# enVision Math Common Core Grade 5 Answer Key Topic 12 Convert Measurements

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## enVision Math Common Core 5th Grade Answers Key Topic 12 Convert Measurements

enVision STEM Project: Grand Canyon
Do Research Use the Internet and other sources to learn about the Grand Canyon and the Colorado River. Where is the Grand Canyon? How was it formed? What do the different rock layers tell us? Predict how you think the canyon dimensions will change in a million years.
Journal: Write a Report Include what you found. Also in your report:
• Describe the canyon’s dimensions.
• Describe the Colorado River’s dimensions.
• Define erosion.
• Make up and solve problems involving measurement units and conversions.

Review What You Know

A-Z Vocabulary

Choose the best term from the box. Write it on the blank.

• customary
• multiplication
• subtraction
• exponent
• metric

Question 1.
A meter is a unit of length in the ___ system of measurement.

A meter is a unit of length in the Metric system of measurement.

Question 2.
A foot is a unit of length in the ____ system of measurement.

A foot is a unit of length in the British imperial and United States customary system of measurement.

Question 3.
The division has an inverse relationship with _____

The division has an inverse relationship with Multiplication.

Question 4.
A(n) ____ shows the number of times a base is used as a factor.

An Exponent shows the number of times a base is used as a factor.

Multiplication

Find each product.

Question 5.
60 × 6

60 × 6 = 360

Question 6.
24 × 103

24 × 103

= 24000

Question 7
16 × 7

16 × 7 = 112

Question 8.
102 × 1.6

102 × 1.6 = 160

Question 9.
100 × 34

100 x 34 = 3400

Question 10.
104 × 0.37

104 × 0.37 = 3700

Question 11.
46.102 × 102

46.102 × 102 =

= 4702. 404

Question 12.
101 × 0.005

0.05

Division
Find each quotient.

Question 13.
1,000 ÷ 100

1,000 ÷ 100

Quotient = 10

Question 14.
176 ÷ 16

176 ÷ 16

Quotient = 11

Question 15.
3,600 ÷ 60

3,600 ÷ 60

Quotient = 60

Question 16.
120 ÷ 24

120 ÷ 24

Quotient = 5

Measurement
Circle the more appropriate unit of measure for each item.

Question 17.
The capacity of a swimming pool: liters or milliliters

Question 18.

The length of an ear of corn: yards or inches

Question 19.
The mass of a gorilla: grams or kilograms

Question 20.
The weight of a tennis ball: ounces or pounds

Question 21.

Would you use more centimeters or meters to measure the length of car? Explain.

meters is more useful to measure the length of the car.

meters are used to measure the length of the car. Because centimeters are shorter than meters.

Pick a Project
PROJECT 12A
What makes a treehouse so cool?
Project: Build a Model of a Treehouse

PROJECT 12B
What would you weigh on Mars?
Project: Make a Mobile Display of the Solar System

PROJECT 12C
Have you ever heard of National Punch Day?
Project: Plan a Class Party

PROJECT 12D
What are the characteristics of Florida panthers?
Project: Design a Zoo Space for Florida Panther Cubs

### Lesson 12.1 Convert Customary Units of Length

Activity

Solve & Share
William has a piece of wire that measures 1 yard long. He will use wire to fix several electrical outlets in his house. How many inches long is the wire? Solve this problem by using bar diagrams.

You can show the relationship between yards and inches in a bar diagram. Show your work!

Look Back! Generalize How can you convert inches to yards? Would you multiply or divide when converting from a smaller unit to a larger unit? Explain.

Visual Learning Bridge

Essential Question How Do You Change from One Leon Unit of Length to Another?

A.
Some frogs can jump 11$$\frac{1}{4}$$ feet. What are some other ways to describe the same distance?

The table shows equivalent measures.

B.
To change larger units to smaller units, multiply.

You know 1 foot equals 12 inches.

You know 3 feet is equal to 1 yard.

C.
To change smaller units to larger units, divide.
Ed’s frog jumped 11 feet. How many yards is this?

11 ÷ 3 = 3 R2 So, 11 feet = 3 yards, 2 feet.

Convince Me! Generalize In the example above, explain how you could use a mixed number to write 11 feet as an equivalent measure in yards.

Guided Practice

Do You Understand?

Question 1.
If you want to convert yards to feet, what operation would you use?

To convert a yard measurement to a foot measurement, multiply the length by the conversion ratio. The length in feet is equal to the yards multiplied by 3.

Question 2.
If you want to convert feet to miles, what operation would you use?

To convert a foot measurement to a mile measurement, divide the length by the conversion ratio.

Question 3.
What are some tools you could select to measure length? Explain when you would use them.

The most common way to measure length is by using the scale on some sort of hand-held tool or implement, but you can also measure length — or distance — with radar, sonar, and laser beams.

Do You Know How?

In 4-8, convert each unit of length.

Question 4.
9 ft = ___ yd

Question 5.
8 ft 7 in. = ___ in.

103 inches

Question 6.
5$$\frac{1}{2}$$ ft = __in.

Question 7.
288 in. = __ yd

8 yards

Question 8.
219 in. = ___ ft ___ in. or. ___ ft

18 feet 3 inches

18.25 ft

Independent Practice

In 9 and 10, complete the table to show equivalent measures.

Will the number in your answer be greater than or less than the number in the given measurement?

Question 9.

1 feet = 12 inches

2 feet = 24 inches

3 feet = 36 inches

4 feet = 48 inches

Question 10.

1 yard = 3 feet

2 yard = 6 feet

3 yard = 9 feet

4 yard = 12 feet

In 11-16, convert each unit of length.

