Envision Math Common Core 4th Grade Answers Key Topic 11 Represent and Interpret Data on Line Plots

Essential Questions:
How can you solve problems using data on a line plot? How can you make a line plot?
Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 1

enVision STEM Project: Safety and Data
Do Research Use the Internet or other sources to find what causes an earthquake and how the power of an earthquake is measured. Tell how people can stay safe during earthquakes.
Journal: Write a Report Include what you found. Also in your report:

  • The size, or magnitude, of an earthquake is measured with the Richter scale. Explain how the scale is used.
  • Research the magnitudes of at least 6 earthquakes that have occurred in your lifetime. Make a table showing when they occurred and their magnitudes, and then show their magnitudes on a line plot.

Review What You Know
Vocabulary
Choose the best term from the box. Write it on the blank.

  • compare
  • data
  • line plot
  • scale

Question 1.
A _________ is a way to organize data on a number line.
Answer:
A __line plot_______ is a way to organize data on a number line.

 

Question 2.
Numbers that show the units used on a graph are called a __________
Answer:
Numbers that show the units used on a graph are called a __scale________.

 

Question 3.
_________ are pieces of information.
Answer:
___Data______ are pieces of information.

 

Comparing Fractions
Write >, <, or = in the Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 2.
Question 4.
\(\frac{7}{8}\) Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 2 \(\frac{3}{4}\)
Answer:
\(\frac{7}{8}\) > \(\frac{3}{4}\).

Explanation:
\(\frac{7}{8}\) Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 2 \(\frac{3}{4}\)
=> 0.875  __>__  0.75.

 

Question 5.
\(\frac{1}{2}\) Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 2 \(\frac{5}{8}\)
Answer:
\(\frac{1}{2}\) < \(\frac{5}{8}\).

Explanation:
\(\frac{1}{2}\) Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 2 \(\frac{5}{8}\)
=> 0.5   __<___  0.625.

 

Question 6.
\(\frac{1}{4}\) Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 2 \(\frac{2}{8}\)
Answer:
\(\frac{1}{4}\) = \(\frac{2}{8}\)

Explanation:
\(\frac{1}{4}\) Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 2 \(\frac{2}{8}\)
=> 0.25  __=___  0.25.

 

 

Fraction Subtraction

Find the difference.
Question 7.
10\(\frac{3}{8}\) – 4\(\frac{1}{8}\) = _______
Answer:
10\(\frac{3}{8}\) – 4\(\frac{1}{8}\) = 6\(\frac{1}{4}\).

Explanation:
10\(\frac{3}{8}\) – 4\(\frac{1}{8}\) = ???
=> 6\(\frac{1}{4}\) .

 

Question 8.
5\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = _______
Answer:
5\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = 1\(\frac{1}{2}\).

Explanation:
5\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = ???
=> 1\(\frac{1}{2}\).

 

 

Question 9.
7\(\frac{4}{8}\) – 2\(\frac{4}{8}\) = __________
Answer:
7\(\frac{4}{8}\) – 2\(\frac{4}{8}\) = 5.

Explanation:
7\(\frac{4}{8}\) – 2\(\frac{4}{8}\) = ???
=> 5.

 

 

Interpreting Data
Use the data in the chart to answer each exercise.
Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 3
Question 10.
What is the greatest snake length? What is the least snake length?
Answer:
The greatest snake length is 24 inches.
The least snake length is 12 \(\frac{1}{2}\) inches.

 

Question 11.
Which of the snake lengths are recorded more than once? Which length was recorded the most?
Answer:
The snake lengths are recorded more than once are 12 \(\frac{1}{2}\) inches, 16 inches and 17 inches.
Length that was recorded the most is 16 inches.

 

Question 12.
What is the difference between the greatest length and the shortest length recorded?
Answer:
The difference between the greatest length and the shortest length recorded is 11 \(\frac{1}{2}\) inches.

Explanation:
The difference between the greatest length and the shortest length recorded is:
The greatest snake length – The least snake length
= 24 inches – 12 \(\frac{1}{2}\) inches.
= 11 \(\frac{1}{2}\) inches.

 

 

Pick a Project
PROJECT 11A
What are fun ways to get up off the couch and move?
Project: Design a Park
Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 4
Answer:
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Pick a Project-PROJECT 11A

 

PROJECT 11B
What are the most commonly chosen state insects?
Project: Write a Poem and Make a Graph about a State Insect
Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 5rtijuo
Answer:
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Pick a Project-PROJECT 11B

 

PROJECT 11C
Have you ever baked a pie?
Project: Make a Pamphlet of Pie Recipes
Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 6
Answer:
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Pick a Project-PROJECT 11C

 

3-ACT MATH PREVIEW
Math Modeling
It’s a Fine Line
Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 7
I can… model with math to solve a problem that involves analyzing and interpreting data on line plots.

Lesson 11.1 Read Line Plots

Solve & Share
Emily went fishing. She plotted the lengths of 12 fish caught on the line plot shown below. What was the length of the longest fish caught? What was the length of the shortest fish caught?
I can … interpret data using line plots.
Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 8

Look Back! What other observations can you make from the line plot about the lengths of fish caught?
Answer:
Other observations can be made from the line plot about the lengths of fish caught is that every quarterly he caught new fish added one more than it.

