Content Knowledge Focus Fractions

Purpose: Mini workshop sessions (30 - 45 mins) based on a specific focus that you could lead after school as opt-in sessions

Split for your choice:• Stage 6 to 7• Stage 4 to 5

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 1 Stage 2-4 (AC) Stage 5 (EA)Unequal Sharing Equal Sharing Use of Addition and

known facts e.g. 4 + 4 + 4 = 12

Use your framework to explore fraction knowledge developed at

stages 4-5• Identifies symbols for halves, quarters, thirds

and fifths and tenths• Identifies symbols for improper fractions,

e.g. 5/4

• Order fractions with like denominators (and unit fractions)

• Know doubles and halves to 20

Key Idea 1

Task: Draw two pictures of one quarter

Key Idea 1: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.

Key Idea 2 :

(Moving to EA) Develop use of addition to solve fraction problems rather than equal sharing.

The Strategy Teaching Model

Using Number PropertiesUsing Imaging

Using Material

s

New Knowledge & Strategies

Existing Knowledge & Strategies

Using Materials

Find one quarter of this shape

Find one quarter of this shape

Find one quarter of this shape

Now find one quarter of 12(using equal sharing - Stage 4)

Now find one quarter of 12 Using halving and halving again

66

33

33

Now find one quarter of 12 using addition facts - Stage 5

?

??

?3

3

3

3

? + ? + ? + ? = 12

Find one quarter of 12 using imaging

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

3

33

3

Using Number Properties

Find one quarter of 40, 400, 4000

Recapping Key Idea 2 :

(Moving to EA) Develop use of addition to solve fraction problems rather than equal sharing.

Linking the use of regions and sets helps to do this.

Key Idea 3What fraction is shaded?

3 sevenths 3 out of 7 7/3 7 thirds

5 views of fractions

€

37

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”

12

23

35

The problem with “out of”

23 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

Fractional vocabulary

One half

One third

One quarter

Don’t know

Emphasise the ‘ths’ code

1 dog + 2 dogs = 3 dogs1 fifth + 2 fifths = 3 fifths1/5 + 2/5 =

3/5

3 fifths + ?/5 = 11 - ?/5 = 3/5

1 - ?/20 = 3/2017

Recapping Key Idea 3

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.

Play Which Mystery Letter Am I?

6 is one quarter of what number?

This is one quarter of a shape. What does the whole look like?

Key Idea 4

24

6 is one quarter of what number?

6

??

?6

6

6

6

6 + 6 + 6 + 6 = 24

Recapping Key Idea 4 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.

Key Idea 5

Which letter shows 5 halves as a number?

0 1 2 3

A B C D E F

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

1 521/2

5 halves

Using fraction number lines to consolidate understanding of denominator and numerator

Push over 1

0 1 half 2 halves 3 halves 4 halves

0 1/2 2/2

3/2 4/2

0 1/2 1 11/2 2

Using Fraction Circles

Which is bigger 3/4 or 9/8?

Three in a row (use two dice or numeral cards)A game to practice using improper fractions as numbers

0 1 2 3 4 5 6

e.g. Roll a 3 and a 5

Mark a cross on either 3 fifths or 5 thirds.

The winner is the first person to get three crosses in a row.

X X

Summary of Fractions Key Ideas(Stages 2 - 5 )

1. Use sets as well as shapes/regions from early on 2. Fraction Language - use words first and introduce symbols

carefully3. Fractions are a context for add/sub and mult/div strategies4. Go from Part-to-Whole as well as Whole-to-Part.5. Fractions are not always less than 1, push over 1 early to

consolidate meaning of fraction symbols.

How could you adapt known games to practice fraction knowledge?

• Identifies symbols for halves, quarters, thirds and fifths and tenths

• Identifies symbols for improper fractions, e.g. 5/4

• Order fractions with like denominators (and unit fractions)

• Know doubles and halves to 20

Fraction / Number Mat

Fraction Snakes and

Chances

FractionDominoes

FractionI have, Who

Has

FractionBingo

FractionMemory/ Happy

Families