1. Progression In Calculations at Lyndhurst First School. Multiplication and Division Mathematical Calculations in School Today. The phases indicate progression in the development of children’s jottings to support their calculations. The phases do not represent any specific Year Group or National Curriculum level. Remember each child progresses at their own pace.

2. Phase 1 - Understanding Multiplication as repeated addition. Vocabulary/Language Lots of, groups of Double Repeated addition Once, twice, three times….. Explanation. Children need to experience physically counting repeated groups of the same size. This is best done in a ‘real-life’ context. Children could count out repeated groups of the same size using sweets, pencils, counters etc. 2 add 2 add 2 makes 6 2 + 2 + 2 = 6 3 lots of 2 makes 6

3. Phase 1 –Understanding Division as sharing. Vocabulary/Language Share, share equally, share between Halve How many each? Explanation Children need to experience sharing a set of objects equally between people or teddies, initially between 2. It is important that they realise that things must be shared equally. Share 10 sweets between 2 friends. One for you, one for me, one for you…. Until all shared out equally. Count both piles to ensure that they are equal.

4. Phase 1 –Understanding Division as grouping. Vocabulary/Language Share, share equally, share between Divide Halve How many each? Explanation Children need to experience dividing a set of objects by grouping them equally or repeatedly taking away groups of equal size. Share 10 sweets between 2 friends by repeatedly taking away groups of 2 and counting how many piles there are.

5. Phase 1 – Recognising Patterns in Numbers. Vocabulary/Language Count on in twos, fives, tens… Add, plus, more than, count on Digits, pattern Multiples of… Explanation Working with a hundred square helps develop a childs’ understanding of the number system. Looking at the patterns in numbers created by colouring in steps of the same size can help a child to learn and predict the times tables. 12345678910 11121314151617181920 21222324252627282930 31323334353637383940 41424344454647484950 51525354555657585960 61626364656667686970 71727374757677787980 81828384858687888990 919293949596979899100 By counting on in twos and colouring in the numbers it is clear to see the pattern created. This helps children to understand odd and even numbers and recognise what multiples of 2 end with. This activity can be done with any times table and allows children to see patterns in the times tables which may help them to learn them.

6. Phase 2 – Multiplication on a Number Line. Vocabulary/Language Lots of, groups of, times, multiplied by Repeated addition Explanation Blank number lines can be used to enable children to count in jumps of repeated sizes. Children are taught to draw their own blank number lines, enabling them to do calculations within any range of numbers, although initially they learn the 2, 5 and 10 times tables. 0 2 4 6 8 0 5 10 15 20 25 30 4 lots of 2 is 8 2 + 2 + 2 + 2 = 8 2 x 4 = 8 6 lots of 5 is 30 5 + 5 + 5 + 5 + 5 + 5 = 30 5 x 6 = 30 Multiplication can be understood as a series of additions on a number line. It is important to start at 0 and ensure that each jump is the same size.

7. Phase 2 – Division on a Number Line. Vocabulary/Language Share, share equally, share between Divide, division, grouping Explanation Blank number lines can be used to enable children to count back in jumps of repeated sizes. Children are taught to draw their own blank number lines, enabling them to do calculations within any range of numbers. Initially they need to work with ÷ 2, 5 and 10 with no remainders. Division can be understood as repeated subtraction on a number line. It is important to remember that the answer will be found by counting how many times the number was repeatedly subtracted until 0 was reached. 0 5 10 15 -5 -5 -5 15 ÷ 5 = 3 3 groups of 5 were subtracted from 15 to reach 0.

8. Phase 2 – Multiplication as an Array. Vocabulary/Language Lots of, groups of, times, multiplied by, multiplication, product Equals Array, grid, representation Explanation The arrangement of circles clearly represents the number sentence and can aid visual learners to understand multiplication. This can be developed to grids used as a visual model. 2 lots of 3 = 6 3 lots of 2 = 6 3 x 2 = 6 2 x 3 = 6

9. Phase 3 – Multiplication on a Grid. Vocabulary/Language Lots of, groups of, times, times by, multiplied by, multiplication, multiply, product Repeated addition Equals Explanation The grid method of multiplication is a development of the Array and allows more complex problems to be broken down into more manageable calculations. Children would be working on problems with TU x U, progressing to TU x TU. 210 35 30 5 7 7 x 35 7 x 30 = 210 7 x 5 = 35 245 60020 903 30 1 20 3 23 x 31 600 + 90 + 20 + 3 = 713

10. Phase 3 – Division with Remainders. Vocabulary/Language Share, share equally, share between Divide, division, grouping Remainder, R, left over Explanation When children understand division and are able to accurately solve TU ÷ U with no remainders, then they are ready to solve more complex problems that do involve remainders. Initially this would be with remainder 1, moving on to other remainders when they understand the concept. It is important to remember that the answer will be found by counting how many times the dividing number was repeatedly subtracted until it is impossible to subtract the same number again without going past 0. The left over amount is the remainder and cannot be greater than or equal to the dividing number. 0 1 6 11 16 21 -5 -5 21 ÷ 5 = 4 R1 4 groups of 5 were subtracted, with 1 left over.