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© 2020 Adept Education LimitedFollows Stage 5 of the New ZealandMathematics CurriculumAges 8-9 | Year 4Created byLucy Patston
© 2020 Adept Education Limited2Book 11Able to use doubles of teens to solve addition and subtractionAble to understand equalityAble to use standard partitioning to add 2-digit numbersAble to use tidy numbers to add 2-digit numbersAble to use compensation to add 2-digit numbersAble to use difference to subtract 2-digit numbersAble to use standard partitioning to subtract 2-digit numbersAble to use tidy numbers to subtract 2-digit numbersAble to use the combination of notes and coins Book 12Knows compatible numbers (in ones) to 100Understands equal sharingUnderstands making equal groupsKnows multiplication facts x 3Knows multiplication facts x 9Has knowledge of the distributive property of multiplicationHas knowledge of the doubling and halving strategyKnows multiplication facts x 4Book 13Able to read, write and order 3-digit numbersKnows the value of digits in 3-digit numbersAble to round 3-digit numbers to the nearest 10 or 100Able to use compensation to add 3-digit numbersAble to use tidy numbers to add 3-digit numbersAble to use standard partitioning to add 3-digit numbersAble to use standard partitioning to subtract 3-digit numbersAble to use difference to subtract 3-digit numbersAble to give changeBook 14Understands sizes of fractions in relation to the wholeAble to order unit fractionsAble to find ½, ¼, ⅓ and ⅕ using additive strategiesUnderstands division as sharing or groupingAble to use a calculator efficientlyAble to select an appropriate operation to solve a problemAble to solve multi-step problemsAble to solve problems involving moneyOverview of Books 11 to 14
© 2020 Adept Education LimitedApple AppsZap ZapFractions ExtendedBy Visual Math Interactive This is a lovely set of tutorials mixed with practices and games that take learners through the beginnings of fractions.Fractions – by BrainingcampBy BrainingcampThis is a large and well-constructed FREE app. It includes a nice introduction with multiple parts and goes on to assist in comparing, adding & subtracting, multiplying and dividing fractions. These menus will be used in later books.Splash MathBy StudyPad, Inc.This app is well designed and aligned to our learning intentions, so it provides a good resource for moving through the books. There is a free version of this app, but the full version will be useful for many books to come. Android AppsSimply Fractions (Lite), MathBy Simply Learning AidThis is a simple app that does the job. Simply Learning do a higher level fraction app also that we will be utilizing in later books.Splash MathBy StudyPad, Inc.This app is well designed and aligned to our learning intentions, so it provides a good resource for moving through the books. There is a free version of this app, but the full version will be useful for many books to come. The app is also available on computer.3* 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@reacheducation.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.Book 14 Apple and Android Applications*
© 2020 Adept Education LimitedLearning Intention Date Sticker27.Understands sizes of fractions in relation to the whole28.Able to order unit fractions29.Able to find ½, ¼, ⅓ and ⅕ using additive strategies30.Understands division as sharing or grouping31.Able to use a calculator efficiently32.Able to select an appropriate operation to solve a problem33.Able to solve multi-step problems34.Able to solve problems involving moneyReview of Books 11, 12, 13 & 144Book 14 Learning Intention Sticker Chart
