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## Bridges in Mathematics Grade 5 Student Book Answer Key Unit 6 Module 4

**Bridges in Mathematics Grade 5 Student Book Unit 6 Module 4 Session 1 Answer Key**

**More of Caleb’s Flags**

Caleb just got an order for 2 more flags. Use his sketch plans to figure out how many square feet of cloth it will take to make each flag.

Question 1.

The first order is for a flag that is 2\(\frac{1}{2}\) feet wide and 4\(\frac{1}{2}\) feet long.

a. Write an expression to represent the area of this flag.

Answer: 2\(\frac{1}{2}\) x 4\(\frac{1}{2}\) = \(\frac{5}{2}\) x \(\frac{9}{2}\) = 11.25

Expression to represent the area of this flag is 2\(\frac{1}{2}\) x 4\(\frac{1}{2}\)

= \(\frac{5}{2}\) x \(\frac{9}{2}\) = 11.25

b. Here are three different estimates for the answer. Choose the one that is most reasonable, and explain why it is most reasonable.

9 square feet

10 square feet

11 square feet

Answer: 11 square feet

2\(\frac{1}{2}\) x 4\(\frac{1}{2}\) = \(\frac{5}{2}\) x \(\frac{9}{2}\) = 11.25

Expression to represent the area of this flag is 2\(\frac{1}{2}\) x 4\(\frac{1}{2}\)

= \(\frac{5}{2}\) x \(\frac{9}{2}\) = 11.25

c. Here is the plan Caleb has sketched out for this flag. Use his sketch to solve the problem. Show all of your work.

It will take ______________ square feet of cloth to make this flag.

Answer: 11.25 square feet

2\(\frac{1}{2}\) x 4\(\frac{1}{2}\)

= \(\frac{5}{2}\) x \(\frac{9}{2}\) = 11.25

Question 2.

The second order is for a flag that is 3\(\frac{1}{2}\) feet wide and 4\(\frac{3}{4}\) feet long.

a. Write an expression to represent the area of this flag.

Answer: 3\(\frac{1}{2}\) x 4\(\frac{3}{4}\) = \(\frac{7}{2}\) x \(\frac{19}{4}\) = 16.625

Expression to represent the area of this flag is 3\(\frac{1}{2}\) x 4\(\frac{3}{4}\)

= \(\frac{7}{2}\) x \(\frac{19}{4}\) = 16.625

b. Here are three different estimates for the answer. Choose the one that is most reasonable, and explain why it is most reasonable.

12 square feet

14 square feet

16 square feet

Answer: 16 square feet

3\(\frac{1}{2}\) x 4\(\frac{3}{4}\) = \(\frac{7}{2}\) x \(\frac{19}{4}\) = 16.625

Expression to represent the area of this flag is 3\(\frac{1}{2}\) x 4\(\frac{3}{4}\)

= \(\frac{7}{2}\) x \(\frac{19}{4}\) = 16.625

c. Here is the plan Caleb has sketched out for this flag. Use his sketch to solve the problem. Show all of your work.

It will take _____________ square feet of cloth to make this flag.

Answer: 16.625 square feet

3\(\frac{1}{2}\) x 4\(\frac{3}{4}\) = \(\frac{7}{2}\) x \(\frac{19}{4}\) = 16.625

Question 3.

CHALLENGE Find at least two different pairs of dimensions for a flag that has an area of 8\(\frac{1}{2}\) square feet. Show your work.

Answer: First pair: \(\frac{51}{4}\) feet wide and \(\frac{2}{3}\) feet long

Second pair: \(\frac{51}{16}\) feet wide and \(\frac{8}{3}\) feet long

8\(\frac{1}{2}\) square feet = \(\frac{17}{2}\) square feet

**Aaron’s Arrays**

Question 1.

Aaron is setting up an array to solve 2\(\frac{1}{3}\) × 4\(\frac{1}{4}\).

a. Fill in the blanks on the array.

