How to teach subtraction

Start by modelling 'taking away' with objects, then 'finding the difference' by comparing two groups. Link every subtraction fact to an addition fact using fact families, use a number line to count back, and only introduce regrouping or borrowing once single-digit facts are secure.

Subtraction usually begins in Kindergarten with taking objects away from a group, and develops through Grade 4. Facts within 20 come first, then two-digit subtraction, then borrowing across columns. The written borrowing method typically appears around Grade 2, after the meaning of subtraction is well understood.

Take away means removing an amount from a group, such as having 8 and eating 3 to leave 5. Difference means comparing two groups to see how many more one has, such as the gap between 8 and 5. Both are subtraction, but children find comparison harder, so teach take away first.

Subtraction is the inverse of addition, so every subtraction fact has a matching addition fact in the same fact family. From 2, 3 and 5 you get 5 minus 3 equals 2 and 3 plus 2 equals 5. Teaching them together means learning one fact gives the others for free.

A common error is subtracting the smaller digit from the larger in each column regardless of position, which avoids borrowing. Borrowing across a zero is especially tricky. Children also confuse 'take away' with 'difference'. Securing addition facts and practising borrowing on a number line first usually helps.

Borrowing, also called regrouping, is used when the top digit in a column is smaller than the one below it. You take ten from the next column left and add it to the current column so the subtraction works. Only introduce it once single-digit subtraction facts are secure.

Once addition and subtraction within 20 are fluent, children move on to multiplication and division, which are the next inverse pair. Multi-digit subtraction with borrowing and multi-step word problems also build on secure subtraction facts, so fluency here makes later arithmetic much smoother.