Question 11.
3 yd = ___ in.

3 yd = 108 inches

Question 12.
324 ft =__ yd

324 ft = 108 yd

Question 13.
2$$\frac{2}{3}$$ mi = ___ ft

2 2/3 miles = 14080 feet

Question 14.
56 ft = ___ yd ___ ft

56 ft = 18 yd 2 ft

Question 15.
12$$\frac{1}{2}$$  = ___ in.

12 1/2 feet = 150 inches

Question 16.
6 in. = ___ ft

6 in = 0.5 feet

In 17-19, compare lengths. Write >,<, or = for each

Question 17.
100 ft 3 yd

100 ft >3 yd

Question 18.
74 in. 2 yds 2 in.

74 in = 2 yd 2 in

Question 19.
5,200 ft 145 in. 1 mi 40 in.

5200 ft 145 in > 1 mi 40 in.

Problem Solving

Question 20.
Number Sense Which number would be greater, the height of a tree in feet or the height of the same tree in yards?

1 feet = 30.48 centimeters

1 yard = 91.44 centimeters.

Question 21.
Reasoning The dimensions of the nation’s smallest post office are 8 feet 4 inches by 7 feet 3 inches. Why would you use the measurement 8 feet 4 inches instead of 7 feet 16 inches?

16 inches = 1 foot 4 inches

1 foot is added to 7 inches

Therefore,

The measurement 8 feet 4 inches instead of 7 feet 16 inches

Question 22.
Roger earns $24 a week mowing lawns. He spends $$\frac{1}{6}$$ of his earnings on lunch and $$\frac{2}{3}$$ of his earnings on music. He saves the rest. How many dollars does Roger save? Tell me how you found the answer. Answer: Given that, Roger earns$24 a week

