Return to flip book view
1© 2020 Adept Education LimitedFollows Stage 4/5 of the New ZealandMathematics CurriculumAges 7-8 | Year 3Created byLucy Patston
2© 2020 Adept Education LimitedBook 81. Knows the multiplication facts x22. Knows the multiplication facts x103. Able to recall addition and subtraction facts to 204. Able to use “equals” to balance equations (advanced)5. Able to skip count in threes and fours6. Able to work with, and round to, tens7. Able to solve number problems8. Understands the NZ denominations of money9. Able to solve problems using money Book 91. Knows the multiplication facts x52. Understands the link between skip counting and multiplication3. Able to solve multiplication problems by skip counting (advanced) 4. Knows multiplication is commutative5. Knows compatible numbers (in fives) to 1006. Able to estimate using known number facts7. Able to add 9 using + 10 – 18. Able to subtract 9 using – 10 + 1Book 101. Able to understand equality2. Understands equal sharing3. Understands making equal groups4. Able to recognise halves and quarters of shapes (advanced)5. Able to find half or quarter of a set using doubles6. Able to add a single-digit to a double-digit number using the part/whole method7. Able to subtract a single-digit from a double-digit number using the part/whole method8. Able to use a calculatorOverview of Books 8, 9 and 10
3© 2020 Adept Education LimitedLearning Intention Date Sticker10.1Able to understand equality10.2Understands equal sharing10.3Understands making equal groups10.4Able to recognise halves and quarters of shapes (advanced)10.5Able to find half or quarter of a set using doubles10.6Able to add a single-digit to a double-digit number using the part/whole method10.7Able to subtract a single-digit from a double-digit number using the part/whole method10.8Able to use a calculator efficientlyBook 10 Learning Intention Sticker Chart
4© 2020 Adept Education LimitedLI Year 3 Year 410.1Able to understand equality E13 F13 G12 H1210.2Understands equal sharing H1 H2 H310.3Understands making equal groups H7 H810.4Able to recognise halves and quarters of shapes (advanced) W110.5Able to find half or quarter of a set using doubles W2 W3 W410.6Able to add a single-digit to a double-digit number using the part/whole method G2 G310.7Able to subtract a single-digit from a double-digit number using the part/whole method H2 H3for Book 10Summary of Activities
5© 2020 Adept Education Limited5Activities✓1.Sheet 10.16: Sharing quantities between three friends.2.Sheet 10.17: Sharing quantities between six friends.3.Sheet 10.18: A beaker and some test tubes.4. nz.ixl.com: Year 4 – H7 Divisibility rules for 2, 5, and 10. 5. nz.ixl.com: Year 4 – H8 Division input/output tables. Learning Intention 10.3: Understands making equal groupsGrouping, sometimes thought of as repeated addition, is splitting a bigger set up into smaller sets. “How many fives in 15?” is a grouping problem. These problems encourage recognition of the commutative nature of multiplication and division. See Learning Intention 9 in Book 9 for when we first approached this idea.practicepracticepractice© 2023 Adept Education Limited
6© 2020 Adept Education Limited3|Now share them with Jack as well. 4|Share 18 equally between the friends.5|Add 2 counters and include yourself.6|Share 28 between the four of you.7|Share 30 with Jack and Judy. 8|How many counters would you need to add to give yourself and Neeta the same number?6Neeta, Judy and Jack are working on grouping in class. Using 30 counters they’ve decided to use the ovals they’ve drawn around themselves to help them solve the problems. You do the same with your 30 counters. How many each?1|Share 21 counters equally between the friends. NeetaJudyJack2|Share 24 counters equally between Neeta and Judy.Learning Intention 10.3: Understands making equal groupsSheet 10.16
