In this activity, we will learn how to express an odd number as 'double a number plus one' and then identify whether the result is an odd or even number.

Example
Write this odd number as 'double a number plus one'. Then say whether the answer is odd or even. 

209  =  2 x   ______   + 1

Answer

To solve this, we need to start with the answer of 209 and do the opposite (inverse) to it.

The inverse of adding 1 is subtracting 1.

The inverse of multiplying by 2 (doubling) is to divide by 2 (halving)

So, we do 209 - 1 = 208 

208 ÷ 2 = 104

209  =  2  x 104 + 1, which is the same as 'double 104 plus one'.

The number 104 is an even number, since it is divisible by 2. 

Does that make sense?

Let's try some questions.