Letter: Answer: Letter:

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34. Year 8 emPowerED Maths ©2021 . com What do you notice about the area of the rectangle and trapezium? —> They are the SAME! So we see that the area of a trapezium is the SAME as the area of a rectangle with the same height. But what is the length of the base? The base of the rectangle is the average of the parallel sides of the trapezium. To find the base: (Base 1 + Base 2) ÷ 2 Area of a Trapezium Formula: Area = (Base 1 + Base 2) ÷ 2 x Height OR Area = (b1 + b2) ÷ 2 x h A = (b1 + b2) ÷ 2 x h A = (b1 + b2) ÷ 2 x h A = (12 + 8) ÷ 2 x 3 A = (9 + 5) ÷ 2 x 11 A = 30 m2 A = 77 cm2 What happens when we add two numbers then halve the sum? Is there a special name for this? Why might we need to know this to find the area of a trapezium? A trapezium is a shape with 4 sides and only 1 pair of parallel lines. MEASUREMENT Area of Trapeziums Tuhinga o mua Learning Intention:  We are learning how to calculate the area of a trapezium. What is a trapezium? Using the definition of a trapezium... • Do you think a trapezium is a parallelogram? Why or why not? • Do you think a trapezium is a regular or irregular quadrilateral? Why or why not? A trapezium is NOT a parallelogram because a trapezium only has 1 pair of parallel lines and a parallelogram has 2 pairs. All trapeziums are quadrilaterals since they have 4 sides but they are always irregular because their sides are not equal. Remember that area is the amount of space inside a shape. We measure area by the number of square units it takes to cover a shape. To find the area of a trapezium, we can count the number of squares it takes to cover the shape. To find the area quickly, we can see if we can rearrange a parallelogram to make another shape. 8 m 3 m 12 m 5 cm 11 cm 9 cm Pop corn

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35. Year 8 emPowerED Maths ©2021 . com Did you meet your Success Criteria? Yes / No What is one big thing you learned today? ___________________________________ ___________________________________ Where can you use this knowledge again? ___________________________________ ___________________________________ MEASUREMENT Area of Trapeziums Tuhinga o mua Show all working and write in the formula. 1. Base 1 = Base 2 = Height = Area of a Trapezium Formula = A = (b1 + b2) ÷ 2 x h Area = 2. Formula: Area: 3. Formula: Area: 7 cm 6 cm 10 cm 7 m 9 m 11 m 5 mm 10 mm 9 mm Extension: Success Criteria:  I can identify the bases and height of a trapezium.  I can calculate the area of a trapezium. 1. Formula: Area: 2. Formula: Area: 3. Find the missing base and height of the trapezium if the area is 216 m2. (Hint: the average of the bases is 13.5) Base 1 = Base 2 = Height = 24 m 39 m 18 m 7 m 9.4 m 16 m __ m ___ m 18 m Formula: Area: Formula: Area: Formula: Area: 4 mm 3 mm 6 mm 7 m 20 m 15 m 5 m 8.3 m 10.8 m

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36. Year 8 emPowerED Maths ©2021 . com TUATAHI: How to calculate the area of a trapezium. Me pēhea te tatau i te rohe o te tāwhiti. Worked Example: What is the area of the trapezium-shaped shopping bag? Calculate the area of these trapeziums. Calculate the area of these trapeziums. 1. 4. Answer: Answer: 2. 5. Answer: Answer: Step it up! 3. 6. What is the area of the weight in m²? (purple section) Answer: Answer: POP- CORN 9 cm 10 cm 8 cm Don’t forget to add the top and bottom lengths together first. Number Correct: __ / 6 How strong is your understanding? Measurement Level 3/4: Use sides and edge lengths to find trapeziums. What is your tip of the day? Divide the sum of the top and bottom sides by two. This formula is similar to the area of a triangle. 40 cm A = (b1 + b2) x h 2 A = (31 + 45) x 40 2 A = 1520 cm² 72 cm 50 cm 16 cm 16 cm 12 cm 21 cm 17 cm 9 cm 10 cm 7 m 9 m 6 m Use: A = (b1 + b2) x h 2 Use: A = (b1 + b2) x h 2 Use: A = (b1 + b2) x h 2 Use: A = (b1 + b2) x h 2 Use: A = (b1 + b2) x h 2 Use: A = (b1 + b2) x h 2

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37. Year 8 emPowerED Maths ©2021 . com TUARUA: How to calculate the area of a trapezium. Me pēhea te tatau i te rohe o te tāwhiti. Worked Example: A = (b1 + b2) x h 2 A = (10 + 8) x 19 2 A = 171 cm² What is the area of the trapezium-shaped bucket? Calculate the area of these trapeziums. Calculate the area of these trapeziums. 1. 4. Answer (mm2): Answer: 2. 5. Answer: Answer (cm2): 3. Next Level! 6. What is the area of the planter box? Answer (cm2): Answer (m2): 49 cm 26 cm 23 cm 17 cm 9 mm 22 mm 15 mm 33 cm 240 mm 0.4 m 200 mm 185 mm 15 cm Number Correct: __ / 6 How strong is your understanding? Measurement Level 4: Use sides and edge lengths to find trapeziums. 8 cm 19 cm 10 cm What is your tip of the day? Divide the sum of the top and bottom sides by two. This formula is similar to the area of a triangle. 1.5 m 73 cm 1.10 m Once you have added the length of the top and the bottom, divide by two. Use: A = (b1 + b2) x h 2 Use: A = (b1 + b2) x h 2 Use: A = (b1 + b2) x h 2

