Return to flip book view

Ages 11 12 Year 7 Follows Stage 6 7 of the New Zealand Mathematics Curriculum Created by Lucy Patston 2021 Adept Education Limited

Adept Education Publishing 13A Flavia Place Lynfield Auckland 1042 New Zealand www adepteducation co nz Adept Education Publishing 2021 The Reaching Competence Mathematics Programme has been produced by Adept Education Ltd and is protected under the New Zealand Copyright Right Act 1994 Photocopying or printing for production beyond personal use is prohibited 2021 Adept Education Limited

Book 21 Able to use a range of strategies for addition Able to use a range of strategies for subtraction Able to identify and estimate addition and subtraction problems Able to use a range of strategies for multiplication Able to multiply double digits using area Able to use a range of strategies for division Able to divide using a written method Book 22 Able to understand and compare positive and negative integers Able to use squares cubes and square roots Able to order operations to solve problems Able to reverse operations to solve problems Able to use multiplication to find equivalent fractions Able to use benchmarking to order fractions Able to find a fraction of a quantity Able to covert between fractions and decimals Book 23 Overview of Books 21 23 Understands percentages and their relationship to fractions and decimals Able to use a range of strategies to add decimal numbers Able to use a range of strategies to subtract decimal numbers Able to multiply integers and decimal numbers Able to divide integers and decimal numbers Able to express large numbers using exponents 3 2021 Adept Education Limited

Book 21 Learning Intention Checklist Learning Intention 1 Able to use a range of strategies for addition 2 Able to use a range of strategies for subtraction 3 Able to identify and estimate addition and subtraction problems 4 Able to use a range of strategies for multiplication 5 Able to multiply double digits using area 6 Able to use a range of strategies for division 7 Able to divide using a written method 4 2021 Adept Education Limited Date Reward

practice practice practice Learning Intention 1 Able to use a range of strategies for addition Strategies are techniques students are taught from early on that are used to solve addition and subtraction problems mentally and in the written form Such mental strategies include using tidy numbers using doubles and standard partitioning As children mature they should come to know which strategies work best for them and which strategies work best in particular situations For instance adding a number to 299 should be done using tidy numbers the tidy number 300 as this method would be the most efficient in this situation Activities 1 Sheet 21 01 Using tidy numbers to add large numbers Tidy numbers depend on the scale of the numbers being added They usually end with a zero or zeros For example a tidy number for 19 is 20 for 199 is 200 and for 149 is 150 Tidy numbers make mental calculations much easier 2 Sheet 21 02 Using doubles to add large numbers Doubling usually involves two or even three mental steps but can be very useful in the right situations For example 208 195 can be thought of as 200 200 8 5 203 and simpler still 205 195 can be thought of as 200 200 5 5 200 Essentially the double is dealt with first and then the stragglers Watch for errors when the double numbers are rounded up AND down as in the equations above 3 Sheet 21 03 Using standard partitioning to add large numbers Standard partitioning is when students most effectively use their place value The largest place value numbers like thousands or hundreds are added first then tens then ones This method becomes exhausting when values on both sides rise above 5 e g 868 976 as opposed to 114 210 4 Sheet 21 04 Using the written method to add large numbers You were probably taught this way 5 2021 2021Adept AdeptEducation Education Limited Limited

Learning Intention 1 Able to use a range of strategies for addition We can use tidy numbers to add when one number is close to a zero number Here s a quick reminder how it works 400 540 398 540 400 940 2 938 540 938 940 2 Number lines are not to scale 1 What would the number line for this equation look like 173 594 Use tidy numbers to solve the following equations There is space to write your working but see if you can do them in your head first Mental answer 2 294 437 3 1 496 287 4 602 366 5 444 2 997 6 305 995 7 2 907 363 8 883 1 008 Working space 6 2021 Adept Education Limited Worked answer Sheet 21 01

Learning Intention 1 Able to use a range of strategies for addition We can use doubles to add when both numbers are nearly the same value Here are some examples A When both the numbers are greater than the double number 402 406 400 400 800 800 2 6 B When both the numbers are less than the double number 808 195 197 200 200 400 400 5 3 392 C When one number is greater than the double number and the other is less than the double number 354 347 350 350 700 700 4 3 701 Are these an A problem a B problem or a C problem 1 202 205 3 898 896 5 606 601 2 152 141 4 593 608 6 492 505 Solve the following additions using doubles Use the space at the end for notes if needed 7 650 649 8 457 452 9 692 702 10 1 001 1 005 11 893 899 12 298 295 7 2021 Adept Education Limited Sheet 21 02