7© 2020 Adept Education Limited5|If you give everyone, including yourself, 7 counters, how many counters do you need?6|If you give 4 friends 5 counters each, how many counters do you need?7|Share 42 counters equally between the 6 friends. 8|Can you still share 42 with yourself added in?7NeetaJudyJoshJosh, Ken and Jacinda have joined the game. Using 60 counters help them solve the problems. How many each?1|Share 54 counters equally with the whole group.2|Now share those counters with only 3 friends.3|Add 2 counters and share with you and all the friends.4|Share 36 counters equally between the 6 friends.Learning Intention 10.3: Understands making equal groupsSheet 10.17
8© 2020 Adept Education LimitedA small test tube holds 10mL and a large test tube holds 50mL. A small beaker holds 100mL and a large beaker holds 500mL.810mL 50mL100mL 500mL1| How many times could you fill the 50mL test tube with water and pour it into the 500mL beaker?4| How much of the 100mL beaker could you pour into the 50mL test tube?5| Which combination of test tubes and/or beakers could you use to fill the 500mL beaker to half way?2| How many times could you fill the 10mL test tube with water and pour it into the 50mL test tube?3| How many times could you fill the 100mL beaker with water and pour it into the 500mL beaker?6| How many times could you fill the 10mL test tube with water to fill 1/5 of the 500mL beaker?© 2023 Adept Education LimitedLearning Intention 10.3: Understands making equal groupsSheet 10.18
9© 2020 Adept Education Limited9Activities✓1.Sheet 10.19: Adept Problem Solvers 8.2.Sheet 10.20: Adept Problem Solvers 9.Learning Intention 10.3: Understands making equal groupsapply© 2023 Adept Education Limited
10© 2020 Adept Education LimitedJade NinaBethany CliveCyril RichieClaude JasmineTina GinaMonty VivaanNisha RizaMoana LachlanThe students in Miss Knowles’ class have been tasked with sorting themselves into quiz teams. They decide to use their eye colour for teams: blue eyes, green eyes, brown eyes, and hazel eyes. 1| How many are in each team?2| How many students are there in Miss Knowles’ class?3| Is the grouping fair? Explain.4| What fraction of the classmates have blue eyes?5| What fraction of the classmates have green eyes?6| What fraction of the classmates have brown eyes?7| What fraction of the classmates have hazel eyes?10Learning Intention 10.3: Understands making equal groupssolvers8Team How many?1. Blue2. Green3. Brown4. HazelSheet 10.19
11© 2020 Adept Education LimitedJade162cmNina160cmBethany159cmClive157cmCyril156cmRichie156cmClaude154cmJasmine153cmTina152cmGina152cmMonty152cmVivaan151cmNisha150cmRiza149cmMoana148cmLachlan147cmThe students decide instead to make 4 equal teams. 3|Could the teams have been equal if they had been at school?4| How could they have made equal teams with Toni and Bella included?___________________________________11Learning Intention 10.3: Understands making equal groupssolvers91. Team Tall3. Team KindaShort2. Team Nearly Tall4. Team Short1| How many will be in each team?2| If they use their heights from tallest to shortest, which students will be allocated to each team?Toni and Bella are away today. Sheet 10.20
12© 2020 Adept Education LimitedHere’s some other pages you’ll see in this book.www.adepteducation.co.nz
13© 2020 Adept Education LimitedIf we take a whole pizza and cut it down the centre we have cut it in half (or ).Two halves make a whole. We write one half like this: We write two halves like this: 1 wholeIf we cut each half of the pizza in half again, we have cut it into quarters (or ).Two halves make a whole andfour quarters make a whole. We write one quarter like this: We write two quarters like this: We write three quarters like this: We write four quarters like this: Can you see that two quarters is the same as one half?1|If I eat of my pizza, how much is left?2|If I eat of my pizza, how much is left?3|If I eat of my pizza, how much is left?Remember that both halves are the same size and each quarter is the same size.Learning Intention 10.4: Able to recognise halves and quarters of shapes (advanced)Sheet 10.21