The amount he spends on his lunch = 1/6 of his earnings

Which means, 1/6 x 24 = 4

Also given, he spends 2/3 of his earnings on music

This means, 2/3 x 24 = 16

Total amount he spend = 16 + 4 = 20

Remaining amount = 24 – 20

A 250 mL container of juice costs $1.69. One liter of juice in half-liter packs costs,$2.39 x 2 = $4.78. One liter of juice in 250 mL packs costs,$1.69 x 4 = $6.76. So, Terry should buy 6 half-liter packs of juice and spend$2.39 x 6 = $9.56 to get 3 liters at the lowest price. What steps do you need to do to solve this problem? Assessment Practice Question 28. A birdbath holds 4 liters of water. How many milliliters of water does it hold? A. 400 ml B. 800 mL C. 4,000 mL D. 8,000 mL Answer: C. 4,000 mL 1 litre = 1000 milliliters So, 4 litres = 4000 millilitres. Question 29. You are filling a 2-liter bottle with liquid from full 80-milliliter containers. How many containers will it take to fill the A. 400 B. 250 C. 40 D. 25 Answer: 1 litre = 1000 millilitres So, The number of 80 mL containers need are 2000/80 = 25 Therefore, 25 containers are required. ### Lesson 12.6 Convert Metric Units of Mass Activity Solve & Share In chemistry class, Rhonda measured 10 grams of a substance. How many milligrams is this? Solve this problem any way you choose. Answer: 1 gram = 1000 mg So, 10 grams = 10000 milligrams. Look for Relationships You can use patterns to help you see a relationship between the units. Look Back! How many kilograms did Rhonda measure? Write an equation to model your work. Visual Learning Bridge Essential Question How Do You Convert Metric Units of Mass? A. The three most commonly used units of mass are the milligram (mg), the gram (g), and the kilogram (kg). Converting metric (units of mass is like converting other metric units. B. A whistle has a mass of about 5 grams. How many milligrams is this? To change from a larger unit to a smaller unit, multiply. Find 5 × 103 5 × 103 = 5 × 1,000 = 5,000 So, 5 g = 5,000 mg So, a whistle has a mass of about 5,000 milligrams. C. How many kilograms is the whistle? To change from a smaller unit to a larger unit, divide. Find 5 ÷ 103 5 ÷ 103 = 5 ÷ 1,000 = 0.005 So, 5 g = 0.005 kg. So, a whistle has a mass of about 0.005 kilograms. Convince Me! Use Structure in the picture above, what is the football player’s mass in grams and in milligrams? How can you tell? Guided Practice Do You Understand? Question 1. A-Z Vocabulary How does the relationship between meters and millimeters help you understand the relationship between grams and milligrams? Answer: 1 meter = 1000 millimeters. 1 Gram = 1000 milligrams. Question 2. Which has the greater mass: 1 kilogram or 137,000 milligrams? Explain how you made your comparison. Answer: 137,000 is greater Because, 1 kg = 1000000 Therefore, 137,000 is greater than 1 kg Do You Know How? In 3 and 4, convert each unit of mass. Question 3. 9.25 g = ___ mg Answer: 9250 mg Question 4. 190 g = __ kg Answer: 0.19 kg In 5 and 6, compare. Write >,<, or = for each Question 5. 7,000 mg 7,000 g Answer: 7,000 mg < 7,000 g Question 6. 102 kg 104 g Answer: 102 kg > 104 g Independent Practice In 7-12, convert each unit of mass. Question 7. 17,000 g = ___ kg Answer: 17,000 = 17 kg Question 8. 18 kg = ___ g Answer: 18 kg = 18000 g Question 9. 4,200 mg = ___ g Answer: 4.2 g Question 10. 0.276 g = ____ mg Answer: 276 mg Question 11. 4.08 kg = ___ g Answer: 4080 g Question 12. 43 mg = ___ g Answer: 0.043 g In 13-18, compare. Write >, <, or = for each Question 13. 2,000 g 3 kg Answer: 2000 g < 3 kg Question 14. 4 kg 4,000 g Answer: 4 kg = 4000 g 4 kg = 4,000 g Question 15. 104 mg 13 g Answer: 104 mg < 13 g Question 16. 7 kg 7,000 g Answer: 7 kg < 7000 g Question 17. 9,000 g 8 kg Answer: 9000 g > 8 kg Question 18. 8,000 g 5 kg Answer: 8000 > 5 kg In 19 and 20, complete each table. Question 19. Answer: 1 grams = 1000 milligrams 10 grams = 10000 milligrams 100 grams = 100000 milligrams Question 20. Answer: 500 grams = 0.5 kg 5000 grams = 5 kg 50000 grams = 50 kg Problem Solving Question 21. Make Sense and Persevere Sheryl has a recipe for pasta with vegetables. The recipe calls for 130 grams of vegetables and twice as much pasta as vegetables. What is the total mass in grams of the recipe? Answer: Given, The mass of vegetables = 130 grams Also given, the mass of pasta is twice as vegetables Which means, 130 x 2 = 260 Total mass = 260 + 130 = 390 grams Therefore, the total mass of the recipe = 390 grams. Question 22. Terri is beginning a science experiment in the lab. The instructions call for 227 milligrams of potassium. Calculate the difference between this amount and 1 gram. Answer: We know that, 1 gram = 1000 milligrams Given that, The weight of potassium = 227 milligrams Now, The difference between the amount = 1000 – 227 = 773 grams. Therefore, the difference between the amount and 1 gram = 773 grams. Question 23. Number Sense One of the world’s heaviest hailstones weighed 2.2 pounds. Which is more appropriate to express its mass, 1 kilogram or 1 gram? Answer: 2.2 pounds = 0.997 kg 2.2 pounds = 997. 9 grams Therefore, 1 kilogram is more appropriate to express the mass. Question 24. Higher Order Thinking A cook has 6 onions that have a total mass of 900 grams and 8 apples that have a total mass of 1 kilogram. All onions are the same size, and all apples are the same size. Which has the greater mass, an onion or an apple? Explain. Answer: Given, Number of onions = 6 Total mass = 900 grams Weight of each onion = 900/6 = 150 grams. Number of apples = 8 Total mass = 1 kg or 1000 grams Weight of each apple = 1000/8 = 125 grams. Therefore, Onion has a greater mass than apple. In 25 and 26, use the given information and the picture. enVision® STEM If a man weighs 198 pounds on Earth, his mass on Earth is 90 kilograms. Question 25. What is this man’s weight on the Moon? Answer: Given, The weight of the person on the moon is 1/6 weight on earth. Also given, the mass on earth = 90 kgs The weight of man’s weight on the moon = 90/6 =15 or 14.9 approx. Question 26. What is his mass in grams? Answer: 1 kg = 1000 grams. 15 kg = 15000 grams Assessment Practice Question 27. Write the following masses on the lines from least to greatest. Answer: 5000 mg > 500 g > 50 kg Question 28. If you convert grams to milligrams, what operation would you use? A. Addition B. Subtraction C. Multiplication D. Division Answer: Multiplication. ### Lesson 12.7 Convert Units of Time Activity Solve&Share Emily played softball all weekend. She was wondering the difference in time between the shortest game and the longest game. Can you help her figure it out? Select a common unit of time to help compare game times. Look Back! Make Sense and Persevere Mateo saw a professional baseball game, which lasted 2$$\frac{1}{2}$$ hours. How many minutes longer was the professional game than Emily’s Game 3? Explain. Visual Learning Bridge Essential Question How Do You Solve Problems that Involve Different Units of Time? A. Kendall’s family is driving to the theater to see a 2-hour movie. Kendall notices this sign at the parking lot closest to the theater. Do you think they should park there? You can convert one of these times so you are comparing like units. B. One Way: Convert 2 hours to minutes. Then compare. To change from larger units to smaller units, multiply. Remember, 1 hour equals 60 minutes. 