Learning Intention 1 Able to use a range of strategies for addition When we use standard partitioning to add there is a lot of information to organise Here are the steps to follow Step 1 Expand 2 695 3 164 2 000 600 90 5 3 000 100 60 4 3 000 Step 2 Add thousands 2 000 Step 3 Add hundreds 600 5 000 Step 4 Add tens 90 100 Step 5 Add ones 5 700 150 4 9 60 Step 6 Sum totals 5 859 Try writing this one in full and then see if you can do the following mentally 1 224 1 Step 1 Expand 5 313 Step 2 Add thousands Step 3 Add hundreds Step 4 Add tens Step 5 Add ones Step 6 Sum totals 2 6 147 1 352 5 9 332 1 015 3 2 230 5 264 6 1 252 2 207 4 4 312 4 272 7 13 421 5 428 8 2021 Adept Education Limited Sheet 21 03

Learning Intention 1 Able to use a range of strategies for addition Here s a reminder of how we carry ones tens and hundreds over when we re using the written method 5 187 3 965 1 Add the ones 2 Add the tens 1 5 1 8 7 3 9 6 5 2 7 5 12 Write in the 2 of 12 and carry the 1 to the tens column 5 1 8 7 3 9 6 5 3 Add the hundreds 1 1 1 5 1 8 7 3 9 6 5 52 4 Add the thousands 1 1 1 1 1 5 1 8 7 3 9 6 5 9 1 5 2 5 1 8 7 3 9 6 5 152 1 8 6 15 1 1 9 11 1 5 3 9 10 80 60 150 100 100 900 1 100 Write the 5 of 15 and carry the 1 to the hundreds column Write the 1 of 11 and carry the 1 to the thousands column 1 000 5 000 3 000 9 000 Write the 9 and you re done Rewrite the following addition equations in the standard written form Then solve them 1 2 587 6 769 3 5 659 3 487 5 22 569 1 681 2 5 8 7 2 8 453 6 867 4 10 806 8 838 6 15 597 11 747 1 0 8 0 6 9 2021 Adept Education Limited Sheet 21 04

apply Learning Intention 1 Able to use a range of strategies for addition Activities 1 Sheet 21 05 Deciding which strategy to use 2 Sheet 21 06 Solve the story problems 3 Sheets 21 07 and 21 08 Adept Problem Solvers 1 This is a challenging task with many variables to consider Students should work slowly and methodically attempting one door at a time If their solutions are not as suggested in the answer section this is not a concern so long as their chosen methodology brings them to the correct answer Similarly if they are attempting to use the suggested method but make a calculation error that leads to an incorrect answer it is important to focus on the fact that their logic was correct if indeed their mathematics was not The answer section may be of some use 10 2021 2021Adept AdeptEducation Education Limited Limited

Learning Intention 1 Able to use a range of strategies for addition Which strategy would you use to solve the following equations Equation e g 238 237 1 547 299 2 495 348 3 427 374 4 727 455 5 429 426 Equation 6 2 558 6 748 7 628 399 8 2 534 2 542 9 3 865 876 10 4 998 2 475 Tidy Numbers Doubles Standard Partitioning Written Method Tidy Doubles Standard Partitioning Written Method 11 2021 Adept Education Limited Sheet 21 05

Learning Intention 1 Able to use a range of strategies for addition Solve the story problem using the method indicated You can use the space for working Tidy Numbers 1 Doubles There were 349 people travelling on one aeroplane and 226 on another How many people were travelling on aeroplanes 3 There were 543 beads in my collection and 545 in my sister s collection How many beads did we have altogether 2 On holiday we drove 1 842km the first week and 599km the second week How many km did we travel altogether 4 A new laptop costs 1 246 The extra accessories cost 1 244 How much would the whole purchase cost Standard Partitioning 5 Written Method On Valentine s Day the florist sold 564 worth of red roses and 435 worth of white roses How much money did the florist make from roses that day 7 A brick layer needs 5 648 standard bricks and 2 482 special bricks to complete a job How many bricks will be used on the job 6 The biologist estimated there were 823 bacteria on one Petri dish and 317 on the other How many bacteria were on both Petri dishes 8 Dad s car cost 3 672 Mum s car cost 8 583 How much did the couple spend in total 12 2021 Adept Education Limited Sheet 21 06

