We included HMH 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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