Ages 7 to 9 Follows Level 2 of the New Zealand Mathematics Curriculum Created by Lucy Patston 2020 Adept Education Limited t a Reach Education
Contents Introducing Reaching Competence 5 Overview of Fraction Books 7 Apple and Android Apps List 8 Learning Intention Sticker Chart 9 Learning Intention 9 Understands sizes of fractions in relation to the whole 10 Learning Intention 10 Able to order unit fractions early 21 Learning Intention 11 Able to find and using additive strategies 29 Learning Intention 12 Understands division as sharing or grouping 37 Learning Intention 13 Able to find non unit fractions of shapes 45 Learning Intention 14 Able to find non unit fractions of numbers 52 Learning Intention 15 Able to add and subtract fractions with the same denominator 61 Learning Intention 16 Able to recognise improper fractions 69 Answers to Level 2 Fractions 74 About the Author 81 Print Cut Resources 83 Board Games 84 Certificates of Competence 85 2020 Adept Education Limited t a Reach Education
Reaching competence Introducing Reaching Competence by Reach Education The Reaching Competence programme has been designed to enable parents and caregivers to mentor their own children at home in mathematics The programme progresses caregivers and children together along the mathematics curriculum being taught in schools In this way parents and caregivers are empowered to understand the curriculum and help children with their understanding At the same time parents and caregivers become knowledgeable as to which ways their children struggle and excel In addition learning can be conveniently popped into quiet moments or scheduled sessions depending on the family s needs Lucy Patston PhD Psychology Founding Director of Reach Education I wish you all the best in your maths journey with your child or children I hope you enjoy your time together 3 2020 Adept Education Limited t a Reach Education
Level 1 Able to recognise symbols for half and quarter Able to find halves and quarters of shapes early Able to find halves and quarters of sets Able to find halves and quarters of shapes advanced Able to find half or quarter of a set using doubles Able to recognise symbols for third and fifth Able to find thirds and fifths of shapes Able to recognise wholes with fractions left over Level 2 Understands sizes of fractions in relation to the whole Able to order unit fractions Able to find and using additive strategies Understands division as sharing or grouping Able to find non unit fractions of shapes Able to find non unit fractions of numbers Able to add and subtract fractions with the same denominator Able to recognise improper fractions Level 3 Overview of Fractions Books Able to order unit fractions advanced Able to use improper fractions and mixed numbers Knows simple equivalent fractions Able to solve simple ratio problems using repeated replication Understands percentages as special fractions Knows common percentages 4 2020 Adept Education Limited t a Reach Education
Level 2 Fractions Apple and Android Applications Apple Apps Zap Zap Fractions Extended This is a lovely set of tutorials mixed with practices and games that take children through the beginnings of fractions By Visual Math Interactive Fractions by Brainingcamp By Brainingcamp Third Grade Splash Math By StudyPad Inc This 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 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 Apps Simply Fractions Lite Math By Simply Learning Aid Splash Math For PC Create an account at https www splashmat h com mathskills third grade Simply Fractions 3 Lite This is a simple app that does the job Simply Learning do a higher level fraction app also that we will be utilizing in later learning intentions Here we are switching to the computer to make the most of the Splash Math online programme that taps the curriculum so beautifully Take a leap of faith and make an account for your child ren You will have to pay before long but it will be worth it This is another of the Simply Learning apps that nicely fits into our learning intention frame work By Simply Learning Aid Reach 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 Reach 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 children at this stage 5 2020 Adept Education Limited t a Reach Education
Learning Intention Sticker Chart Learning Intention 9 Understands sizes of fractions in relation to the whole 10 Able to order unit fractions early 11 Able to find and using additive strategies 12 Understands division as sharing or grouping 13 Able to find non unit fractions of shapes 14 Able to find non unit fractions of numbers 15 Able to add and subtract fractions with the same denominator 16 Able to recognise improper fractions 6 2020 Adept Education Limited t a Reach Education Date Sticker