solvers 1 Learning Intention 1 Able to use a range of strategies for addition The awesome foursome are looking for clues to solve a 200 year old mystery that will reveal the whereabouts of the blueprint for a machine that makes unlimited energy for free So far they ve been led to a bunch of creepy doors in a castle in England Each door has a coded lock Help the team open the doors by selecting the best member to work on the maths on the next page Strengths Addition Written method Tidy numbers Strengths Addition Subtraction Doubles Written method Weaknesses Subtraction Spiders actually any bugs Weaknesses Rats Joseph Stella Strengths Subtraction Tidy numbers Doubles Strengths Subtraction Addition Standard partitioning Weaknesses Written method Cobwebs Weaknesses None that he admits to Moana Jacob 13 2021 Adept Education Limited Sheet 21 07

solvers 1 Learning Intention 1 Able to use a range of strategies for addition 1 3 5 Equation 401 555 Best method Team member Working and Answer Equation 151 156 Best method Team member Working and Answer Equation 1 245 1 323 Best method Team member Working and Answer 2 4 6 Equation 5 574 1 675 Best method Team member Working and Answer Equation 3 320 2 126 Best method Team member Working and Answer Equation 1 238 499 Best method Team member Working and Answer 14 2021 Adept Education Limited Sheet 21 08

Here are some other pages you ll see in this book www adepteducation co nz 2021 Adept Education Limited

Learning Intention 2 Able to use a range of strategies for subtraction Let s have a look at how we handle regrouping when there are zeros in the top number 10 304 3 465 Step 1 1 0 3 0 4 3 4 6 5 We can t subtract 5 ones from 4 ones and there are no tens to borrow from Step 2 2 1 0 3 10 4 3 4 6 5 So we need to regroup one of the hundreds into 10 tens and then we need to regroup one of the tens into 10 ones Step 3 Move a hundred to the tens Change the 300 to 200 and add a 1 to the tens column Now we have 9 tens left 2 9 1 0 3 10 14 3 4 6 5 9 Move a ten to the ones Change the 10 to a 9 14 5 9 And we have 14 ones to subtract our 5 ones from Have a go at these when you ve finished looking at the next page 1 8 084 4 258 2 9 705 5 631 3 7 500 3 248 16 2021 Adept Education Limited Sheet 21 12

Learning Intention 2 Able to use a range of strategies for subtraction Let s have a look at how we handle regrouping when there are zeros in the top number 10 304 3 465 Step 4 2 We can progress as normal until we hit another zero 9 10 14 1 0 3 3 4 6 5 3 9 9 0 6 0 3 0 Step 5 1 000 x10 1 000 1 000 1 000 1 000 2 9 1 0 3 10 14 3 4 6 5 3 9 We need to regroup one of the thousands into ten hundreds Step 6 We can t subtract 400 from 200 but we do have 10 thousands to borrow from Now we have 9 thousands left x9 0 1 000 1 000 9 12 9 1 10 3 10 14 3 4 6 5 8 3 9 1 000 x10 Move a thousand to the hundreds Change the 10 into a 9 12 00 4 00 8 00 And we have 12 hundreds to subtract our 4 hundreds from Step 7 0 9 12 9 1 10 3 10 14 3 4 6 5 6 8 3 9 We can finish the subtraction 9 000 3 000 6 000 Have a go at these 1 85 040 14 225 2 60 104 32 738 3 20 000 8 464 17 2021 Adept Education Limited Sheet 21 13

Learning Intention 2 Able to use a range of strategies for subtraction Circle the strategy you will use and then write out your working to solve the story problems Tidy Numbers Standard Partitioning Written Method Tidy Numbers 1 There are 13 532 sheep on the farm The farmer sells 4 710 of them How many does the farmer have left Tidy Numbers Standard Partitioning Standard Partitioning Written Method 3 The vet charges 1 034 for an operation on a large dog Luckily today there is 399 off the fee How much does the operation cost today Written Method Tidy Numbers 2 The cycle race is 665km long You have ridden 341km so far How much further is it to ride to get to the finish line Standard Partitioning Written Method 4 Layla sold 5 843 worth of beeswax wraps for her business They cost her 974 to make What is her profit Profit is the difference between the amount earned and the amount spent 18 2021 Adept Education Limited Sheet 21 14

