Unit 5 Multiplicative Comparison And Measurement — Unit Plan

TitleAssessment
Lesson 1
Times as Many
Three Times as Many Cubes

Here is an image of connecting cubes.

Connecting Cube Tower, 2.

Which of the following shows 3 times as many cubes as in the image? Explain your reasoning.

A
connecting cube tower, 5.

B
connecting cube tower, 6.

C
connecting cube tower, 3.

Show Solution

B has 6 cubes, which is 3 times as many as 2.

Lesson 2
Interpret Representations of Multiplicative Comparison
Comparing Cubes

  1. Circle the statement and the multiplication equation that show a comparison of Tyler’s and Elena’s cubes.

    diagram. two rectangles.
    diagram. two rectangles. Top rectangle, Tyler's cubes. partitioned into 20 equal parts. 4 blue, 4 yellow, 4 blue, 4 yellow, 4 blue. Bottom rectangle, Elena's cubes. Partitioned into 4 equal parts, same size as each of the parts in top rectangle.

    Tyler has 4 more cubes than Elena.

    6×4=246 \times 4 = 24

    Elena has 5 times as many cubes as Tyler.

    2×10=202 \times 10 = 20

    Tyler has 5 times as many cubes as Elena.

    4×4=164 \times 4 = 16

    Tyler has 4 times as many cubes as Elena.

    5×4=205 \times 4 = 20

  2. Explain your choices.

Show Solution
  1. Tyler has 5 times as many cubes as Elena. 5×4=205 \times 4 = 20
  2. Sample responses:
    • We can see Elena has 4 and Tyler has 20. The diagram shows that Tyler has 5 groups of 4 cubes, so he has 5 times as many as Elena, who has 4 cubes.
    • The equation 5×4=205 \times 4 = 20 shows that the number of cubes that Tyler has, 20, is 5 times 4, the number of cubes that Elena has.
Lesson 3
Solve Multiplicative Comparison Problems
Back at the Book Drive

Kiran donated 28 books to the book drive. Jada donated some books, too. Kiran donated 4 times as many books as Jada.

How many books did Jada donate? Explain or show your reasoning.

Show Solution

7 books. Sample responses:

  • diagram
  • ?×4=28{?} \times 4 = 28 or 4×?=284 \times {?} = 28
Lesson 4
Solve Multiplicative Comparison Problems with Large Numbers
Represent Multiplicative Comparison

Priya read some pages on Monday. Jada read 63 pages, which is 7 times as many pages as Priya read. 

  1. Write an equation to show the comparison. Use a symbol for the unknown.
  2. How many pages did Priya read?
Show Solution
  1. Sample response: 7×?=637 \times {?} = 63
  2. Priya read 9 pages.
Lesson 5
One- and Two-Step Comparison Problems
Comics and Posters

At a book fair, students spent $27 on comics and 5 times as much on posters. How much money did students spend on comics and posters during the book fair? Explain or show your reasoning.

Show Solution

$162. Sample responses:

  • They spent 5×27=1355\times27=135 on comics, so the total spent on comics and posters is 27+135=16227+135=162.
  • Comics and posters is 27+(5×27)27+(5\times 27), which is 6×276\times 27.
Lesson 6
Ten Times as Many
What’s the Value?

diagram. two rectangles. bottom rectangle, B. partitioned into 10 equal parts. Top rectangle, A. Same size as one of the 10 parts of the bottom rectangle.

  1. A has a value of 3. What is the value of B?
  2. A has a value of 30. What is the value of B?
  3. A has a value of 300. What is the value of B?
  4. Write one true statement comparing 3, 30, and 300 with the phrase “as much as.”
Show Solution
  1. 30
  2. 300
  3. 3,000
  4. Sample response: 300 is 10 times as much as 30, which is 10 times as much as 3. 
Section A Check
Section A Checkpoint
Problem 1

The diagram represents the cost, in dollars, of a card game and a video game.

diagram. two rectangles.
diagram. two rectangles. bottom rectangle, video game. partitioned into 7 equal parts, total length 42. Top rectangle, card game. Same size as one of the 7 parts of bottom rectangle.

  1. Write a statement that compares the cost of the card game and the cost of the video game.
  2. Write a multiplication equation that compares the cost of the card game and the cost of the video game.
Show Solution

Sample responses:

  1. The cost of the video game is 7 times as much as the cost of the card game. 
  2. 7×?=427 \times {?} = 42 or ?×7=42{?} \times 7 = 42 or 7×6=427 \times 6 = 42 or 6×7=426 \times 7 = 42
Problem 2

Han ran 12 miles in a week. That's 3 times as far as Andre ran. How many miles did Andre run during the week? Explain or show your reasoning.

Show Solution

4 miles. Sample responses:

  • Students draw a diagram to show the multiplicative comparison.
  • Andre ran 4 miles because 12÷3=412 \div 3 = 4.
  • 3×?=123\times?=12, so Andre ran 4 miles.
Problem 3

Jada has 23 pennies in her piggy bank. Elena has 4 times as many pennies as Jada in her piggy bank. How many pennies do Jada and Elena have altogether in their piggy banks? Explain or show your reasoning.

