# Into Math Grade 6 Module 15 Lesson 1 Answer Key Explore Mean as Fair Share

We included HMH Into Math Grade 6 Answer Key PDF Module 15 Lesson 1 Explore Mean as Fair Share to make students experts in learning maths.

## HMH Into Math Grade 6 Module 15 Lesson 1 Answer Key Explore Mean as Fair Share

I Can find both the fair share and the balance point of a data set using a model or a number line.

A florist needs to make 10 bouquets with 40 carnations, 36 red roses, 24 yellow roses, and 24 lilies. How many flowers should there be in each bouquet, so that each bouquet has the same number of flowers? Justify your answer. 12 flowers should be there in each bouquet.

Explanation:
40 + 36 + 24 + 24
76 + 24 + 24
100 + 24
124 flowers.
We need to make 10 bouquets.
So latex]\frac{124}{10}[/latex]
So 12 flowers should be there in each bouquet.

Turn and Talk Suppose the florist has to put the same number of each type of flower in each bouquet. How many total flowers should there be in each bouquet, and how many will be left over? Explain.

Build Understanding

If everyone has a fair share of a group of items, they all have the same number of items.

Question 1.
While at the beach, three friends found 6, 1, and 5 seashells. The friends agreed to divide the shells evenly. How many shells should each person get? Each person should get 4 seashells.

Explanation:
Three friends found 6, 1, and 5 seashells.
Total 12 seashells. And these are divided among three friends.
Therefore latex]\frac{12}{3}[/latex] = 4 seashells
Each person should get 4 seashells.
A. Look at the model shown. For each friend to have the same number of shells, or a fair share of shells, what needs to happen? Each friend should have 5 shells.

Explanation: B. Explain how you could rearrange the shells in Part A so that each friend has the same number of shells. Then sketch the fair shares.
Explanation: C. Suppose the three friends had found 9, 1, and 5 seashells. How many shells would each person get? Explain your reasoning
Each person would get 5 seashells.

Explanation:
Three friends found 9, 1, and 5 seashells.
Total of 15 seashells.
These shells should be divided among three friends.
latex]\frac{15}{3}[/latex]
5 seashells.

Turn and Talk Describe another way to find the fair share of shells each friend should have in Part C.

Question 2.
How can you find the balance point of a data set?
A. Look back at the data in Task 1, Part A. Complete the dot plot to represent the data. The balance point of a data set is 4

Explanation:
Number of sea shells are 1, 2, 3, 4, 5, 6, 7
total number of sea shells are 1 + 2+ 3+ 4+ 5+ 6+ 7 = 28
latex]\frac{28}{7}[/latex] = 4

B. Now, circle the number that represents the fair share number from Task 1 on the dot plot in Part A. What is the distance from each data point to the fair share number?
The distance from 1 to is . The distance from 5 to is .
The distance from 6 to is .
The distance from 1 to 4 is 3. The distance from 5 to 4 is 1.
The distance from 6 to 4 is 2.

C. What do you notice about the total distances from the data points on the left side and the right side of the fair share number? Explain.

D. A balance point of a data set is the point on a number line where the data distribution is balanced. What number from the dot plot in Part A represents the balance point for the data set 6 shells, 1 shell, and 5 shells? Explain.
4

Explanation:
The data set 6 shells, 1 shell, and 5 shells.
6 + 1 + 5 = 12
latex]\frac{12}{3}[/latex] = 4

Turn and Talk How are fair share and balance point related? Explain.

Check Understanding

Question 1.
Three friends have 7, 5, and 9 marbles. The friends agreed to divide the marbles evenly. How many marbles should each person get? Each person should get 7 marbles.

Explanation:
Given
7 + 5 + 9 = 21 marbles.
There are three friends.
Should divide equally.
So latex]\frac{21}{3}[/latex] = 7 marbles.

Question 2.
What is the balance point for the data set 3, 7, 8?
6

Explanation:
Given set = 3, 7, 8
3 + 7 + 8 = 18
latex]\frac{18}{3}[/latex]
= 6

Question 3.
Felipe has a bowl of fruit with 2 apples, 7 bananas, 2 oranges, 3 pears, and 1 plum. He wants to share the fruit with 4 friends. A. How many pieces of fruit will each person get?
60 pieces of fruit for each person.

B. How should Felipe distribute the fruit so everyone gets a fair share? Show your work.
Felipe has a bowl of fruit with 2 apples, 7 bananas, 2 oranges, 3 pears, and 1 plum
Total of 2 + 7 + 2 + 3 + 1 = 15 fruits
He wants to share with 4 friends
So 15 × 4 = 60 pieces of fruit for each person.

Question 4.
Attend to Precision What is the balance point for the set of data 3, 1, 8, 4, 6, 8?
A. Make a dot plot for the data.  B. What is the balance point?
5 is the balance point.

