We included **H****MH Into Math Grade 5 Answer Key**** PDF** **Module 8 Lesson 1 Explore Groups of Equal Shares to Show Multiplication** to make students experts in learning maths.

## HMH Into Math Grade 5 Module 8 Lesson 1 Answer Key Explore Groups of Equal Shares to Show Multiplication

I Can find a fractional part of a group by using a visual model to solve a problem.

**Spark Your Learning**

Ayesha writes a children’s story about quartets of cat musicians. In her story, \(\frac{1}{4}\) of the cats in two quartets play the cello. How many cats in two quartets play the cello?

Answer:

The number of cats in two quartets playing the cello is 2 cats.

Explanation:

Given that Ayesha writes a children’s story about quartets of cat musicians and in her story, \(\frac{1}{4}\) of the cats in two quartets play the cello. So the number of cats in two quartets playing the cello is \(\frac{1}{4}\) × 8 which is 2 cats.

**Draw a visual model to show how you can find the number of cats in two quartets that play the cello. Justify your reasoning.**

**Turn and Talk** How could you find the number of cats that do not play the cello?

**Build Understanding**

1. After their concert, the cat quartet invites their friends to a party. Of the total number of cats shown, \(\frac{1}{6}\) of the cats have striped tails. How many cats have striped tails?

Answer:

The number of cats that have striped tails is 6 cats.

Explanation:

Given that \(\frac{1}{6}\) of the cats have striped tails. So the number of cats that have striped tails is \(\frac{1}{6}\) × 12 which is 6 cats.

**Draw a visual model to show how you can find the number of cats that have striped tails.**

A. How is the unit fraction \(\frac{1}{6}\) represented in your visual model?

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B. How can you use your visual model to find the number of cats that have striped tails?

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C. How many cats have striped tails?

Answer:

2 cats.

Explanation:

The number of cats that have striped tails is 2 cats.

**Turn and Talk** How would your visual model change if you wanted to find \(\frac{1}{2}\) of the cats at the party instead of \(\frac{1}{6}\)?

2. Four more cats join the party. Of the cats shown, \(\frac{3}{4}\) have solid-colored tails. How many cats have solid-colored tails?

Answer:

The number of solid-colored tails will be 12 cats.

Explanation:

Given that four more cats join the party and \(\frac{3}{4}\) have solid-colored tails. So the number of solid-colored tails will be \(\frac{3}{4}\) × 16 which is 3×4 = 12 cats.

**Draw a visual model to show how you can find the number of cats that have solid-colored tails.**

A. How many equal-sized groups did you draw? why?

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B. How many cats are represented in each group? ______________________

C. How many of these groups represent cats with solid-colored tails? How do you know?

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D. How many cats have solid-colored tails?

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Answer:

12 cats.

Explanation:

The number of cats that have solid-colored tails is 12 cats.

**Check Understanding Math Board**

Question 1.

At nine o’clock, \(\frac{5}{8}\) of the 16 cats at a party go home. How many cats go home at nine o’clock? Draw a visual model to find the answer.

Answer:

The number of cats go home at nine o’clock is 10 cats.

Explanation:

Given that at nine o’clock, \(\frac{5}{8}\) of the 16 cats at a party go home. So the number of cats go home at nine o’clock is \(\frac{5}{8}\)×16 which is 5×2 = 10 cats.

**On Your Own**

Question 2.

**Reason** Walt has twenty $1 bills. He uses \(\frac{3}{5}\) of his $1 bills to pay for a new winter hat. How much does Walt pay for his new winter hat? How do you know?

Answer:

Walt pay for his new winter hat is $12.

Explanation:

Given that Walt has twenty $1 bills and he uses \(\frac{3}{5}\) of his $1 bills to pay for a new winter hat. So Walt pay for his new winter hat is \(\frac{3}{5}\)×20 which is 3×4 = $12.

Question 3.

**Use Repeated Reasoning** Seth buys a carton of eggs. Find the number of eggs in each fraction of the total.

- \(\frac{2}{3}\) of the eggs ______
- \(\frac{5}{6}\) of the eggs ______
- \(\frac{1}{9}\) of the eggs ______
- \(\frac{6}{9}\) of the eggs ______

Answer:

\(\frac{2}{3}\) of the eggs 12 eggs,

\(\frac{5}{6}\) of the eggs 15 eggs,

\(\frac{1}{9}\) of the eggs 2 eggs,

\(\frac{6}{9}\) of the eggs 12 eggs.

Explanation:

Given that Seth bought a carton of eggs, so for \(\frac{2}{3}\) of the eggs it will be

\(\frac{2}{3}\) × 18 which is 2×6 = 12 eggs,

\(\frac{5}{6}\) × 18 which is 5×3 = 15 eggs,

\(\frac{1}{9}\) × 18 which is 1×2 = 2 eggs,

\(\frac{6}{9}\) × 18 which is 6×2 = 12 eggs.

**Draw a visual model to solve.**

Question 4.

\(\frac{2}{5}\) of 15 ____

Answer:

\(\frac{2}{5}\) of 15 = 6.

Explanation:

Given that \(\frac{2}{5}\) of 15 which is 2×3 = 6.

Question 5.

\(\frac{5}{6}\) of 12 ____

Answer:

\(\frac{5}{6}\) of 12 = 10.

Explanation:

Given that \(\frac{5}{6}\) of 12 which is 5×2 = 10.

Question 6.

**Use Tools** Use the number line to find \(\frac{7}{8}\) of 24. ____

Answer:

\(\frac{7}{8}\) of 24 = 21.

Explanation:

Given that \(\frac{7}{8}\) of 24 which is

= \(\frac{7}{8}\) × 24

= 7 × 3

= 21.

**I’m in a Learning Mindset!**

What strategies did I use to show a fractional part of a group?

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