Doubling, Halving, Odd, and Even

The big idea

To double a quantity, make two equal copies and combine them. To halve an even whole-number quantity, split it into two equal groups. The operations undo one another: doubling 7 gives 14, and halving 14 returns to 7.

An even number can be paired with nothing left over. An odd number leaves one unpaired object, so it cannot be divided into two equal whole-number groups.

Worked example

Double 9 by adding two copies: 9 + 9 = 18. Half of 18 is 9 because 18 ÷ 2 = 9.

If 15 objects are placed into pairs, 7 pairs use 14 objects and 1 remains. Therefore 15 is odd, and a whole-number half would not be possible without splitting an object.

How children may show it

Children may make pairs, arrange an even number into two equal rows, draw two matching groups, use a number line, or use known doubles facts. For a changing process, recording each state in a table prevents the child from losing track of which quantity was doubled or halved.

Common mix-up

Halving is not subtracting 2, and doubling is not adding 2. The word describes a multiplicative relationship. Another common error is deciding that a number is even merely because it is large or familiar; pairing or checking the ones digit provides evidence.

Try it together

Choose a number from 1 to 20. Predict whether it can be split into two equal whole-number groups, then verify with counters. If it is even, name its half and rebuild the original by doubling. If it is odd, identify the single object that remains unpaired.