Subtraction Facts Strategies

Est. Class Sessions: 2–3

Developing the Lesson

Part 1. Subtraction Facts Strategies

Using Tens. The Subtraction Facts Strategies pages in the Student Guide begin with a discussion between John, Suzanne, and their teacher about three subtraction facts: 15 − 10, 13 − 10, and 15 − 9. Through their discussion, students review subtraction facts strategies.

After students read the two pages of dialog, ask questions like the following:

What strategy do you use to solve the problem 15 − 10? (Possible response: I know when you subtract ten, the difference is the same as the ones digit in the number you are taking the ten from.)
John thinks facts with tens are the easiest. He solves two of them. What are other examples of facts with tens? (Examples will vary: 17 – 10, 16 – 10, 18 – 10, 12 – 10)

After listing a few facts with tens on the board, ask:

What are the answers to these subtraction facts?
What patterns do you see? (Possible response: I see that the difference is the same as the ones digit in the first number.)
Explain to a friend why John might think these are easy.

Refer to Suzanne's explanation to introduce “facts with nines.” Ask the class to generate a list of problems similar to 15 − 9, such as 13 − 9 or 17 − 9.

Ask:

What is 13 − 9? (4)
How did you solve it? (Possible strategy: 13 – 10 = 3 so 13 – 9 = 3 + 1, or 4.)
Use Suzanne's method of counting up to solve 13 − 9. (Start at 9 and count up to 10, 11, 12, 13. That's 4 numbers. So the answer is 4.)
Describe how Suzanne is “using tens” to help her solve 15 − 9. (Possible response: It was easier for her to think about adding 1 to 9 so she could use a ten. Then she could easily count up 5 from 10 to 15. Altogether, she counted up 6, so 15 – 9 = 6.)

Discuss Subtraction Strategies. Class discussion of strategies helps students verbalize number relationships and encourages them to think about the problems in new ways. In the class discussion between John, Suzanne, and the teacher, John uses addition to help him solve 15 – 9. This strategy can help students identify fact families relating addition to subtraction.

It is important to emphasize that a strategy that works well for one person may not be helpful to another. The strategies mentioned here are suggestions students may find useful. Encourage students to develop and share their own strategies as well. Sharing strategies increases the opportunities for students to encounter helpful strategies that will make learning the subtraction facts easier. Students who already demonstrate fluency with the facts may find that using a strategy is more work. Emphasize that these strategies will be more helpful when they solve problems such as 25 − 9 or 33 − 19.

Ask student pairs to discuss Questions 1–6 in the Student Guide. It is not necessary for students to remember the names of the strategies, but they should remember how to use them. Students may use different strategies to do the same problem. Pairs can report their answers and methods in a class discussion.

Ask:

What strategy did you use to solve 16 − 9? (Possible response: I know 16 − 10 is 6. Since subtracting 9 from 16 takes away one less than subtracting 10, I know the answer is not 6, but 7.)
Tell me the strategy you used to solve 16 − 7. (Possible response: I think about what I need to get from 7 to 16 and I use counting up. From 7 to 10 is 3, and from 10 to 16 is 6 more. 3 + 6 = 9, so 16 − 7 = 9.)
What strategies can you use to solve 18 − 10? (Possible response: I think, “10 plus what number makes 18?” I know that 10 + 8 = 18, so 18 − 10 must be 8.)

Thinking Addition. After discussing the strategies, remind students that addition can also be used to check the facts that they think they “just know.” Ask them to read the Thinking Addition section in the Student Guide and then solve Questions 7–11. In these problems, students write an addition sentence that they can use to check each subtraction problem. Encourage them to always check subtraction problems with addition. Usually they should do this using mental math instead of writing out full sentences, though this strategy helps develop this habit.