Body Fractions Game Arm Span = 1 One arm = half What is a quarter? Make one half, three quarters, one, etc With a partner three halves In a group of four…

Dotty Pairs Game You need two sets of cards 1-6 The children play in pairs. One child takes dots, the other takes crosses. The players take turns turning over two cards. The numbers are used to form a fraction e.g 2 and 5 are turned over - could make two fifths or five halves. One fraction is chosen and marked on a 0-6 number line with the players identifying mark. Winner is the person who can get three uninterrupted marks on the number line. If a fraction is already marked on the number line the player misses that turn

Dotty Pairs Game What stage do you think the game appears at? What knowledge do the children need to successfully play the game? Why is it important? What understandings does it develop? Advanced Counting - Early Additive Book 7 page 22

Book 7 Teaching Fractions, Decimals and Percentages Contains Key Ideas for fractions, decimals and percentages - page 2&3 An introduction to Rational Numbers and Proportional Reasoning Key Mathematical Ideas and Diagnostic Snapshots for each stage. Spend some time becoming familiar with these ideas before working with your class on Fractions, Decimals and Percentages.

Assess Your Fraction Strategies and Fraction Knowledge

Fraction Snapshots Here are 12 jelly beans to spread on the cake. If you ate one third of the cake how many jelly beans will you eat? Stage 1Stage 2-4 (AC)Stage 5 (EA) Unequal SharingEqual SharingUse of Addition and known facts e.g = 12

Fraction Snapshots (cont’d) What is 3 / 4 of 80? Stage 6 (AA) Using multiplication 16 is four ninths of what number? Stage 7 (AM) Using division To make 8 aprons it takes 6 metres of cloth. How many metres would you need to make 20 aprons? Stage 8 (AP)

What misconceptions may young children have when beginning fractions? Misconceptions about finding one half when beginning fractions: Share without any attention to equality Share appropriate to their perception of size, age etc. Measure once halved but ignore any remainder So what do we need to teach to move to equal sharing? Introduce the vocabulary of equal / fair shares with both regions and sets for halves and then quarters.

Draw two pictures of one quarter

Discrete and continuous models One Quarter: Continuous Discrete (regions/lengths) (sets) Label your drawings as discrete or continuous models. Children need experience with both models from the very start.

Key Idea 1 Work with both shapes and sets of fractions from early on.

Linking regions/shapes and sets Find one quarter

The Strategy Teaching Model Using Number Properties Using Imaging Using Material s New Knowledge & Strategies Existing Knowledge & Strategies Using Materials

Using Materials - fraction regions Find one quarter

Using Materials - fraction regions Find one quarter of 12

The Strategy Teaching Model Using Number Properties Using Imaging Using Material s New Knowledge & Strategies Existing Knowledge & Strategies Using Materials

Using Imaging Find one quarter of 12 Key idea: quarters means you need 4 equal groups. One quarter is the number in one of those groups.

The Strategy Teaching Model Using Number Properties Using Imaging Using Material s New Knowledge & Strategies Existing Knowledge & Strategies Using Materials

Using Number Properties Find one quarter of 40, 400, 4000

Develop early additive thinking by using addition facts Find one quarter of 12 ? ?? ?

Using Materials - cubes Four birds found a worm in the ground 20 smarties long. What proportion of the worm do they each get? How many smarties will each bird get?

Key Idea 2 3 sevenths 3 out of 7 7/3 7 thirds

5 views of fractions 3 over 73 : 7 3 out of 7 3 ÷ 7 3 sevenths

+ = “I ate 1 out of the 2 sandwiches in my lunchbox, Kate ate 2 out of the 3 sandwiches in her lunchbox, so together we ate 3 out of the 5 sandwiches” The problem with “out of” 2323 x 24 = 2 out of 3 multiplied by 24 !!!!!

Fraction Language Use words before and use symbols with care. e.g. ‘one fifth’ not 1 / 5 How do you explain the top and bottom numbers? 1 2 The number of parts chosen The number of parts the whole has been divided into Let the fraction do the talking!

