# How to subtract numbers

### Let's have fun with math!

## How can "subtract" with simple methods:

**calculate**how many school days

**left**...

*1. Partitioning *

This involves splitting one quantity into two or more sub-quantities. This is the inverse of the â€˜Combiningâ€™ model for addition.

Some examples of this are:

typical word problem for this kind of subtraction is:

â€œIn a box are 5 cars. Two are Johnâ€™s and the rest are Tomâ€™s. How many are Tom's?

*2. Reduction *

This type of subtraction involves reducing the value of one quantity. This subtraction structure is often known as â€˜take awayâ€™. It should be evident from this that â€˜take awayâ€™ is not an appropriate description for other types of subtraction and therefore the commonly-held view that â€˜subtractionâ€™ and â€˜take awayâ€™ are interchangeable terms with the same meaning is mistaken. This is a common misconception among children who may have been incorrectly taught or who have rarely encountered any other form of subtraction. The â€˜reductionâ€™ form of subtraction is the inverse of the â€˜augmentationâ€™ model for addition.

## Misconceptions about teaching "subtraction"

Additional confusion can be caused by the use of specific language in this algorithm for earlier grades. The large number of different ways in which subtraction tasks can be phrased in words means that children become unsure what operation is required to solve the particular problem. Also, some words can have various meanings in different syntactic structures.

Language-related problems can be seen also to inappropriate or imprecise use of language. Teachers have to be cautious to use appropriate mathematical language when talking to children. In particular, be aware that the âˆ’sign as â€˜subtractâ€™ or â€˜minusâ€™ and the = sign as â€˜equalsâ€™. Children often read + as â€˜andâ€™ and = as â€˜makesâ€™ which seems acceptable until they become confronted with a statement of the form 7= 3 + 4 whereupon reading it as 7 makes 3 and 4 doesn't make sense!