© 2020 Adept Education Limited5Activities✓1.Revise Book 10.Learning Intention 19: Here we looked at recognising halves and quarters.2.Revise Book 10.Learning Intention 21: Here we looked at recognising thirds and fifths.3.Sheet 14.01: A quick recap using Unifix rods. You will find the substitute apparatus in the Resource Section. 4.Revise Book 10. Learning Intention 20: Here we learned how to find half or quarter of a set.5.Revise Book 10.Learning Intention 22: Here we learned the fraction words numerator, denominator, proper fraction, improper fraction and mixed fraction, and we worked through how to turn improper fractions into mixed fractions and vice versa.6.Sheet 14.02: Creating fractions from wholes.Learning Intention 27: Understands sizes of fractions in relation to the wholeEnsure your learner understands the terminology of denominator (the bottom number) and numerator (the top number) of a fraction. At this point it is a good idea to relate the language of fractions to something familiar in your learner’s life, like pizza or a birthday cake. Start reminding your learner often (and definitely when any confusion arises) that the denominator is the number of equal slices of the wholepizza (or birthday cake) and that the numerator is the number of slices they will get to eat. So, if a pizza has 4 equal slices, 4 is the denominator. If they get 1 slice to eat, 1 is the numerator, and their share was, therefore, of the pizza. Remember to keep your example consistent, so if you choose pizza, always use pizza!practicepracticepractice© 2020 Adept Education Limited
© 2020 Adept Education LimitedStart by lining up your colour Unifix rods in order from black to dark blue and then answer the following questions. Allow your learner to move the rods around and line them up beside each other to work out the answers.1|Which colour rod is of the dark blue rod?2|Which colour rod is of the orange rod?3|Why are the answers to Q1 and Q2 different when they are both asking for halves?___________________________________________________________________4|Which colour rod is of the orange rod?5|Which colour rod is of the light blue rod?6|Which colour rod is of the green rod?6Now, line up your number Unifix rods in order from 1 to 10 and answer the questions.7|Which number rod is of the 4 rod?8|Which number rod is of the 9 rod?9|Which number rod is of the 8 rod?10|Which number rod is of the 10 rod?11|The 1 rod is of which number rod?12|The 2 rod is of which number rod?Learning Intention 27: Understands sizes of fractions in relation to the wholeSheet 14.01
© 2020 Adept Education LimitedJudy is cutting shapes into different fractions. Help her know which lines to cut using a marker pen.She has started work on Question 1.74|Judy wants to cut this hexagon into thirds.1|Judy wants to cut this circle into sixths.5|Judy wants to cut this pentagon into fifths.2|Judy wants to cut this square into quarters.6|Judy wants to cut this triangle into halves.3|Judy wants to cut this octagon into eighths.7|Judy wants to cut this decagon into fifths.Learning Intention 27: Understands sizes of fractions in relation to the wholeSheet 14.02
© 2020 Adept Education Limited8applyActivities✓1.Sheet 14.03: Colour the fractions.2.Sheet 14.04: Adept Problem Solvers 28.3.Sheets 14.05 and 14.06: Adept Problem Solvers 29.4.Sheets 14.07 & 14.08: Folding fractions.5. Zap Zap Fractions Extended.When we last concentrated on fractions in Book 10, we completed Chapter 1 of this app. Either review this chapter if you’ve worked through this app before, or complete 1 through to 3 of Chapter 1: Understanding Fractions. ORSimply Fractions (Lite), Math. Play Shade-a-fraction, Fill the beaker and Compare.Learning Intention 27: Understands sizes of fractions in relation to the whole© 2020 Adept Education Limited
© 2020 Adept Education LimitedName the shape and colour in the fraction specified.91| _______________3| ________________5| ________________2| ________________4| ________________6| ________________7| 9| 11| 8| 10| 12| Try colouring these challenging shapes. Some of the shapes are not divided into equal parts,so be careful with your choices. Put a cross beside the unequal ones.Learning Intention 27: Understands sizes of fractions in relation to the wholeSheet 14.03
© 2020 Adept Education LimitedThe friends are all making statements about the pictures they’ve been given. Mark the statements as correct with a or incorrect with a .10Learning Intention 27: Understands sizes of fractions in relation to the wholesolvers1|the animals are cows.4|of the insects are caterpillars.7|of the jellybeans are orange.2|of the animals are sheep.5|There are 3 butterflies for every caterpillar.8|There are 3 red jellybeans for every green one.3|There are twice as many sheep as there are cows.6|of the insects are butterflies.9|the jellybeans are red.28Sheet 14.04
