Back to Subtract

You are using the online sample of the Teaching Mental and Written computation CDROM. Not all linked pages are accessible in this version. For further information about the complete CDROM, click here.

Teaching algorithms for subtraction

In the primary school children are normally taught a formal written computational procedure for subtraction. The most commonly taught procedure is the decomposition (also known as renaming) algorithm. The other procedure sometimes taught is the equal additions algorithm. Many older people were taught equal additions.

Prior to the introduction of the formal algorithms, it is important for children to be familiar with basic subtraction facts, learned in conjunction with basic addition facts. There are many games that help children consolidate knowledge of basic number facts.

When introducing formal algorithms, continued use of concrete materials is important. Both the decomposition and the equal additions algorithms can be modelled using place value material (e.g. MAB - MultiBase Arithmetic Blocks), or cubes, unifix or icy pole sticks bundled into tens and hundreds etc ). The algorithms should be demonstrated step by step before being applied in an abstract way.

Children should be taught that before applying any algorithm it is always a good idea to first estimate the approximate difference to use as a rough guide for the answer. Rough estimates can be found in many different ways. For example, one way would be to approximate this subtraction as 70 take away 40, so that the answer is about 30.

 Decomposition algorithm Click on the images below to watch movies of the decomposition algorithm. standard standard standard variation Click here to read a written description of decomposition with accompanying photos of Reuben using place value materials. Click here to see how the decomposition algorithm is done with place value material.

 Look at the decomposition logo and the equal additions logos below, and think how they illustrate the main principle involved in each of the algorithms.