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38. Year 8 emPowerED Maths ©2021 . com TUATORU: How to calculate the area of a trapezium. Me pēhea te tatau i te rohe o te tāwhiti. Worked Example: What is the area of the trapezium-shaped light shade? A = (b1 + b2) x h 2 A = (12 + 16) x 21 2 A = 294 cm² Calculate the area of these trapeziums in cm². Calculate the area of these trapeziums in mm². 1. 4. Answer (cm2): 2. Answer (mm2): 5. Answer (cm2): Answer (mm2): 3. Extension! 6. What is the area of the green trapezium of this wheelbarrow in cm²? Answer (cm2): 1.2 m 1.4 m 190 cm 160 mm 35 cm 20 cm Number Correct: __ / 6 How strong is your understanding? Measurement Level 4: Use sides and edge lengths to find trapeziums. What is your tip of the day? Divide the sum of the top and bottom sides by two. This formula is similar to the area of a triangle. 16 cm 120 mm 210 mm 1.3 m 1.2 m 96 cm 450 mm 60 cm 1.02 m 750 mm 640 mm 800 mm 90 mm 19 cm 150 mm A trapezium’s area is the equal to a rectangle’s. Use: A = (b1 + b2) x h 2 Answer (cm2):

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39. Year 8 emPowerED Maths ©2021 . com LEARNING INTENTION:  We are learning how to calculate the area of a trapezium. Kai te ako mātau me pēhea te tatau i te rohe o te tāwhiti. MEASUREMENT - AREA OF TRAPEZIUMS INSTRUCTIONS:  Work out the following questions and find the answer in the code below.  Write the letter in the space provided then unscramble the letters to reveal the answer to the joke. Unscramble the letters below to find the answer to “What do you call a person who hates long sentences?” A _C_ ___ ___ ___ ___ ___ ___ ___ ! A B C E I K L M N O P R S T U 44 303.24 360 98 108 180 147.6 151.62 54 88 295.2 49 590.4 216 176 Code Problem: Working: Answer: Letter: 5 m 12 m 13 m 8.4 m 23.4 m Find the area. Find the area. Find the area. Find the area. Find the area. Find the area. Find the area. Find the area. 5 cm 7 cm 9 cm 8 mm 11 mm 16 mm 4 m 9 m 3.2 cm Area of a Trapezium = (Base 1 + Base 2) 2 x Height

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40. Year 8 emPowerED Maths ©2021 . com Sometimes a group of ordered pairs can be joined together to create a path or image. Start at the first co-ordinate then continue on to the next one, drawing a line to connect them. (-4,3)(-2,4)(-1,3) (1,3)(2,4)(4,3) (3,1)(3,-2)(1,-4) (-1,-4)(-3,-2) (-3,1)(-4,3) Plot these on the cartesian plane. A (3,-2) B (-1,3) C (2,-4) D (-3,1) Indicate which dice is at… (3,-2) (-4,1) (-2,-3) (1,1) Join these ordered pairs together to create a shape. (2,-3)(-2,-3) (-2,2)(0,4)(2,2)(2,-3) New line: (-2,2)(2,2) Geometry Co-ordinates Taunga Learning Intention:  We are learning how to plot and identify co-ordinates on a Cartesian plane. Co-ordinates are ordered pairs that tell us the location of points on the Cartesian plane. The first number in the brackets is the x-coordinate (horizontal) and the second is the y-coordinate (vertical). Example: (3, 4) means 3 to the right and 4 up On the x-axis to the right and on the y-axis going up, these numbers are positive. On the x–axis to the left and on the y-axis going down, these numbers are negative. Which object is represented for each ordered pair? Draw a line from the ordered pair to the fruit. (4,-3) (-1,-1) (-3, 3) (2,3) x-axis y-axis Origin (0,0) 4 3 2 1 1 2 3 4 5 Y-axis 4 3 2 1 -4 -3 -2 -1 -1 1 2 3 4 5 -2 -3 -4 4 3 2 1 -4 -3 -2 -1 -1 1 2 3 4 5 -2 -3 -4 4 3 2 1 -4 -3 -2 -1 -1 1 2 3 4 5 -2 -3 -4 4 3 2 1 -4 -3 -2 -1 -1 1 2 3 4 5 -2 -3 -4 4 3 2 1 -4 -3 -2 -1 -1 1 2 3 4 5 -2 -3 -4 Origin (0,0) Y-axis 4 3 2 1 -4 -3 -2 -1 -1 1 2 3 4 5 -2 -3 -4 Origin (0,0) x-axis y-axis x-axis y-axis

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41. Year 8 emPowerED Maths ©2021 . com Did you meet your Success Criteria? Yes / No How would you rate your effort in Maths class today? (out of 10) ___________________________________ What is one big thing you learnt today? ___________________________________ ___________________________________ Geometry Co-ordinates Taunga Identify the letter that best represents the co-ordinate. (4,3) Letter __ (-4,-3) Letter __ (2,-3) Letter __ (2,2) Letter __ Write the ordered pairs for the indicated letter. Letter K ( ) Letter A ( ) Letter I ( ) Letter E ( ) Letter B ( ) Extension: Join all the ordered pairs to create 3 separate shapes. Puzzle: With a partner, play Battleship. Place 3 of each ship on the grid (see example) note the co-ordinates the ships are on. Take turns guessing co-ordinates. If the correct co-ordinate is guessed, cross out the piece of the ship. The winner is the first person to sink the other person’s ships. Success Criteria:  I can add three numbers (up to 6 digits).  I can add four numbers (up to 6 digits). 4 3 2 1 -4 -3 -2 -1 -1 1 2 3 4 5 -2 -3 -4 A B H K D J G E C F I 4 3 2 1 -4 -3 -2 -1 -1 1 2 3 4 5 -2 -3 -4 8 7 6 5 4 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 -6 -7 -8 -9 -10 10 -2 -3 -4 -5 -6 -7 -8 8 7 6 5 4 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 -6 -7 -8 -9 -10 10 -2 -3 -4 -5 -6 -7 -8 8 7 6 5 4 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 -6 -7 -8 -9 -10 10 -2 -3 -4 -5 -6 -7 -8 Ship E x a m p l e Use this grid to help you keep track of the co-ordinates you have guessed. Shape 1 Shape 2 Shape 3 (-5,-4) (0,-3) (1,-1) (-7,1) (-2,-4) (3,7) (-5,6) (-2,-7) (10,7) (-3,1) (6,-7) (8,-1) (-5,-4) (6,-3) (1,-1) (0,-3) A B H K D J G E C F I

