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Book 4 Reaching Competence

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© 2023 Adept Education LimitedFollows Stage 3 of the New ZealandMathematics CurriculumAges 6 to 7Created byLucy Patston

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© 2023 Adept Education LimitedIntroducing Reaching Competence ………………………………………………………………5Overview of Books 1 to 4 ……………………………………………………………………………..7Book 4 Apple and Android Applications ………………………………………………………..8Book 4 YouTube Suggestions ………………………………………………………………………..9Book 4 Learning Intention Sticker Chart ……………………………………………………....10IXL Summary of Activities for Book 4 …………………………………………………………….11Learning Intention 4.1: Able to use a number line to solve addition and subtraction ……………………………………………………………………………………………….12Learning Intention 4.2: Able to solve addition and subtraction by counting on from largest number ……………………………………………………………………………19Learning Intention 4.3: Able to use the “=“ symbol in number sentences …….28Learning Intention 4.4: Knows groupings within 10 ………………………………………34Learning Intention 4.5: Able to skip count in twos and tens ………………………….42Learning Intention 4.6: Able to recall doubles facts to 10 …………………………….51Learning Intention 4.7: Able to recall facts with 5 …………………………………………56Adept Explains: The Punch Method ………………………………………………………………60Answers to Book 4 ………………………………………………………………………………………..63Resources …………………………………………………………………………………………………….67About the Author ………………………………………………………………..……………………….83Contents

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© 2023 Adept Education Limited3About the ProgrammeThe Reaching Competence Mathematics Programme by Adept Education covers the mathematics curriculum up to high school. Each book is divided into learning intentions that are appropriate for your learner’s age group. Learning intentions are maths skills that can be thought of as knowledge pieces that build on each other as students develop a deeper understanding of the concepts of mathematics.Book 4 covers the 7 learning intentions for learners aged about 6 to 7 years old. At this level, learners can now hold numbers in their minds without having to look at all the objects. They need to learn to count on from the highest number for addition, and back for subtraction, e.g., 9 and 4 is (10, 11, 12, 13) 13!Setting the pace Students will progress through each learning intention at a different pace. One may take a few minutes to master and apply, while another may take a few hours, a week, or more. This is normal, but if frustration arises, move on to another learning intention and return to the difficult one after the next has been mastered.Practice and ApplyLearning intentions are divided into Practice and Apply sections that should be worked through from start to finish. The Practice sections are developed to ‘drill the skill’ that the students are learning. The grey boxes at the beginning of these pages are to aid parents’ understanding and to explain how the learning intentions link in with other parts of the programme.The Apply sections are developed to ensure students can apply their new knowledge or skill to a problem-solving situation. Problem solving is emphasised in the Reaching Competence programme as this is a critical skill to have, and often one that students have difficulty with. Activities in the Apply sections are designed to broaden students’ understanding and enjoyment of their new maths skills.There is also a section containing the answers to all pages marked with the ‘Q?A’ icon.Adept supportIf you have any questions as you move through the programme, please don’t hesitate to email us at support@adepteducation.co.nzWe will be happy to support you in helping your learner’s confidence and maths ability grow, and are keen to hear any feedback you may have on our programme.

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© 2023 Adept Education LimitedBook 11. Knows the names of the main colours2. Able to sort by up to two attributes3. Able to match one to one4. Able to copy and create a simple repeating pattern5. Able to count to 106. Able to recognise numerals to 67. Able to count a set of objects to 6 8. Able to order numerals to 69. Able to give the number before and after in the range 0-6Book 21. Able to recognise numerals to 102. Able to count a set of objects to 10 3. Able to count backwards from 104. Able to recognise patterns to 55. Knows groupings within 56. Able to partition a set into two subsets7. Able to order numbers to 108. Able to give the number before and after up to 109. Able to recognise and copy number patternsBook 31. Able to solve addition and subtraction by counting all 2. Able to record using pictures, diagrams and words3. Able to use + and – to record number facts4. Able to recognise numerals to 205. Able to count forwards and backwards in range 0-206. Able to count a set of objects up to 207. Able to order numbers to 208. Able to give number before and after up to 209. Able to predict number patternsBook 41. Able to use a number line to solve addition and subtraction2. Able to solve addition and subtraction by counting on from the largest number3. Able to use the “=“ symbol in number sentences4. Knows groupings within 105. Able to skip count in twos and tens6. Able to recall doubles facts to 107. Able to recall facts with 5Overview of Books 1 to 4

