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National Curriculum - Knowing and using number facts : Key Stage 2 : Mathematics Content Knowledge


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Key Stage 2
National Curriculum - Knowing and using number facts
Question 1 of 11

1. 1. How confident are you that you can

a. a. derive and remember multiplication facts up to 12 × 12 and the corresponding division facts using the patterns and relationships within and between multiplication tables?


Example

Fluency with multiplication facts builds on an understanding of multiplication as repeated addition. This might develop through activities such as:

  • counting on and back along the number line in steps of constant size
  • counting on and back around a clock face in steps of 5.

Multiplication tables can be connected to each other. For example, children can reason that:

  • three times a number is half of six times a number;
  • four times a number is double twice the number, e.g. since 6 × 2 = 12, it follows that 6 × 4 = 24.

Children should know the commutative principle a × b = b × a. Realising that the number of multiplication facts to be remembered is halved aids fluency. Division does not have this property.

Children can reason with trios of numbers such as 63, 9 and 7: multiplication and division facts can be learned by applying inverse operations and developing families; for example,

9 × 7 = 63       7 × 9 = 63       63 ÷ 7 = 9       63 ÷ 9 = 7

If one fact is known, the other three can quickly be derived.

Children may also be helped by exploring patterns of multiples, e.g. on a multiplication square. This square shows multiples of four.

 Multiplication square

They can also explore the patterns formed by last digits, e.g. when repeatedly adding 4.

Sign of Four

Write a multiplication in the middle of the board. Invite children to discuss how they would work out the result, and record their different methods.

For example:

What this might look like in the classroom

Problem 1:
If
3 × 8 = 24
write down at many multiplication and division facts that you can work out that are connected to this one.

Possible solutions:
24 ÷ 3 = 8
24 ÷ 8 = 3
6 × 8 = 48
48 ÷ 6 = 8
48 ÷ 8 = 6
3 × 4 = 12
12 ÷ 3 = 4
12 ÷ 4 = 3
 

Ask the children to discuss how they arrived at their answers. Further class discussion may lead to connections such as 30 × 8 = 240. Ask the children to reason why:

3 × 8 = 24 leads to 6 × 8 = 48
and
12 ÷ 3 = 4 leads to 24 ÷ 3 = 8
but
24 ÷ 3 = 8 does not mean 24 ÷ 6 = 16.

Taking this mathematics further

Children can use these skills to solve problems involving fraction and percentage calculations e.g.

 

12  of 12 = 6
 

14  of 12 = 3
 

12 + 14  = 34

so 34 of 12 = 6 + 3 = 9

34 + 12 = 114

 so 114 of 12 = 9 + 6 = 15

12 of a 14 = 18

 so 18 of 12 = 32 = 112 or 1.5


100% is equivalent to £240
50% = £120
25% = £60
10% = £24
1% = £2.40
11% = £25.40

In addition to whole numbers, fractions and percentages you could use the same idea for minutes in an hour linking to fractions.

Begin with open ended question such as ‘I know that 14 of an hour is 15 minutes. What else do I know?’

 

Making connections

Children need to be fluent with times tables facts. They begin this skill when they start counting in steps of 10 and then five. They then learn to count in twos and build up the knowledge that for example 10 × 2 = 20. This progresses to the point where they should be able to recall the table facts to 12 × 12. The progression shows that they practise counting in steps of a multiple and then begin to learn the associated times−table facts.

Once the children are confident counting forwards and backwards in steps of different sizes from zero to the twelfth multiple and are beginning to remember the associated times−table facts, practise doing this along a counting stick. Move your finger backwards and forwards randomly e.g. 7, 14, 35, 63, 35, 42 and see how the children keep up. Ask for numbers between the different multiples e.g.10.5 is half way between seven and 14. When they are confident repeat this idea for multiples of ten or tenths of that number e.g. 70, 140, 210 etc., 700, 1400, 2100 etc., 0.7, 1.4, 2.1 etc. To do this they are using their knowledge of the times table to generate other facts.

When multiplying they will use this skill to help them to work out calculations such as 374 x 6

Example of thought processes:

300 × 6 = 3 × 6 × 100 = 18 × 100 = 1800

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