14© 2020 Adept Education LimitedWhat about ? How many jellybeans would Judy have eaten then? is 3.is 3 lots of 3 = 9.The answer is 9.If Judy had 12 jellybeans and she ate half of them, how many would she have eaten?of12=3of12=6of12=9of12=12We can find quarters by halving and halving againWhat is half of 12? 6.Now, what is half of 6? 3.If Judy had 12 jellybeans and she ate one quarter of them, how many would she have eaten?6 jellybeans eaten.What is half of 12? 6.6 jellybeans left.3 jellybeans eaten.9 jellybeans left.Or 3 x 3Learning Intention 10.5: Able to find half or quarter of a set using doublesSheet 10.28
15© 2020 Adept Education Limited1|Mark whereis on the 8cm line. Score: ___2|Mark whereis on the 8cm line. Score: ___3|Mark whereis on the 4cm line. Score: ___Neeta is playing a game where she tries to place a fraction exactly in the right spot on a line. Here, she is placing a pink mark at of the way along a 12cm line.Neeta knows that of 12cm is 6cms, so next she measures where 6cms is and makes a blue mark.Now Neeta carefully measures how close her pink mark was to where the blue mark is. This will tell her how close she was to the true mark.Neeta’s pink mark is about 5mm before the blue mark. That’s between 4 & 6mm. Neeta scores 6 points this time!Here are some lines for you to mark so you can play too.Note: line lengths may not be perfect.SCORINGBetween 0 & 2mm either way: 10 ptsBetween 2 & 4mm either way: 8 ptsBetween 4 & 6mm either way: 6 ptsBetween 6 & 8mm either way: 4 ptsMore than 8mm either way: 2 pts1|of 8cm is 4cm. 1 x 4 = 4cm2|of 8cm is 2cm. 1 x 4 = 2cm3|of 4cm is 1cm. 1 x 1 = 1cmLearning Intention 10.5: Able to find half or quarter of a set using doublesSheet 10.30
16© 2020 Adept Education LimitedLook at the pictures of the Base 10 tens rods and ones units. Count the tens and the ones and fill in the table. Write the number in words also.Tens rods OnesHow many tens?How many ones?What’s the number?2 8 28Twenty eight1|2|3|4|Learning Intention 10.6: Able to add a single-digit to a double-digit number using the part/whole methodSheet 10.31 Sheet 10.32
17© 2020 Adept Education LimitedJosh is using a number line to help him add a single-digit number to a double-digit number.Josh’s equation is 27 + 6.Josh decides that because 27 + 3 = 30 (his tidy number), he should use 3 + 3 = 6.3 more takes him to 33. So 27 + 6 = 33.1|29 + 6 =5|18 + 8 = 2|55 + 7 =6|47 + 8 = 3|86 + 8 = 7|74 + 7 =4|38 + 5 =8|66 + 9 =212223242526272829313233343536373839302040+ 3+ 3Draw a number line to show how you would find the answers to the following additions.Learning Intention 10.6: Able to add a single-digit to a double-digit number using the part/whole method65326Sheet 10.38
18© 2020 Adept Education LimitedSome naughty cockroaches have been sneaking through these houses at night collecting numbers. They start at the front door and exit through the back door. The number on their back is the sum of all the rooms they passed through. Can you help the owners work out which path they’ve been taking through the houses? Draw the path in with a pencil.3 4 92 5 81 6 73| Josh’s House2| Jack’s House 1 2 34 5 67 8 91 4 72 5 83 6 918311 | Judy’s House 29Front doorBack doorFront doorFront doorBack doorBack doorsolvers11Learning Intention 10.6: Able to add a single-digit to a double-digit number using the part/whole methodSheet 10.41
19© 2020 Adept Education Limited191| Jesse has found an interesting chest along with a box containing the key to the chest, but the box has a code for the combination lock. Help him solve the problems so he can unlock the chest to see what’s inside.The combination is:The combination is:Your notes:====++=–=+=+=x–=85Learning Intention 10.7: Able to subtract a single-digit from a double-digit number using the part/whole methodsolvers13Sheet 10.49