Show Solution

115. Sample response: Elena has 4×234 \times 23 or 92 pennies in her piggy bank. Then 23+92=11523 + 92 = 115.

Lesson 7
Meters and Centimeters
The Longest Creatures
  1. The longest stick insect ever found was more than 62 centimeters long. Is that insect shorter or longer than 1 meter? Explain your reasoning.
  2. The world’s longest snakes can grow up to 9 meters long. What is that length in centimeters?
Show Solution
  1. Shorter than 1 meter, because 1 meter is 100 centimeters, and 62 is less than 100.
  2. 900 centimeters long, because 9×100=9009 \times 100 = 900.
Lesson 8
Meters and Kilometers
How Far Away from School?
  1. Kiran lives 7 kilometers from school. How many meters from school does he live? Explain or show your reasoning.

  2. Clare lives 800 meters from school. Does she live closer or farther away from school than Kiran? Explain your reasoning.

Show Solution
  1. 7,000 meters. Sample reasoning: 1 kilometer is 1,000 meters, so 7 kilometers is 7×1,0007 \times 1,000, which is 7,000.
  2. Clare lives closer to school. Sample reasoning: One kilometer is 1,000 meters, and 800 meters is not even 1 kilometer, so it is much less than 7 kilometers.
Lesson 9
Grams and Kilograms, Liters, and Milliliters
A Chef and a Host
  1. A chef bought 3 kilograms of flour on Monday and 4,000 grams on Friday. On which day did they buy more flour? Explain or show your reasoning.
  2. A party host bought 8 bottles of sparkling water. Each bottle contains 1 liter. How many milliliters of sparkling water did they buy?
Show Solution
  1. Friday. Sample response: 3 kilograms is 3,000 grams, which is less than 4,000 grams.
  2. 8,000 milliliters.
Lesson 10
Multi-Step Measurement Problems
Hydration Here and There

Halfway through a soccer game, Han drank 210 mL of water. At the end of the game, he drank 4 times as much as he did at halftime.

Did Han drink more or less than 1 L of water in total? Explain or show your reasoning.

Show Solution
More than 1 L. Sample response: One liter is 1,000 mL. At the end of the game, Han drank 4×2104 \times 210 or 840 mL. Combined with the 210 mL from halftime, that is 840+210840 + 210 or 1,050 mL. This is 50 mL more than 1 L.
Lesson 11
Pounds and Ounces
Hungry Birds

The table shows the pounds of food that 3 species of birds consume in a week.

bird pounds of food a week ounces of food a week
golden eagle 7
pelican 20
cardinal 3123\frac{1}{2}

Complete the table to show how many ounces of food each species eats in a week.

Show Solution
bird pounds of food a week ounces of food a week
golden eagle 7 112
pelican 20 320
cardinal 3123\frac{1}{2} 56
Lesson 12
Hours, Minutes, and Seconds
Time on Chores

Clare and Andre both do chores on weekends. 

  1. Each month, Clare spends 6 hours on chores. How many minutes does Clare spend on chores each month?
  2. Andre says, “I spend about 400 minutes on chores each month, which is about 8 hours.” Do you agree that Andre spends 8 hours on chores? Explain your reasoning.
Show Solution
  1. 360 minutes.
  2. Disagree. Sample responses: 
    • Eight hours is 480 minutes, because 8×60=4808 \times 60 = 480, so Andre spends more than an hour less than 8 hours. 
    • Four hundred minutes is 40 minutes more than 360 minutes or 40 minutes more than 6 hours, which is much less than 8 hours.
Lesson 13
Multi-Step Measurement Problems with Fractions
Fish Tank

Priya needs sand and rocks for her fish tank. She needs 3 pounds of sand. That amount is 4 times as much as the amount of rocks that she needs. How many ounces of rocks does she need? Explain or show your reasoning.

Show Solution

12 ounces. Sample response: One pound is 16 ounces, and 3 pounds is 3×163 \times 16, which is 48 ounces, so she needs 48 ounces of sand. 48÷4=1248 \div 4 = 12, so she has 12 ounces of rocks.

Section B Check
Section B Checkpoint
Problem 1

How many ounces are in 5 pounds? Explain or show your reasoning.

Show Solution
80 ounces. There are 16 ounces in 1 pound, and 5×16=805 \times 16 = 80.
Problem 2

Select the longest measurement.

A. 200,000 cm
B. 400 m
C. 3 km
D. 60 cm

Show Solution
 3 km
Problem 3

Tyler is going to the zoo for a field trip. He will stay at the zoo for 3123 \frac{1}{2} hours. The table shows how long Tyler plans to spend at each attraction within the zoo.

attraction amount of time
Monkey and Gorilla Gymnasium 50 minutes
Bird House 25 minutes
Reptile Terrarium 45 minutes
African Safari 1 hour and 10 minutes

Does Tyler have enough time to visit all the attractions? Explain or show your reasoning.