 

Essential Question
How Can You Read Data in a Line Plot?
Answer:
It is read easily because the line plot is clear stating its refers to lengths of different fishes caught and represented on the line its catching points of intervals, by this way I can read given Data in a Line Plot.

 

 

Visual Learning Bridge
A line plot shows data along a number line. Each dot above a point on the line represents one number in the data set.
The table below shows the distance Eli walked his dog each day for seven days.
Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 9

Here is how the data look on a line plot.
Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 10
The numbers along the bottom of the line plot are the scale of the graph.

Interpret the data on the line plot.
The most dots are above 1 on the line plot.
The most common distance walked is 1 mile.
The longest distance walked is 3 miles.
The shortest distance walked is \(\frac{1}{2}\) mile.

What is the difference between the longest distance and the shortest distance Eli walked his dog?
3 – \(\frac{1}{2}\) = \(\frac{6}{2}\) – \(\frac{1}{2}\)
= \(\frac{5}{2}\) or 2\(\frac{1}{2}\) miles

Convince Me! Model with Math Write and solve an equation to find how many miles m, Eli walked his dog in all for the 7 days.
Answer:
Total distance walked by Eli his dog in all for the 7 days = 9 \(\frac{1}{2}\) miles.

Explanation:
Distance walked by Eli on Monday = \(\frac{1}{2}\) mile.
Distance walked by Eli on Tuesday = 1 \(\frac{1}{2}\) miles.
Distance walked by Eli on Wednesday = 1 mile.
Distance walked by Eli on Thursday = 1 \(\frac{1}{2}\) miles.
Distance walked by Eli on Friday = 3 miles.
Distance walked by Eli on Saturday = 1mile.
Distance walked by Eli on Sunday = 1mile.
Total distance walked by Eli his dog in all for the 7 days = Distance walked by Eli on Monday + Distance walked by Eli on Tuesday + Distance walked by Eli on Wednesday + Distance walked by Eli on Thursday  + Distance walked by Eli on Friday  + Distance walked by Eli on Saturday + Distance walked by Eli on Sunday
= 1 + \(\frac{1}{2}\) + 1 \(\frac{1}{2}\) + 1 + 1 \(\frac{1}{2}\) + 3 + 1
= 1 \(\frac{1}{2}\)+ 1 \(\frac{1}{2}\) + 1 + 1 \(\frac{1}{2}\) + 3 + 1
= 3 + 1 + 1 \(\frac{1}{2}\) + 3 + 1
= 4 + 1 \(\frac{1}{2}\) + 3 + 1
= 5 \(\frac{1}{2}\) + 3 + 1
= 8 \(\frac{1}{2}\) + 1
= 9 \(\frac{1}{2}\) miles.

 

 

 

Guided Practice
Do You Understand?
Question 1.
How can you tell the longest distance Eli walked his dog from the line plot?
Answer:
It can be said the longest distance Eli walked his dog from the line plot by checking and comparing the numerical values given in the given data and finding out the highest among them in all.

 

Question 2.
If a line plot represented 10 pieces of data, how many dots would it have? Explain.
Answer:
If a line plot represented 10 pieces of data, dots would be of 10 because the data is of 10 pieces.

 

 

Do You Know How?
For 3-5, use the line plot below.
Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 11
Question 3.
How many giraffes are 14 feet tall?
Answer:
Two or 2 giraffes are 14 feet tall.

 

Question 4.
What is the most common height?
Answer:
The most common height is 15 feet.

 

Question 5.
How tall is the tallest giraffe?
Answer:
16 feet is the tallest giraffe.

 

Independent Practice
For 6-10, use the line plot at the right.
Envision Math Common Core 4th Grade Answer Key Topic 11 Represent and Interpret Data on Line Plots 12
Question 6.
How many people ran the 100-meter sprint?
Answer:
20 people ran the 100-meter sprint.

 

Question 7.
Which time was the most common?
Answer:
11 hours is the most common time.

 

Question 8.
What is the difference between the fastest sprint and the slowest sprint?
Answer:
The difference between the fastest sprint and the slowest sprint is 3 \(\frac{3}{4}\) seconds.

Explanation:
The fastest sprint = 10 \(\frac{1}{4}\).
The slowest sprint = 12 \(\frac{2}{4}\).
The difference between the fastest sprint and the slowest sprint:
= 12 \(\frac{2}{4}\) – 10 \(\frac{1}{4}\)
= 6 – 2 \(\frac{1}{4}\)
= 3 \(\frac{3}{4}\) seconds.

 

Question 9.
How many more people ran 100 meters in 11\(\frac{2}{4}\) seconds than in 10\(\frac{1}{4}\) seconds?
Answer:
2 more people ran 100 meters in 11\(\frac{2}{4}\) seconds than in 10\(\frac{1}{4}\) seconds.

Explanation:
More people ran 100 meters in 11 \(\frac{2}{4}\) seconds than in 10 \(\frac{1}{4}\) seconds
= 2.

