Section C Practice Problems

Problem 1

  1. Explain or show 2 different ways that you see equal groups in the array.

    Array. 3 rows of 6 dots.

  2. Rearrange the dots to make a different array.

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Solution
  1. Sample response:
    • There are 3 rows, and each row has 6 dots.
    • There are 6 columns, and each column has 3 dots.

  2. Sample response:

    Array.

Problem 2

Rearrange the circles to make an array in 2 different ways.

A group of 12 dots.

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Solution

Sample response:

Array.
Array.

Problem 3

There are 4 rows of water bottles in the box. There are 5 bottles in each row.

  1. Draw an array to represent the situation.
  2. Write a multiplication expression to represent the number of bottles.
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Solution

Sample responses:

  1. Array.
  1. 4×54 \times 5 or 5×45 \times 4

Problem 4

There are 5 rows of chairs in the room. There are 4 chairs in each row. How many chairs are in the room?

  1. Write a multiplication equation to represent the situation.
    Use a symbol for the unknown.

  2. Find the value that makes your equation true.

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Solution
  1. 5×4=?5 \times 4 = {?} or 4×5=?4 \times 5 = {?}
  2. 5×4=205 \times 4 = 20 or 4×5=204 \times 5 = 20 There are 20 chairs in the room.

Problem 5

  1. Write a multiplication equation that represents each array.

    A
    an array.

    B
    an array.

  2. How are the arrays alike? How are they different?
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Solution
  1. Sample response:
    1. ​​​​​​3×5=153 \times 5 = 15 or 5×3=155 \times 3 = 15
    2. 5×3=155 \times 3 = 15 or 3×5=153 \times 5 = 15
  2. Sample response: Both arrays have 15 circles in 3 rows and 5 columns. The first one shows the 3 rows of 5, and the second one shows the 5 columns of 3.

Problem 6

Andre says that there are an odd number of circles in this picture.

Do you agree with Andre? Explain or show your reasoning.

5 rows of circles. First row, 1 circle. Second row, 2 circles. Third row, 3 circles. Fourth row, 4 circles. Fifth row, 5 circles.

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Solution
Sample response: Yes. The circles that are not on the dotted line can be put in pairs: 4 pairs for the first row and column and 2 pairs for the second row and column. The line goes through 3 more circles, which is 1 pair and 1 leftover circle.

Problem 7

Find a collection of objects in the classroom or at home that is arranged in an array.

  1. Describe the objects.
  2. Create a drawing of the objects.
  3. Write an equation showing how many objects there are.
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Solution
Sample response:
  1. There are 13 rows of seats on the bus. Two kids sit in each row.

  2. Array.

  3. 2×13=262 \times 13 = 26 or 13×2=2613\times2=26