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Calculating : Adult Learning : Mathematics Content Knowledge


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Calculating
Question 1 of 38

1. How confident are you that you can use an empty number line to model the mental calculations:

a. 48 + 36?


Example

Mental addition and subtraction can be developed with a number of strategies, such as the following.

Counting on

  • Put the larger number first and count on: 4 + 27 = 27 + 4; count on from 27
  • Count on from the smallest number: 25 – 17; count on from 17 to 20 and 20 to 25
  • Count on in tens: 45 + 26 = 45, 55, 65 + 6
  • Count on in ones and tens: 72 – 48 = 48 to 50, 60, 70 to 72

Partitioning

28 + 15 = 28 + 2 + 13 = 30 + 13
76 – 33 = 76 – 30 – 3 = 46 – 3

Using near numbers

39 + 42 = 40 + 40 – 1 + 2

Breaking numbers into tens and units

36 + 42 = 30 + 40 + 6 + 2 = 70 + 8

Combinations of these strategies may also be used.

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

48 + 36 = 84

Number line

or:

Number line


Additional User Example

Doubling near numbers:

40+38= 40+ 40 - 2= 80 - 2=78


 

 

 

What this might look like in the classroom

Question:
Use an empty number line to work out the answer to 48 + 36 using three different ways.
Answer:
Possibility 1
number line

Possibility 2
number line

Possibility 3-

Taking this mathematics further

The history of the use of the empty number line is explained in the document in the following link.

Making connections

To be able to develop mental calculation strategies for addition, children first need to be able to:
  • count on and back in ones and tens,
  • know or calculate number pairs to ten, understand the place value of numbers and partition them into tens and ones,
  • understand the concept of addition and its inverse operation of subtraction.
Children need to be able to apply the concept of addition to real−life applications, for example the total cost of two items costing 48p and 36p. They may then need to be able to convert their answer into the appropriate units.

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