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© 2023 Adept Education LimitedApple AppsSkip CountingBy HAVOCThis is a simple, attractive and effective app for skip counting. Learners are asked to drag numbers to their correct positions in the skip counting grid (clouds with a child superhero). Line ‘em UpBy Classroom Focused SoftwareThis app is an elegant version of a number line where learners are asked to drag numbers to their correct location in a grid. Use the settings to adjust the app to suit your learner’s level. There are also suggestions embedded in this programme.Math Slide: Add & SubtractBy Math AdventuresThis app is limited in content but nicely designed so that learners, or kids and their caregivers(!), can race each other on the same questions at the same time. It allows 4 players to sit around a device and play together. We suggest spending the money and getting the full worth.Android Apps Numbers and Math for KidsBy EDUBUZZKIDSThis is a nice wee app that targets a few skills not necessarily found in other learners’ mathematics apps, and there is an emphasis on problem solving.Skip Counting –Montessori MathBy Mobile MontessoriThis app gives learners a good concept of the hundred board while they practice their skip counting, the precursor to times tables. The app requires players to choose the correct multiples of the table and to drag these numbers to their correct place in the hundred board.Addition and SubtractionBy AplityThis is another simple, yet effective free app. It’s a shame the numbers are always represented with eyes, etc., for the practice trials, but if you can get past this then this app adds value. The “Exams” mode is particularly useful as players type in their answers, so choice (and chance!) are eliminated here.5Book 4 Apple and Android Applications** Adept Education does not endorse the apps recommended here. We have spent time researching apps, on both Apple and Android devices, to find those we feel best suit our programme for the least amount of expenditure to caregivers. It should be noted that Adept Education is not in any way in partnership with the owners of these applications, which may be updated without our knowledge. Please contact us at support@adepteducation.co.nz if you believe a recommended app has been changed significantly from what we describe here, or you can recommend apps you feel would better suit the needs of learners at this stage.

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© 2023 Adept Education LimitedLearning Intention Date Sticker4.1Able to use a number line to solve addition and subtraction4.2Able to solve addition and subtraction by counting on from the largest number4.3Able to use the “=“ symbol in number sentences 4.4Knows groupings within 104.5Able to skip count in twos and tens4.6Able to recall doubles facts to 104.7Able to recall facts with 56Book 4 Learning Intention Sticker Chart

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© 2023 Adept Education Limited7LI Year 1 Year 24.1Able to use a number line to solve addition and subtraction B3 B8 D9 F3 H9 H104.2Able to solve addition and subtraction by counting on from the largest number C2 C3 G2 G34.5Able to skip count in twos and tens F1 F5 F2 F64.6Able to recall doubles facts to 10 E1 I2for Book 4Summary of Activities

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© 2023 Adept Education Limited8Activities✓1.Sheet 4.01: Use the number ladder to find the answers (addition).Show learners how to use the number ladder/line by starting at the higher number and counting on in “jumps”. Remind them that we count “jumps”, not numbers. Let them use their fingers to point to the sequence of numbers while they count to the number to be added.2. nz.ixl.com: Year 2 – B3 Addition sentences using number lines – sums up to 10. 3. nz.ixl.com: Year 2 – D8 Addition sentences using number lines – sums up to 18. 4.Sheet 4.02: Use the number ladder to find the answers (subtraction).As with Sheet 4.01, help your learner to count jumps moving backwards through the number ladder/line. Again, reinforce the fact that we count “jumps”, not numbers.5. nz.ixl.com: Year 2 –F3 Subtraction sentences using number lines – numbers up to 10. 6. nz.ixl.com: Year 2 –H9 Subtraction sentences using number lines – numbers up to 18. Learning Intention 4.1: Able to use a number line to solve addition and subtractionpracticepracticepracticeYour learner should now be confident using their fingers or appropriate equipment to calculate simple addition and subtractions. The next step is to encourage your learner to imagine numbers in their head. A number line is a useful image for learners to use. Here, we give the option of using the vertical ladder or the horizontal number line.© 2023 Adept Education Limited

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© 2023 Adept Education Limited9Activities✓7.Sheet 4.03: Climbing steps (multiple additions).Here we ask students to keep adding along the number line multiple times.8.Sheet 4.04: Descending steps (multiple subtractions).9. nz.ixl.com: Year 2 – D9 Addition word problems – sums up to 18. 10. nz.ixl.com: Year 2 – H10 Subtraction word problems –numbers up to 18. Learning Intention 4.1: Able to use a number line to solve addition and subtraction continued…practicepracticepractice© 2023 Adept Education Limited

