Section C Practice Problems

Problem 1

How many tens are there in 50?
How many tens are there in $7 \times 50$ ? Explain your reasoning.
What is the value of $7 \times 50$ ? Explain your reasoning.

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Solution

5 tens
35 tens. Sample response: There are 7 groups of 5 tens. That’s $7 \times 5$ tens.
350 tens. Sample response: 30 tens are 300, and then there are 5 more tens, or 50.

Problem 2

There are 4 lunch tables. There are 12 students at each table. How many students are at the tables? Show your thinking using objects, a drawing, or a diagram.

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Solution

48 students. Sample response:

Problem 3

What do the 60 and 24 in the diagram represent?
Explain how to use the diagram to find the value of $14 \times 6$ .

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Solution

Sample responses:

The 60 is the area, in square units, of the smaller 6 by 10 rectangle. The 24 is the area, in square units, of the smaller 6 by 4 rectangle.
The two smaller rectangles make up the 6 by 14 rectangle. The area of that larger rectangle is the sum of the areas of the two smaller rectangles: $60+24$ , or 84 unit squares.

Problem 4

There were 18 days of school in the month. There were 7 hours of school each day. How many hours of school were there during the month?

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Solution

126 hours. Sample response:

7 \times 10 = 70

7 \times 8 = 56

, and

70 + 56 = 126

Problem 5

Find the value of each expression. Explain or show your reasoning.

$2 \times 47$
$3 \times 25$

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Solution

94. Sample response: I found $47 + 47$ , which is $80 + 14$ , or 94.
75. Sample response: I know that $3 \times 20$ is 6 tens, or 60, and then $3 \times 5$ is 15 more.

Problem 6

A rope is 640 inches long. Andre cuts off 5 pieces of rope that are each 16 inches long. How much rope is left?

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Solution

560 inches. Sample response: Andre cut off $5 \times 16$ inches of rope, which is 80 inches: $(5 \times 10) + (5 \times 6)$ . Then $640 - 80$ is $560$ .

Problem 7

Here is Mai’s strategy for finding the value of $4 \times 21$ : “First, I double 21, and that’s 42. Then I double 42, and that’s 84.”

Explain why Mai’s strategy works.
Use Mai’s strategy to find $4 \times 23$ .

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Solution

Sample response: 4 is the same as $2 \times 2$ , so multiplying by 4 is the same as multiplying by $2 \times 2$ , which is doubling twice. So doubling 21 twice will give four 21s.
92. Sample response: If I double 23, that’s 46. If I double 46, that’s 92. So $4 \times 23 = 92$ .

Problem 8

Make a list of the whole numbers greater than 0 and less than 20 that do not appear in the multiplication table.
What do these numbers have in common?
Choose 1 of these numbers and count out that number of objects. Can you make an array out of the objects? Explain your reasoning.

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Solution

11, 13, 17, 19
Sample response: Sample response: These numbers are all odd. They’re all greater than 10. They are all teen numbers.
Sample response: I can make a line with that number of dots but I can’t make an array with more than 1 row or more than 1 column.

Problem 9

Look at the 2 different diagrams representing the same multiplication expression:

<p>Area diagram. Rectangle divided into 2 parts. One part labeled 60 with a top measurement of 10, the other labeled 18, with a top measurement of 3. Left side measurement 6.</p>

<p>Base ten blocks. 6 tens. 18 ones.</p>

What multiplication expression do the 2 diagrams represent?
Can you show a third way to represent the same expression?
What is the value of the expression?
Write a story problem to match the expression.

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Solution

$6 \times 13$ or $13 \times 6$
Sample response:
78
Sample response: Noah bought 6 “baker’s dozens” of bagels for his whole grade’s end-of-year party. (A baker’s dozen is a count of 13 items.) How many bagels did Noah buy?