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National Curriculum - Number: addition, subtraction, multiplication and division : Key Stage 1 : Mathematics Content Knowledge


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Key Stage 1
National Curriculum - Number: addition, subtraction, multiplication and division
Question 1 of 17

1. 1. How confident are you that you can:

a. a. use a number line to model and record addition and subtraction calculations: such as 7 + 3 = 10, and 20 – 4 = 16


Example

A number line can help pupils to record their steps forwards and backwards when trying to find the result of different addition and subtractions questions. If pupils are using the number line with smaller numbers they are more likely to show their calculations with single steps:

7 + 3 = 10

number line

Or 20 – 6 = 14

number line

When pupils are familiar with number lines they may also use them to record their thinking when doing more difficult calculations, with larger numbers.

An empty number line helps to record the steps to calculating a total. Here are two possible ways to do 48 + 36. There are others.

48 + 36 = 84

number line

or:

number line

Pupils are most likely to use different approaches when doing larger subtraction questions:

For example 83 – 25 could be calculated as
83 – 3 – 20 – 2

number line

Additional User Example

Children will have different ways of counting up, so it is important for them to put their own ideas forward about how they will be counting up. It is also important to that children know that addition questions can be done forwards or backwards.

Here are some more examples of doing this same question:

48 + 36
is the same as 36 + 48
so we can do 36 + 4 to make 40
Then 40 + 40 to make 80
Then 80 + 4 to make 84

or
48 + 36 is the same as 36 + 48
so we can do 36 + 24 to make 60 and then
60 + 24 to make 84.

It is sometimes better to start with the bigger number.

Some children will confidently be using the skill of doubling and halving numbers.

It is a good idea for children to look at the numbers and see how they fit together before deciding on an approach.

What this might look like in the classroom

Question 1:

Use a number line.

Choose a starting number (for example 3) and a number to repeatedly add on to the previous number (for example + 4). What results do you get?

Answer 1:

number line

Question 2:

Use a number line

Choose a starting number (for example 63 and a number to repeatedly subtract from the previous number (for example – 7). What results do you get?

Answer 2:

number line

Taking this mathematics further

Question 3:

Use the same process in questions 1 and 2 to explore additions and subtractions with larger numbers. For example start at 89 and subtract 22.

For example start at 12 and add 35

Answer 3:

number line

number line

  • Consider the use of ‘time lines’ to solve problems involving addition of time.

Making connections

  • Number lines provide a visual model for sequencing and comparing numbers. In the early years, children may use them in practical situations to support counting or measuring. For example they may use a height chart to measure how tall they are and make comparisons.
  • These early experiences lead into the use of a fully marked number line to support counting and calculation. Children may use these for addition, initially by counting forward in ones.

    number line
     
  • Number lines can help learners become aware of relationships between numbers. This growing sense of number supports effective decision−making about how to carry out calculations. For example, they may become more efficient by using known number bonds to bridge on multiples of 10 and by counting in tens. Learners make choices about the exact steps they use depending on the particular numbers involved in the calculation and their own number confidence. Drawing empty number lines, where only key numbers are noted, is one effective way to record the steps used to work out a particular calculation.

      Number line

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