Explaining, convincing and proving

In these addition games, you'll need to think strategically to get closest to the target.

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

Can you place these quantities in order from smallest to largest?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Try out this number trick. What happens with different starting numbers? What do you notice?

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick ten numbers from the bags so that their total is 37?

How many possible symmetrical necklaces can you find? How do you know you've found them all?

Here are shadows of some 3D shapes. What shapes could have made them?

This problem looks at how one example of your choice can show something about the general structure of multiplication.