Learning Intention 2 Able to use a range of strategies for subtraction Your students have submitted their subtraction tests They get 1 mark for choosing an appropriate strategy and 1 mark for providing the correct working answer What are their scores Name Helena 1 17 381 9 685 1 7 38 1 9 6 85 1 2 3 0 4 2 635 199 635 200 435 1 436 Name Mark 16 1 17 381 9 685 5 11 14 3 62 515 3 664 6 2 5 11 5 3 6 6 4 5 8 8 5 1 12 17 1 7 3 8 11 9 6 8 5 7 6 9 6 2 635 199 600 100 500 30 90 60 5 9 4 500 60 4 436 4 736 544 700 500 200 130 40 90 6 4 2 292 5 11 14 6 2 5 1 5 3 62 515 3 664 3 61 6 4 5 8 8 5 1 5 1 333 699 1 333 700 633 1 634 4 736 544 730 540 210 6 4 212 10 5 1 333 699 1 333 700 633 1 632 10 19 2021 Adept Education Limited Sheet 21 15

solvers Learning Intention 2 Able to use a range of strategies for subtraction 2 The awesome foursome are still cracking codes to creepy castle doors Use the information on Sheet 21 07 to solve these subtraction equations with the best team member strategy 1 3 5 Equation 834 417 Best method Team member Working and Answer Equation 703 450 Best method Team member Working and Answer Equation 5 751 916 Best method Team member Working and Answer 2 4 6 Equation 8 463 6 857 Best method Team member Working and Answer Equation 885 584 Best method Team member Working and Answer Equation 3 198 600 Best method Team member Working and Answer 20 2021 Adept Education Limited Sheet 21 16

Learning Intention 3 Able to identify and estimate addition and subtraction problems What is the answer to the following equation 4 3x5 There are TWO different answers you may have calculated Did you decide to do it this way or this way 4 3x5 7x5 35 4 3x5 4 15 19 The correct answer is 19 This is because we work out the multiplication part of the equation first and then carry out the addition part Mathematics has to be very precise and for this reason there exists an order of operations B E Brackets Exponents 2 Brackets come first Exponents come second D Division M A S Multiplication Addition Subtraction x These two come next We order them left to right These two come last We order them left to right Use the order of operations to find the answers to these equations 1 6 x 8 10 4 17 4 x 5 7 40 5 x 7 2 9 2 50 5 10 2 x 8 8 12 8 2 3 5 9 4 6 40 x 3 2 9 30 6 x 2 21 2021 Adept Education Limited Sheet 21 20

Learning Intention 4 Able to use a range of strategies for multiplication Circle the correct answer or colour the array 1 57 2 Read the scenario and then circle the correct answer to the questions What is the product of 5 x 7 35 45 33 Scenario A Miss Jones helps 12 people across the road each day What is the product of 8 x 6 84 56 54 9 48 How many people does Miss Jones help in 3 days 24 3 What is the product of 7 x 7 49 64 42 10 36 11 4x5 38 66 56 74 How many people does Miss Jones help in 8 days 84 4 36 How many people does Miss Jones help in 6 days 72 Colour the arrays 32 92 96 108 5 3 x 6 Scenario B The police officer visits 3 schools per week 12 6 2x4 How many schools are visited over 3 weeks 7 5 x 6 27 13 8 9 x 11 6 9 How many schools are visited over 9 weeks 9 14 13 27 14 30 How many schools are visited over 13 weeks 144 22 2021 Adept Education Limited 30 39 33 Sheet 21 23

Learning Intention 4 Able to use a range of strategies for multiplication We can use standard partitioning to solve multiplication equations Let s see how it works 226 x 3 200 x 3 600 20 x 3 60 6x3 18 678 Draw in the notes and coins for this example and solve 132 x 4 Try these without the visualisation 1 2 326 x 3 3 812 x 5 5 561 x 7 x3 x5 x3 x5 x3 x5 439 x 4 4 477 x 6 6 274 x 8 x4 x4 x4 23 2021 Adept Education Limited Sheet 21 27

