I invented “Cross Sums” to help students who struggle with Proportional Reasoning. The philosophy includes:

All proportional reasoning sums are essentially the same – times 2 numbers and divide by a third. If one of the numbers is one, then it’s just a multiply or a divide.

Students who get used to working a problem “forwards” often struggle to work backwards, but mathematically there is no difference!

Skills gained working with ratios can be applied to shopping, percentages, similar shapes, stratified sampling, speed, density, and other “per” problems, Direct and Inverse proportion, currency conversions, unit conversions and the Sine Rule, without learning shed loads of new stuff.

Students often get in a muddle because they do sums and lose hold of the units of numbers so although they get a correct answer they don’t realise what it means! Cross Sums hold the units of numbers as well as the numbers themselves.

Students sometimes try to mix different units inappropriately in their working. With cross sums this is much less likely.