2 × 60 minutes = 120 minutes 120 minutes > 90 minutes, so Kendall’s family should not park in that lot. C. Another Way: Convert 90 minutes to hours. Then compare. To change from smaller units to larger units, divide. 90 ÷ 60 = $$\frac{90}{60}$$ = 1$$\frac{1}{2}$$ hours 1$$\frac{1}{2}$$ hours < 2 hours, so Kendall’s family should not park in that lot. Convince Me! Make Sense and Persevere explain how to convert 4 hours, 15 minutes to minutes. Another example! There is often more than one way to show converted units of time. Find the missing numbers. Divide. Write the quotient with a remainder. 210 ÷ 60 = 3 R 30 So, 210 seconds = 3 minutes, 30 seconds Remember, 1 minute equals 60 seconds. 210 seconds = ___ minutes Divide. Write the quotient as a mixed number. $$\frac{210}{60}$$ = 3$$\frac{30}{60}$$ = 3$$\frac{1}{2}$$ So, 210 seconds = 3$$\frac{1}{2}$$ minutes Guided Practices Do You Understand? Question 1. Which is the longest time: 5 minutes, 25 seconds, or 315 seconds? Explain. Answer: 5 hours 25 seconds Explanation : 1 minute = 60 seconds So, 5 minutes = 300 seconds Now, 300 +25 = 325 seconds Therefore, 325 seconds is longer than 315 Question 2. How many minutes are in a quarter-hour? How do you know? Answer: Quarter hour = 15 minutes We know that 15 minutes = quarter. Do You Know How? In 3-6, convert each time. Question 3. 240 seconds = ___ minutes Answer: 4 Minutes. Question 4. 2 hours, 18 minutes = ___ minutes Answer: 120 + 18 138 minutes Question 5. 4$$\frac{1}{2}$$ minutes ___ seconds Answer: 4 minutes = 4 x 60 = 240 seconds 1/2 minute = 30 seconds Now, 240 + 30 = 270 Seconds Therefore, 4 1/2 Minute = 270 seconds. Question 6. 80 minutes = ___ Seconds Answer: 1 minute = 60 seconds 80 minutes = 80 x 60 = 480 seconds. Independent Practice In 7-10, convert each time. Question 7. 6 hours = ___ minutes Answer: 1 hour = 60 minutes So, 6 hours = 6 x 60 = = 360 minutes. Question 8. 390 seconds = ___ minutes Answer: 60 seconds = 1 minute Now, 360 seconds = 6 minutes 30 seconds = 1/2 minute 390 seconds = 6 1/2 minutes. Question 9. 208 minutes = ___hours, ___ minutes Answer: 1 hour = 60 minutes 3 hours = 180 minutes And 208 – 180 = 28 minutes Therefore, 208 minutes = 3 hours 28 minutes. Question 10. 7 minutes, 12 seconds = ___ seconds Answer: 1 minute = 60 seconds 7 minutes = 7 x 60 = 420 seconds 420 + 12 = 432 seconds . Therefore, 7 minutes, 12 seconds = 432 seconds In 11-12, compare. Write >, <, or = for each Question 11. 330 minutes 7.5 hours Answer: 330 minutes < 7.5 hours Question 12. 45 minutes $$\frac{3}{4}$$ hour Answer: 45 minutes = 3/4 hour Problem Solving Question 13. Brock spends 15 minutes walking to school and 15 minutes walking home each day. By the end of the school week (5 days) how many hours has Brock spent traveling between home and school? Answer: Given, Brock spends 15 minutes walking to school 15 minutes walking home Total = 15 + 15 = 30 Number of days = 5 Now, 5 x 30 = 150 minutes 1 hour = 60 minutes 150 minutes = 2.5 hours Therefore, Brock spent 2.5 hours traveling between home and school Question 14. A television station shows commercials for 7$$\frac{1}{2}$$ minutes each hour. How many 45-second commercials can it show per hour? Answer: 1 minute = 60 seconds 7 minutes = 60 x 7 = 420 seconds 420 + 30 = 450 450/45 = 10 Therefore, 10 45 second commercials it can show per hour. Question 15. Leslie is making these two recipes. Which takes longer to make, the strawberry bread or the spaghetti sauce? How many minutes longer? Answer: The time is taken to prepare spaghetti sauce is 1 hour 40 minutes Also, the time taken to prepare strawberry bread is 1 hour 15 minutes Therefore spaghetti sauce takes longer Now, 1 hour 40 minutes – 1 hour 15 minutes = 25 minutes spaghetti sauce takes 25 minutes longer than strawberry bread. Question 16. Critique Reasoning The school day is 6 hours, 15 minutes long. Jenna says that it’s 6$$\frac{1}{4}$$ hours. Henry says it’s 6.25 hours. Can they both be correct? Explain. Answer: Jenna is correct. Given, the time of the school day = 6 hours 15 minutes long 1 hour = 60 minutes 1/4 hour = 15 minutes and 6 hours Total: 6 1/4 hour 6.25 hours means 25 minutes more But the school day is only 15 minutes long Therefore, Jenna is correct. Question 17. Higher-Order Thinking How many seconds are there in 1 hour? In 10 hours? Explain. Answer: 1 hour = 60 minutes 1 minute = 60 seconds 60 minutes = 60 x 60 = 3600 seconds 10 hours = 10 x 60 = 600 minutes 600 minutes = 600 x 600 = 36000 seconds. Assessment Practice Question 18. Three hikers reported how long it took to hike a trail. Write the names of the hikers from fastest to slowest. ___ ____ _____ Answer: Anita – First – 70 minutes Brad – second – 75 minutes Sanjay – Third – 90 minutes ### Lesson 12.8 Solve Word Problems Using Measurement Conversions Activity Solve&Share Amy wants to frame a poster that has a width of 8 inches and a length of 1 foot. What is the perimeter of the poster? Solve this problem any way you choose. Make Sense and Persevere You can use measurement conversions in real-world situations. Show your work! Look Back! Which measurement did you convert? Can you find the perimeter by converting to the other unit of measurement? Visual Learning Bridge Essential Question How Can You Convert Units of Session Measurement to Solve a Problem? A. A city pool is in the shape of a rectangle with the dimensions shown. What is the perimeter of the pool? You can convert one of the measures so that you are adding like units. B. What do you know? The dimensions of the pool: l = 25 yards w = 60 feet What are you asked to find? The perimeter of the pool You can use feet for perimeter. C. Convert 25 yards to feet so you can add like units. 1 yard = 3 feet To change from larger units to smaller units, multiply. 25 × 3 feet = 75 feet So, 25 yards = 75 feet. D. Substitute like measurements into the perimeter formula. Perimeter = (2 × length) + (2 × width) P = (2 × l) + (2 × w) P = (2 × 75) + (2 × 60) P = 150 + 120 P = 270 feet The perimeter of the pool is 270 feet. Convince Me! Be Precise If the width of the pool is increased by 3 feet, what would be the new perimeter of the pool? Explain. length = 75 feet width = 63 feet Perimeter = 2 ( l+b) 2 (75+63) 2 ( 138 ) = 276 feet. Guided Practice Do You Understand? Question 1. In the example on the previous page, how could you find the perimeter by converting all measurements to yards? Answer: 75 feet = 25 yards 60 feet = 20 yards perimeter = 2 ( 25 + 20 ) = 2 ( 45) perimeter = 90 feet Question 2. Write a real-world multiple-step problem that involves measurement. Answer: Multiple-step problem : Robert had 16 marbles. His brother gave him 3 more bags of marbles. If each bag contained 5 marbles, how many marbles does Robert have now? Do You Know How? Question 3. Stacia needs enough ribbon to wrap around the length (l) and height (h) of a box. If the length is 2 feet and the height is 4 inches, how much ribbon will she need? Answer: Given length = 2 feet And height = 4 inches Perimeter = 2 (l+b) = 2 ( 2 + 4) = 2 (6) = 12 feet 1 feet = 12 inches Now, 12 feet = 12 x 12 = 144 inches. Question 4. If ribbon is sold in whole number yards and costs$1.50 per yard, how much will it cost Stacia to buy the ribbon?