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42. Year 8 emPowerED Maths ©2021 . com TUATAHI: How to read a scale on a map and plot coordinates. Me pēhea te pānui i tētahi tauine i runga i tētahi mahere me te tuhi me te tā i ngā taururu. Worked Examples: How big is this object in real life? What are the coordinates for these fish? Each of these objects have different scales. Use the scale provided to indicate the object’s size in real life. Using this Cartesian plane of a spring, write down the coordinates of the following: 1. 2. 3. Match the letters to the correct coordinate on the Cartesian plane. Using the scale on the map below, answer the questions with the distance in real life. Plot these numbers on the Cartesian plane according to the coordinates. 4. How far is it from Town A to Town B? 5. How far is it from Town C to Town A? 6. How far is it from Town B to the Hockey turf? Step it up! 7. Katie decides to take a walk from Town B to the sea. How far is this? 23. What is the next coordinate to finish this rectangle? Number Correct: __ / 23 How strong is your understanding? Geometry Level 3/4: Communicate and interpret locations and directions. What is your tip of the day? Measure the distance before using the scale. The x-axis is horizontal; the y-axis is vertical. 1 cm = 10 cm 1 cm = 5.5 cm 1 cm = 12 cm Town A Town B Town C sea zzz Hockey turf zz 3 2 1 2 3 4 5 y x Fish Coordinates ( , ) 8. ( , ) 9. ( , ) 10. ( , ) 11. ( , ) 12. -4 -3 -2 -1 0 1 2 3 4 y x 4 3 Letter Coordinates (-1,4) 13. (4,1) 14. (2,4) 15. (-4,3) 16. (0,1) 17. y -4 -3 -2 -1 0 1 2 3 4 4 3 Number Coordinates (-3,2) 18. (2,4) 19. (-1,3) 20. (1,0) 21. (-4,1) 22. x Scale: 1 cm = 1 km Multiply the scale by the actual measurement. 1 cm = 1.5 metres 4 cm The car measures 4 cm. So 4 x 1.5 = 6 metres 3 2 1 1 2 3 y x Fish Coordinate (1,3) (2,2) (3,3) (3,1) -2 -1 0 1 2 y x 3 Start/Finish -2,3 2,1 -2,1

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43. Year 8 emPowerED Maths ©2021 . com TUARUA: How to read a scale on a map and plot coordinates. Me pēhea te pānui i tētahi tauine i runga i tētahi mahere me te tuhi me te tā i ngā taururu. Worked Examples: How far does Katie travel from home to the basketball court? = 450 m What are the coordinates for these pets? Each of these objects have different scales. Use the scale provided to indicate the object’s size in real life. Using this Cartesian plane of a spring, write down the coordinates of the following: 1. 2. 3. Use the scale on the map below to answer the questions. Disregard the roads, direct route only. Measure to nearest ½ cm. 14. Plot and join these coordinates on the Cartesian plane below to create an object. 4. Katie walked from home to the dairy. How far is this? (nearest ½ cm) Next Level! 5. She then walked from the dairy to the hotel. How far did she walk? 6. From the hotel she walked to the Town Hall. How far did she walk? (nearest ½ cm) 7. How far is it from the Town Hall to the Police Station? (nearest ½ cm) 8. Katie walks to and from home to the hospital where she works. How far does she walk in 5 days? (nearest ½ cm) The x-axis runs from left to right. Number Correct: __ / 15 How strong is your understanding? Geometry Level 3/4: Communicate and interpret locations and directions. What is your tip of the day? Measure the distance before using the scale. The x-axis is horizontal; the y-axis is vertical. 3 2 1 1 2 3 y x Pet Coordinate (3,1) (1,3) (1,1) (2,2) Katie’s Pets Library Home Student accommodation Shop Supermarket University Basketball court 1 cm = 100 m 1 cm = 5 cm 1 mm = 2 cm 1 mm = 1.25 cm Library Home Hotel Police Town Hall Hospital Dairy Scale: 1 cm = 100 m Letter Coordinates ( , ) 9. ( , ) 10. ( , ) 11. ( , ) 12. ( , ) 13. -4 -3 -2 -1 0 1 2 3 4 y x 4 3 Order Coordinates Start at... (4,3) then (-1,3) then (-3,1) then (2,1) then (4,3) then (4,-2) then (2,-4) then (-3,-4) then (-3,1) -4 -3 -2 -1 0 1 2 3 4 y x 4 3 -1 -2 Coordinates Item (-3,0) (1,1) (0,-2) (2,4) (2,-1) (-2,2) (-1,4) y x -1 -2 4 3 -4 -3 -2 -1 0 1 2 3 4 15. Record the objects at each point given. (nearest ½ cm)