Learning Intention 4 Able to use a range of strategies for multiplication In a way the written method 1 is just standard partitioning but working backward from ones instead of forward from hundreds Remember to keep place value as you work tens ones hundreds add 5 2 3 x 4 1 2 5 2 3 x 4 1 2 8 0 5 2 3 x 4 1 2 8 0 2 0 0 0 5 2 3 x 4 1 2 8 0 2 0 0 0 2 0 9 2 4 x 3 12 4 x 20 80 4 x 500 2 000 12 80 2 000 2 092 1 Fill in this next example tens ones 6 7 4 x 5 5x hundreds 6 7 4 x 5 5x add 6 7 4 x 5 5x 6 7 4 x 5 Fill in the equations and solve Keep the method going to complete those with thousands 2 3 8 2 1 x 8 2 7 6 5 x 5 4 5 5 2 9 x 6 3 4 4 9 x 3 24 2021 Adept Education Limited 6 7 3 8 5 x 7 6 3 8 5 x 4 Sheet 21 28

Learning Intention 4 Able to use a range of strategies for multiplication The written method 2 is sometimes referred to as the old fashioned way but some people like it and it comes in handy later when multiplying by 2 or 3 digit factors Here s how we do it complete with GOL 3 1 4 1 8 3 x 4 1 6 7 3 2 Multiply the ones 4 x 3 12 Write the 2 and carry the 1 10 Multiply the tens 4 x 8 32 32 tens Add the 1 we carried 33 33 tens Write the 3 and carry the 3 300 Multiply the hundreds 4 x 1 4 4 hundreds Add the 3 we carried 7 7 hundreds Write the 7 Multiply the thousands 4 x 4 16 thousand Write the 16 Fill in the equations and solve 1 4 7 1 5 3 x 2 6 8 2 2 x 1 2 9 x 5 3 x 4 3 x 2 6 5 1 7 4 25 Grouchy Old Lady 6 9 2 3 2 4 7 x 5 6 x 5 2 3 2 0 4 7 4 8 3 3 6 x 8 2021 Adept Education Limited x 6 9 3 Sheet 21 29

Learning Intention 5 Able to multiply double digits using area Now that we can visualise a 1 digit x 2 digit multiplication let s look at the same method for two 2 digit numbers 24 x 62 60 2 A 60 x 20 1 200 B 60 x C 60 x 20 1 200 20 2 D 2 240 x 20 40 x 4 4 8 1 488 60 x 4 240 4 2x4 8 2 x 20 40 You try FYI The diagram above is to scale but the ones below are not 1 2 35 x 27 3 73 x 48 26 x 63 A C A C A C B D B D B D A x A x A x B x B x B x C x C x C x D x D x D x 26 2021 Adept Education Limited Sheet 21 36

solvers 6 Learning Intention 5 Able to multiply double digits using area Emiel the carpenter is preparing a large commercial building for carpeting and needs to give the dimensions of each room to the carpet layer Use the dimensions Emiel has measured to provide the carpet layer with the number of square metres needed for each room 13 138 69 23 13 23 23 26 39 92 23 78 39 69 69 91 52 65 13 26 46 13 1 The pink room 5 The purple room 2 The grey room 6 The green room 3 The red hallway 7 The orange room 4 The blue room 8 The yellow room 27 2021 Adept Education Limited 46 23 Sheet 21 38

Have a go at these logic puzzles Each of the Awesome Foursome have a different favourite colour Use the clues and the table to decide the favourite colour for each character 1 Clue 1 Joseph does not like red or blue Red Clue 2 Stella doesn t like red or green Joseph Clue 3 Moana doesn t like any of the three primary colours Stella Yellow Blue Green 138cm 145cm Moana Jacob Use the clues and the table to decide the height of each character 2 Clue 1 Josephs height is between Stella and Jacob s Clue 2 Moana is the shortest Clue 3 Stella is shorter than Jacob 132cm 134 cm Joseph Stella Moana Jacob The Awesome Foursome and their other two friends Tui and Drew are sitting around a table Use the clues to work out which coloured seat each of them is sitting on 3 Clue 1 Moana and Joseph are sitting opposite each other Clue 2 Drew is sitting next to Joseph Clue 3 Tui is sitting on the blue seat and next to Drew Clue 4 Jacob is sitting opposite Drew and next to Moana Clue 5 Drew is not sitting on the purple seat 28 2021 Adept Education Limited Sheet 21 54

