00467-2010PPT-EN-04 - © Crown copyright 2010 Slide 1 Primary mathematics: support for subject knowledge Unit 1: Teaching division in Years 1, 2 and 3.

00467-2010PPT-EN-04 - © Crown copyright 2010

Slide 1

Primary mathematics: support for subject knowledge Unit 1: Teaching division in Years 1, 2 and 3


In this unit you will: consider how to secure children's understanding of division review the use of models, images and language in the teaching of

division review progression in division up to the end

of Year 3 consider how children can be helped to learn division facts.

Slide 2


Discussion point 1Think of three different 'stories' that involve different interpretations of this division calculation.

12 ÷ 2

Slide 3


Possible interpretations of 12 ÷ 2 Equal sharing of 12 between 2, for example ‘Share 12 sweets

equally between two children.’ Finding one-half of 12, for example ‘Joe spends half of £12.

How much does he spend?’ Grouping 12 into twos, for example, ‘How many 2p coins

make 12p?’

Grouping includes:

- counting forwards in twos from 0 to 12,or repeatedly adding twos to reach 12

- counting back in twos from 12 to 0, or repeatedly subtracting 2 from 12.

Slide 4


Discussion point 2What different ways are there to read this calculation?

12 ÷ 2 12 divided by 2 12 divided into 2 equal parts 12 shared equally between 2.

It is sometimes helpful to interpret '12 divided by 2’ as 'How many twos make 12?'

Slide 5


The language of division The use of ‘divided by’ teaches children that, as with

addition, subtraction and multiplication:– the structure and language of calculation follow a

consistent pattern– the structure and language have an associated image

that supports the method of calculation.

Slide 6


Discussion point 3

What images could you use to help secure a child’s understanding of this calculation?

12 ÷ 2

Slide 7


Models of division for 12 ÷ 2

Sharing between two or finding ½

Slide 8



Grouping into twos

Counting forwards (or backwards) in twos

Slide 9

0 8 1242 6 10



Repeatedly subtracting 2 from 12

Deriving from knowledge of multiplication facts

Slide 10

12 – 2 = 10 6 – 2 = 4 10 – 2 = 8 4 – 2 = 2

8 – 2 = 6 2 – 2 = 0

6 2 = 12 12 ÷ 2 = 6

2 6 = 12 12 ÷ 6 = 2



Sharing or finding ½ Grouping

How many in one column? How many rows are there?

Slide 11


Sharing secures understanding of halving and one-to-one

correspondence between objects

requires little knowledge or skill beyond counting

as the divisor increases:

– becomes difficult to visualise

– becomes inefficient, for example try sharing 63 between 9, counting out one for you, one for you)

provides no image to support later understanding of how to represent a remainder as a fraction of the divisor.

Slide 12


Grouping secures understanding that the divisor is important in the calculation

links to counting in equal steps on a number line

requires sound knowledge of addition and subtraction facts

provides an image to support understanding of what to do with remainders

is more efficient as the divisor increases

provides a firmer basis on which to build children's understanding of division.

Slide 13


Discussion point 5 In your school, in which year groups do children learn to derive and

recall multiplication facts quickly? In which year groups do children learn to derive the division facts for

a given times table so that they can recall them nearly as quickly as they can recall multiplication facts?

Slide 14


Discussion point 5The expectations in the Primary Framework for mathematics are:

Year 2: derive and recall multiplication facts for the 2, 5 and 10 times tables and the related division facts

Year 3: derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10 times tables and the corresponding division facts

Year 4: derive and recall multiplication facts up to 10 10 and the corresponding division facts

Year 5: recall quickly multiplication facts up to 10 10 and derive quickly corresponding division facts.

How do you help children to recall these facts quickly?

Slide 15


Supporting the learning of division factsUsing a number line

Using a horizontal counting stick

Slide 16

0 1 2 3 4 5 6 7 8 9 10

0 6 12 18 24 30 36 42 48 54 60

0 6 12 18 24 30 36 42 48 54 60

0 1 2 3 4 5 6 7 8 9 10


Supporting the learning of division factsUsing a verticalcounting stick

Slide 17

0 ÷ 6 = 0

6 ÷ 6 = 1

12 ÷ 6 = 2

18 ÷ 6 = 3

24 ÷ 6 = 4

30 ÷ 6 = 5

36 ÷ 6 = 6

42 ÷ 6 = 7

48 ÷ 6 = 8

54 ÷ 6 = 9

60 ÷ 6 = 10

0 0

6 1

12 2

18 3

24 4

30 5

36 6

42 7

48 8

54 9

60 10


Supporting the learning of division factsUsing a number dial

Slide 18

10 %10 %10 %

10 %

10 %

10 %

10 %

10 %10 %10 %

1

2

3

45

6

7

8

910

6

12

18

2430

36

42

48

5460

÷ 66


Supporting the learning of division factsUsing ‘tables trios’

I am thinking of a tables trio.Two of the numbers are 48 and 6.What is the third number?

One of the numbers is 56. What could the other two numbers be?

What are the four facts associated with this trio?

Slide 19

48

6 ? 56

? ? 27

9 3


Discussion point 6 Apart from learning division facts, what other knowledge and

understanding of division are children expected to have by the end of Year 2?

What is the expected progression across Year 3?

Slide 20


Crown copyright• The content of this publication may be reproduced for non-commercial research, education or training purposes

provided that the material is acknowledged as Crown copyright, the publication title is specified, it is reproduced accurately and not used in a misleading context.

• For any other use of this material please apply to OPSI for a Click-Use, PSI Licence, or by writing to:

Office of Public Sector Information

Information Policy Team

National Archives

Kew

Richmond

Surrey

TW9 4DU

Email: [email protected]

Web: www.opsi.gov.uk/click-use/index.htm

• The permission to reproduce Crown copyright protected material does not extend to any material in this publication which is identified as being the copyright of a third party, or to Royal Arms and other departmental or agency logos, nor does it include the right to copy any photographic or moving images of children or adults in a way that removes the image or footage from its original context.

Slide 21

00467-2010PPT-EN-04 - © Crown copyright 2010 Slide 1 Primary mathematics: support for subject knowledge Unit 1: Teaching division in Years 1, 2 and 3.

Documents

crown copyright

learning of division

division calculation

number dial slide

models of division

language of division

related division facts

vertical counting stick