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

PPT-EN-04 - © Crown copyright 2010 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

PPT-EN-04 - © Crown copyright 2010 Discussion point 1 Think of three different 'stories' that involve different interpretations of this division calculation. 12 ÷ 2 Slide 3

PPT-EN-04 - © Crown copyright 2010 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

PPT-EN-04 - © Crown copyright 2010 Discussion point 2 What 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

PPT-EN-04 - © Crown copyright 2010 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

PPT-EN-04 - © Crown copyright 2010 Discussion point 3 What images could you use to help secure a childs understanding of this calculation? 12 ÷ 2 Slide 7

PPT-EN-04 - © Crown copyright 2010 Models of division for 12 ÷ 2 Sharing between two or finding ½ Slide 8

PPT-EN-04 - © Crown copyright 2010 Models of division for 12 ÷ 2 Grouping into twos Counting forwards (or backwards) in twos Slide 9

PPT-EN-04 - © Crown copyright 2010 Models of division for 12 ÷ 2 Repeatedly subtracting 2 from 12 Deriving from knowledge of multiplication facts Slide – 2 = 10 6 – 2 = 4 10 – 2 = 8 4 – 2 = 2 8 – 2 = 6 2 – 2 = = 1212 ÷ 2 = = 1212 ÷ 6 = 2

PPT-EN-04 - © Crown copyright 2010 Models of division for 12 ÷ 2 Sharing or finding ½ Grouping How many in one column?How many rows are there? Slide 11

PPT-EN-04 - © Crown copyright 2010 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

PPT-EN-04 - © Crown copyright 2010 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

PPT-EN-04 - © Crown copyright 2010 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

PPT-EN-04 - © Crown copyright 2010 Discussion point 5 The 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 and the corresponding division facts Year 5: recall quickly multiplication facts up to and derive quickly corresponding division facts. How do you help children to recall these facts quickly? Slide 15

PPT-EN-04 - © Crown copyright 2010 Supporting the learning of division facts Using a number line Using a horizontal counting stick Slide 16

PPT-EN-04 - © Crown copyright 2010 Supporting the learning of division facts Using a vertical counting stick Slide 17

PPT-EN-04 - © Crown copyright 2010 Supporting the learning of division facts Using a number dial Slide 18 6

PPT-EN-04 - © Crown copyright 2010 Supporting the learning of division facts Using 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 ?56 ??27 93

PPT-EN-04 - © Crown copyright 2010 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

PPT-EN-04 - © Crown copyright 2010 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 Web: 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