I hope you’ve been enjoying my ideas for teaching mental maths. So far we’ve looked at the counting on strategy and near doubles strategy. Today we’re looking at the compatible numbers strategy. It’s important for your students to realize that mental calculations can be simplified by learning particular strategies, such as the compatible numbers strategy.

What are compatible numbers?

Compatible numbers are numbers that when added produce a ‘tidy sum’, one that usually ends in zero, or multiples of 10. For example, 7 and 3; 6 and 4; 8 and 2; and 9 and 1 are considered compatible because when added they total 10 (end in zero). Also, 70 and 30; 16 and 84; 38 and 62 are also compatible numbers because when added they total 100 (end in zero). For younger students, you could use strips of 10 that can be broken up to show the compatible numbers, as in the picture below.

Compatible numbers activity

For this activity you will need a whiteboard. On the whiteboard write a list of compatible numbers in random order within a frame. Below is an example of compatible numbers you could use that total 10 (for younger students) as well as some that total 100.

Explain the compatible numbers strategy to your students (numbers that when added produce a tidy sum – usually ending in a zero) and then ask your students to list the pairs of compatible numbers. Some discussion questions you can ask your students include:

• Do the two numbers add together to make the tidy sum?
• How did you choose the pairs of numbers?
• How did you work that out?
• What was your strategy?
• Why did you use that strategy?

You can then get your students to make their own compatible numbers that total an amount that suits the level of your students, such as 10, 20, 50 or 100. See below for some more examples of grids you could use.

Some ways that you could adapt this activity include:

• Get your students to write as many compatible numbers (that total a specific amount) as they can in a certain time (such as 1 minute).
• Get your students to make up their own grids and swap with another student who must find the compatible numbers.
• You could also ask for 3 numbers that make a tidy sum.
• You could also have a number of different frames made up as task cards for a math center. Students need to find the compatible numbers on the card and write them down with the total.

I hope this has given you some more ideas for how you can teach the compatible numbers strategy. Tomorrow we’ll look at the partitioning strategy.

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Graphic Credits: Graphics From the Pond