Explanation:
Given,
Data set = 3 + 1 + 8 + 4 + 6 + 8 =30
latex]\frac{30}{6}[/latex] = 5
Therefore 5 is the balance point.

C. Explain how you found the balance point.
Given,
Data set = 3 + 1 + 8 + 4 + 6 + 8 =30
latex]\frac{30}{6}[/latex] = 5
Therefore 5 is the balance point.

Question 5.
Open-Ended Make a data set that has 5 numbers and a balance point of 12.

I’m in a Learning Mindset!

What strategies for representing a fair share can I talk about?

Lesson 15.1 More Practice/Homework

Question 1.
Four friends fished for crabs. They caught 5, 9, 8, and 6 crabs. The friends agreed to divide the crabs evenly.
A. How many crabs should each person get?
Each person will get 7 crabs.

B. Describe how the crabs should be distributed among the four people.
There are four friends.
they caught 5, 9, 8,  and 6 crabs.
Their friends agreed to divide the crabs evenly is 5 + 9 + 8 + 6 = 28
latex]\frac{28}{4}[/latex] = 7 crabs.

Question 2.
Reason Five pages of a photo album contain 6, 7, 9, 10, and 13 pictures. Can the pictures be rearranged so that there is an equal number of pictures on each page? Explain why or why not.
9 pictures on each page.

Explanation:
Given,
6 + 7 + 9 +10 + 13 pictures = 45
latex]\frac{45}{5}[/latex]
9 pictures on each page.

Question 3.
Open-Ended How could the cubes be stacked so there is the same number of cubes in each stack? The same number of cubes in each stack is 5.

Question 4.
Tatiana has three dogs. She has the following amounts of dog food left.
17 cups of Brand A dog food
12 cups of Brand B dog food
13 cups of Brand C dog food
If the food is to be distributed evenly to the three dogs, how many cups of dog food should each dog get?
14 cups of dog food should each dog get.

Explanation:
Given
17 cups of Brand A dog food
12 cups of Brand B dog food
13 cups of Brand C dog food
A total of 42 cups of dog food.
Food should be distributed evenly to the three dogs so, latex]\frac{42}{3}[/latex] = 14 cups

Test Prep

Question 5.
In which ways could the cubes be stacked so there is the same number of cubes in each stack? Select all that apply. (A) 2 stacks of 5 cubes
(B) 2 stacks of 6 cubes
(C) 3 stacks of 4 cubes
(D) 4 stacks of 3 cubes
(E) 2 stacks of 12 cubes
(B) 2 stacks of 6 cubes
(C) 3 stacks of 4 cubes
(D) 4 stacks of 3 cubes

Question 6.
Alex has 36 pennies. He wants to stack them in equal rows. Select all the stacks that Alex can make.
(A) 3 stacks of 10 pennies
(B) 3 stacks of 12 pennies
(C) 5 stacks of 7 pennies
(D) 6 stacks of 6 pennies
(E) 8 stacks of 4 pennies
Alex can make 3 stacks of 12 pennies and 6 stacks of 6 pennies.

Question 7.
What is the balance point for the data set?
1, 5, 7, 3, 4
4

Explanation:
1 + 5 + 7 + 3 + 4 = 20
latex]\frac{20}{5}[/latex]
4 is the median for the data set.

Spiral Review

Question 8.
Find the volume of a rectangular prism with a length of 6$$\frac{1}{2}$$ feet, a width of 4$$\frac{3}{4}$$ feet, and a height of 3$$\frac{1}{2}$$ feet.
The volume of a rectangular prism is 108.06 cubic feet.

Explanation:
Given,
l =  6$$\frac{1}{2}$$ feet = $$\frac{13}{2}$$
w = 4$$\frac{3}{4}$$ = $$\frac{19}{4}$$
h = 3$$\frac{1}{2}$$ = $$\frac{7}{2}$$
Volume = l × b × h
Volume = $$\frac{13}{2}$$ × $$\frac{19}{4}$$ × $$\frac{7}{2}$$
= $$\frac{1729}{16}$$
= 108.06 cubic feet.

Question 9.
Ms. Castillo spent $87.75 on shrimp. The shrimp cost$9.75 per pound. How many pounds of shrimp did Ms. Castillo buy?
9 pounds.

Explanation:
Castillo spent = $87.75 Shrimp cost =$9.75 per pound
Castillo bought $$\frac{87.75}{9.75}$$
= 9 pounds.

Question 10.
Janelle earns $12 per hour. What equation can be used to find how many hours Janelle worked if she earned$360?
Janelle earns $12 per hour. She earned$360.
$360 =$12 × x per hour.
x = $$\frac{360}{12}$$