Addition Strategies

True or False? Tell students a number sentence is true if the quantities on both sides of the equal sign have the same value. That is, a number sentence is true if the symbols on both sides of the equal sign represent the same number.

Continue to practice with the following number sentences. Encourage students to think of tools or mental strategies they can use to justify their answers.

A. 10 = 11

False

B. 10 = 7 + 3

True

C. 5 + 5 = 10

True

D. 5 + 5 = 7 + 3

True

E. 7 + 3 = 7 + 4

False

For D and E, students can use number lines or cubes as described above. Alternatively, they can use mental strategies. For D, they can reason that 5 + 5 = 7 + 3 because 5 + 5 = 10 and 7 + 3 = 10, so both sides equal 10. You can model this thinking for students as shown:

For the last sentence (E), students can add both sides to find that the sentence is false. However, they can reason that since 3 is one less than 4, 7 + 3 must be one less than 7 + 4. Therefore, the sentence must be false.

Ask students to work with a partner to decide whether the sentences in Questions 6 and 7 in the Student Guide are true or false. Remind them that they need to be ready to justify their thinking using tools or strategies as in Question 8. As students work, talk with them about their reasoning. See the Content Note for information on students' use of the equal sign and possible misconceptions.

Solve Open Number Sentences. Display the following open number sentences. Ask students to work with a partner to fill in the missing numbers to make each number sentence a true statement. Encourage them to use strategies similar to those they used to decide if the number sentences were true or false. Discuss students' strategies. See the Sample Dialog of a classroom discussion of the last number sentence in the list.

5 + 6 = + 5

5 + 1 = 6 +

5 + 6 = 10 +

5 + 5 + = 5 + 6

15 + 6 = + 5 + 6

X

15 + 6 = + 5 + 6

Teacher: What number should be in the empty box to make this number sentence a true number sentence? Tell me your thinking.

Shannon: Twenty-one goes in the box. Fifteen and six are twenty-one.

Nicholas: I think that 10 goes in the box. It has to be the same on both sides, so 15 + 6 is the same as 10 + 5 + 6.

Teacher: Let's look at these choices and decide which one makes a true number sentence. [The teacher writes the number sentences on the board.]

15 + 6 = 21 + 5 + 6 15 + 6 = 10 + 5 + 6

Talk with your partner and decide which number sentence is true and which is false. Remember that the numbers on both sides of the equal sign must equal the same thing. Be ready to show how you decided. Think of tools and words to explain your thinking. [Students work in pairs for a few minutes. Shannon raises her hand.] Shannon, what did you and Keenya decide?

Shannon: We think Nicholas is right.

Teacher: Why?

Shannon: Well, we looked at the first one. Keenya said we had to make a train for each side. We made this train for the first side. [Shannon shows a train of 21 cubes.] But we didn't even have enough cubes to make the train for the other side, so it was going to be a lot longer. So, they aren't the same. So, twenty-one can't go in the box.

Teacher: What about Nicholas' number sentence. Is it true?

Ming: It's right.

Teacher: How did you decide that 15 + 6 = 10 + 5 + 6?

Ming: I added on both sides. I added the first side and I got 21.

Teacher: [Teacher writes the following on the board.] How did you decide that 10 went in the box?

Ming: I added the numbers on the other side that weren't in the box and I got 11. I used the number line to see that 10 should go in the box.

Teacher: How did you use the number line?

Ming: I looked and saw that you have to go ten more to get from 11 to 21. [Points to the class number line, moving from 11 to 21.]

Teacher: So, on the first side you have 21 and on the other side you have 21. Right? [Teacher writes the following on the board.]

Teacher: Is that the way you thought about it Nicholas?

Nicholas: I didn't even add the numbers at first. I split the 15 into 10 and 5. So, 10 can go in the box. Then it's easy to add.

Ask students to find the missing number sentences in Question 9. Remind them to be ready to justify their solutions in Question 10.