© 2020 Adept Education LimitedChelsea’s CheesecakesChelsea’s Cheesecakes sell three types of cheesecake:11Learning Intention 27: Understands sizes of fractions in relation to the wholeChelsea cuts her chocolate cheesecake into sixths.Chelsea cuts her berry cheesecake into eighths.Chelsea cuts her lemon cheesecake into tenths.Chocolate Berry Lemon1|Draw in the lines for Chelsea’s cuts on her second cheesecake (the centre is shown).Chocolate Berry Lemon2|Chelsea sells 12 slices of chocolate cheesecake on Monday. How many whole cheesecakes is that?3|On Tuesday, Chelsea sells only 7 slices of chocolate cheesecake. How many whole cheesecakes and pieces is that?1234567891011121234567solvers29Sheet 14.05
© 2020 Adept Education LimitedChelsea’s CheesecakesChelsea’s Cheesecakes sell three types of cheesecake:12Learning Intention 27: Understands sizes of fractions in relation to the wholeChelsea cuts her chocolate cheesecake into sixths.Chelsea cuts her berry cheesecake into eighths.Chelsea cuts her lemon cheesecake into tenths.Chocolate Berry Lemon4|Help Chelsea keep a record of her cheesecake sales for the week.Pieces WholesM 12 2T 71 W 9Th 6F 8Pieces WholesM 8 1T 101 W 15Th 16F 13Pieces WholesM 5T 10 1W 13Th 20F 17solvers29Sheet 14.06
© 2020 Adept Education LimitedUse the next page to cut out strips and fold. Then open your shapes out flat and lay them on the template below to answer the questions.a|The half point has been marked and labelled. Lay your opened up triangle strip on the template and use it to mark and label the point.b|Lay your square strip on the template and mark and label the point.c|Check your point is half way to the point.d|Now, one by one, lay down your pentagon and label the point, then lay downyour hexagon and label the point, and then lay down your octagon and label the point.1|Are your labels getting closer to the left end of your template?2|Does this mean the fractions are getting smaller or bigger?3|Complete the sentence: Fractions get ___________ as the denominator gets ___________.4|Why is this? ____________________________________________________13All your labels should be on the other half of the template.5|Is a smaller or a bigger fraction than ?6|Is a smaller or a bigger fraction than ?Learning Intention 27: Understands sizes of fractions in relation to the wholeSheet 14.07
© 2020 Adept Education Limited141|Fold this strip into a triangle with 3 sides.2|Fold this strip into a square with 4 sides.3|Fold this strip into a pentagon with 5 sides.4|Fold this strip into a hexagon with 6 sides.5|Fold this strip into an octagon with 8 sides.Here’s a spare strip if you need it.Learning Intention 27: Understands sizes of fractions in relation to the wholeSheet 14.08
© 2020 Adept Education LimitedHere’s some other pages you’ll see in this book.www.adepteducation.co.nz
© 2020 Adept Education LimitedWhat fractions are shown below?161|2|1/63|4|5|6|What happens to the size of the fraction as the denominator gets bigger?______________________________________________________________7|12|8|13|9|14|10|15|11|16|Learning Intention 28: Able to order unit fractionsSheet 14.10
© 2020 Adept Education LimitedFraction: Fraction: Fraction:1| First, colour in 2 segments of each shape, then label the fraction.Next, cut out the shapes along the dotted lines.Glue them into your workbook in order from smallest to largest.172| Colour in 3 segments and do as you did in Question 1.3| Colour in 4 segments and do as you did in Question 1.Fraction: Fraction: Fraction:Fraction: Fraction: Fraction:Learning Intention 28: Able to order unit fractions Sheet 14.12
