1. Primary National Strategy Mathematics 3 plus 2 day course: Session 4

2. © Crown copyright 2003 Primary National Strategy Slide 4.1 Objectives To discuss the approach to teaching short division To consider the tasks for Day 2 of the course (a self-study day)

3. To divide 81 by 3 Slide 4.2 81 ÷ 3= (60 + 21) ÷ 3 = (60 ÷ 3) + (21 ÷ 3) = 20 + 7 = 27

4. To divide 672 by 4: ‘hundreds’ stage Slide 4.3 672 ÷ 4= (400 + 272) ÷ 4 = (400 ÷ 4) + (272 ÷ 4) = 100 + (272 ÷ 4)

5. To divide 672 by 4: ‘tens’ stage Slide 4.4 272 ÷ 4= (240 + 32) ÷ 4 = (240 ÷ 4) + (32 ÷ 4) = 60 + (32 ÷ 4)

6. To divide 672 by 4: ‘units’ or ‘ones’ stage Slide 4.5 272 ÷ 4= (240 + 32) ÷ 4 = (240 ÷ 4) + (32 ÷ 4) = 60 + (32 ÷ 4) 32 ÷ 4= 8

7. Types of short division calculations Slide 4.6 no exchange, no remainder 4 ) 848 no exchange, with remainder 3 ) 635 with exchange, no remainder 7 ) 994 with exchange, with remainder 3 ) 470 empty place at start of quotient 7 ) 287 noughts in the quotient 4 ) 8168 ) 5608 decimal dividend 5 ) 61.53 ) 4.26

8. © Crown copyright 2003 Primary National Strategy Slide 4.7 Day 2: a self-study day Following up Day 1 on division Putting ideas into practice Preparing for Day 3 on problem solving Allow about 4 hours 15 minutes plus some normal teaching time with your own class.

9. © Crown copyright 2003 Primary National Strategy Slide 4.8 Following up the day on division Read, reflect on and annotate the article Divide and rule 2, a follow-up paper on division. Allow about 1 hour 15 minutes for this task. Check the summary. Does this pick out the key points arising from your annotations and from your reflections on the first day of your course? Think through the self-assessment tasks. Refer back to the article to check your responses. Consider whether you need to adjust your teaching plans in any way as a result of Day 1 and your reading. If so, make notes on what needs to be done.

10. © Crown copyright 2003 Primary National Strategy Slide 4.9 Putting ideas into practice Prepare and teach two lessons on division – one to your own class and one to a colleague’s class (preferably a different age group). Allow about 2 hours plus some normal teaching time with your own class for this task. Choose the lessons from those in Participant’s pack 2. Adapt them as necessary to suit the pupils that you will teach. After each lesson, complete the evaluation form provided in the pack. Be prepared to discuss the lessons on Day 3 of the course.

11. © Crown copyright 2003 Primary National Strategy Slide 4.10 Preparing for Day 3 on problem solving Read the article Some strategies for solving problems and consider the summary of key points at the end. Pick a problem from the paper Problems to solve, suitable for the pupils in your class. Give it to the pupils to tackle as part of a normal lesson. Identify one solution based on a systematic approach, and one where it is not. Bring the two examples with you to Day 3 of the course. Allow about 1 hour plus about 30 minutes normal teaching time with your own class for this task.

12. © Crown copyright 2003 Primary National Strategy Slide 4.11 Six lessons on division Doubling and halving Multiplication and division facts and TU  U Multiplication and division as inverse operations HTU ÷ U (whole-number answers) Expressing a quotient as a fraction or decimal Tests of divisibility

13. © Crown copyright 2003 Primary National Strategy Slide 4.12 Links are to these autumn term units: Year 4 Unit 9 (Multiplication and division) Year 5 Unit 2 (Multiplication and division 1) Year 5 Unit 3 (Multiplication and division 2) Year 6 Unit 2 (Multiplication and division, mental methods) Year 6 Unit 3 (Multiplication and division, written methods)

14. © Crown copyright 2003 Primary National Strategy Slide 4.13 TASK: Six lessons on division Browse through the six lessons. Consider which you might choose to teach. Make some preliminary decisions about the possible modifications that you might make to suit your particular pupils.

15. © Crown copyright 2003 Primary National Strategy Slide 4.14 QCA’s advice on division Put more emphasis on: 1997developing informal methods towards greater efficiency 1998representing remainders as fractional or decimal parts division as the inverse of multiplication 1999developing standard written methods ‘missing number’ problems, e.g. 527 ÷  = 31 2000developing informal methods into formal approaches and recognising that standard methods are more efficient

16. © Crown copyright 2003 Primary National Strategy Slide 4.15 QCA’s advice on division Put more emphasis on: 2001dividing by 10 developing more compact written methods solving ‘missing number’ problems working with ratios simple proportional reasoning 2002using inverse operations rather than trial and improvement in ‘missing number’ and ‘what is my number?’ problems solving problems involving proportion, e.g. finding the cost of 10 cakes given the cost of 6 cakes, dividing a line in a given ratio