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44. Year 8 emPowerED Maths ©2021 . com TUATORU: How to read a scale on a map and plot coordinates. Me pēhea te pānui i tētahi tauine i runga i tētahi mahere me te tuhi me te tā i ngā taururu. Worked Examples: What is the compass direction and distance from the tree to the park bench? Join the coordinates together to form a shape. Use the compass and scale on the map to find the quickest pathway to a given destination. 9. Using the table of values, plot the points on the Cartesian plane. Join them with a line. 1. Give the distance and compass directions for Tama to walk from home to school. Plot and join the coordinates to finish the picture. 2. Give distance and compass directions for Tama to walk from school to the Church. 3. Give distance and compass directions for Tama to walk from the Church to the Hospital. What are the coordinates for the letters? Extension! y x 3 2 -3 -2 -1 0 1 2 3 -1 -2 Number Correct: __ / 21 How strong is your understanding? Geometry Level 3/4: Communicate and interpret locations and directions. What is your tip of the day? Measure the distance before using the scale. The x-axis is horizontal; the y-axis is vertical. Town Hall School Church Entertainment Hospital Park Falls Letter Coordinates A ( , ) 4. B ( , ) 5. C ( , ) 6. D ( , ) 7. E ( , ) 8. -4 -3 -2 -1 0 1 2 3 4 y x 4 3 -1 -2 Home Coordinates 10. (3,1) 11. (-2,1) 12. (-1,3) 13. (-2,4) 14. (-3,1) 15. (-5,1) 16. (-5,-1) 17. (4,-1) x -3 -2 -1 0 1 2 3 y -5 -4 -3 -2 -1 0 1 y 4 3 -1 -2 x -4 -3 -2 -1 0 1 2 3 4 18. (4,2) 19. (3,3) 20. (3,1) Coordinates (-3,2) (-2,-1) (1,-2) (3,0) (2,3) -3 -2 -1 0 1 2 3 y x 3 2 -1 -2 21. Tama plays darts and throws 5 darts on the board. What is his total using the points above? Coordinates Order (3,-3) Start... (0,-1) then (-3,1) then (-2,3) then (3,1) then Scale: 2.8 cm = 28 m = 3 = 4 = 2 = 1 -4 -3 -2 -1 0 1 2 3 4 y x 4 3 -1 -2 A B D E C Scale: 1 cm = 10 m Scale: 1 cm = 1 m Always state the compass direction first before the distance.

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45. Year 8 emPowerED Maths ©2021 . com INSTRUCTIONS:  There is a hidden picture in this grid. Connect the coordinates below with lines to reveal the picture. Line 1: (4,-9),(4,-8),(1,-7),(1,-6),(3,-7),(5,-6),(7,-7),(5,-3),(7,-4),(4,1),(6,-1),(3,4),(5,2),(3,5),(3,7),(-3,6),(-3,4),(-6,2),(-4,2),(-7,-1),(-5,0),(-7,-4),(-5,-3),(-8,-7),(-6,-6), (-4,-7),(-1,-6),(-1,-7),(-4,-8),(-4,-9),(4,-9) Line 2: (0,3),(-1,4),(-2,4),(-3,3),(-3,1),(-2,0),(-1,0),(0,1),(1,0),(2,0),(3,1),(3,3),(2,4),(1,4),(0,3) Line 3: (-3,-1),(-1,-3),(1,-3),(3,-1),(-3,-1) 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 10 9 8 7 6 5 4 3 2 1 GEOMETRY - CO-ORDINATES LEARNING INTENTION:  How to plot and identify co-ordinates on a Cartesian plane. Me pēhea te tā me te tohu i ngā whakaritenga ā-hoa i runga i tētahi waka rererangi Cartesian.

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46. Year 8 emPowerED Maths ©2021 . com This means that the 1st term in the sequence is 7, the 2nd term is 12, the 3rd term is 17 and so on. Step 2: Start writing your rule. Assign variables (letters) to represent the values in the top row which is the term number and a different letter for the values in the bottom row which is the number sequence. Begin writing the rule with the bottom letter followed by an equal sign then the top letter and a times sign. Bottom letter = Top letter x b = a x Step 3: Find the difference between the numbers. Figure out how much the pattern is going up by (or down by) then write that number next to the times sign. b = a x 5 Step 4: Add or subtract to get the first term. Choose a top and bottom pair from the table and substitute the values into the rule. Substitute the pair into your equation. b = a x 5 --> 12 = 2 x 5 We can see this equation is not true. What can we add or subtract on the right side to make it true? 12 = 2 x 5 + 2 b = a x 5 + 2 Step 5: Test your rule. Choose a different pair then substitute the values into your rule. If the equation is true then your rule is correct! b = a x 5 + 2 --> 17 = 3 x 5 + 2 ALGEBRA Number Sequences Ngā Tauira Tau Learning Intention:  We are learning how to continue a number sequence and write an algebraic rule. Katie earns $15 each week for washing her parents’ cars. Complete the table below. Tama decides to grow tomatoes. He plants a seed and records the plant’s height. He finds it doubles in height every month and it was 3 cm in the second month. Complete the table below. We can represent real-life patterns using number sequences. A number sequence can be increasing (going up) or decreasing (going down). An increasing sequence looks like this: Here the sequence starts at 7 and is going up by 5. A decreasing sequence looks like this: Here the sequence starts at 45 and is going down by 3. Writing a Rule for Number Sequences: Step 1: Write the term numbers above. Make a row above the number sequence and write the term numbers. 4 9 14 19 24 29 34 39 44 65 60 55 50 45 40 35 30 25 a 1 2 3 4 5 6 7 8 9 b 7 12 17 22 27 32 37 42 47 +5 +5 +5 +5 +5 +5 +5 +5 1 2 3 4 5 6 7 8 9 a 7 12 17 22 27 32 37 42 47 b Week 1 2 3 4 5 6 7 Total Earned ($) Month Height (cm)

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47. Year 8 emPowerED Maths ©2021 . com Did you meet your Success Criteria? Yes / No How would you rate your attitude in Maths class today? (out of 10) ___________________________________ How can you improve your Maths learning tomorrow? ___________________________________ ___________________________________ ALGEBRA Number Sequences Ngā Tauira Tau Write a rule for the following number sequence: Step 1: Write the term numbers above. Step 2: Start writing your rule. Step 3: Find the difference between the numbers. Step 4: Add or subtract to get the first term. Step 5: Test your rule. Completing Number Sequences: Identify the pattern and complete the number sequence. 1. 2. 3. 4. 5. Success Criteria:  I can identify and complete a number pattern.  I can write an algebraic rule for a number sequence. 6. 7. Writing Rules for Number Sequences: Complete the table and find an algebraic rule for each sequence. 8. Rule: _____________________ 9. Rule: _____________________ 10. Use the rule b = 4a - 3 to complete the table below. 11. What number would be in the 21st term? 12. What term number would the number 45 be? 13. What term number would the number 89 be? 21 24 27 30 33 36 39 42 45 2 5 8 11 4 9 14 19 7 11 15 11 17 23 20 24 28 17 27 42 43 55 67 a 2 4 6 8 10 12 14 16 18 b a 5 9 13 17 21 25 29 33 37 b 1 2 3 4 5 6 7 8 9 a b ________ ________ ________ a 21 24 27 30 33 36 39 42 45 b