144 x $1.05 = 151.2 Therefore it costs approx$151 to buy the ribbon.

Independent Practice

In 5-7, use conversions to solve each problem.

Edging means she will put bricks around the perimeter of the hexagon.

Question 5.
Becca wants to edge her hexagonal garden with brick. All sides are equal. The brick costs $6 per yard. What is the perimeter of the garden? How much will it cost to buy the edging she needs? Answer: The perimeter of the hexagon = Number of sides = 6 Now, 12 x 6 = 72 feet The perimeter of hexagon = 72 feet or 24 yards Given, the cost of the brick =$6

Now, 24 x $6 =$144

Therefore, it costs $144 to buy the edging. Question 6. Isaac buys milk to make milkshakes for his friends. He buys 1 quart of milk and $$\frac{1}{2}$$ gallon of milk. How many cups of milk does he buy? Answer: 1 quart = 4 cups 1/2 gallon = 8 cups Total = 4 + 8 = 12 cups Therefore, he bought 12 cups of milk. Question 7. Maggie buys 1$$\frac{1}{2}$$ pounds of walnuts, 8 ounces of pecans, and pound of almonds. How much do the nuts weigh in all? Answer: 1 1/2 pounds of walnuts = 24 ounces 8 ounces of pecans 1 pound of walnuts = 16 ounces Total : 24 + 8 + 16 = 48 ounces Therefore, the nuts weigh 48 ounces Problem Solving Question 8. Reasoning Matt’s family is thinking about buying a family pass to the city pool. The pass is$80 for a family of 4. Individual passes are $25 each. How much money can Matt’s family save by purchasing a family pass instead of 4 individual passes? Answer: Given, the amount of family pass =$80

Also given, the price of an individual pass = $25 Total number of family members = 4 Now,$25 x 4

= $100 So,$100 – $80 =$20

Therefore, Matt’s family saves $20 by purchasing a family pass instead of 4 individual passes Question 9. Marcia walked 900 meters on Friday. On Saturday, she walked 4 kilometers. On Sunday, she walked 3 kilometers, 600 meters. How many kilometers did Marcia walk over all three days? Answer: Given, On Monday she walked 900 meters On Tuesday she walked 4 kilometers 1 km = 1000 m 4 km = 4000 m On Sunday, she walked 3 km,600 m 3 km =3000 m + 600 m = 3600 m Total : 900 + 4000 + 3600 = 8500 meters. 8500 meters = 8.5 kilometers Therefore, Marica walked 8.5 kilometers. Question 10. Higher-Order Thinking Raul wants to put wood shavings in his rabbit’s cage. The floor of the cage measures 1 yard wide by 5 feet long. One bag of shavings covers 10 square feet. How many bags will Raul have to buy to cover the floor of the cage? Explain. Answer: 1.5 bags Explanation: Width = 1 yard = 3 feet Length = 5 feet Area of the floor = 5ft × 3ft = 15sqft 1 bag = 10sqft x bag = 15sqft x bags = (15 × 1)/10 = 1.5 bags Therefore, Raul needs 1.5 bags. Question 11. Cheryl’s fish tank is 2 yards long by 24 inches wide by 3 feet high. What is the volume of Cheryl’s tank in cubic inches? Answer: Given, length = 2 yards 2 yards = 72 inches wide = 24 inches Height = 3 feet 3 feet = 36 inches Volume of the tank = length x width x height Question 12. Some statistics about a typical adult Royal antelope are shown in the data table. a What is a typical Royal antelope’s tail length in millimeters? b. How many centimeters high can a typical Royal antelope jump? c. What is the mass of a typical Royal antelope in grams? Answer: a. Given, tail length = 6 cm 1 cm = 10 mm 6 cm = 6 x 10 = 60 mm b. Given, vertical leap = 2 meters 1 m = 1000 cm Now, 2 meters = 2 x 1000 = 2000 cm Therefore, it can jump 2000 cm c. 2.4 kg = mass of antelope 1 kg = 1000 grams 2.4 kg = 2000 + 400 = 2400 grams. Therefore, the mass of a typical Royal antelope in grams= 2400 grams Assessment Practice Question 13. Joann wants to put a wallpaper border around her room. The border costs$3 per foot. The diagram shows Joann’s room. How much money will the border cost?
A. $120 B.$102
C. $84 D.$60

