B. Number · Adding and Subtracting

Mental Math: Make Ten and Estimate

B2.3 B2.1About 30 minutes

Learning goals

I can add 10 and a number in my head, like 10 + 6 = 16.
I can use the make ten strategy, like 8 + 5 = 8 + 2 + 3.
I can subtract by going back through 10.
I can estimate if an answer is more or less than 10 or 20.

Words to know

make ten
A strategy where you break one number apart to fill up a ten first.

teen numbers
Numbers from 11 to 19. Each one is 10 and some more.

estimate
A smart guess about how much, without working it all out.

Teen numbers are 10 and some more

Every number from 11 to 19 is one full ten and some ones. That makes adding to 10 super easy!

One full ten frame and 4 more. 10 + 4 = 14. Fourteen is 10 and 4.

Fact	Teen number
10 + 1	11
10 + 2	12
10 + 3	13
10 + 4	14
10 + 5	15
10 + 6	16
10 + 7	17
10 + 8	18
10 + 9	19
10 + 10	20

10 plus a number. Look: the ones digit is the number you added!

The make ten strategy

What is 8 + 5? Here's a clever trick.

8 is close to 10. It needs 2 more to make 10. So take 2 from the 5. That leaves 3.

8 + 5 = 8 + 2 + 3 = 10 + 3 = 13.

🟡🟡🟡🟡🟡🟡🟡🟡

Start: 8 in the first ten frame. 2 spaces are empty.

🟡🟡🟡🟡🟡🟡🟡🟡🟡🟡

🟡🟡🟡

Move 2 of the 5 into the first frame to fill it. The other 3 go in the second frame. 10 + 3 = 13.

8 + 5: jump 2 to get to 10, then jump 3 more to 13.

Worked example

Example 1: Make ten

What is 9 + 6?

9 is closest to 10. It needs 1 more to make 10.
Break 6 into 1 and 5.
9 + 1 = 10.
10 + 5 = 15.

9 + 6 = 15. I made a ten first.

Nines and eights love the make ten trick

Adding 9? Make 10 by taking 1 from the other number. 9 + 4 is the same as 10 + 3 = 13.

Adding 8? Take 2 from the other number. 8 + 6 is the same as 10 + 4 = 14.

Worked example

Example 2: Make ten with a story

A hockey team scored 7 goals in the first game and 6 goals in the second game. How many goals in all?

We are putting goals together: 7 + 6.
7 needs 3 to make 10. Break 6 into 3 and 3.
7 + 3 = 10. Then 10 + 3 = 13.
Another way: 6 + 6 = 12 is a double, and 7 is one more, so 13. Same answer!

The team scored 13 goals.

Back through 10 to subtract

What is 14 − 6?

First take away 4 to get down to 10. (14 − 4 = 10)

You still have 2 more to take away (because 6 is 4 and 2). 10 − 2 = 8.

14 − 6: jump back 4 to 10, then back 2 more to 8.

Worked example

Example 3: Subtract two ways

What is 13 − 5?

Way 1, back through 10: 13 − 3 = 10. 5 is 3 and 2, so take 2 more: 10 − 2 = 8.
Way 2, think addition: 5 + ? = 13. 5 + 5 = 10, then 3 more to 13. 5 + 3 = 8. So the answer is 8.
Check: 8 + 5 = 13. Yes!

13 − 5 = 8

Estimating

Sometimes we just need to know about how much. We estimate to check if an answer makes sense.

Is 6 + 3 more or less than 10? 6 + 4 would be 10. 3 is less than 4, so less than 10.
Is 9 + 8 more or less than 20? 10 + 10 = 20. Both numbers are less than 10, so less than 20.
Is 7 + 5 more or less than 10? 7 + 3 = 10, and 5 is more than 3, so more than 10.

Does it make sense?

If someone says 9 + 8 = 7, you can tell it's wrong right away! When you add, the answer is bigger than each number (unless you add 0). 7 is smaller than 9. Estimate first, then solve!

Just for fun

Why does 9 always want to stand next to 1?

Because together they make a perfect 10!

Hands-on activity

Ten frame flash

You need: an egg carton with 2 cups cut off (so it has 10 cups), and 20 small things like dry beans or pom-poms. Or draw two ten frames on paper.

A grown-up says a fact like 9 + 4.
Put 9 beans in the first frame and 4 beside it.
Move beans to fill the frame up to 10. How many are left over? Say the fact: "10 + 3 = 13, so 9 + 4 = 13."
Try 8 + 7, 9 + 9, 7 + 4 and 6 + 8.

Estimation challenge: Before you solve each one, say "more than 10" or "less than 10". Were you right?

Math talk: "How many did you need to move to make ten?"

Your turn

10 + 7 = ?

9 + 5 = ? Use make ten.

8 + 4 = ?

7 + 5 = ?

15 − 7 = ?

12 − 4 = ?

Without solving, is 4 + 3 more or less than 10?

Ava says 8 + 6 = 12. Is that right? Explain.

More practice: warm-up

10 + 5 = ?

🔵🔵🔵🔵🔵

🔵🔵🔵

A full ten frame and 3 more dots. What number is it?

9 needs __ more to make 10.

6 needs __ more to make 10.

True or false: 10 + 9 = 19

More practice: on your own

9 + 3 = ? Use make ten.

8 + 7 = ? Use make ten.

13 − 4 = ? Go back through 10.

Without solving, is 6 + 5 more or less than 10? How do you know?

7 kids go down the toboggan hill in the morning. 8 kids go down in the afternoon. How many kids is that in all?

Challenge

Find the mistake. Mo says 9 + 7 = 15. Use make ten to check.

Show two ways to solve 14 − 5.

Jen has 8 red apples and 4 green apples. Paul says, "That is less than 10 apples." Is Paul right? Find the total.

Check your understanding

Quiz

What is 10 + 8?

To solve 9 + 7 with make ten, what do you break 7 into?

What is 8 + 5?

What is 16 − 7?

Which sum is more than 10?

To solve 8 + 6 with make ten, what do you break 6 into?

What is 11 − 3?

For parents and teachers

Big idea: Our number system is built on tens. Making a ten is the most powerful mental math strategy children will learn, and they will use it in later grades for bigger numbers (like 38 + 5). Estimation (part of B2.3) helps children notice answers that don't make sense.

Common mistakes:

Not knowing the partners of 10 well enough. Make ten only works when 8 + 2, 7 + 3, and so on are automatic. Go back to Lesson 2 games if needed.
Forgetting the leftover. For 8 + 5, a child may get to 10 and stop. Ask: "You used 2 of the 5. How many are left to add?"
Writing teen numbers backwards (writing 41 for fourteen, because we hear "four" first). Show that fourteen is 1 ten and 4 ones, so the 1 is written first.

How to help: An egg carton with 10 cups is a perfect home ten frame. Ask "more or less than 10?" before solving, so estimating becomes a habit.