20© 2020 Adept Education LimitedOur friends have been using their calculators to do some tricky additions and subtractions. Using your estimating skills, can you tell who has entered their equations correctly and who has made a mistake? Tick correct or mistake.49 + 15 =58 + 22 =82 + 47 =76 – 35 =82 – 71 =56 – 29 =27correctmistake1|2|4|5|3| 6|64correctmistakecorrectmistakecorrectmistakecorrectmistakecorrectmistake1031192131Learning Intention 10.8: Able to use a calculator efficientlySheet 10.51
21© 2020 Adept Education Limited1| How many groups of 3 are there in 42?4| There are 23 people in Room 1, 55 people in Room 2 and 82 people in Room 3. How many altogether?5| If 18 flowers each had 6 petals, how many petals would there be altogether?7| The groceries cost $45.85. If I paid with a $100 note, how much change would I get?2| What is the difference between 297 and 56?8| What is the total of 327, 389 and 25?3| I have 5 chocolate bars, each with 9 rows of 6 pieces. How many pieces of chocolate do I have?6| I’m running a 42km marathon. If I’ve run 13km, how much further do I have to go?Use your calculator to solve each story problem. Write the equation down to show which buttons you pressed.21Learning Intention 10.8: Able to use a calculator efficientlySheet 10.53
22© 2020 Adept Education LimitedNeeta’s HouseSwimming PoolSupermarketJosh’s HouseSchool Library Judy’s House Jack’s House Doctor180m145m155m500m195mJudy has drawn up a map of her suburb, showing all the places where she spends her time. Use the map and your calculator to answer the questions below.1|How far is it from Judy’s house to Neeta’s house?4|Judy goes from school to the library, and then home. How far does she walk?2|If Josh wants to walk Jack to school, how far does he walk in total?5|Josh and Neeta meet at the pool on Saturdays. Who has to walk the farthest?3|How far does Neeta have to walk to get to the supermarket and back?6|How much further does Neeta have to walk than Judy to go to the doctor?Learning Intention 10.8: Able to use a calculator efficientlySheet 10.57
23© 2020 Adept Education Limited© 2023 Adept Education LimitedSheet 10.011|2|3|4|5|6|7|8|8 + 8 = 7 + 910 + 8 = 12 + 63 + 9 = 6 + 610 + 5 = 7 + 814 + 16 = 10 + 2010 + 4 + 10 = 2 + 2210 + 9 = 5 + 10 + 45 + 5 + 5 = 6 + 9Sheet 10.021|2|3|4|5|6|7|8|9|10|20 – 7 = 4 + 920 – 3 = 12 + 534 – 10 = 20 + 420 + 12 = 40 – 810 + 10 = 25 – 518 – 9 = 2 + 71 + 2 + 2 = 10 – 520 – 9 = 5 + 65 x 5 = 30 – 510 + 2 + 4 = 4 x 4Sheet 10.031|2|3|4|5|6|7|8|9|10|56 > 4239 < 8122 < 2584 > 7066 > 658 + 9 > 7 + 212 + 3 > 7 + 65 + 5 < 11 + 29 + 5 > 4 + 73 + 6 < 5 + 8Sheet 10.041|2|3|4|5|6|7|9 + 5 = 4 + 10: A2 x 3 < 4 + 4: C30 – 6 > 20 + 2: A20 – 1 > 6 x 3: N5 x 3 = 11 + 4: D2 + 10 < 17 – 4: L5 x 5 < 3 x 10: ESheet 10.051|2|3|4|5|6|11 + 11 < 33 – 10: B2 x 6 = 3 x 4: R2 x 9 > 11 + 6: E36 – 3 > 10 x 3: A20 + 4 = 6 x 4: T15 – 5 < 2 x 6: HSheet 10.061|2|3|4|5|6|7|8|6 + 3 = 93 + 6 = 95 + 5 = 10 kiwifruit3 + 2 = 5 mangoes10 + 5 = 15Half of 20 is 10. There are 9 oranges left, 20 – 9 = 11 sold. 11 is more than 10. Yes20 – 10 = 10 kiwifruit sold.20 – 9 = 11 apples sold. 10 < 11, so Ma did NOT sell more kiwifruit than apples.Ma sold 11 apples.Ma sold 11 oranges.Ma sold 10 kiwifruitMa sold 15 mangoes.11 + 11 + 10 + 15 = 47 pieces of fruit sold.She sold 15, so 15.Mangoes, because 15 is greater than 11, 11 and 10.Sheet 10.071|2|3|4|5|6|75c group50c group$1.50 group$2.00 group50c group$1.00 groupSheet 10.081|2|3|4|5|6|7|8|9|10|11|12|4 (6 x 4 = 24)2 (8 x 2 = 16)4 5 x 4 = 20)5 (6 x 5 = 30)36 (6 x 6)42 (7 x 6)Yes, 8 x 4 = 32Yes, 4 x 8 = 32No, 6 x 5 = 30 and 6 x 6 = 3625 (5 x 5)8 (1 x 1), (2 x 2) etc to (8 x 8)4 (2 x 6), (3 x 4), (4 x 3), (6 x 2) Note, 1 x 12 and 12 x 1 cannot be constructed on the 8 x 8 gridSheet 10.101|2|16 ÷ 2 = 8 because 8 x 2 = 1610 ÷ 5 = 2 because 2 x 5 = 10Sheet 10.111|2|3|4|12 ÷ 3 = 4 because 4 x 3 = 12$25 ÷ 5 = $5 because 5 x $5 = $25, so 32 ÷ 4 = 8 because 8 x 4 = 328 ÷ 4 = 2 because 2 x 4 = 8