Given,

The cost of border per foot = $3 Now, 11 x 3 =$33

3 yards = 9 feet

9 feet = 9 x 3 = $27 Total :$33 + $27 =$60

The border cost $60. ### Lesson 12.9 Precision Problem Solving Solve & Share Beth wants to make a picture frame like the one pictured below. She recorded the outside dimensions as 5 cm by 7 cm. Measure the outside dimensions of the frame in millimeters. Compare your measurements to Beth’s. Do you think her measurements are precise enough? Explain. Thinking Habits Think about these questions to help you attend to precision. • Am I using numbers, units, and symbols appropriately? • Am I using the correct definitions? • Am I calculating accurately? • Is my answer clear? Look Back! Be Precise What is the difference between the perimeter based on the measurements Beth made and the perimeter based on the measurements you made? Explain how you found the answer. Visual Learning Bridge Essential Question How Can You Be Precise When Solving Math Problems? A. Chad and Rhoda are hanging a swing. Chad cut a piece of chain 6 feet 2 inches long. Rhoda cut a piece of chain 72 inches long. When they hung the swing, it was crooked. Use precise language to explain why. Be Precise means that you use appropriate math words, symbols, and units as well as accurate calculations when you solve problems. B. How can I be precise in solving this problem? I can • calculate accurately. • give a clear answer. • use the correct units. Here’s my thinking. C. Convert 6 ft 2 inches to inches to see if Chad and Rhoda cut equal lengths of chain. 6 ft 2 in. = ___ in. 6 × 12 = 72, so 6ft = 72 in. 6 ft 2 in. = 72 +2 = 74 in. Chad’s chain is 74 inches long, but Rhoda’s chain is only 72 inches long. Since Chad and Rhoda used unequal lengths of chain, the swing is crooked. Convince Me! Be Precise What recommendations would you make to Chad and Rhoda so that the swing hangs level? Guided Practice Mary needs a board 4 feet 8 inches long. She cut a board 56 inches long. Remember to be precise by converting measurements accurately. Question 1. What measurements are given? Are the same units used for each measurement? Explain. Answer: No The measurements are mentioned with different units. Question 2. Explain how you can convert one of the measurements so that both use the same unit. Answer: 4 feet 8 inches can be converted into 56 inches as 1 foot = 12 inches Now, 4 feet = 4 x 12 = 48 inches 48 + 8 = 56 inches. Question 3. Is the board Mary cut the right length? Give a clear and appropriate answer. Answer: Yes, mary cut the right length. 4 feet 8 inches can be shown as 56 inches Therefore, mary cut the right length. Independent Practice Be Precise Sean is making meat loaf. He used the amount of catsup shown in the measuring cup. Question 4. Are the units that Sean used to measure the catsup s the same as those given in the recipe? Explain. Answer: No, the units that Sean used to measure the catsup s the same as those given in the recipe. Question 5. How can you convert one of the measurements so that both use the same unit? Answer: 1 fl oz = 0.125 cups So, 6 fl oz = 0.75 cups. Question 6. Did Sean use the right amount of catsup? Give a clear and appropriate answer. Answer: No, 6 fl oz = 0.75 cups 0.75 cups = 3/4 But sean used 2/3 cup of catsup. Problem Solving Performance Task Shipping a Package A customer is using regular delivery to ship a package. Northside Shipping Company discovered that its old scale is not very accurate. It registers a weight that is 2 ounces too heavy. A new, accurate scale shows that the actual weight of the customer’s package is 2 pounds 11 ounces. Question 7. Make Sense and Persevere Which information do you need to determine the total shipping cost using either scale? Answer: We need the weight of the package and delivery charges to the total shipping cost using either scale Question 8 Be Precise Why do you need to convert measurements to determine total shipping costs? Answer: Because To make the answer accurate we have to convert the measurements. To be precise, you need to check that the words, numbers, symbols, and units you use are correct and that your calculations are accurate. Question 9. Model with Math Show how to convert the measurements you described in exercise 8. Answer: 1 pound =16 ounces. 2 pounds 11 ounces = 43 ounces. Question 10. Be Precise What would the total cost be if the package is weighed on the new scale? What would the total cost be if the package is weighed on the old scale? Show your work. Answer: The weight on the new scale =$ 25. 95

The weight on the old scale = \$27.15

### Topic 12 Fluency Practice

Activity

Point&Tally

Find a partner. Get paper and a pencil. Each partner chooses light blue or dark blue.
At the same time, Partner 1 and Partner 2 each point to one of their black numbers. Both partners find the product of the two numbers.
The partner who chose the color where the product appears gets a tally mark. Work until one partner has seven tally marks.

Topic 12 Vocabulary Review

Glossary

Word List

• capacity
• centimeter
• cup
• fluid ounce
• foot
• gallon
• gram
• inch
• kilogram
• kilometer
• liter
• mass
• meter
• mile
• milligram
• milliliter
• millimeter
• ounce
• pint
• pound
• quart
• ton
• weight
• yard

Understand Vocabulary

Choose the best term from the Word List. Write it on the blank.

Question 1.
One ___ is equivalent to twelve ___

one foot is equivalent to 12 inches

Question 2.
The measure of the amount of matter in an object is known as ___

Question 3.
The volume of a container measured in liquid units is its ____

Question 4.
There are 1,000 meters in one ____

Question 5.
Finding how light or how heavy an object is means measuring its _____

Question 6.
There are 2 cups in one _____

For each of these objects, give an example and a non-example of a unit of measure that could be used to describe it.

Milk is measured in liters

person’s height is measured in feet

shoe’s length is measured in centimeters or inches

Use Vocabulary in Writing

Question 10.
Explain the relationship among the metric units of mass in the Word List.

