Developing an understanding in number

1. Understanding number

As a result of planned experiences it is expected that children will develop key understandings that form the basis of sound mathematical knowledge.

1. Counting a collection tells us how many there are in it. To be able ‘to count’ a collection of things a child must remember the number names in the right order and be able to use them to decide ‘How many?’. We match the numbers in order as we point to or look at each object exactly once and we know the last number said, answers the ‘How many?’ question.
   
   
2. The same number fact will be true no matter how you count the objects, or what the objects are. Through experimentation you can help your child to see that, no matter how you rearrange them, or from where you start to count, or what the items are, five items together with seven items will give twelve items.
   
   
3. There are patterns in the way we say whole numbers. Hearing patterns in the way we say the counting numbers helps children to recite the number names in order. We need to assist children from an early age to notice these patterns by emphasizing them orally. Children need to use these patterns to say, for example, what comes after 79 and also what comes before 80 – counting both forwards and backwards from any number. Our place value system is based on the pattern established by the initial ones, tens and hundreds places repeated. This allows us to say and write bigger numbers and to get a feel of how big they are.
   
   
4. There are patterns in the way we write whole numbers. Place value is central in understanding how we say, read, write and calculate with whole numbers. Digits mean different things in different places, the order of the digits makes a difference to the number and zero is used as a place holder to show when there are none of a particular quantity, are all important characteristics of our place value system. Children should understand that it is the pattern in the way we put the digits together that allows us to write any number of whole numbers and order them.
   
   
5. We can rearrange the numbers of a problem in different ways without changing the total quantity. Children should develop the idea that to fi nd 8 + 274 you must get the same result if you start at 274 and count on 8 as if you start with 8 and count forward 274. To fi nd 274 + 8 you can also think of 8 as 6 + 2, use the 6 to ‘fi ll up’ the seventies and then add 2. Children can use a known fact to work out facts they do not know yet, for example, 8 + 9 must be double 4 plus 1 because 9 is 8 + 1. They can also use known basic addition facts to work out subtraction facts.
   
   
6. With practise we can do many calculations in our head. There are strategies which help us store the bits of the calculation in our head as we go along. Children should learn to see mental arithmetic as the fi rst resort when they need to calculate. Children rarely get better at mental computation from practising written computation. As children proceed through the primary years, they should demonstrate an increasing repertoire of mental strategies to assist in calculating and estimating mentally.
   
   
7. There are some special calculating methods that you could choose when calculations are too hard to do in your head. The development of mental strategies should be developed fi rst, followed by the extension of children’s existing strategies to enable them to deal with larger numbers easily. We would be concerned if a child tried to calculate vertically the answer to 10 000–9 998 instead of thinking and using number sense. It is also important that children be expected to estimate the results of calculations prior to using any procedure, to evaluate the ‘reasonableness’ of their calculation.
   
   
8. Rounding, imagining a number line and using what we know about numbers and operations, help us to estimate calculations. Good estimation and approximation skills enhance our ability to deal with everyday situations. Children should be provided with ample opportunity to estimate fi rst, decide how close the estimate is to the calculation and refl ect on this for further estimations.
   
   
9. To use a calculator well you need to enter and interpret the information and know about its functions. Children should have ready access to calculators from the earliest years of schooling to develop calculator skills which they will use in their everyday life. Calculators help children develop many mathematical concepts earlier and more thoroughly than they can without having the use of calculators.
   
   
10. Thinking about what makes sense helps us to check and interpret the results of calculations. Children should be expected to routinely check their answers are reasonable by using both their mathematical knowledge and their contextual knowledge. They need to check whether their answers make sense and that if they don’t, they should see that some correction is likely to be necessary.