practice practice practice Learning Intention 10 Able to order unit fractions early Children need to practice comparing fractions and understand that the larger the denominator the smaller the equal parts Activities 1 1 2 5 1 Sheet Frac2 09 Ordering fractions to 2 Sheet Frac2 10 Introducing sixths sevenths eighths ninths and tenths 3 Sheet Frac2 11 Ordering fractions to 4 Zap Zap Fractions If you re new to Zap Zap Fractions complete 4 through to 6 of Chapter 1 Understanding Fractions 1 1 6 10 7 2020 Adept Education Limited t a Reach Education
Learning Intention 10 Able to order unit fractions early Use the fraction table to complete the activities One whole 1 1 2 1 2 1 3 1 3 1 4 1 3 1 4 1 5 1 4 1 5 1 4 1 5 1 5 1 5 Put these fractions in order from smallest to largest 1 1 5 1 4 1 _____ _____ _____ _____ 2 3 2 2 2 _____ 1 3 1 2 _____ 2 5 _____ _____ Use the greater than and
Learning Intention 10 Able to order unit fractions early What fractions are shown below 1 6 1 2 3 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 9 2020 Adept Education Limited t a Reach Education Frac2 10
Learning Intention 10 Able to order unit fractions early Use the fraction table to complete the activities 1 6 1 7 1 8 1 9 1 10 1 6 1 6 1 7 1 7 1 8 1 9 1 10 1 6 1 7 1 8 1 9 1 10 1 7 1 8 1 9 1 6 1 8 1 9 1 10 1 10 1 7 1 8 1 9 1 10 1 8 1 9 1 10 1 6 1 7 1 8 1 9 1 10 1 9 1 10 1 10 Put these fractions in order from smallest to largest 1 1 8 1 9 _____ 1 10 _____ _____ 2 9 2 _____ _____ 2 6 2 7 _____ 1 6 1 7 _____ _____ Use the greater than and
apply Learning Intention 10 Able to order unit fractions early Activities 1 Sheet Frac2 12 Colour the fractions and order 2 Play the Reach game Fully Fledged Family An example of a winning board is below 3 Simply Fractions Lite Math Play Name Memory and Word Problems 4 1 3 2 10 4 5 2 4 2 tenths 1 third 2 quarters 4 fifths 7 sevenths 11 2020 Adept Education Limited t a Reach Education 7 7
Learning Intention 10 Able to order unit fractions early 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 Fraction Fraction Fraction 2 Colour in 3 segments and do as you did in Question 1 Fraction Fraction Fraction 3 Colour in 4 segments and do as you did in Question 1 Fraction Fraction 12 2020 Adept Education Limited t a Reach Education Fraction Frac2 12
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solvers 6 Learning Intention 11 Able to find and using additive strategies Mr 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 KEY Silver ring Gold ring Ruby ring Diamond ring 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 9 What fraction are ruby rings 10 What fraction are diamond rings 14 2020 Adept Education Limited t a Reach Education Frac2 15
solvers 9 Learning Intention 12 Understands division as sharing or grouping Break the code to reveal the answers to the riddles 1 2 3 4 5 6 7 8 9 10 11 A C E I L N O R S T Y 1 When you have me you feel like sharing me But if you do share me you don t have me What am I 1 3 8 8 2 1 4 of 27 15 5 20 10 1 2 of 16 24 8 1 3 of 30 What word in the dictionary is spelled incorrectly of 16 18 3 1 5 of 10 35 5 32 4 16 2 30 10 1 4 of 8 15 2020 Adept Education Limited t a Reach Education 1 2 of 20 1 3 of 15 22 2 Frac2 24
Learning Intention 13 Able to find non unit fractions of shapes Divide the following shapes into equal parts by drawing lines straight across the shapes 1 Divide these shapes into halves 3 Divide these shapes into thirds 4 Divide these shapes into fifths 5 Divide these shapes into sixths 6 Divide these shapes into eighths 2 Divide these shapes into quarters 16 2020 Adept Education Limited t a Reach Education Frac2 25
Chelsea s Cheesecakes solvers 10 Learning Intention Able to find non unit fractions of shapes Chelsea s Cheesecakes sell six types of cheesecake Each cheesecake type is sliced into different fractions Show how the round cheesecakes are sliced by drawing straight lines Strawberry halves Blueberry thirds Caramel quarters Lemon fifths Chocolate sixths Raspberry eighths Using the key above answer the following questions 1 Which type of cheesecake has the largest slices 2 Which type of cheesecake has the smallest slices 3 Is 1 slice of strawberry cheesecake the same amount as 2 slices of the caramel cheesecake 4 Is 1 slice of the blueberry cheesecake the same amount as 2 slices of the chocolate cheesecake 17 2020 Adept Education Limited t a Reach Education Frac2 28
Chelsea s Cheesecakes solvers 11 Learning Intention Able to find non unit fractions of shapes Help Chelsea fill in her table to show what fractions of her cheesecakes her customers are buying Slice and colour the customer s cheesecakes Have they bought more than half a cheesecake Customer Description 1 Monica 2 slices of blueberry 2 Colleen 3 slices of raspberry 3 Philip 4 slices of lemon 4 Florence 1 slice of strawberry 5 Chester 3 slices of caramel 6 Jack 4 slices of chocolate Colleen Fraction More than half ______ Monica Florence Chester Philip 18 2020 Adept Education Limited t a Reach Education Jack Frac2 29