Length = meter, kilometer

Mass = gram, kilogram

volume = liter, milliliter.

### Topic 12 Reteaching

Set A
pages 489-492, 517-520

Convert 3 yards to inches.
1 foot (ft) = 12 inches (in.)
1 yard (yd) = 3 ft = 36 in.
1 mile (mi) = 1,760 yd = 5,280 ft
1 yard = 36 inches. To change larger units to smaller units, multiply: 3 × 36 = 108.
So, 3 yards = 108 inches.

Remember to divide when changing smaller units to larger units.
Convert.

Question 1.
7 ft = ___ in.

Question 2.
7,920 ft = ___ mi

Question 3.
Max wants to put a fence around his triangular garden. If each side is 6 yards, how many feet of fencing does Max need?

Given, the side of the triangle = 6 yards

Perimeter = 6 x 6 x 6

= 18 yards

1yd/3 ft x 18/18

Now, 18/ 54

Therefore, Max have 54 feet of fencing.

Set B
pages 493-496
Convert 16 cups to pints.
2 cups = 1 pint. To change smaller units to larger units, divide: 16 ÷ 2 = 8.
So, 16 cups = 8 pints.

Remember that 1 gal = 4 qt, 1 qt = 2 pt, 1 pt = 2 c, and 1 c= 8 fl oz.

Convert.

Question 1.
36C = ___ gal

Question 2.
7 pt = __qt

Question 3.
1$$\frac{1}{2}[latex] gal = ___ fl oz Answer: 1 1/2 gal = 192 fl oz Question 4. 6 pt = ___ c Answer: 1 pt = 2 cups So, 6 pt = 6 x 2 = 12 cups. Set C pages 497-500 Convert 6 pounds to ounces. 1 pound = 16 ounces. To change larger units to smaller units, multiply: 6 × 16 = 96. So, 6 pounds = 96 ounces. Remember that 2,000 pounds = 1 ton. Convert. Question 1. 2[latex]\frac{3}{4}$$ lb = __oz

Question 2.
56 oz = __ lb

Question 3.
4,000 lb = ___ T

Question 4.
6$$\frac{1}{2}$$T = __ lb

Set D
pages 501-504
Convert 2 meters to centimeters.
1 km = 1,000 m
1 m= 100 cm
1 m = 1,000 mm
1 cm = 10 mm
1 meter = 100 centimeters. To change larger units to smaller units, multiply: 2 × 100 = 200.
So, 2 meters = 200 centimeters.

Remember to multiply or divide by a power of 10 to convert metric measurements.

Convert.

Question 1.
5.4 m = ___ cm

Question 2.
2.7 km = ___ m

Question 3.
0.02 km = __ cm

Question 4.
0.025 m = ___ mm

Question 5.
675 mm = ___ m

Question 6.
7,435 cm = ___ m

Set E
pages 505-508
Convert 6,000 milliliters to liters.
1,000 milliliters = 1 liter. To change milliliters to larger units, divide: 6,000 ÷ 1,000 = 6.
So, 6,000 milliliters = 6 liters.

Remember that the most commonly used metric units of capacity are the liter and milliliter.

Convert.

Question 1.
6L = ___ mL

Question 2.
0.15 L = ___mL

Question 3.
2,000 mL = __ L

Question 4.
900 mL = ___ L

Set F
pages 509-512
Convert 6 kilograms (kg) to grams (g).
1 kilogram = 1,000 grams. To change larger units to smaller units, multiply:
6 × 1,000 = 6,000.
So, 6 kg = 6,000 g.

Remember that to convert metric units, you can annex zeros and move the decimal point.

Convert.

Question 1.
30 kg = ___ g

Question 2.
3,000 mg = ___ g

Question 3.
560 g = ___ kg

Question 4.
0.17g = __mg

Set G
pages 513-516
The choir concert is scheduled to last 90 minutes. The band concert is scheduled from 7:00-8:45. Which concert is scheduled to be longer? By how many minutes?
The choir concert will last 90 minutes = 1 hour, 30 minutes. The band concert will last 1 hour, 45 minutes. The band concert will be 15 minutes longer.

Remember to check if the units in the problem are the same.

Convert.

Question 1.
8 minutes = ___ seconds

1 minute = 60 seconds

8 minutes = 8 x 60 = 480 seconds

Question 2.
86 minutes = ___ hour, ___ minutes

1 hour = 60 minutes

86 minutes = 1 hour 26 minutes

Question 3.
A movie starts at 7:10 and ends at 9:03. How long does the movie last? __ hour, ___ minutes

The movie lasts 1 hour 53 minutes

Set H
pages 521-524

Thinking Habits
• Am I using numbers, units, and symbols appropriately?
• Am I using the correct definitions?
• Am I calculating accurately?

Remember that the problem might have more than one step.

Question 1.
Monica bought a 40-pound bag of dog food. Twice a day, she gives her dog 6 ounces of food. How many pounds of dog food will she use in 1 week? Explain.

Given, The amount of dog food Monica bought = 40 pounds

40 pounds = 640 ounces

The amount of food Monica gives dog = 6 ounces

Twice = 6 x 2 = 12 oz

In one week = 12 x 7 = 84 oz

Therefore, Monica gives 84 oz of dog food will she use in 1 week

### Topic 12 Assessment Practice

Question 1.
Which of the following are equivalent to 7 grams? Select all that apply.
0.007 kilogram
70 milligrams
7,000 kilograms
7,000 milligrams
0.007 milligram

0.007 kilogram

7,000 milligrams

Question 2.
Justin’s garden is shown below.

