Mental Math: Early Subtraction

By doing mental math, we help our children use the basic principles of arithmetic to simplify problems so they can think about number relationships, mastering the basic structures of how numbers work.

And the more our children practice these structures in mental math, the better prepared they will be to recognize the same principles in algebra.

The basic idea of subtraction is finding the difference between two quantities: comparing a larger amount to a smaller one, figuring out what’s left when you remove a part, or finding the distance between two measurements (or two points on the number line).

When you work with young children learning subtraction, remember our two key mental-math strategies.

• Use friendly numbers.

For early subtraction with numbers less than 20, the most important friendly numbers are 5 and 10, the pairs of numbers that make 10, and the doubles.

• Estimate, then adjust.

When children apply their creative minds to reasoning about math, they can use friendly numbers to get close to an answer, and then tweak the result as needed.

Let’s Try an Example

For instance, how might children think through a subtraction puzzle such as 17 − 9? If they try to count on their fingers, they’ll probably lose track, so how can we make it easy enough to solve in our heads?

Subtraction is related to addition, so we don’t need to memorize a list of subtraction facts. If your children know addition, then for subtraction they can think, “How far apart are these numbers? How many would I add to get from here to there?”

In the explanations below, I’ll model the thinking on a rekenrek, a useful tool for young children just beginning to explore number relationships. As they grow more comfortable with numbers, they’ll be able to visualize the patterns mentally.

You can buy a rekenrek from your favorite school supply company, or make your own with craft beads.

Make a Friendly Ten

If we start with nine beads, how many more do we need in order to have seventeen? Adding one gets us up to ten, and then we need seven more beads to get the rest of the way to seventeen:

17 − 9

= 1 + 7

Remove a Friendly Ten

Or think about subtraction as taking stuff away, so we would start with seventeen and remove nine. But don’t count — we have to use logic.

If only it was 17 − 10, that would be easy, because we could just get rid of ten beads and keep the seven.

But we were only supposed to remove nine, so we took away too much. We’ll have to put one bead back.

17 − 9

= 17 − 10 + 1

= 7 + 1

Use Friendly Chunks

Or we could take away a little at a time, in easy chunks. We might take away seven beads, so we’ll have ten left. Then we still need to take away two more:

17 − 9

= 17 − 7 − 2

= 10 − 2

Friendly Doubles

Or we could think about doubles: eighteen is double-nine, so it would be easy to take one of the nines away. There would be nine beads left.

But we’re starting with one less than eighteen, which means we’ll end up with one less than nine:

17 − 9

= 18 − 9 − 1

= 9 − 1

Play with the Numbers

Can you find any other ways to think about 17 − 9?

Play around with the calculations in your math book, or let your child choose a subtraction puzzle. How many ways can you find to solve it?

As master teacher George Polya said, “It is better to solve one problem five different ways, than to solve five problems one way.”

Read the Whole Series

Check out all the posts in my Mental Math Series:

• Mental Math Is the Key to Algebra
• Three Basic Principles
• Early Addition
• Early Subtraction
• Coming Soon: Multiplication math facts…