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48. Year 8 emPowerED Maths ©2021 . com Writing an Algebraic Rule for a Pattern: Step 1: Start writing your rule. Assign letters to represent the values in the top row and a different letter for the values in the bottom row. Begin writing the rule with the bottom letter followed by an equal sign then the top letter and a times sign. Bottom letter = Top letter x m = n x Step 2: Find the difference between the numbers. Figure out how much the pattern is going up (or down) by then write that number next to the times sign. +3 +3 m = n x 3 Step 3: Add or subtract to get the first term. Choose a top and bottom pair from the table and substitute the values into the rule. Substitute the pair into your equation. m = n x 3 --> 4 = 1 x 3 We can see this equation is not true. What can we add or subtract on the right side to make it true? 4 = 1 x 3 + 1 Step 4: Test your rule. Choose a different pair then substitute the values into your rule. If the equation is true then your rule is correct! m = n x 3 + 1 --> 7 = 2 x 3 + 1 m = n x 3 + 1 --> 10 = 3 x 3 + 1 ALGEBRA Spatial Patterns Ngā Tauira Mokowā Learning Intention:  We are learning how to continue a spatial pattern and write an algebraic rule. Where have you seen a pattern in real life? Draw these patterns in the space below: We can use a table to help us look for patterns. For example: Now we can see what is different between the terms. --> We are adding three new matchsticks each time. Circle then square then triangle. (repeat 3 times) 3 triangles then 2 squares. (repeat 3 times) Term Number 1 2 3 4 Number of Matchsticks 4 7 10 13 Term Number 1 2 3 4 Number of Matchsticks 4 7 10 13 Term Number = n 1 2 3 4 Number of Matchsticks = m 4 7 10 13 Term Number 1 2 3 4 Number of Matchsticks 4 7 10 13 Term Number 1 2 3 4 Number of Matchsticks 4 7 10 13

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49. Year 8 emPowerED Maths ©2021 . com ALGEBRA Spatial Patterns Ngā Tauira Mokowā Write a rule for the following patterns: Step 1: Start writing your rule. Step 2: Find the difference between the numbers. Step 3: Add or subtract to get the first term. Step 4: Test your rule. 1. Rule: _____________________ 2. Rule: _____________________ Success Criteria:  I can create a table based on a spatial pattern.  I can write an algebraic rule for a spatial pattern. Did you meet your Success Criteria? Yes / No How would you rate your effort in Maths class today? (out of 10) ___________________________________ What is one big thing you learnt today? ___________________________________ ___________________________________ 3. Rule: _____________________ Extension: 1. Use the rule y = 3x - 2 to complete the table below. 2. How many matchsticks would be in the 119th term? 3. What term number would have 49 matchsticks in it? 4. What term number would have 619 matchsticks in it? Puzzle: Multiply the two outside circles together to calculate the middle square values. Term Number = n 1 2 3 6 Number of Matchsticks = m Term Number = n 1 2 3 7 Number of Matchsticks = m Term Number = n 1 2 3 10 Number of Matchsticks = m ________ ________ ________ Term Number = x 1 2 3 8 13 17 38 Number of Matchsticks = y 15 7 23 33 396 492 Term Number = n 1 2 3 8 Number of Matchsticks = m

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50. Year 8 emPowerED Maths ©2021 . com TUATAHI: How to continue a pattern and write an algebraic rule. Me pēhea te haere tonu i tētahi tauira me te tuhi tātai mō tētahi raupapa tau. Worked Examples: Find the missing numbers in the pattern. Complete the table and write the rule. 1. 13. 2. 3. 14. How many matchsticks are needed to create the 15th pattern? 4. 15. 5. 6. 16. How many matchsticks are needed to create the 20th pattern? 7. 17. 8. 9. 18. How many matchsticks are needed to create the 22nd pattern? 10. Step it up! Step it up! 11. An average tree grows 3 metres per year. If a tree is 4 metres tall, how tall will it be 2, 3 and 5 years from now? 19. 12. Continuing in the same growth rate, how tall will the tree be in 11 years from now? 20. What pattern number would use 51 matchsticks? 15 17 19 21 23 25 27 29 31 Number Correct: __ / 20 How strong is your understanding? Number and Algebra Level 3/4: Form and solve simple linear equations. What is your tip of the day? A number pattern can go up or down. Add or subtract to find the other bits of the pattern. So we can have patterns with numbers or shapes. Find the missing numbers to make the pattern correct. + 2 Look at the shape pattern (p). Write a rule for the pattern. 7 12 17 +5 Rule: 5p + 2 3 5 7 13 17 6 11 16 31 46 4 11 32 39 60 7 16 34 70 2 8 14 38 50 5 8 11 23 11 15 23 39 4 9 24 44 5 12 26 40 9 20 31 64 Pattern (p) 1 2 3 4 8 12 Rule: Matchsticks (m) 5 9 13 m= Pattern (p) 1 2 3 4 8 12 Rule: Matchsticks (m) 6 10 14 m= Pattern (p) 1 2 3 4 8 12 Rule: Matchsticks (m) 8 11 14 m= Pattern (p) 1 2 3 4 8 12 Rule: Matchsticks (m) m=

