Book Drive Math Detectives

Check each strategy and tell why it works.

Place value clues

Use tens and ones to solve. Then choose the best reason.

Room 12 collected 46 books for the book drive. Then they got 3 more bags with 10 books in each bag. How many books do they have now?

46 + 30 = books

When Room 12 added 30 books to 46 books, the tens digit changed but the ones digit stayed 6. Why?

A. 30 is a bigger number than 6, so the ones do not count.B. 30 is 3 tens and 0 ones, so only tens are added.C. When you add, the ones digit always stays the same.

Match each problem to its answer. Think about which digit changes.

Ms. Rivera's class brought 38 books. Mr. Chen's class brought 25 books. Jada breaks 25 into 2 and 23 so that 38 can become 40.

38 + 2 =
40 + 23 =
So 38 + 25 = books

Why does Jada get the right total when she breaks 25 into 2 and 23?

A. She makes the problem smaller, so the answer gets smaller too.B. Breaking a number apart always makes the total bigger.C. 2 and 23 together still make 25, so she adds the same number of books.

Doubles and taking away in parts

Fill in the blanks. Then tell why each strategy works.

Leah sorted 25 picture books and 26 chapter books. She knows that 25 + 25 = 50.

25 + 26 = 25 + 25 +
So 25 + 26 = books

Why can Leah use 25 + 25 to help her find 25 + 26?

A. 26 is 1 more than 25, so the total is 1 more than 50.B. 26 is 1 more than 25, so the total is 1 less than 50.C. 25 + 25 and 25 + 26 have the same total.

There were 53 books on a table. Families took 8 books home. Marco breaks 8 into 3 and 5. He takes away 3 first to get to a ten. Then he takes away the rest.

53 − 3 =
50 − 5 =
So 53 − 8 = books

Marco wants to find 72 − 6. Circle every problem that has the same answer as 72 − 6.

Check the work

Decide if each strategy works. Then explain your thinking.

10.

Is each number sentence true? Sort them.

11.

Tyler added 27 + 45. He said 20 + 40 = 60 and 7 + 5 = 12, so he wrote 612. Is he right? Use tens and ones to explain.

12.

Show two different ways to find 34 + 28. Explain why both ways give the same total.