Answer:

b. 2\(\frac{1}{3}\) × 4\(\frac{1}{4}\) = _________ + _________ + _________ + _________ = _________

Answer: 2\(\frac{1}{3}\) × 4\(\frac{1}{4}\) = 2.48 + 2. 48 + 2.48 + 2.48 = 9.91

2\(\frac{1}{3}\) × 4\(\frac{1}{4}\) = \(\frac{7}{3}\) × \(\frac{17}{4}\) = \(\frac{119}{12}\) = 9.91

2.48 + 2. 48 + 2.48 + 2.48 = 9.91

Question 2.

Aaron needs to solve 1\(\frac{4}{5}\) × 2\(\frac{1}{2}\).

a. Sketch and label an array that shows 1\(\frac{4}{5}\) × 2\(\frac{1}{2}\).

Answer: 4.4

1\(\frac{4}{5}\) × 2\(\frac{1}{2}\) = \(\frac{9}{5}\) × \(\frac{5}{2}\) = \(\frac{9}{2}\) = 4.5

b. 1\(\frac{4}{5}\) × 2\(\frac{1}{2}\) = _________ + _________ + _________ + _________ = _________

Answer: 1\(\frac{4}{5}\) × 2\(\frac{1}{2}\) = \(\frac{9}{8}\) + \(\frac{9}{8}\) + \(\frac{9}{8}\) + \(\frac{9}{8}\) = 4.5

1\(\frac{4}{5}\) × 2\(\frac{1}{2}\) = \(\frac{9}{5}\) × \(\frac{5}{2}\) = \(\frac{9}{2}\) = 4.5

\(\frac{9}{8}\) + \(\frac{9}{8}\) + \(\frac{9}{8}\) + \(\frac{9}{8}\) = 4.5

Question 3.

Fill in the blanks:

a. 3\(\frac{1}{2}\) × 14 = ___________ × 7 = ____________

Answer: 3\(\frac{1}{2}\) × 14 = 7 x 7 = 49

3\(\frac{1}{2}\) × 14 = \(\frac{7}{2}\) × 14 = 7 x 7 = 49

7 x 7 = 49

b. 32 × 2\(\frac{1}{4}\) = 16 × __________ = ____________

Answer: 32 × 2\(\frac{1}{4}\) = 16 × 4.5 = 72

32 × 2\(\frac{1}{4}\) = 32 × \(\frac{9}{4}\) =8 x 9 = 72

16 x 4.5 = 72

c. 24 × _________ = 12 × 15 = ____________

Answer: 24 x 7.5 = 12 x 15 = 180

**Review**

Question 4.

Solve. Use the strategy that makes the most sense to you.

Answer:

**Bridges in Mathematics Grade 5 Student Book Unit 6 Module 4 Session 2 Answer Key**

**Thinking About Flags**

Every country in the world has its own flag. Every state in the United States also has its own flag. Cities, sports teams, colleges, and high schools often have their own flags as well. Flags are designed to tell a story about a group of people or an organization. A country’s flag often tells something about the history of that country. For example, the American flag still has 13 red and white stripes, which stand for the original 13 colonies. There are also 50 stars on the American flag, one for each state.

Flag makers use special words to describe the dimensions of a flag. The side of the flag nearest the flag pole—its width—is called the hoist. The side of the flag that extends from the hoist to the free end—its length—is called the fly.

Flags come in all different sizes, from the tiny flags children wave at parades to the huge flags people march out onto football fields at halftime. You may have noticed that the flag for a particular country is usually the same shape, no matter how large or small it is. That is because flag makers use the same ratio for the hoist to the fly, no matter what the size of the flag. The ratio of the hoist to the fly for the American flag is 10:19. If the hoist is 10 inches, the fly is 19 inches. If the hoist is doubled to 20 inches, the fly must also be doubled. Fill in the ratio table below to see some different sizes for the U.S. flag.

**Caleb’s U.S. Themed Flags**

Caleb has decided to design and make a new set of flags. Each of these flags will feature a theme that is uniquely American. Naturally, Caleb wants to use the hoist-to-fly ratio of the American flag, 10:19.

He wants to make the largest of the flags in this new set 10 feet by 19 feet. Then he plans to cut the dimensions in half, and then in half again, and then in half again to make smaller and smaller flags.