© 2020 Adept Education LimitedSilver ringGold ringRuby ringDiamond ringMr Mi has been asked to count all his rings and provide his accountant with some facts. Mr Mi could use your help with his stocktake. Include the rings in the key.1|How many rings does Mr Mi have in stock altogether?2|What fraction are silver rings?3|What fraction are gold rings?4|What fraction are ruby rings?5|What fraction are diamond rings?Mr Mi decides to make more stock. He makes 4 more gold rings, 2 more ruby rings and 2 more diamond rings.6|How many rings does Mr Mi have altogether now?7|What fraction are silver rings?8|What fraction are gold rings?18solversLearning Intention 29: Able to find ½, ¼, ⅓ and ⅕ using additive strategies9|What fraction are ruby rings?10|What fraction are diamond rings?KEY30Sheet 14.15
© 2020 Adept Education Limited19You might have noticed that when we’re sharing we often know how many items we have to share amongst a given number. For example, we might know that we have 6 pancakes to share with 3 people.It’s easy enough to see that Ken, Josh and Jacinda each get 2 pancakes, but things get a bit trickier when the numbers get bigger!What we’ve done here is a division equation based on a multiplication equation we already know.3 x 2 = 6 is the same as 6 ÷ 3 = 23 x 2 = 6 is the same as 6 ÷ 3 = 21| Twenty four (24) eggs are shared equally between 2 recipes. How many eggs does each recipe need?2|Nine (9) apples are shared equally between 3 horses. How many apples does each horse get?Write the multiplication AND division equations for these story problems.2 x 8 = 24 24 ÷ 2 = 2 x 12 = 24 24 ÷ 2 = These are the numbers we already know.This is the number we want to know.Learning Intention 30: Understands division as sharing or groupingSheet 14.19
© 2020 Adept Education LimitedSolve the equation using your calculator. Then turn your calculator upside down, read the word and enter it into the crossword. Use the key at the bottom of this page to help with your letter interpretation, if needed.ACROSSDOWN1|36,589 + 424,7862|48468 ÷ 62|901,594 – 524,9864|64.25 x 83|2669 x 25|81,044,205 – 3,698,5424|926 x 46|14,429 x 47|3.525 ÷ 510|108945 ÷ 38|500,000 + 31,71711|Enter 0.1409|0.1289 x 612|10,609 x 514|0.02 x 513|1 ÷ 215|52,952 – 52,648200 1 2 3 4 5 6 7 8 9O I - E H S G L B -1 152345614121171089133807638076GLOBELearning Intention 31: Able to use a calculator effectivelySheet 14.25
© 2020 Adept Education LimitedTry this trick with your calculator from Dr Mike’s Math Games for Kids.InstructionsExample:29thFebruaryYour birthday:1|Enter the number 772|Multiply by the day of your birth (=)7 x 29 = 2033|Subtract 1 (=)203 – 1 = 2024|Multiply by 13 (=)202 x 13 = 2,6265|Add the month of your birth (=)2626 + 2 = 2,6286|Add 3 (=)2628 + 3 = 2,6317|Multiply by 11 (=)2631 x 11 = 28,9418|Subtract the day of your birth (=)28,941 – 29 = 28,9129|Subtract the month of your birth (=)28,910 – 2 = 28,91010|Divide by 10 (=)28,910 ÷ 10 = 2,89111|Add 11 (=)2,891 + 11 = 2,90212|Divide by 100 (=)2,902 ÷ 100 = 29.0221Adapted from: www.dr-mikes-math-games-for-kids.comTell your friends you’re a maths genius and can provide them with the formula to calculate their birthday (shown as dd.mm). All they have to do is follow your instructions. You have a go, first! Fill out the table with the answer on the calculator as you go.Learning Intention 31: Able to use a calculator effectivelySheet 14.26
© 2020 Adept Education LimitedThis waiter needs to balance his dishes so that he does not tip over. He has worked out how heavy the dishes are and balances them as shown in the pictures below. Can you help him with the following questions?1|If the waiter only had 3 bowls, how many plates would he need?2|If he had 12 plates, how many bowls would he need?3|If the waiter had 1 platter, how many bowls would he need?4|If he had 1 platter, how many plates would he need?5|If he had 4 jugs, how many plates would he need?6|If the waiter had 4 jugs, how many platters would he need?7|If he had 4 jugs, how many bowls would he need?2210 plates5 bowls4 bowls2 platters1 jug3 plates1 bowl equals 2 plates1 jug equals 3 plates1 platter equals 2 bowlssolvers37Note, this activity is challenging.Learning Intention 33: Able to solve multi-step problemsSheet 14.35