Fractional vocabulary One half One third One quarter Don’t know

Emphasise the ‘ths’ code 1 dog + 2 dogs = 3 dogs 1 fifth + 2 fifths = 3 fifths 1 / / 5 = 3 / 5 3 fifths + ? / 5 = ? / 5 = 3 / ? / 20 = 3 / 20 17

Key Idea 2 Fraction language is confusing. Emphasise the ‘ths’ code. Use words before symbols. Introduce symbols with care. The bottom number tells how many parts the whole has been split into,the top number tells how many of those parts have been chosen.

6 is one third of what number? This is one quarter of a shape. What does the whole look like? Key Idea 3

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Key Idea 3 Go from part-to-whole as well as whole-to-part with both shapes and sets. Children need experience in both reconstructing the whole as well as dividing a whole.

Perception check on two key ideas Where in the table does this question fit? Hemi got two thirds of the lollies. How many were there altogether? Part-to-WholeWhole-to-Part Continuous (region or length) Discrete (sets)

Write 3 more questions to fit the other parts of the table. ModelPart - to - WholeWhole - to - Part Continuous (Region or length) Discrete (sets) Hemi got two thirds of the lollies. How many were there altogether?

Extending the idea of going from part-to-whole with non-unit fractions Hemi got three fifths of the lollies and got 12. How many lollies were there altogether? i.e. 12 is three fifths of what number? Draw a diagram/use equipment to help your thinking.

12 is three fifths of what number?

5 children share three chocolate bars evenly. How much chocolate does each child receive? Discuss in groups what you think children would do and then how you would solve this problem. 3 ÷ 5 Key Idea 4

Division 3 ÷ 5 1 / / / 5 = 3 / 5

Key Idea 4 Division is the most common context for fractions when units of one are not accurate enough for measuring and sharing problems. e.g. 5 ÷ 3

Which letter shows 5 halves as a number? 0123 ABCDEF

Key Idea 5 Fractions are not always less than 1. Push over 1 early to consolidate the understanding of the top and bottom numbers /221/2 5 halves

Using fraction number lines to consolidate understanding of denominator and numerator Push over half 2 halves 3 halves 4 halves 0 1 / 2 2 / 2 3 / 2 4 / / / 2 2

1 / 2 is a number between 0 and 1 (number) Find one half of 12 (operator) Key Idea 6 Fractions are numbers as well as operators

Using Double Number Lines Put a peg on where you think 3 / 5 will be. (Fractions as a number). How will you work it out? Use a bead string and double number line to find 3 / 5 of 100. (Fractions as an operator). How will you work it out?

Key Idea 7 Sam had one half of a cake, Julie had one quarter of a cake, so Sam had most. True or False or Maybe

Key Idea 7 Fractions are always relative to the whole. Halves are not always bigger than quarters, it depends on what the whole is.

What is the whole? AA BBBB C DDDDDDDD

Key Idea 8 - Ratios! Write 1 / 2 as a ratio 3: 4 is the ratio of red to blue beans. What fraction of the beans are red? Think of some real life contexts when ratios are used. 1:1 3/73/7

Key Idea 8 There is a link between ratios and fractions. Ratios describe a part-to-part relationship e.g. 2 parts blue paint : 3 parts red paint But fractions compare the relationships of parts with the whole, e.g. The paint mixture above is 2 / 5 blue

Summary of Fractions Key Ideas (Stages 2 - 6) 1.Use sets as well as shapes/regions from early on 2.Fraction Language - use words first and introduce symbols carefully 3.Go from Part-to-Whole as well as Whole-to-Part 4.Division is the most common context for fractions. 5.Fractions are not always less than 1, push over 1 early. 6.Fractions are numbers as well as operators. 7.Fractions are always relative to the whole. 8.Be careful of the relationship between ratios and fractions 9.Fractions are a context for add/sub and mult/div strategies

Resources FIO Proportions and Ratios Digital Learning Objects Fraction Walls Paper and Shapes ARBs Book 7 Lead Teacher Wikispace