solvers 12 Learning Intention Able to find non unit fractions of numbers Carpenter Emiel has a lot of building materials squeezed into his van Help him work out his fractions so he knows what he has 1 Emiel has 8 nails 24 bolts and 16 screws What fraction of each does he have Nails Bolts Screws 3 What fraction of these bricks are Grey 6 6 Carpenter Emiel Building since a long time ago 6 Yellow Brown Hammers Screwdrivers Wrenches Saws 2 Pine is yellow Oak is brown and Indian Silver is grey What fraction of these wood piles is pine 4 Emiel has 4 hammers 18 screwdrivers 6 wrenches and 5 saws What fraction of each does he have 19 2020 Adept Education Limited t a Reach Education Frac2 34
Learning Intention Able to find non unit fractions of numbers Simon Jasper and Sally are being given some yummy choices by their grandmother Which of the three cousins made the best delicious decision 1 For the jelly beans Grandmother s choices are 1 12 2 1 2 of the bowl of 28 1 3 of the bowl of 36 2 3 of the bowl of 48 3 8 of the jar of 112 For the M Ms Grandmother s choices are 4 5 3 of the jar of 180 of the bowl of 35 2 10 of the bowl of 200 For the skittles Grandmother s choices are 2 14 of the jar of 280 1 4 of the jar of 120 20 2020 Adept Education Limited t a Reach Education Frac2 35
Learning Intention 15 Able to add and subtract fractions with the same denominator Here s another way of writing addition for fractions 5 9 3 9 is the same as Solve the fraction addition equations and crack the code 6 9 1 4 7 2 5 8 3 6 9 8 9 Write in the letter associated with your answer for each question 10 1 2 3 4 5 6 7 21 2020 Adept Education Limited t a Reach Education 8 9 Frac2 41
Learning Intention Able to recognise improper fractions Circle the correct answer 1 2 Which of the following fractions is NOT an improper fraction 7 Which of the following sums results in a proper fraction 4 2 4 3 3 3 4 2 3 6 What is the sum of 2 5 2 8 5 3 2 6 7 4 5 7 9 5 3 9 3 2 3 Which of the following is the 8 denominator of the fraction 9 3 8 5 5 4 4 8 9 5 4 10 5 9 8 Which of the following sums results in an improper fraction 5 4 5 5 2 8 6 2 5 6 9 What is the answer to 9 10 2 1 9 3 5 10 9 8 9 Which of the following fractions is NOT a proper fraction 1 6 5 8 3 3 5 6 10 5 10 What is the sum of 5 15 12 15 14 14 4 4 17 7 17 5 0 10 10 5 30 15 15 7 Which of the following is the 4 numerator of the fraction 11 What is the answer to 7 8 2 8 7 7 6 7 4 4 7 4 Which of the following fractions is an improper fraction 12 8 9 9 5 5 8 16 8 Which of the following fractions is a proper fraction 5 2 5 3 20 16 22 18 7 3 5 4 15 30 20 12 22 2020 Adept Education Limited t a Reach Education Frac2 45
Sheet Frac2 02 continued Sheet Frac2 01 1 Red Two of the red rods would be the same length of the dark blue rod 2 Purple Two of the purple rods would be the same length of the orange rod 3 Because the starting rods are different lengths 4 Brown Three of the brown rods would be the same length as the orange rod 5 Purple Three of the purple rods would be the same length as the light blue rod 6 Brown Four of the brown rods would be the same length as the green rod 7 2 Half of 4 is 2 8 9 One third of 9 is 3 9 2 One quarter of 8 is 2 10 2 One fifth of 10 is 2 11 5 One fifth of 5 is 1 12 6 One third of 6 is 2 Sheet Frac2 02 continued 2 4 OR 5 OR 6 Sheet Frac2 02 1 3 7 23 2020 Adept Education Limited t a Reach Education
Instructions Reaching competence Designed by Lucy Patston You will need 2x 1 10 numbered dice Five counters each Several sticky dots and a pen Players take it in turns to roll both dice and create a proper fraction a fraction less than 1 For example if 8 and 2 were rolled the fraction would be 28 Next the player writes the fraction on a dot sticker and places it on a counter Then the player chooses on which duck to place their fraction counter The aim of the game is to order counters from smallest tiny duckling to largest Mother Duck who must be 1 i e a double Use the fraction table to carefully consider how large your fraction is because once placed your counter cannot be moved The winner is the first player to have counters on all five ducks 1 1 One whole 1 1 2 1 2 1 3 1 4 1 3 1 4 1 1 5 5 1 1 1 6 6 6 1 1 1 7 7 7 1 1 1 1 8 8 8 8 1 1 1 1 9 9 9 9 1 1 1 1 1 10 10 10 10 10 1 3 1 4 1 5 1 7 1 9 1 4 1 5 1 5 1 1 1 6 6 6 1 1 1 7 7 7 1 1 1 1 8 8 8 8 1 1 1 1 9 9 9 9 1 1 1 1 1 10 10 10 10 10 2020 Adept Education Limited t a Reach Education
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Explore the mathematics curriculum with your child at your own pace with this guided interactive programme This booklet includes learning intentions 9 through to 16 of 22 for Fractions Level 2 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 Understands sizes of fractions in relation to the whole Able to order unit fractions early Able to find and using additive strategies Understands division as sharing or grouping Able to find non unit fractions of shapes Able to find non unit fractions of numbers Able to add and subtract fractions with the same denominator Able to recognise improper fractions Online and printed versions available at www reacheducation co nz 2020 Adept Education Limited t a Reach Education