© 2020 Adept Education LimitedKya has had 8 adorable puppies.231|How many puppy ears are there?2|How many puppy paws are there?3|How many puppy tails, eyes and paws are there altogether?4|Looking at the graph of puppy weight over 8 weeks, how much did an average puppy weigh at birth?5|How much will an average puppy weigh at 8 weeks old?6|How much weight will each puppy gain over those 8 weeks?7|What fraction of their 8-week weight were the puppies when they were 1 week old?solvers3850004500400035003000250020001500100050000 1 2 3 4 5 6 7 8Write in your equations and solve the questions.Puppy weight in gramsPuppy age in weeksPermission to use the photos on this page was kindly granted by Kevin OttonLearning Intention 33: Able to solve multi-step problemsSheet 14.36
© 2020 Adept Education Limited24a) He will give them $2 more each day, starting with $10 on Monday b) He will give them $100 at the end of the week; orc) He will give them $8 each day plus an extra bonus of $50 on Sunday.Jack and Judy are going to earn some pocket money by helping Judy’s grandfather with his vegetable garden. He has given them some options for payment over the first week. They will share the money equally.Option 1 Option 2 Option 3Monday$10 $8TuesdayWednesdayThursdayFridaySaturdaySunday$22Bonus$50Total1| Which option seems the best straight away? If you had to choose in 3 seconds only, which option would you take?2| Use the table to work out which option they should choose.3| How much money will they get each?solvers39Option:Option:$ororLearning Intention 34: Able to solve problems involving moneySheet 14.39
© 2020 Adept Education LimitedPlot the data from your table onto this graph and rule the lines for each of the three data sets. One line will show Annie’s savings and the other line will show Sandy’s savings.25solvers4201234567 8 91011121314$60$55$50$45$40$35$30$25$20$15$10$5$0Circle and label the point that shows…1|… how much money Annie had on Day 0.2|… how much Sandy had on Day 14.3|… the day Sandy could have stopped saving.4|… when both children had the same amount of money.DayLearning Intention 34: Able to solve problems involving moneyAnnie and Sandy’s School Trip SavingsKey AnnieSandySheet 14.42Amount Saved
© 2020 Adept Education Limited4|5|1|2|3|Here is a beehive addition wall. Can you see how it is constructed?Each of the two numbers below add to the number above.26Race yourself to get to the top of these beehive walls.Time 1:Time 2:Time 3:396121527Time 1:Time 2:11131618191416121512 131711181412181113171915Sheet 14.50Review of Books 11 to 14
© 2020 Adept Education LimitedSheet 14.02 continued…2|OROR3|27Sheet 14.011|2|3|4|5|6|7|8|9|10|11|12|Red. Two of the red rods would be the same length of the dark blue rod.Purple. Two of the purple rods would be the same length of the orange rod.Because the starting rods are different lengths.Brown. Three of the brown rods would be the same length as the orange rod.Purple. Three of the purple rods would be the same length as the light blue rod.Brown. Four of the brown rods would be the same length as the green rod.2. Half of 4 is 2.9. One third of 9 is 3.2. One quarter of 8 is 2.2. One fifth of 10 is 2.5. One fifth of 5 is 1.6. One third of 6 is 2.Sheet 14.021|Sheet 14.02 continued…4|5|6|7|© 2020 Adept Education Limited
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© 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 LimitedExplore the mathematics curriculum with your child at your own pace with thisguided, interactive programme. This book includes Learning Intentions 27 through to34 (of 34) for this level.Includes information about the curriculum for parents and caregivers, learningintention checklist, worksheets, activities, board games, certificates and other print-and-cut resources.The learning intentions covered in this book are:• Understands sizes of fractions in relation to the whole• Able to order unit fractions• Able to find ½, ¼, ⅓ and ⅕ using additive strategies• Understands division as sharing or grouping• Able to use a calculator efficiently• Able to select an appropriate operation to solve a problem• Able to solve multi-step problems• Able to solve problems involving moneywww.adepteducation.co.nzOnline and printed versions available at: adepteducation