Stage 3: The Empty Number Line
Most children should be able to use and empty number line to count on or back by the end of Year 2. The empty number line helps to record or explain the steps in mental subtraction. A calculation like 74 – 27 can be recorded by counting back 27 from 74 to reach 47. The empty number line is also a useful way of modelling processes such as bridging through a multiple of ten.
Again, Cuisenaire rods and number tracks can be used to support the process of counting back for subtraction. The written number line mirrors what the number rods show.
The steps can also be recorded by counting up from the smaller to the larger number to find the difference, for example by counting up from 27 to 74 in steps totalling 47.
With practice, children will need to record less information and decide whether to count back or forward. It is useful to ask children whether counting up or back is the more efficient for calculations such as 57 – 12, 86 – 77 or 43 – 28.
The mental method of counting up from the smaller to the larger number can be recorded using number lines.