Show Solution

Yes. Sample reasoning: 1 hour and 10 minutes is 70 minutes. All the times together make 190 minutes. 3 hours is 180 minutes, and a half hour is 30 minutes so that is 210 minutes.

Lesson 14
Weight and Capacity Measurements
More Clay

An art teacher and a kindergarten teacher are getting clay from the craft store. The art teacher buys 6 pounds of clay. This amount is 4 times as much clay as what the kindergarten teacher buys.

How many ounces of clay do the two teachers buy all together? Explain or show your reasoning.

Show Solution
120 ounces. Sample responses:
  • The art teacher buys 96 ounces, because 1 pound is 16 ounces and 6×16=966 \times 16 = 96. The kindergarten teacher buys 24 ounces, because 4×24=964 \times 24 = 96. In total, they buy 96+2496 + 24 or 120 ounces.
  • The kindergarten teacher buys 64\frac{6}{4} or 1121\frac{1}{2} pounds of clay, because 4×112=64 \times 1\frac{1}{2} = 6. In total, they buy 7127\frac{1}{2} pounds of clay. In ounces, that amount is: (7×16)+(12×16)=112+8=120(7 \times 16) + (\frac{1}{2} \times 16) = 112 + 8 = 120.
Lesson 15
Length Measurements
A Sculptor and a Tower

A sculptor is 5 feet 8 inches tall. Her height is 4 times the height of a stone tower she built.

How tall is her tower in inches? Explain or show your reasoning.

Show Solution
17 inches. Sample response: 5 feet is 5×125 \times 12 or 60 inches and 8 inches more makes 68 inches. 4×17=684 \times 17 = 68.
Lesson 16
Compare Perimeters of Rectangles
Rectangles Y and Z
  1. Rectangle Y has a perimeter of 20 inches. Name a possible pair of side lengths it could have.

  2. Rectangle Z has a perimeter of 180 inches.

    1. Complete this statement:

      The perimeter of Rectangle Z is __________ times the perimeter of Rectangle Y.

    2. If the length of Rectangle Z is 70 inches, how many inches is its width? Explain or show your reasoning. Draw a diagram if it is helpful.
Show Solution
  1. Sample response: 8 inches and 2 inches
    1. 9 times
    2. 20 inches. Sample response: The two sides (lengths) add up to 140 (70+70=14070 + 70 = 140). This means the two other sides (the width) add up to 180−140180-140 or 40 inches, and each side is 20 inches.
Lesson 17
More Perimeter Problems
A Rectangle and a Trapezoid
  1. Find the perimeter of the rectangle. Show your reasoning.

    diagram. Rectangle. length, 3 and 5 eighths feet. width, 1 and 3 eighths feet.

  2. A trapezoid has a perimeter of 10 yards.

    Compared to the perimeter of the rectangle, how many times as long is the perimeter of the trapezoid? Explain or show your reasoning.

Show Solution
  1. 10 feet. Sample responses:
    • 358+138=53\frac{5}{8} + 1\frac{3}{8} = 5 and twice that length is 10.
    • (2×358)+(158×2)=6108+268=8168=10\left(2 \times 3\frac{5}{8}\right) + \left(1 \frac{5}{8} \times 2\right) = 6\frac{10}{8} + 2\frac{6}{8} = 8\frac{16}{8} = 10
  2. 3 times. Sample response: One yard is 3 feet, so 10 yards is 10×310 \times 3 or 30 feet, and 30 is 3 times 10.
Lesson 18
Two Truths and a Lie
No cool-down
Section C Check
Section C Checkpoint
Problem 1

Priya and her aunt wanted to see how far each could throw a disc. Priya’s aunt’s throw was 52 yards, which was 4 times the distance of Priya’s throw.

What was the distance of Priya’s throw in feet? Explain or show your reasoning.

Show Solution

39 feet. Sample responses: 

  • Priya’s throw is 52÷452 \div 4 or 13 yards. One yard is 3 feet, so 13 yards is 13×313 \times 3 or 39 feet.
  • One yard is 3 feet, so 52 yards is 156 feet. This is 4 times Priya’s distance. I know 160=4×40160 = 4 \times 40 and 156 is 4 less than 160, so 156=4×39156 = 4 \times 39.
Problem 2

A rectangle has a width of 2142 \frac {1}{4} inches. The perimeter of the rectangle is 13 inches. What is the length of the rectangle? Explain or show your reasoning.

Show Solution

4144\frac{1}{4} inches. Sample response: The two 2142\frac{1}{4}-inch sides make up 214+2142\frac{1}{4} + 2\frac{1}{4} or 4244\frac{2}{4} inches of the perimeter. The other two sides together are 13−42413 - 4\frac{2}{4} or 8248\frac{2}{4} inches long. Each of those sides is 4144 \frac{1}{4} inches long because 2×414=8242 \times 4\frac{1}{4} = 8\frac{2}{4}.