Use Problem-Solving Strategies

Teacher: [Pointing to intervals on the chart] What interval do you think the answer will be in?

Nicholas: I think it will be in the interval 21–30.

Teacher: Why do you think so, Nicholas?

Nicholas: Because we have 18 and 12 and both of them are bigger than 10. Ten and 10 is 20, so I think it will be bigger than 20.

Teacher: I can see what you're saying. Since both 18 and 12 are bigger than 10, our answer should be larger than the double of 10 or larger than 20. So, you're saying we add to get the answer. What does everyone else think?

Luis: I don't think we should add 18 and 12. I think it's subtracting because one farmer gave him 12 sheep and the other one gave him some more and the shepherd had 18 altogether.

Teacher: So, you're saying that we already have the total, Luis? That's why we're not adding the two numbers?

Luis: Yes, 18 is the total. We can either say 18 − 12 or
12 + = 18.

Teacher: What interval do you think your answer will be in?

Luis: I think it will be a small number because you don't have to count up too much to go from 12 to 18, so I think the interval is 1–10.

Teacher: Okay, let's work the problem. When you finish, see if your exact answer is in the interval 1–10.

Teacher: What was your answer and what strategy did you use to solve the problem?

Katie: My number sentence is 12 + = 18. I knew the total was 18 and one farmer had 12 sheep, so I put 12 in my head and counted up to 18: 13, 14, 15, 16, 17, 18. The answer is 6.

Teacher: Very nice explanation, Katie. Let's call that "Katie's strategy." Did anyone solve the problem a different way?

Maddie: I counted back. I started with 18 and counted back 12. I had to use my number line because I don't have 12 fingers. [pointing to numbers on number line] I counted back 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7. My answer is different from Katie's.

Teacher: We'll call counting back "Maddie's strategy." Why do you think she got a different answer?

Ashley: When she counted back she started with 18. She should have started with 17 and then she would have gotten 6 for an answer.

Teacher: Good answer, Ashley! It's hard to keep track if you're counting back large numbers. Try to use counting back if you're only counting back a few numbers. Who has another strategy?

Romesh: I knew that 18 minus 10 is 8. Then I subtracted 2 more because I'm really supposed to take away 12, not 10. So I got 6.

Teacher: How did you know that 18 minus 10 is 8?

Romesh: I used my 100 Chart. I looked for 18 and went to the row above because that's how you find minus 10. I landed on 8 and then, I went back 2 more and got to 6.

Teacher: That's great, Romesh! We'll call that "Romesh's strategy." I'm going to give you another problem and I'd like all of you to try solving it using Romesh's strategy. How much is 16 − 11? Remember, try solving it using Romesh's strategy. Use your 100 Chart.