A. How can you convert the dimensions of Justin’s garden from yards to inches?
B. What is the perimeter of Justin’s garden in inches?

A.

Given, Length = 8 yards

8 yards = 8 x 36 = 288 inches

6 yards = 6 x 36 = 216 inches.

B.

Perimeter = length x width

288 x 216 = P

62208 = Perimeter

Therefore, The perimeter of Justin’s Garden = 62208  inches.

Question 3.
Which of the following equations can be used to find how many kilograms are in 2,000 grams?
A. 1,000 ÷ 2,000 = 0.5 kilogram
B. 2,000 ÷ 1,000 = 2 kilograms
C. 2,000 × 1,000 = 2,000,000 kilograms
D. 2,000 × 100 = 200,000 kilograms

2,000 ÷ 1,000 = 2 kilograms

Question 4.
A. 10 bales of cotton weigh approximately 5,000 pounds. How can you convert 5,000 pounds to tons?
B. Which comparison is true?
A. 5,000 pounds > 10,000 tons
B. 5,000 pounds = 3 tons
C. 5,000 pounds < 3 tons
D. 5,000 pounds > 3 tons

A.

1 pound = 0.0005 tons

Now, 5000 pounds = 2.5 tons.

B.

5,000 pounds > 3 tons

Question 5.
Tyrell bought 4 liters of fruit punch for a party. He will serve the punch in glasses that can hold 200 milliliters. How many full glasses of fruit punch can he serve?

1 litre = 1000 millilitres

Now, 4 litres = 4000 milliliters.

4000/200 = 20

Therefore, Tyrell can fill 20 glasses of fruit punch.

Question 6.
Select each equation that the number 103 will make true.
? km = 1 mm
? mm = 1 m
? cm = 1 m
?m = 1 km
? dm = 1 m

1000000 km = 1 mm

1000 mm = 1 m

100 cm = 1 m

1000 m = 1 km

10 dm = 1m

Question 7.
Match each measurement on the left to its equivalent measurement.

1 gallon = 4 quarts

1 cup = 8 fl oz

1 quart = 2 pints

1 pint = 2 cups.

Question 8.
Select all lengths that are equal to 6 feet 12 inches.
3 yd 1 ft
7 ft
7 ft 2 in.
2 yd 1 ft
1 yd 4 ft

a. 7 feet

b. 2 yd 1 ft

c. 1 yd 4 ft

Question 9.
Write and solve an equation to find how many milliliters are in 3.4 liters.

1 liter = 1000 milliliters

3.4 liters = 3400 milliliters.

Question 10.
Mason made 5 quarts of salsa. Which of the following can be used to find the number of cups of salsa Mason made?
A. 5 × 2 × 2
B. 5 × 4 × 4
C. 5 ÷ 2 ÷ 2
D. 5 × 4 ÷ 2

1 quart = 4 cups

The answer is 5 x 2 x 2.

Question 11.
Alicia bought 5 pounds of potting soil. She wants to put 10 ounces of soil in each flower pot.
A. How can she convert 5 pounds to ounces?
B. How many flower pots can she fill?

A.

1 pound = 16 ounces

So, 5 pounds = 5 x 16 = 80 ounces

B.

Now, 80/10 = 8

Therefore, she can make 8 flower pots.

Question 12.
The tail of a Boeing 747 is 63 feet 8 inches tall. How many inches tall is the tail?

Given,

The length of tail = 63 feet

1 feet = 12 inches

Now, 63 x 12

= 756

Total = 756 + 8

= 764 inches

Question 13.
Write and solve an equation to convert 0.38 meters to centimeters.

1 meter = 100 centimeters

Now, 0.38 meters = 38 cm.

Orange Juice
Heidi sells freshly-squeezed orange juice in Heidi’s Orange Juice cups.

Question 1.
Use the Information About Oranges. Answer the questions below to find how many pounds of oranges Heidi needs for her orange juice.
Part A
How many oranges does Heidi need to make one large orange juice? Show your work.

Part B
How many pounds of oranges does Heidi need to make one large orange juice? Show your work.

2.5 cups = 20 fluid ounces.

20 fl oz = 1.5 pounds

Question 2.
Answer the following to find the area of Heidi’s Display Shelf.
Part A
What units can you use for the area? Explain.

Part B
What is the area of Heidi’s Display Shelf? Show your work.

4 feet = 48 inches

Area = length x width

= 48 x 15

= 720 sq. inches

therefore, the area of hiedi’s shelf = 720 inches

Question 3.
The Orange Nutrition table shows nutrients in one medium-sized orange that weighs 5 ounces or 140 grams. All the nutrients in the orange are also in Heidi’s orange juice.

Part A
How many grams of potassium are in one large cup of Heidi’s orange juice? Explain how you solved.

Given,

250 milligrams of potassium is there in the juice cup

1 milligram = 0.001

250 mg = 0.25 grams

therefore, there are 0.25 grams of potassium in orange juice.

Part B
How many milligrams of fiber is in one large cup of Heidi’s orange juice? Use an exponent when you explain the computation you used to solve.

1 gram = 1000 milligrams

3.5 grams = 3500 milligrams

Therefore, there is 3500 mg of fiber.

Question 4.
Heidi also sells cartons of orange juice. Use the picture of Heidi’s Orange Juice Carton. Find the volume of the carton in cubic centimeters. Explain.

The measurements of the carton are

10 cm, 50 mm = 5 cm, 0.2 m = 20 cm

Volume = l x w x h

= 50 x 5 x 20

= 500 Cubic centimeters

therefore, volume = 500 cubic centimeters.

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