Section A Practice Problems

Problem 1

<p>Array. 4 rows of 5 dots.</p>

  1. Write a multiplication expression that represents the array.
  2. Write a multiplication equation that represents the array.
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Solution

Sample responses:

  1. 4×54 \times 5 or 5×45 \times 4
  2. 4×5=204 \times 5 = 20 or 5×4=205 \times 4 = 20

Problem 2

Find the area of each rectangle.

A
Area diagram.

B
A rectangle. Left side labeled 4 centimeters. Top labeled 10 centimeters. Other sides unlabeled.

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Solution
  1. 30 square units
  2. 40 square centimeters

Problem 3

The area of the rectangle is 40 square centimeters.

Find the unknown side length of the rectangle. Explain your reasoning.

A rectangle. Left side labeled 5 centimeters. Top labeled question mark. Other sides unlabeled.

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Solution
8 cm. Sample response: I know 5×8=405 \times 8 = 40.

Problem 4

Find the number that makes each equation true.

  1. 8×5=‾8 \times 5 = \underline{\hspace{1cm}}
  2. 5×‾=355 \times \underline{\hspace{1cm}} = 35
  3. ‾×2=18\underline{\hspace{1cm}} \times 2 = 18

Show Solution
Solution
  1. 40
  2. 7
  3. 9

Problem 5

There are 6 volleyball teams in the gym. Each team has 10 players. How many volleyball players are there altogether?

  1. Make a drawing to represent the situation.
  2. Write an equation with a symbol for the unknown that represents the situation.
  3. Solve the problem.
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Solution
  1. Students draw 6 groups of 10.
  2. Sample responses: 6×10=?6 \times 10 = {?} or 10×6=?10 \times 6 = {?}
  3. There are 60 volleyball players on the 6 teams.

Problem 6

For each problem, show your thinking using a drawing or a diagram.

  1. There are 40 apples packed into boxes. There are 8 apples in each box. How many boxes are there?
  2. There are 40 apples packed into boxes. There are 10 apples in each box. How many boxes are there?
Show Solution
Solution
  1. 5 boxes. Sample response:

    Groups of dots.

  2. 4 boxes. Sample response:

    Groups of dots.

Problem 7

For each problem, show your thinking using a drawing or a diagram.

  1. There are 30 oranges. They are packed into 5 bags with the same number of oranges in each bag. How many oranges are in each bag?
  2. There are 30 oranges. They are packed into 3 bags with the same number of oranges in each bag. How many oranges are in each bag?
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Solution
  1. 6 oranges. Sample response:

    Groups of dots.

  2. 10 oranges. Sample response:

    Groups of dots.

Problem 8

  1. Ten people go to the movies in cars. Two people go in each car. How many cars are there? Show your thinking using a drawing or a diagram.
  2. Ten other people go to the movies in cars. They ride in 2 cars with the same number of people in each car. How many people are in each car? Show your thinking using a drawing or diagram.
  3. How are the 2 situations similar? How are they different? How are the diagrams  similar? How are they different?
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Solution
  1. 5 cars. Sample response:

    Groups of dots.

  2. 2 people. Sample response:

    Groups of dots.

  3. Sample response: There are 10 people in each situation, and there is a 2 and a 5 in each situation. In the first situation, 2 is the number in each car and 5 is the number of cars. In the second situation, 5 is the number in each car and 2 is the number of cars.

Problem 9

There are 20 desks in the class. They are divided equally into 5 groups. How many desks are in each group?

  1. Which expression best represents this situation: 20÷420\div4 or 20÷520\div5? Explain your reasoning.

  2. Choose the diagram that represents this situation. Explain your reasoning.

    A
    <p>4 groups of 5 dots.</p>

    B
    5 groups of 4 dots.

Show Solution
Solution
  1. 20÷520 \div 5. Sample response: There are 20 desks divided into 5 equal groups.
  2. B. Sample response: It shows 20 divided into 5 equal groups.

Problem 10

Mai’s family picked 40 peaches. They put 5 peaches in each bag.

  1. Write a division expression that represents the situation.
  2. How many bags of peaches did Mai’s family pick? Explain or show your reasoning.
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Solution
  1. Sample response: 40÷540 \div 5
  2. 8 bags. Sample response:

<p>8 groups of 5 dots.</p>

Problem 11

Complete each problem by putting a number in each blank that makes sense. Draw a diagram to represent and solve each problem.

  1. Mai has __________ stickers. She puts the same number of stickers on each of her 5 notebooks. How many stickers are on each notebook?
  2. Andre has __________ cards. He arranges them in rows of __________ cards each. How many rows of cards does Andre make?
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Solution
Sample responses:
  1. 30. There are 6 stickers on each notebook.

    Groups of dots.

  2. 48 (cards), 8 (cards in each row). He makes 6 rows.

    Groups of dots.

Problem 12

Write a division situation to match each diagram.

A
2 groups of 7 dots.

B
9 groups of 3 dots.

C
6 groups of 4 dots.

Show Solution
Solution

Sample responses:

  1. There are 14 pears in the box in 2 equal rows. How many pears are in each row?
  2. There are 27 students in the class. They are placed in groups of 3. How many groups are there?
  3. There are 24 cards. They are split equally between 6 people. How many cards does each person get?