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51. Year 8 emPowerED Maths ©2021 . com 15 TUARUA: How to continue a pattern and write an algebraic rule. Me pēhea te haere tonu i tētahi tauira me te tuhi tātai mō tētahi raupapa tau. Worked Examples: Find the missing numbers in the pattern. Complete the table and write the rule. 1. 13. 2. 3. 14. How many matchsticks are needed to create the 19th pattern? 4. 15. 5. 6. 16. How many matchsticks are needed to create the 23rd pattern? 7. 8. 17. 9. How many matchsticks are needed to create the 29th pattern? 18. 10. Next level! Next level! 11. Each month Marei collects NZ apple stickers. She starts with 15, then 12 each month after this. How many stickers will she have in 9 months? Teila collects earrings. She starts with three and each week she buys seven new ones. How many earrings will she have at the end of one year? 19. 12. 20. What pattern number would use 37 matchsticks? Number Correct: __ / 20 How strong is your understanding? Number and Algebra Level 3/4: Form and solve simple linear equations. What is your tip of the day? A number pattern can go up or down. Add or subtract to find the other bits of the pattern. 5 9 13 17 21 25 29 33 37 Find the missing numbers to make the pattern correct. + 4 Look at the shape pattern (p). Write a rule for the pattern. 8 11 14 +3 Rule: 3p + 5 Finding a rule for a pattern is kinda cool once you get your head around the process. 7 11 13 19 6 18 22 30 38 9 17 25 37 1 7 19 31 49 4 12 36 60 22 27 42 20 28 44 68 47 42 32 17 55 34 20 13 52 40 28 Pattern (p) 1 2 3 4 8 12 Rule: Matchsticks (m) m= Pattern (p) 1 2 3 4 8 12 Rule: Matchsticks (m) m= Pattern (p) 1 2 3 4 8 12 Rule: Matchsticks (m) m= Pattern (p) 1 2 4 8 11 15 Rule: Matchsticks (m) m=

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52. Year 8 emPowerED Maths ©2021 . com Number Correct: __ / 20 How strong is your understanding? Number and Algebra Level 3/4: Form and solve simple linear equations. TUATORU: How to continue a pattern and write an algebraic rule. Me pēhea te haere tonu i tētahi tauira me te tuhi tātai mō tētahi raupapa tau. Worked Examples: Find the missing numbers in the pattern. Complete the table and write the rule. 1. 13. 2. 3. 14. What pattern number would use 43 matchsticks? 4. 15. 5. 6. 16. What pattern number would use 136 matchsticks? 7. 17. 8. 9. 18. What pattern number would use 95 matchsticks? 10. Extension! Extension! 11. Katie records how much money she saves. She started with $54. She was able to save $29 each week. How much was saved by the end of her ninth week? 19. 12. After the ninth week, she is only able to save $37 every fortnight. How much will Katie have saved by the 21st week? 20. What pattern number would use 237 matchsticks? What is your tip of the day? A number pattern can go up or down. Add or subtract to find the other bits of the pattern. 8 20 26 7 15 21 9 21 33 12 33 54 68 13 33 48 Pattern (p) 1 2 3 8 10 12 Rule: Matchsticks (m) m= Pattern (p) 1 2 3 10 15 21 Rule: Matchsticks (m) m= Pattern (p) 1 2 3 9 17 39 Rule: Matchsticks (m) m= Pattern (p) 1 2 3 8 14 20 Rule: Matchsticks (m) m= 3 7 11 15 19 23 27 31 35 Find the missing numbers to make the pattern correct. + 4 Look at the shape pattern (p). Write a rule for the pattern. 6 10 14 +4 Rule: 4p + 2 Subtract the bigger number from the smaller number then divide by the number of spaces. 24 26.5 31.5 36.5 1.5 6 10.5 12 4.7 5.1 6.3 8.7 12.3 7.35 4.55

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53. Year 8 emPowerED Maths ©2021 . com 1. 4. 8. 11. 15. 3. 6. 10. 12. 1. 3. 6. 8. 13. 2. 5. 7. 9. 14. Down Clues: Across Clues: INSTRUCTIONS:  Complete the missing number in the pattern.  A crossword puzzle has across and down clues. Solve each clue and fill in one digit per box, either across or down according to the clue. LEARNING INTENTION:  We are learning how to continue a pattern and write a rule for a number sequence. Me pēhea te haere tonu i tētahi tauira me te tuhi tātai mō tētahi raupapa tau. ALGEBRA - NUMBER SEQUENCES 142 152 162 172 214 209 204 388 386 382 700 580 520 1318 913 508 381 384 387 8 27 64 520 670 970 264 282 291 343 512 729 337 352 367 153 147 135 2703 3403 3753 6721 6171 5621 838 845 852 974 962 950 266 386 626 1800 450 225 444 888 1776 1 7 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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54. Year 8 emPowerED Maths ©2021 . com TUATAHI: Algebra Test Answer these questions to the best of your ability. 13. 5m x 2 x 8n x m Complete the number sequences. Answer: 1. 14. (18m + 6m) ÷ (4m + 2m) 2. Answer: Solve these equations to find the value of a. 3. 15. a + 8 = 19 16. 29 - a = 13 4. 17. 7a = 35 18. a ÷ 9 = 8 Complete the rule for the pattern. 5. Calculate the value of the blocks below. 19. Add the two bottom blocks to find the block above them. 6. How many matchsticks will be needed to make the 9th shape in the pattern? 7. 20. Multiply the two bottom blocks to find the block above them. How many matchsticks will be needed to make the 7th shape in the pattern? 8. 21. The cost of hiring an e-bike is $25 per hour plus a booking fee of $10. If the total cost is $85, how many hours was the e-bike hired for? 9. 22. Sevi shares his 57 jelly beans among his 8 friends and has one left over. How many jelly beans did each friend receive? 10. How many matchsticks will be needed to make the 11th shape in the pattern? Simplify the following algebraic expressions. 11. 18 + 10m + 9m + 5n - 2m - 4n Answer: 12. 3m² + 5m + 5m² + 7m - 5m² Answer: Number Correct: __ / 22 How strong is your understanding? Show what you know! 38 32 29 20 14 Pattern (p) 1 2 3 4 8 12 Rule: m= Matchsticks (m) Pattern (p) 1 2 3 4 8 12 Rule: m= Matchsticks (m) Pattern (p) 1 2 3 4 8 12 Rule: m= Matchsticks (m) n 5n 4n 5m 5 6m 3 6 9 15 21 27 3 5 9 11 15 19 7 10 19 25 31