24© 2020 Adept Education Limitedx 1 2 3 4 5 6 7 8 9 10 11 121 1 2 3 4 5 6 7 8 9 10 11 122 2 4 6 8 10 12 14 16 18 20 22 243 3 6 9 12 15 18 21 24 27 30 33 364 4 8 12 16 20 24 28 32 36 40 44 485 5 10 15 20 25 30 35 40 45 50 55 606 6 12 18 24 30 36 42 48 54 60 66 727 7 14 21 28 35 42 49 56 63 70 77 848 8 16 24 32 40 48 56 64 72 80 88 969 9 18 27 36 45 54 63 72 81 90 9910810 10 20 30 40 50 60 70 80 9010011012011 11 22 33 44 55 66 77 88 9911012113212 12 24 36 48 60 72 84 96108120132144Multiplication Table
25© 2020 Adept Education LimitedCut out the Bingo boards (yellow and green) and the Bingo cards (white) to make your bingo pack. Only cut along the the dotted lines.Fraction Bingo1218162016121212688644Bingo Board Player 1Bingo Cards Set 1(Mix with Set 2)of 10of 10of 12of 12 of 9of 9of 9of 18of 18of 18of 20of 20of 20of 20of 16of 16of 16of 16of 15of 15of 15of 15of 15of 20of 20of 20of 20of 20of 5of 2410920151215695106353
26© 2020 Adept Education Limited4/5.11|8011|6421|8931|4441|812|7212|6022|1132|5242|123|2513|3823|6733|8343|434|6814|2824|1834|7144|325|6115|4625|4935|2045|706|4516|7026|2136|4846|877|5817|5127|2337|8547|268|3318|3028|6538|8848|249|4119|5329|9039|5049|4210|7420|6330|7640|6750|62You will need:One 1-10 numbered diceStop watch or timerDesigned by Lucy PatstonInstructions:Below are a list of double-digit numbers. Start at 1| and roll the dice. Add the number you roll to the listed number (e.g., if you roll 8, the answer to 1| is 88). Call out your answer to a ‘judge’ and if you’re correct, move on to the next number. If you’re incorrect, stay on that number, roll the dice again and call your answer. Set a timer or stop watch to 3 minutes and see how far through the list you can get. Play again and see if you can beat your previous score!
27© 2020 Adept Education LimitedCertificate ofThis award gives credit toDate:Signed:for achieving Learning Intentions 1 to 4 for Book 10 of the Reaching Competence Mathematics Programme.Certificate ofThis award gives credit toDate:Signed:for achieving Learning Intentions 5 to 8 for Book 10 of the Reaching Competence Mathematics Programme.
28© 2020 Adept Education LimitedAbout the AuthorLucy Patston BA/BSc(Hons), PhDLucy 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.
29© 2020 Adept Education Limited29Overview of the Reaching Competence Mathematics ProgrammeAge and Stage Reaching CompetenceCurriculum Level School YearStudent Age Approx.Maths StageNumberMeasurement, Geometry & Statistics10-1 5-6 0-3 Books 1-4 Lapbooks Years 0-22 6-7 4 Books 5-723 7-85Books 8-10Lapbooks Years 3-4*4 8-9 Books 11-1435 9-106Books 15-17Lapbooks Years 5-6*6 10-11 Books 18-2047 11-127Books 21-23 Book 24*8 12-13Books 25-27*Book 28**Not yet publishedwww.adepteducation.co.nzHelping parents and tutors support their neurodiverse learners
30© 2020 Adept Education LimitedThe learning intentions covered in this book are:1. Able to understand equality2. Understands equal sharing3. Understands making equal groups4. Able to recognise halves and quarters of shapes (advanced)5. Able to find half or quarter of a set using doubles6. Able to add a single-digit to a double-digit number using the part/whole method7. Able to subtract a single-digit from a double-digit number using the part/whole method8. Able to use a calculatorwww.adepteducation.co.nzDownloadable books available at: adepteducationExplore the mathematics curriculum with your child at your own pace with thisguided, interactive programme.Includes information about the curriculum for parents and caregivers, learningintention checklist, worksheets, activities, board games, certificates and other print-and-cut resources.