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© 2023 Adept Education Limited1020191817161514131211109876543210Use the number ladder or number line to find the answers.15and4is1914and4is10and2is6and3is8and5is7and3is7and5is12and4is9and2is12and3is4and3is15and5is4321Learning Intention 4.1: Able to use a number line to solve addition and subtractionSheet 4.01 1|2|3|4|5|6|7|8|9|10|11|12|More01234567891011121314151617181920More1234

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© 2023 Adept Education Limited1120191817161514131211109876543210Use the number ladder or number line to find the answers.19take away4leaves1514take away2leaves16take away6leaves17take away1leaves13take away3leaves20take away4leaves16take away5leaves13take away1leaves19take away7leaves11take away5leaves18take away3leaves12take away6leavesLearning Intention 4.1: Able to use a number line to solve addition and subtractionSheet 4.02 1|2|3|4|5|6|7|8|9|10|11|12|Less or fewer1234012345678910111213141516171819204321Less or fewer

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© 2023 Adept Education Limited12Sheet 4.03 Amavi and Suresh are each climbing some steps. Use the number ladder or number line to find out which step they are on.20191817161514131211109876543210012345678910111213141516171819201|Amavistarts by climbing 4 steps. Then she climbs another 4 steps. Which step is she on now?2|Then Amaviclimbs another 3 steps. Which step is she on now?3|Then Amaviclimbs another 7 steps. Which step is she on now?4|Suresh starts by climbing 9 steps. Then he climbs another 4 steps. Which step is he on now?5|Then Suresh climbs another 4 steps. Which step is he on now?6|Then Suresh climbs another 2 steps. Which step is he on now?7|Who finished on the highest step?Learning Intention 4.1: Able to use a number line to solve addition and subtraction

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© 2023 Adept Education Limited13Sheet 4.04 20191817161514131211109876543210012345678910111213141516171819201|Amavistarts on Step 18. Then she climbs down another 5 steps. Which step is she on now?2|She climbs down another 2 steps. Which step is she on now?7|He climbs down another 2 steps. Which step is Suresh on now?Now, Amavi and Suresh are climbing back down the steps. Use the number ladder or number line to find out which step they are on.3|She climbs down another 8 steps. Which step is she on now?4|How many steps until she reaches the bottom?5|Suresh starts on Step 19. Then he climbs down another 3 steps. Which step is he on now?6|He climbs down another 6 steps. Which step is he on now?x8|How many steps until he reaches the bottom?Learning Intention 4.1: Able to use a number line to solve addition and subtraction

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© 2023 Adept Education Limited14applyActivities✓1.Play Hide the Counters (10): Have your Number Ladder/Line resource handy. Write the numbers 1 to 10 on 10 different counters. Line the counters in order across the table or floor and then ask your learner to close their eyes. Hide the 6 left-most counters under a sheet of paper. Allow your learner to open their eyes and ask “How many counters are under the paper?” If your learner struggles to answer, remind them that the counters are like a number line and move the paper straight down so that the 6 counters are revealed. Repeat with 3 other numbers (e.g., hide 3, 8 and 5).2.Play Hide the Counters (20):Play the same game as above, but this time have 10 more counters labelled 11 to 20 in your lines. Hide 14, 16, 10 and 17.3. Line ‘em up.This game asks learners to complete a number line one number at a time with a few placeholders given. Ensure settings are on Use 20 Tiles, One Pile andstarting from 1. Press the puzzle piece to start. ORNumbers and Math. Choose Arrangement. This game asks learners to drag numbers in ascending and descending order with picture support. Learning Intention 4.1: Able to use a number line to solve addition and subtraction1234567 8 9 10© 2023 Adept Education Limited

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© 2023 Adept Education LimitedHere’s some other pages you’ll see in this book.www.adepteducation.co.nz

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© 2023 Adept Education Limited216My washing machine always takes socks away from my washing!The green one takes 2 socks away. How many socks will come out?6 32 9How many socks will come out if I put in:Take away 24 take away 2 leaves 24Sheet 4.07 1|2|3|4|5|6|7|8|Learning Intention 4.2: Able to solve addition and subtraction by counting on from the largest number

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© 2023 Adept Education Limited1| Megan has 5 books and she borrowed 4 more from the library. How many books does Megan have now?3| Kimiora has 7 red pencils and 3 blue pencils. How many pencils does Kimiora have?2| Jack has 6 little dinosaurs and 2 big dinosaurs. How many dinosaurs does Jack have?4| Kevin has 3 blue cars and 3 yellow cars. How many cars does Kevin have?Solve these addition story problems by finding the largest number on the number line and counting on.17Learning Intention 4.2: Able to solve addition and subtraction by counting on from the largest numberSheet 4.09 01234567891011121314151617181920More

