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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.

Equal additions algorithm


Click on the images below to watch movies of the equal addition algorithm. 
Standard 
standard

standard

Click
here to read a written
description of equal addition.

Click
here to see how the
equal additions 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. 