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55. Year 8 emPowerED Maths ©2021 . com TUARUA: Algebra Test Answer these questions to the best of your ability. 13. 6c⁴ x 8d³ 12c² Complete the number sequences. Answer: 1. 14. 7c⁴ x 9d³ 3d² 2. Answer: Solve these equations to find the value of b. 3. 15. 7b - 16 = 5 16. 4b² = 144 4. 17. 12b ÷ 3 = 32 18. b² + 39 = 103 Complete the rule for the pattern. 5. Calculate the value of the blocks below. 19. Multiply the two bottom blocks to find the block above them. 6. How many matchsticks will be needed to make the 20th shape in the pattern? 7. 20. Multiply the two bottom blocks to find the block above them. How many matchsticks will be needed to make the 15th shape in the pattern? 8. 21. A group of 219 students went to Water World. Nine mini buses were filled plus 12 students travelling in cars. How many students were in each mini bus? 9. 22. New NZ regulations require an accompanying adult per bus. If 5 students were also absent, how many students now must travel by car? 10. How many matchsticks will be needed to make the 22nd shape in the pattern? Simplify the following algebraic expressions. 11. 23c + 9d - c + 7d + 4c - 8d Answer: 12. 5c⁵d³ x 7d³c³ Answer: 13 37 73 109 Pattern (p) 1 2 3 10 12 14 Rule: m = Matchsticks (m) Pattern (p) 1 2 3 8 11 14 Rule: m = Matchsticks (m) Pattern (p) 1 2 3 5 9 15 Rule: m = Matchsticks (m) 147d³ 21d d 6m² 3m 4n 45 51 57 66 17 22 37 47 38 56 74 Number Correct: __ / 22 How strong is your understanding? You’ve got this!

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56. Year 8 emPowerED Maths ©2021 . com TUATORU: Algebra Test Answer these questions to the best of your ability. 13. 72e⁴ ÷ 9e x 3g Complete the number sequences. Answer: 1. 14. 81f⁴ ÷ 3f x 6g 2. Answer: 15. 12e⁵ x 6f² 9ef 16. 15e x 4f³ 10e⁵f² 3. Answer: Answer: 4. Solve these equations to find the value of c. Complete the rule for the pattern. 17. 65 - 9 x c + 3c = 17 18. -5 + 3c x 2c = 19 5. Answer: Answer: 19. 6c + 8c x 4 = 190 20. 5c + 3c x 2 = 77 6. How many matchsticks will be needed to make the 15th shape in the pattern? Answer: Answer: 7. 21. Multiply the two bottom blocks to find the block above them. How many matchsticks will be needed to make the 19th shape in the pattern? 8. 22. Teila has some marbles. Sevi has twice as many marbles as Teila. Mani has 12 more marbles than Teila. In total, they have 76 marbles. How many marbles does Sevi, Mani and Teila each have? 9. 23. On a Saturday afternoon, Marei sent m messages each hour for 7 hours, and Mani sent n messages each hour for 6 hours. Write an algebraic expression to represent the total amount of messages sent. 10. How many matchsticks will be needed to make the 28th shape in the pattern? Simplify the following algebraic expressions. 11. 19e + 7f + 11e + 24f - 6g Answer: 12. 28 + 18f² - 9f³ + 13f² - 15f³ Answer: 16 46 76 121 Pattern (p) 1 2 3 6 9 12 Rule: s = Squares (s) Pattern (p) 1 2 3 5 7 9 Rule: s = Squares (s) Pattern (p) 1 2 3 7 12 15 Rule: s = Squares (s) 216a³b² 24a²b 3ab 55 46 37 97 76 48 48 96 132 Number Correct: __ / 23 How strong is your understanding? You can do it!

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57. Year 8 emPowerED Maths ©2021 . com TUATAHI: How to solve word problems involving fractions and percentages. Me pēhea te whakatika i ngā hautanga me te ōrautanga o ngā raruraru kupu. 1. Katie studies on Monday for 1 2/5 hours and Tuesday for 2 5/6 hours. How many hours did she spend studying in total? Working space ... 2. For five consecutive days, Tama runs 3 3/5 laps around the track. What was the total distance he ran during the five days? 3. Tama walks 1 2/6 km, then ran for 1 4/5 km. What was his total distance travelled as a fraction? 4. Teila collected 24 stamps from around the world. Two thirds of the stamps are from Australia. How many stamps are from AUS? 5. In a store, a $25 pair of trousers is marked ‘20% off’. What is the sale price for the trousers? Total:

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58. Year 8 emPowerED Maths ©2021 . com TUARUA: How to solve word problems involving fractions and percentages. Me pēhea te whakatika i ngā hautanga me te ōrautanga o ngā raruraru kupu. 1. On a bus, there are 108 passengers. One third of them are teenagers. How many people are not teenagers? Working space ... 2. A recipe calls for 2 1/4 cups of flour, 3/8 cups of sugar, 5/8 cups cocoa and 1/3 cup of mashed banana. How many cups of dry ingredients are needed in total? 3. There are 3 5/8 pizzas leftover. They are equally divided between 5 people. How much of the leftover pizza will each person receive? 4. A 5 L jug of juice is shared among 200 mL cups. How many cups can be completely filled? 5. A shoe shop has a 35% discount on all shoes. A pair of shoes originally costs $120. What is the new sale price? Total:

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59. Year 8 emPowerED Maths ©2021 . com TUATORU: How to solve word problems involving fractions and percentages. Me pēhea te whakatika i ngā hautanga me te ōrautanga o ngā raruraru kupu. 1. Tama pays a 25% deposit for a new computer on credit. If the computer costs $1 255, how much does he have left to pay? Working space ... 2. Katie’s mum buys a painting for $28 000 and sells it for 18% more. What was the selling price? 3. Katie works a basic week of 40 hours and her hourly rate of pay is $21.50. If she puts 22% in savings, how much does she have left to spend? 4. Teila and Sevi earn $408 together for a cleaning company. They earn the same hourly rate of pay. If Teila worked 2/3 more than Sevi and Sevi worked 9 hours, how much did Teila earn? 5. In Tama’s year level, 3/8 of the students have a brother. 1/2 of those students also have a sister. If Tama’s year level has 304 students, how many have both a sister and a brother? Total:

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60. Year 8 emPowerED Maths ©2021 . com Māori Taonga akomanga Classroom objects Koronga Ako:  E ako ana mātou me pēhea te tatau ahanoa akomanga.  We are learning how to count classroom objects. Have a good look around the classroom at these objects. Practice naming them by pointing and saying the words in Māori. In Māori, there are different words to represent “the” for a single object and multiple objects. te - ‘the’ for one (singular) ngā - ‘the’ for many (plural) We can use these words to answer questions about how many objects there are. The structure of the question and the answer are the same. E hia ngā _______? E.g. E hia ngā inarapa? E _______ ngā ______. E.g. E toru ngā inarapa. Why might it be helpful to have two different words for ‘the’? Notice Understand Think About It Look at the translations and the cartoons for an example. E hia nga ___? E (number) te/nga (object) Sevi has asked Teila the question: “E hia ngā pene?” How many pens are there? Teila has answered with: “E whā ngā pene” There are four pens. E hia ngā pene? E whā ngā pene. Object/Ngā Ahanoa Māori pen pene pencil penerākau rubber inarapa book pukapuka desk tēpu chair tūru Worked Examples Worked Examples The use of ‘te’ The use of ‘ngā’ E hia ngā tēpu? E hia ngā tūru? E rua ngā tūru. Kotahi te tēpu. E hia ngā pukapuka? E hia ngā penerākau? We can also use ‘me’ which means ‘and’. E hia ngā ahanoa? E hia ngā ahanoa? E rima ngā penerākau. E wha ngā rapa me rua ngā penerākau. E toru ngā pukapuka. Kotahi te pukapuka me rua ngā pene.

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61. Year 8 emPowerED Maths ©2021 . com Did you meet your Success Criteria? Yes / No How would you rate your attitude in Maths class today? (out of 10) ___________________________________ How can you improve your Maths learning tomorrow? ___________________________________ ___________________________________ Māori Taonga akomanga Classroom objects Complete the questions below. Our Turn Extension: Remember to use ‘me’ for ‘and’. Success Criteria:  I can count in Māori.  I can state how many classroom objects there are. Your Turn Pause and Reflect Ahanoa (objects) E hia ngā ahanoa? 1. 2. 3. 4. .2. Ahanoa (objects) E hia ngā ahanoa? 1. 2. 3. 4. 5. 6. 7. 8. Ahanoa (objects) E hia ngā ahanoa? 1. 2. 3. 4. 5. 6. 7. 8.

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62. Year 8 emPowerED Maths ©2021 . com Overall Total: / 60 1. 6 x 7 = 1. 5 + 9 = 1. 3 + 8 x 5 = 2. 4 x 6 = 2. 12 - 4 = 2. 7 - 5 x 2 = 3. 5 x 8 = 3. 7 + 6 = 3. 4 + 8 - 9 = 4. 4 x 3 = 4. 15 - 9 = 4. 3 x 7 - 3 + 6 = 5. 7 x 9 = 5. 3 + 6 = 5. 4 + (9 - 2 x 1) = 6. 12 x 6 = 6. 18 - 13 = 6. 9 x 4 + 21 ÷ 3 = 7. 9 x 5 = 7. 5 + 6 = 7. 8 + 4 x 2 = 8. 11 x 12 = 8. 11 - 7 = 8. 8 x 2 - 7 = 9. 7 x 11 = 9. 7 + 15 = 9. 81 ÷ 9 + 7 = 10. 9 x 8 = 10. 21 - 18 = 10. 33 - 2 x 6 = 11. 36 ÷ 3 = 11. 6 + 11 = 11. 4 x 9 - 28 ÷ 4 = 12. 49 ÷ 7 = 12. 19 - 15 = 12. 56 ÷ 7 + 4 x 5 = 13. 72 ÷ 6 = 13. 14 + 28 = 13. 72 ÷ 6 - 5 x 9 = 14. 64 ÷ 8 = 14. 17 - 8 = 14. 7 x 3 + 17 - 6 = 15. 44 ÷ 4 = 15. 7 + 13 = 15. 5 x 3 + (16 + 20) = 16. 56 ÷ 7 = 16. 22 - 16 = 16. 7 + 6 x (25 - 18) = 17. 144 ÷ 12 = 17. 19 + 26 = 17. 8 x (27 ÷ 9 + 16) = 18. 42 ÷ 6 = 18. 34 - 19 = 18. 20 - 7 x 4 + 8 x 3 = 19. 48 ÷ 12 = 19. 15 + 27 = 19. 15 + 9 x 9 - 6 x 6 = 20. 60 ÷ 12 = 20. 46 - 39 = 20. 16 + 7 x 2 - 3 x 2 = Total Correct: Total Correct: Total Correct:

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Year 8 Maths ©2021 .com This book is copyrighted material. All rights are reserved. It is against the law to make copies of this material without getting specific written permission in advance from ebmcresources.com. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means: electronic, mechanical, photocopying, recording, or otherwise, without prior written permission of the publisher. This is a work of fiction. Unless otherwise indicated, all of the names, characters, places, events and incidents in this document are the product of the author’s imagination. Printed in Wellington, New Zealand by YourBooks.co.nz. Marketing and cover design by Nettle.co.nz. Publishing by Redshift.co.nz. Thank you to our cartoon models Teila, Sevi, Katie and Tama, A.S Colour and our work colleagues for their ongoing support. resources.com Copyright © 2021