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© 2023 Adept Education LimitedDraw a picture by filling in the remaining number of items to help you solve the following problems. Make the children equal to 10.There are 10 children in Miss Lewis’ class. Four (4) of them are boys.How many girls are there in Miss Lewis’ class?There are ___ girls in the class.Make the balls equal to 7.Wendy had 7 blue and orange balls. Two (2) balls were orange.How many of Wendy’s balls were blue?___ balls were blue.Make the eggs equal to 9.There were 9 eggs in the nest. Three (3) of them are still to hatch. How many eggs have hatched already?___ eggs have hatched already.18Learning Intention 4.2: Able to solve addition and subtraction by counting on from the largest numberSheet 4.11

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© 2023 Adept Education Limited1|5|4 = 4 =2|6|8 = 8 =3|7|= =4|8|= =19Learning Intention 4.3: Able to use the “=“ symbol in number sentencesSheet 4.13 Draw the correct number of blocks to balance the scales. Then write the equation underneath.

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© 2023 Adept Education Limited1| My right hand has 5 fingers and my left hand has 5 fingers. I have 10 fingers altogether.4| Jacob had 8 oranges so he gave 4 to his friend. Jacob had 4 oranges left.7| There were 20 cocoons on the swan plant when 3 of them hatched into butterflies. There were 17 cocoons left.5 + 5 = 102| I have 3 girls and a boy. I have 4 children altogether.5| Mary had 5 red jellybeans and 3 yellow ones. She had 8 jellybeans altogether.8| There were 14 cars on the race track when 2 more joined them. Now there are 16 cars on the race track. 3| There were 8 candles on my birthday cake. Mum added 4 more. I am 12 today.6| I had 9 pages left to read in my book. I read another 6 pages today, so now I only have 3 pages left to read in my book. 9| Last month I had 10 baby teeth but 3 more have fallen out. I only have 7 baby teeth left!20Learning Intention 4.3: Able to use the “=“ symbol in number sentencesSheet 4.15 Write the number sentence for the story problem using the correct symbols (+ – =)

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© 2023 Adept Education Limited21Learning Intention 4.4: Knows groupings within 10Neeta and Mei Hsin’s teacher has set them the task to find out all the groupings within 10! They’re going to need your help.Count out 10 counters and place them all on the left side of the oval. This is the grouping 10-0 (see table). Next, move one counter to the right side of the oval. This is the grouping 9-1 (see table).Different groupings within 1010-09-18-?- - - - - - -0-10Sheet 4.16 Keep moving one counter to the right at a time until you get to the last grouping, 0-10. Record your discovery in the table below. How many groupings were there?

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© 2023 Adept Education LimitedSally has been using her peg board to make groupings within 10. Write in the number sentences to match the rows she has created. Which groupings has she missed? Use the empty space to list all the groupings in a sensible order and then cross out the ones Sally already has. Choose 3 of those she has missed and colour in the last three rows. 1|3 + 7 = 102|3|4|5|6|7|8|9|10|22Learning Intention 4.4: Knows groupings within 10Sheet 4.19 Groupings within 10 (in order)

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© 2023 Adept Education LimitedFind 10 counters and pretend they are Jan and May’s grapes.Jan took 4 grapesMay took 6 grapes1| How else could they have shared the grapes?Draw another way below by tracing around your counters.0-10 | 1-9 | 2-8 | 3-7 | 4-6 | 5-5 | 6-4 | 7-3 | 8-2 | 9-1 | 10-023Learning Intention 4: Knows groupings within 10Sheet 4.21

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© 2023 Adept Education Limited24Learning Intention 4.5: Able to skip count in twos and tensSheet 4.24 012345678910111213141516171819202| Write in the missing numbers on the number line for skip counting in twos.02481014201| Circle the correct numbers on the number line for skip counting in twos.3| Circle the correct numbers on the number line for skip counting in tens.051015202530354045504| Write in the missing numbers on the number line for skip counting in tens.0104050701002122232425262728293031323334353637383940222628343638556065707580859095100

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© 2023 Adept Education Limited1|2|3|4|5|6|25Sheet 4.27 Learning Intention 4.5: Able to skip count in twos and tensSkip count in twos or tens to find how many items there are.