Question 1.

Fill in the ratio table below to help Caleb plan the different sizes. Use fractions, rather than decimals, when the answers are not whole numbers.

Answer:

Question 2.

Caleb uses the area of a flag to help figure out how much to charge for it. The area of the largest flag on the ratio table is 10′ × 19′ = 190 ft^{2}. Help him find the area of each of the other flags on the ratio table in square feet. Label each sketch with the dimensions of the flag. Then use the sketch to find the area of that flag.

Flag b is ____________ × ____________.

Area = ______________ ft^{2}

Answer: Flag b is 5′ x 9.5 ‘

Area = 47.5 square ft

Flag c is ____________ × ____________.

Area = ______________ ft^{2}

Answer: Flag c is 2.5′ x 4.75′

Area = 11.875 square feet

Flag d is ____________ × ____________.

Area = ______________ ft^{2}

Answer: Flag d is 1.25 x 2.375′

Area = 2.96875 square feet

**CHALLENGE** Flag e is ____________ × ____________.

Area = ______________ ft^{2}

Answer: Flag e is 0.625 x 1.1875

Area = 0.74218 square feet

**Sophia’s Work**

Question 1.

Sophia solved 2\(\frac{1}{6}\) – 1\(\frac{2}{3}\) like this:

a. Sophia did not get the correct answer. Can you explain why?

Answer: Sophia answer is not correct.

2\(\frac{1}{6}\) – 1\(\frac{2}{3}\) = \(\frac{13}{6}\) – \(\frac{5}{3}\)

= \(\frac{13}{6}\) – \(\frac{10}{6}\)

= \(\frac{3}{6}\)

= \(\frac{1}{2}\)

b. How would you solve 2\(\frac{1}{6}\) – 1\(\frac{2}{3}\)?

Answer: \(\frac{1}{2}\)

2\(\frac{1}{6}\) – 1\(\frac{2}{3}\) = \(\frac{13}{6}\) – \(\frac{5}{3}\)

= \(\frac{13}{6}\) – \(\frac{10}{6}\)

= \(\frac{3}{6}\)

= \(\frac{1}{2}\)

Question 2.

Sophia has to read 5 books each month. By the middle of April, she had read 1\(\frac{5}{8}\) books. How many more books does Sophia need to read before the end of April?

Answer: \(\frac{27}{8}\)

Sophia has to read 5 books each month.

By the middle of April, she had read 1\(\frac{5}{8}\) books

The number of more books Sophia needs to read before the end of April is = 5 – 1\(\frac{5}{8}\)

= 5 – \(\frac{13}{8}\)

= \(\frac{40}{8}\) – \(\frac{13}{8}\)

= \(\frac{27}{8}\)

Question 3.

Write a story problem for this expression: 2\(\frac{1}{4}\) × 1\(\frac{3}{8}\). Then solve the problem.

Answer: \(\frac{99}{32}\)

Story: Sophia spends 2\(\frac{1}{4}\) time daily for reading books. she spent 1\(\frac{3}{8}\) days. How much time did she spent ?

2\(\frac{1}{4}\) × 1\(\frac{3}{8}\) = \(\frac{9}{4}\) × \(\frac{11}{8}\)

= \(\frac{99}{32}\)

Question 4.

Fill in the blanks.

\(\frac{8}{8}\) × ___________ = 12

\(\frac{18}{9}\) × ____________ = 10

\(\frac{5}{5}\) × 5 = ______________

Answer: \(\frac{8}{8}\) × **12** = 12

\(\frac{18}{9}\) × **5** = 10

\(\frac{5}{5}\) × 5 = \(\frac{1}{1}\) = **1**

**Bridges in Mathematics Grade 5 Student Book Unit 6 Module 4 Session 3 Answer Key**

**Design-a-Flag Challenge**

Most countries have flags with ratios that are easier to work with than 10:19. Here are some of the more common ratios, and some of the countries that use those ratios.

You are going to design your own flag today. Here are your instructions:

Question 1.

Choose one of the ratios above for your flag.

Answer: 1:2

From the above ratios selecting 1:2.

