Teaching mathematics
Teaching mathematics

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Teaching mathematics

1.2 Making the connection between quantity and number

Young children learn about quantity in a natural, intuitive way and are able to understand that you can have more of one thing than another. Quantity is a measure of how much you have of something. In order to be able to indicate the quantity, you need to use numbers (and a measure, so that you can say you have a number of kilograms or metres of something; but, for our current purposes, you are thinking of discrete objects which can be counted).

Children are taught to count and to name the numbers used in counting. The next stage of their development in understanding number is to put quantity and number together. Specifically, children need to be able to link the final number in the counting sequence with the size of the quantity of objects which they have counted. This is not an easy concept to develop and can take several years in primary school..

Children learn that adding 1 to a number gives the next number in the sequence. However, it is more difficult to grasp the effect of adding 2 to a number.

Early calculation skills which are taught in primary school

  • a.Counting forwards from 1 and backwards to 1.

  • b.Starting from different numbers and then counting forwards and backwards.

  • c.Addition by counting. For example, you want to add 7 biscuits to 4 biscuits. In order of sophistication, you could do this in three ways:

  • Count all – you could count out 7 biscuits, then you could count out 4 biscuits. Then, after you have put the two groups together, you could count the total number of biscuits.
  • Count on – you could keep the number 4 in our head and then count on 7 from there.
  • Count on from larger number – you could save yourself some effort by beginning with the larger number, i.e. 7, and count on 4 from there.

This all seems very easy, but you need to remember that young children do not have the ready familiarity with numbers that you have. To try to imagine how tricky it can be for a young child to use counting skills in addition, try the following activity (without converting the letters into numbers!).

Activity 2 Adding numbers when you are unfamiliar with their names

Timing: Allow 5 minutes

Suppose the counting sequence is Y, J, A, P, K, T, B, M.

  • Count from A to B.
  • What is J + K?
  • Count back from M to P.
  • Count back from B to J.
  • What is T – A?
  • What is K – Y?

Discussion

From A to B is P.

J + K = B

From M to P is P

From B to J is K

T – A = A

K – Y = P

How did you do?

TM_1

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