PRIMARY ADVANTAGE

MATHEMATICS PROGRAMME

A MODEL OF BEST PRACTICEKS1 Parents Workshop –

Mathematics

Elizabeth Winterton, Jane Woolley and Catherine Thomas

The Fundamentals – Year 1

The Fundamentals – Year 2

Experience and the National Curriculum

What does this mean for how we

teach?

Procedural Fluency

Conceptual Understanding

Primary Advantage

Maths Programme

Key Concepts - CPA

The concrete-pictorial-abstract approach, based on research by psychologist Jerome Bruner, suggests that there are three steps (or representations) necessary for pupils to develop understanding of a concept.

Reinforcement is achieved by going back and forth between these representations.

Concrete Pictorial Abstract

3 + 4 = 7

Addition – Mental Methods

5 + 31 32 + 8 60 + 60

32 + 19 15 + 16 27 + 36 + 13Did you:•Count on from the largest number?•Re-order the numbers?•Partition the numbers into tens and ones?•Bridge through 10 and multiples of 10?•Add 9, 11, etc. by adding a multiple of 10 and compensating?•Use near doubles?•Use knowledge of number facts?These are all strategies that children need to be aware of when carrying out addition calculations.

Models for Addition

Combining two sets of objects (aggregation)

Tom had two sweets and John had three sweets: how many did they have altogether?

Adding onto a set (augmentation)

Tom had two sweets and bought two more. How

many sweets does he have now?

Counting on with a bead bar/number line

12 5 0

+ 7

10 +2+5

Counting on with straws

+ =

Models for Addition

25 + 47

Models for addition

25 + 47

Models for Addition

25 + 47

Models for Addition

Use the deines to complete these sums: 1.17 + 14

1.22 + 19

2.16 + 16

1.172 + 50

Your turn:

Remember to use the terms regroup and rename.

T O

Expanded MethodModels for Addition

20 + 510 + 4 +30 + 9

20 + 710 + 5 +40 + 210

regrouped and renamed

Subtraction – Mental Methods

95 - 86 32 - 8 60 - 30

30 - 14 25 - 9 27 - 18Did you:•Count up from the smallest number?•Round the numbers?•Partition the numbers into tens and ones?•Adjust the place value?•Subtract 9, 11, etc. by subtracting a multiple of 10 and compensating?•Use near halves?•Use knowledge of number facts?These are all strategies that children need to be aware of when carrying out subtraction calculations.

12

Removing items from a set (reduction or take-away)

- 1- 2- 3- 4- 5 = 7

Comparing two sets (comparison or difference)

Seeing one set as partitioned

Seeing 12 as made up of 5

and 7

Models for Subtraction

Counting back on a number line

Finding the difference on a number line

12 0

- 5

7

12 0 5

7

5 2 10

10-2-3

- 5 =

Models for Subtraction

72 - 47

Models for Subtraction

72 - 47

Models for Subtraction

72 - 47

This is now “Sixty-twelve”

7 126

Models for Subtraction

72 - 47

Models for Subtraction

72 - 47

Models for Subtraction

72 - 47 = 25

Models for Subtraction

Use the deines to complete these sums: 1.17 - 14

1.22 - 9

2.32 - 16

1.172 - 61

Your turn:

T O

32 – 16

1 6

Remember to use the terms regroup and rename.

= 16

Expanded MethodModels for Subtraction

20 + 510 + 4 -10 + 1 20 + 3

10 + 5 -+

30

10

10

8

Bead Bar

Number Line

Fingers“6” “9” “12”“3”

0 3 6 9 12

Lots of the ‘same thing’

Models for Multiplication

3 44 3

Models for Multiplication

Four groups of 3 Three groups of 4

x x

Multiplication is commutative

How can it be represented?

12 ÷ 3

41 2

The power of the place value counters for larger numbers

Models for Division

11

11

11

11

11

11

11

11

11

11

11

11

3

11

1111

11

11

11

11

11

1111

1111

The Facts

• Number bonds within 10

• Number bonds to 10

• Number bonds to 20

• Doubles and halves to 20

• Two times tables

• Five times tables

• Ten times tables

1. Look, cover, write and check

1. I say, you say

1. Five minutes whenever you get the chance

Have a go…

www.discoveryeducation.co.uk

Username: student20561

Password: trinity