Question 2.

No matter which ratio you choose, the hoist of your flag will be 9 inches. What fraction of a foot is 9 inches? Show your work.

Answer: 4.5 inches

(1/ 2 ) x 9 = 4.5 inches

Question 3.

Fill in the ratio table to figure out how long your flag’s fly will be if the hoist is 9″.

ex: My ratio is 4:7 (This is a real ratio, used in the flags of Mexico.)

a. My ratio is _______________.

Think: What do I have to multiply the first number in my ratio by to make 9? When you figure that out, multiply the second number in your ratio by the same number. Use the example above to help you. Draw a flag and label the ratios or dimensions if you like.

Answer:

Question 4.

The hoist of my flag will be 9 inches. The fly of my flag will be inches.

a. What is the fly of your flag in feet? Show your work.

Answer: The fly of the flag is 15\(\frac{3}{4}\) feet

b. In the space below, draw an outline of your flag. Use a scale of 1 centimeter per inch. For example, if your flag is going to be 9 inches by 15\(\frac{3}{4}\) inches, measure and draw a rectangle that is 9 cm by 15\(\frac{3}{4}\) cm.

Answer:

c. Label your sketch with its dimensions given in feet.

Answer:

d. Find the area of your flag in square feet. Show all your work.

The area of my flag is _____________ ft^{2}.

Answer: area of my flag is 141.75 square feet.

Area = length x width

area = 9 x 63 /4 = 141.75

**Boxes & Banners**

Question 1.

Ebony’s cousin Jada is away at college this year. Ebony wants to send her a package with some candy in it. She has the three boxes shown below. Which box should she use if she wants to send Jada as much candy as possible?

a. What do you need to know about the boxes in order to answer the question above?

Answer: Their volume

We need to know the volume of the each box to answer the above question.

b. Solve the problem. Show all your work.

Answer: Ebony wants to send Jada box B.

Volume of the each box shown here is:

Box A: 52 x 22 x 8 = 9152 cm^{3}

Box B: 22 x 22 x 22 = 10648 cm^{3}

Box C: 22 x 17 x 15 = 5610 cm^{3}

Question 2.

Ebony also made a banner for Jada to hang on the door of her dormitory room. The banner is 1\(\frac{1}{4}\) feet wide and 2\(\frac{1}{2}\) feet long.

a. Mark the bubble to show which flag-making ratio Ebony used.

2:3

3:5

1:2

3:4

Answer: 1:2

The banner is 1\(\frac{1}{4}\) feet wide and 2\(\frac{1}{2}\) feet long.

1\(\frac{1}{4}\) : 2\(\frac{1}{2}\)

\(\frac{5}{4}\) : \(\frac{5}{2}\) = 1 : 2

b. What is the area of the banner? Make a labeled sketch to model and solve this problem. Show all of your work.

Answer:

Area = 2 + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{8}\) = 3 \(\frac{1}{8}\) sq. ft.

**Bridges in Mathematics Grade 5 Student Book Unit 6 Module 4 Session 4 Answer Key**

**Simplifying Fractions Review**

Question 1.

Divide the numerator and denominator of each fraction by the largest factor they have in common (the greatest common factor) to show each fraction in its simplest form. A fraction is in its simplest form when its numerator and denominator have no common factor other than 1. Some of the fractions below may already be in simplest form.

Answer:

Question 2.

Write two fractions that are equal to the fraction shown.

ex:

a. \(\frac{6}{12}\) = and \(\frac{6}{12}\) =

Answer: \(\frac{6}{12}\) = \(\frac{1}{2}\) and \(\frac{6}{12}\) = \(\frac{12}{24}\)

b. \(\frac{3}{15}\) = and \(\frac{3}{15}\) =

Answer: \(\frac{3}{15}\) = \(\frac{1}{5}\) and \(\frac{3}{15}\) = \(\frac{9}{45}\)

c. \(\frac{7}{12}\) = and \(\frac{7}{12}\) =

Answer: \(\frac{7}{12}\) = \(\frac{14}{24}\) and \(\frac{7}{12}\) = \(\frac{21}{36}\)