Progression In Calculations.

Multiplication

Mathematical Calculations in East Worthing Schools.

This document has been discussed and agreed by all East Worthing Maths Leaders and is designed to help you to understand the calculation methods your child will be taught in school. When supporting your child at home with Maths work it would be helpful if you could reinforce these methods rather than teach them the way that you were taught. Your child’s teacher will be able to direct you to the appropriate method within this document to use at home.

Remember each child progresses at their own pace.

Understand Counting in Different Size Steps.

Children could count out repeated groups of the same size using sweets, pencils, counters etc. 3 lots of 2 makes 6

Begin to know doubles to double 5

Explore counting in steps of 2’s and 10’s. Do 10’s up to 100 and initially do 2’s up to 10 and then gradually develop being able to count in 2’s up to 20. Then introduce counting in 5’s up to 50.

This counting can be done in a range of contexts to make children familiar with the patterns in the numbers… count in 10’s as you go up the stairs…. Count in 2’s as you sort out the shoes/socks…. How many fingers are in the room? Count the hands of the people in the room in 5’s.. Etc.

Key Question/Vocabulary

Double, add, add on Once, twice, three times…..

How many groups are there?

How many items are in each group?

Explanation.

physically counting repeated is best done in a ‘real-life’

Success Criteria

• I can count out groups of equal sizes.

• I can talk about how many I have using the appropriate vocabulary.

Understand Multiplication as Repeated Addition.

Children could count out repeated groups of the same size as before, using sweets, pencils, counters etc. This time relate the vocabulary of addition to the vocabulary of multiplication.

Using Numicon to show 2 x 3 for eg, get out three 2 shapes and then use them to cover the 6 shape to show it is the same.

2 add 2 add 2 makes 6 2 + 2 + 2 = 6 3 lots of 2 makes 6 2 x 3 = 6 Continue counting in steps of 2’s, 5’s and 10’s regularly. Then ask your child questions such as ‘What is 2 x 6?’, helping them to understand that if they count 6 times in 2’s they will reach the answer.

Key Question/Vocabulary

Add, addition, repeated addition, Times, multiply, multiplied by, lots of How many groups are there?

How many items are in each group?

Explanation.

Children need to experience physically counting repeated This is best done in a ‘real life’ context, eg counting toys

Success Criteria

• I can count out groups of equal sizes and understand that if I add them I reach the same total as if I had counted in steps the size of the groups.

Recognising Patterns in Numbers.

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. (Eg, recognising that multiples of 10 end in 0, that multiples of 5 end in 0 or 5 etc) 51 61 71 81 1 11 21 31 41 91 52 62 72 82 2 12 22 32 42 92 53 63 73 83 3 13 23 33 43 93 54 64 74 84 4 14 24 34 44 94 55 65 75 85 5 15 25 35 45 95 56 66 76 86 6 16 26 36 46 96 57 67 77 87 7 17 27 37 47 97 58 68 78 88 8 18 28 38 48 98 59 69 79 89 9 19 29 39 49 99 60 70 80 90 10 20 30 40 50 100

Key Questions/Vocabulary

Count on in twos, fives, tens… Add, plus, more than, count on Digits, pattern Multiples of… Explanation Working with a hundred square helps number system. Looking at the patterns in numbers created by can help a child to learn and predict the times tables.

Success Criteria

• I can recognise and discuss patterns in numbers.

Multiplication on a Number Line.

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. 4 lots of 2 is 8 2 + 2 + 2 + 2 = 8 2 x 4 = 8 (read as ‘2 four times’) Encourage children to look at multiplications as ‘What have I got and how many times have I got it?’ So the first number relates to what you have and the second number indicates how many times you have it (5 x 4 would be you’ve got 5 four times) 6 lots of 5 is 30 5 + 5 + 5 + 5 + 5 + 5 = 30 5 x 6 = 30 (read as ‘5 six times’) 0 2 4 6 8 0 5 10 15 20 25 30

Key Questions/Vocabulary

Lots of, groups of, times, multiplied by Repeated addition Eg 2 x 4... What have you got? (2) How many times have you got it? (4) Explanation Blank number lines can be used to enable children to count in jumps of repeated sizes. their own blank number lines, calculations within any range of numbers, although initially times tables.

Know doubles up to double 10 and corresponding halves. Know facts for 2, 5 and10 times tables.

Success Criteria

• I can understand multiplication and represent it as jumps on a number line.

Look for arrays in the environment. ... Egg boxes, window panes, some trays of apples or chocolates.

An array can be made up of any shape or item. Try creating arrays using sweets or other items.

Multiplication as an Array.

2 three times = 6 3 two times = 6 2 + 2 + 2 = 6 3 + 3 = 6 2 x 3 = 6 3 x 2 = 6 e.g.

or

Key Questions/Vocabulary

Lots of, groups of, times, multiplied by, multiplication, Equals, commutative Array, grid, representation What have you got?

How many times have you got it?

Explanation The arrangement of images clearly represents the number sentence and can aid visual learners to understand multiplication. Children need to understand at this stage that multiplication is COMMUTATIVE, that is that 2 x 3 will be the same as 3 x 2.

or

Know by heart the 2, 5 and 10 times tables.

Success Criteria

• I can identify an array and the multiplication that it represents.

• I can draw an array to represent a given multiplication.

Multiplication on a Grid.

15 x 7=? To begin, partition the 15 into 10 and 5. 10 5 7

70 35

Know the 2, 3, 4, 5 and 10 times tables. Begin to know the 8 times tables.

10 x 7 = 70 70 + 35 = 105 5 x 7 = 35 So 15 x 7 = 105

Key Questions/Vocabulary

Lots of, groups of, times, times by, multiplied by, multiplication, multiply, 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 need to be able to partition numbers into tens and units as they would be working on problems with TU x U, then progressing to TU x TU. You can see the arrays leading to the grid method on the right.

Success Criteria

• I can solve a harder multiplication by breaking it down using the grid method.

Short Multiplication / Multiplication on a Grid.

Know all your times tables Key Questions/Vocabulary

Lots of, groups of, times, times by, multiplied by, multiplication, multiply, Repeated addition Equals Explanation Short multiplication refers to a 2-digit, 3 digit, 4-digit or larger number x by a 1 digit number. Always work from the right of the top number.

Once the children are confident with these calculations they can move onto 2-digit x 2 digit and larger calculations reverting back to grid method as necessary before long multiplication.

3 20 31 x 23 30 1

600 20 90 3

30 x 20 = 600 30 x 3 = 90 1 x 20 = 20 1 x 3 = 3

713

So 31 x 23 = 713

Success Criteria

•I can use short multiplication to calculate •I can solve a harder multiplication by breaking it down using the grid method.

Long Multiplication

Know all your times tables Key Questions/Vocabulary

Lots of, groups of, times, times by, multiplied by, multiplication, multiply, Repeated addition Equals Explanation Long multiplication refers to a 2-digit, 3 digit, 4-digit or larger number x by a 2 digit number. Always work from the right of the top number.

The children once secure in these methods should also look at decimal multiplication using u.th x u (see additional example)

Success Criteria

•I can use long multiplication to calculate