getting three

place four digits in the boxes
multiply across and add the two products
multiply down and add the two products
how can you get a difference of 3 between these two totals?









3 has been chosen as an initial target because any four consecutive numbers give this difference (but there are plenty of other ways to obtain 3)

proving that four consecutive numbers give a difference of 3 is good practice in expanding brackets

how can you get a difference of 0?

explore how you can predict the difference from the original chosen digits without doing too much work...

students might be able to appreciate what is going on from a numerical perspective:
6 x 5 - 6 x 2 = 6 x 3
7 x 5 - 7 x 2 = 7 x 3

the '3' is present from 5 - 2
the result is 1 x 3 because 6 and 7 differ by '1'