Exchanging across zero
When needing to exchange from a zero, pupils may misapply a process without understanding what is happening to the numbers.
In the first example, the pupil has exchanged from the hundreds, leaving 2 hundreds, but has then put this hundred directly into the units to incorrectly make 14. In example 2, the pupil has recalled that zeroes change to nines when subtracting, but has failed to actually exchange one of the hundreds.
Such mistakes may commonly occur when shortcuts to the method have been seen, which omit the step of first writing the exchanged 1 into the zero column to make 10. Pupils need encouraging to work systematically through the method, without taking shortcuts, using base 10 equipment for reinforcement as needed.
Clear and accurate recording of exchanging is important to avoid further errors occurring. In the following examples, only part of the newly formed ‘10’ has been crossed out.
See our How To video for an example of this.
In example 4, the zero is clearly crossed out, but the 1 remains, seeming to make 19. In example 5, the 1 has been crossed out but the 0 remains, seeming to make 90. Such ambiguity can lead to confusion, particularly in more complicated calculations. Using \ rather than / makes it easier to cross out both digits clearly.