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© 2023 Adept Education Limited26When children begin to count (using their fingers most often), they can get caught in the process by counting the first number as well as the number they wish to add (or subtract) – giving them an incorrect answer.The “punch method” provides a way of getting to the correct number each time, by allowing that first (or starter) number to be spoken (and acted upon), but not added to the equation (so to speak). (Before a learner can use this method, they need to be able to recognise the number of fingers they are holding up and be able to count up and down easily. Practice these skills first.)Here’s how the “punch method” goes for 5 + 2:© 2023 Adept Education LimitedMethod Example: 5 + 2 = ?Say the first number while punching (5)“Five,Say the next number (6)six,Keep going until you are holding up the correct number of fingers (2).The answer is the last number you say (7).seven!”

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© 2023 Adept Education Limited27© 2018 Adept Education Limited (t/a Reach Education)Sheet 4.011|2|3|4|5|6|7|8|9|10|11|12|15 and 4 is 1914 and 4 is 1810 and 2 is 126 and 3 is 98 and 5 is 137 and 3 is 107 and 5 is 1212 and 4 is 169 and 2 is 1112 and 3 is 154 and 3 is 715 and 5 is 20Sheet 4.021|2|3|4|5|6|7|8|9|10|11|12|19 take away 4 leaves 1514 take away 2 leaves 1216 take away 6 leaves 1017 take away 1 leaves 1613 take away 3 leaves 1020 take away 4 leaves 1616 take away 5 leaves 1113 take away 1 leaves 1219 take away 7 leaves 1211 take away 5 leaves 618 take away 3 leaves 1512 take away 6 leaves 6Sheet 4.031|2|3|4|5|6|7|Step 8Step 11Step 18Step 13Step 17Step 19SureshSheet 4.041|2|3|4|5|6|7|8| Step 13Step 11Step 33 stepsStep 16Step 10Step 88 stepsSheet 4.051|2|3|4|5|6|7|8|4 add 2 is 68 add 2 is 102 add 2 is 47 add 2 is 99 add 2 is 111 add 2 is 33 add 2 is 55 add 2 is 7Sheet 4.061|2|3|4|5|6|7|8|2 add 3 is 56 add 3 is 94 add 3 is 77 add 3 is 101 add 3 is 48 add 3 is 115 add 3 is 83 add 3 is 6Sheet 4.07 continued…5|6|7|8|6 take away 2 leaves 42 take away 2 leaves 03 take away 2 leaves 19 take away 2 leaves 7Sheet 4.081|2|3|4|5|6|7|8|3 take away 3 leaves 09 take away 3 leaves 64 take away 3 leaves 16 take away 3 leaves 38 take away 3 leaves 510 take away 3 leaves 75 take away 3 leaves 211 take away 3 leaves 8Sheet 4.071|2|3|4|7 take away 2 leaves 510 take away 2 leaves 88 take away 2 leaves 65 take away 2 leaves 3Sheet 4.091|2|3|4|5 – 6, 7, 8, 96 – 7, 8 7 – 8, 9, 103 – 4, 5, 6Sheet 4.101|2|3|4|10 – 9, 8, 7, 6, $58 – 7, 6, 5, 49 – 8, 7, 65 – 4, 3Sheet 4.111|2|3|10 – 4 = 6 girls7 – 2 = 5 blue balls9 – 3 = 6 hatched eggs© 2023 Adept Education Limited

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© 2023 Adept Education Limited20191817161514131211109876543210Number LadderPrint on white cardboard (160-200gsm).Less or fewerMoreNumber Line20191817161514131211109876543210Less or fewerMore

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© 2023 Adept Education LimitedInstructions:Take it in turns to roll the dice. If you roll a double on any of the dice, put a counter on the correct circle. The winner is the player with the most counters on the board after an amount of time you choose.You will need:Three 1-6 dot diceTwelve counters of the same colour for each playerDesigned by Lucy Patston448810101222666

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© 2023 Adept Education Limited01 02 03 04 05 06 07 08 09 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99100Cut out the strip at the bottom. Cut only on the dotted lines. Leave the hundred board intact.Hundred Board

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© 2023 Adept Education LimitedFor full content please purchase from the website.www.adepteducation.co.nz

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© 2023 Adept Education LimitedThe learning intentions covered in this book are:• Able to use a number line to solve addition and subtraction• Able to solve addition and subtraction by counting on from the largest number• Able to use the “=“ symbol in number sentences• Knows groupings within 10• Able to skip count in twos, fives and tens• Able to recall doubles facts to 10• Able to recall facts with 5Explore the mathematics curriculum with your child at your own pace with this guided,interactive programme.Includes information about the curriculum for parents and caregivers, learningintention checklist and sticker chart, suggested Apple and Android applications,worksheets, activities, board games, certificates and other print-and-cut resources.www.adepteducation.co.nzDownloadable books available at: adepted ucation