Sheet 21 01 Sheet 21 03 1 173 594 173 600 773 6 767 600 173 767 773 6 2 294 437 300 437 737 6 731 3 1 496 287 1 500 287 1 787 4 1 783 4 602 366 600 366 966 2 968 5 444 2 997 444 3 000 3 444 3 3 441 6 305 995 300 995 1 295 5 1 300 7 2 907 363 2 900 363 3 263 7 3 270 8 883 1 008 883 1 000 1 883 8 1 891 Sheet 21 02 1 2 3 7 8 9 10 11 12 A 4 C C 5 A B 6 C 1 299 C 909 A 1 394 C 2 006 A 1 792 B 593 B Sheet 21 05 1 Step 1 1 000 200 20 4 5 000 300 10 3 Step 2 1 000 5 000 Step 3 200 300 Step 4 20 10 Step 5 4 3 Step 6 6 000 500 30 7 6 537 2 7 499 3 7 494 4 8 584 5 10 347 6 3 459 7 18 849 Sheet 21 04 1 Sheet 21 06 1 1 1 1 1 1 1 1 1 2 5 8 7 6 7 6 9 9 3 5 6 2 3 4 8 4 5 3 6 8 6 7 1 5 3 2 0 5 6 5 9 3 4 8 7 9 1 4 6 1 1 1 0 8 0 6 8 8 3 8 1 9 6 4 4 5 1 1 1 1 1 1 2 2 5 6 9 1 6 8 1 2 4 2 5 0 6 1 Tidy numbers 2 Tidy numbers 3 Standard Partitioning or Written Method 4 Standard Partitioning or Written Method 5 Doubles 6 Standard Partitioning or Written Method 7 Tidy numbers 8 Doubles 9 Standard Partitioning or Written Method 10 Tidy numbers 1 5 5 9 7 1 1 7 4 7 2 7 3 4 4 29 2021 Adept Education Limited 2020 Adept Education Limited 1 349 226 350 226 576 1 575 2 1 842 599 1 842 600 2 442 1 2 441 3 543 545 545 x2 1 090 2 1 088 4 1 246 1 244 1 245 x 2 2 490 1 1 5 564 435 500 400 60 30 4 5 999 6 823 317 800 300 20 10 3 7 1 140 7 5 648 2 482 1 1 1 5 6 4 8 2 4 8 2 8 1 3 0 8 3 672 8 583 1 1 3 6 7 2 8 5 8 3 1 2 2 5 5

For full content please purchase from the website www adepteducation co nz 2021 Adept Education Limited

About the Author Lucy Patston BA BSc Hons PhD Lucy has 20 years of teaching experience and a strong academic background She has expertise in neuroscience psychology and human development and gained her doctorate for research investigating how childhood learning affects brain functioning in adulthood Lucy is a mum to three very energetic children all of whom have recently entered the school system As a parent and a teacher she understands how important it is for students to grasp key mathematical concepts and for parents to be actively engaged in this process where possible Lucy was raised in New Zealand during a time when the school curriculum was taught very differently to today and provides the Reaching Competence Programme direct to parents also In the Programme Lucy spends an equal amount of time helping parents understand the curriculum as she does students She believes that if parents can communicate effectively with their children about the concepts they are currently learning in the classroom then children will not only feel supported in their learning but will be open to realising how important maths is in our everyday lives When parents and teachers are using the same terminology and strategies to help their learners with numeracy our kids are winning 31 2021 Adept Education Limited

Explore the mathematics curriculum with your child at your own pace with this guided interactive programme This booklet includes learning intentions 1 through to 7 of 21 for this level Includes information about the curriculum for parents and caregivers learning intention checklist worksheets activities board games certificates and other printand cut resources The learning intentions covered in this book are Able to use a range of strategies for addition Able to use a range of strategies for subtraction Able to identify and estimate addition and subtraction problems Able to use a range of strategies for multiplication Able to multiply double digits using area Able to use a range of strategies for division Able to divide using a written method Online and printed versions available at www adepteducation co nz adepteducation 2021 Adept Education Limited