Understanding Multiplication: practice solutions, Grade 3 – download the PDF

1 Plates of cookies ★★★

1. There are 5 plates with 2 cookies each: \( 2 + 2 + 2 + 2 + 2 \).
2. 5 groups of 2: \( 5 \times 2 \).
3. Count by twos: 2, 4, 6, 8, 10. So \( 5 \times 2 = 10 \). There are 10 cookies.

2 From addition to multiplication ★★★

1. 6 is added 4 times: \( 4 \times 6 = 24 \).
2. 9 is added 3 times: \( 3 \times 9 = 27 \).
3. 2 is added 7 times: \( 7 \times 2 = 14 \).

3 Stickers in an array ★★★

1. There are 3 rows and 4 columns.
2. 3 rows of 4: \( 3 \times 4 = 12 \). 4 columns of 3: \( 4 \times 3 = 12 \). There are 12 stickers.

4 Skip counting by 5 ★★★

Five jumps of 5: 5, 10, 15, 20, 25. So \( 5 \times 5 = 25 \).

5 Zeros and ones ★★★

1. \( 7 \times 1 = 7 \) (7 groups of 1).
2. \( 1 \times 9 = 9 \) (1 group of 9).
3. \( 8 \times 0 = 0 \) (8 groups of nothing).
4. \( 0 \times 6 = 0 \) (no groups at all).

6 Name the parts ★★★

The factors are 4 and 7, because they are multiplied. The product is 28, because it is the answer.

7 Jumps on a number line ★★★

1. There are 3 jumps, and each jump is 4 long.
2. They land on 4, 8, and then 12. They end at 12.
3. \( 3 \times 4 = 12 \).

8 True or false? ★★★

1. True. Factors can switch places, and both products are 18.
2. True. 5 is added 3 times, and both sides equal 15.
3. False. Any number times 0 is 0, so \( 3 \times 0 = 0 \).
4. False. \( 4 \times 1 = 4 \), but \( 4 + 1 = 5 \).

9 Bike shop ★★★

6 groups of 2 wheels: \( 6 \times 2 = 12 \). Also, by the commutative property, \( 2 \times 6 = 12 \). There are 12 wheels.

10 Theater seats ★★★

The seats form an array with 7 rows and 3 columns. \( 7 \times 3 = 21 \). Check by skip counting: 3, 6, 9, 12, 15, 18, 21. The theater has 21 seats.

11 Bundles of pencils ★★★

Count by tens, eight times: 10, 20, 30, 40, 50, 60, 70, 80. So \( 8 \times 10 = 80 \). There are 80 pencils.

12 Switch the factors ★★★

1. \( 4 \times 7 = 28 \).
2. \( 9 \times 6 = 6 \times 9 \). The box is 9.
3. \( 5 \times 8 = 8 \times 5 \). The box is 8.

13 Arrays for 12 ★★★

Three possible arrays: 1 row of 12 (\( 1 \times 12 = 12 \)), 2 rows of 6 (\( 2 \times 6 = 12 \)), and 3 rows of 4 (\( 3 \times 4 = 12 \)). Flipping them gives 4 rows of 3 and 6 rows of 2, which are also correct.

14 Find the mistake ★★★

Leo added the factors (5 + 4 = 9) instead of finding 5 groups of 4. The correct work is \( 4 + 4 + 4 + 4 + 4 = 20 \), so \( 5 \times 4 = 20 \).

15 The hopping frog ★★★

1. Skip count by 6: 6, 12, 18, 24, 30, 36, 42. The frog lands on 42, and \( 7 \times 6 = 42 \).
2. Yes. 30 is the 5th landing spot, since \( 5 \times 6 = 30 \).
3. No. The frog lands on 36 and then 42, so it skips over 40.

16 Marching band ★★★

First find the total: \( 8 \times 5 = 40 \). Then subtract the players who left: \( 40 - 4 = 36 \). There are 36 players still on the field.

17 Write your own story ★★★

Sample story: “A zoo has 4 pens. Each pen has 9 rabbits. How many rabbits are there?” Repeated addition: \( 9 + 9 + 9 + 9 = 36 \). So \( 4 \times 9 = 36 \), and there are 36 rabbits. (Any story with 4 equal groups of 9 is correct.)

18 Which is greater? ★★★

1. \( 6 \times 4 = 24 \) and \( 4 \times 7 = 28 \). Since 24 < 28, 6 groups of 4 is less.
2. \( 3 \times 8 = 24 \) and \( 6 \times 4 = 24 \). They are equal.

19 Two arrays in one ★★★

1. \( 5 \times 3 = 15 \) tiles and \( 5 \times 4 = 20 \) tiles.
2. The big array has 5 rows and \( 3 + 4 = 7 \) columns.
3. \( 5 \times 7 = 35 \), and \( 15 + 20 = 35 \). Both ways give 35 tiles.

20 Zero and one puzzles ★★★

1. 1, because \( 9 \times 1 = 9 \).
2. \( 5 \times 0 = 0 \) and \( 1 \times 7 = 7 \), so \( 0 + 7 = 7 \). Ben has 7 stickers.
3. 0, because \( 12 \times 0 = 0 \).

21 Pick the right model ★★★

Repeated addition: \( 4 + 4 + 4 + 4 + 4 + 4 = 24 \). Skip counting by 4: 4, 8, 12, 16, 20, 24. Multiplication: \( 6 \times 4 = 24 \). All three give 24 cartons.