1. LEARNING OBJECTIVE: TO UNDERSTAND DIVISION AS GROUPING (REPEATED SUBTRACTION)

2. SMK Language: groups, set, divide, division, divided by, (÷), remainder, inverse operation, multiplication, multiply, times by, counting on, counting back, (quotient, divisor, dividend) The inverse of division is multiplication i.e. 20÷5=4 and 5x4=20. Pupils can check their answers using inverse operation, however they would need secure knowledge of the multiplication facts to do this. Division is repeated subtraction until 0 i.e. 20÷5 is 20-(5-5-5-5) which gives (4 lots of 5) Division should be shown as both sharing and grouping (repeated subtraction) to consolidate pupils learning. When you divide a number by 2, you are also halving it. If a number ends in a 5 or a 0, it is divisible by 5. If a number ends in an even digit, it will be divisible by 2.

3. ESSENTIAL Use practical objects to show grouping. e.g. “How many groups of 2 marbles can I get from a set of 12 marbles?” 12÷2=6

4. WIDER Show grouping by repeated subtraction using a number line. This can be demonstrated using IWB whilst pupils use their own interactive number line:

5. For key stage 1, children should be able to count on and back in 2’s 5’s and 10’s. Explain to children that we are counting back in groups of 2, so we are using repeated subtraction each time until we get to 0.

6. EFFECTIVE RESOURCES. USE AN INTERACTIVE NUMBER LINE. DON’T USE A RULER AS A NUMBER LINE.

7. DEEPER Division and multiplication are inverse processes, so it is important that children see how they are linked. This can be shown practically and by using a number line. First the practical method: 12 ÷ 2 = 6 6 x 2 = 12

8. DEEPER This can be explained more fully using a number line: By using a number line to show repeated subtraction, we can also show how division is linked to multiplication: “How many groups of 2 are there? “There are 6 groups of 2 which we write as 6x2. So 12 ÷ 2 = 6 and 6 x 2 = 12

9. MISCONCEPTIONS & MISUNDERSTANDINGS. Children may struggle with the language of division; groups, sets etc. It is important that the language of grouping is used within the correct context.

10. WORD PROBLEMS It is important to show division as grouping (as well as by sharing), because children will experience word problems which use this mathematical language: E.g. 1. Jane has to sort 24 boxes into groups of 6. How many groups will she have in total? 2. Jane has to share 24 boxes between 6 people. How many boxes will each person receive?

11. USEFUL RESOURCES: For number lines etc. www.sparklebox.co.uk & www.mrspancake.comwww.sparklebox.co.uk To improve your pedagogical knowledge: Mathematics Explained for Primary Teachers. Derek Haylock and: Primary Mathematics. Teaching Theory and Practice. Claire Mooney et al. Your tutors – Laurence and Antony!

12. ANY QUESTIONS?