 

Question 10.
Curtis said more than half the people ran 100 meters in less than 11 seconds. Do you agree? Explain.
Answer:
Yes, I agree with what Curtis said because its 17 people who ran 100 meters in less than 11 seconds.

 

 

Problem Solving
For 11-12, use the line plot at the right.
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 13
Question 11.
Reasoning Mr. Dixon recorded the times it took students in his class to complete a project. Which time was most often needed to complete the project?
Answer:
3 Hours was most often needed to complete the project.

 

Question 12.
How much longer was the greatest amount of time spent completing the project than the least amount of time?
Answer:
1 hour longer was the greatest amount of time spent completing the project than the least amount of time.

Explanation:
The greatest amount of time spent completing the project = 3 \(\frac{2}{4}\) hours.
The least amount of time spent completing the project = 2 \(\frac{2}{4}\) hours.
Difference:
The greatest amount of time spent completing the project – The least amount of time spent completing the project
= 3 \(\frac{2}{4}\) – 2 \(\frac{2}{4}\)
= 1 hour.

 

 

Question 13.
Number Sense Jorge collects sports cards. He displays his cards in an album. There are 72 pages in the album. Each page holds 9 cards. Explain how to decide whether or not the album holds more than 600 cards.
Answer:
Yes, the album holds more than 600 cards because by the calculation of total number of cards and result is 648.

Explanation:
Number of pages in the album = 72.
Number of cards in each page = 9.
Total number of cards the album holds = Number of pages in the album × Number of cards in each page
= 72 × 9
= 648.

 

 

Question 14.
Higher Order Thinking Bob and 2 friends each were able to juggle with bean bags for \(\frac{3}{4}\) minute. How long did they juggle altogether?
Answer:
Total time taken by them = \(\frac{9}{4}\) minutes.

Explanation:
Number of people were juggling with bean bags = 3.
Time taken for each to juggle with bean bags = \(\frac{3}{4}\) minute = 3/4 minute.
Total time taken by them = Number of people were juggling with bean bags × Time taken for each to juggle with bean bags
= 3 × \(\frac{3}{4}\) minute
= \(\frac{9}{4}\) minutes.

 

Assessment Practice
For 15-16, use the line plot at the right.
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 14
Question 15.
How much longer is the longest nail than the shortest nail?
A. 1\(\frac{1}{4}\) inches
B. 1\(\frac{2}{4}\) inches
C. 1\(\frac{3}{4}\) inches
D. 2\(\frac{1}{4}\) inches
Answer:
1\(\frac{2}{4}\) inches is the longest nail than the shortest nail.
B. 1\(\frac{2}{4}\)

Explanation:
The longest nail = 2 \(\frac{1}{4}\) inches.
The shortest nail = \(\frac{3}{4}\)  inches.
Difference:
The longest nail – The shortest nail
= 2 \(\frac{1}{4}\) – \(\frac{3}{4}\)
= 1\(\frac{2}{4}\) inches.

 

Question 16.
Ed measured the nails that were 2\(\frac{1}{4}\) inches long incorrectly. They were each actually \(\frac{3}{4}\) inch longer. What was the length of the nails?
A. \(\frac{3}{4}\) inch
B. 1\(\frac{2}{4}\) inches
C. 3 inches
D. 3\(\frac{1}{4}\) inches
Answer:
1\(\frac{2}{4}\) inches is the the length of the nails.
B. 1\(\frac{2}{4}\)

Explanation:
Wrong measurement of nails = 2\(\frac{1}{4}\) inches.
Correct measurement of nails = \(\frac{3}{4}\) inch.
the length of the nails = Wrong measurement of nails  – Correct measurement of nails
= 2\(\frac{1}{4}\) – \(\frac{3}{4}\)
= 1\(\frac{2}{4}\) inches.

 

 

 

Lesson 11.2 Make Line Plots

Solve & Share
The manager of a shoe store kept track of the lengths of the shoes sold in a day. Complete the line plot using the data from the shoe store. What length shoe was sold the most?
I can … make a line plot to represent data.
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 15

Look Back! Generalize How can you use a line plot to find the data that occur most often?
Answer:
We can use a line plot to find the data that occur most often by counting the number of times which occurred more in the given data.

Explanation:
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Lesson 11.2 Make Line Plots-Solve & Share

Essential Question
How Can You Make Line Plots?
Answer:
We can make line plots by using the data given representing it on line. To create a line plot, ​first create a number line that includes all the values in the data set.

 

 

Visual Learning Bridge
Serena measured the lengths of her colored pencils. How can Serena make a line plot to show these lengths?
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 16

Making a Line Plot

Step 1
Draw a number line and choose a scale based on the lengths of Serena’s pencils. Mark halves, fourths, and eighths. The scale should show data values from the least to the greatest.

Step 2
Write a title for the line plot. Label the line plot to tell what the numbers represent.

Step 3
Draw a dot for each pencil length.
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 17

Convince Me! Model with Math Write and solve an equation to find the difference , in length between Serena’s two shortest colored pencils.
Answer:
Difference , in length between Serena’s two shortest colored pencils = \(\frac{1}{4}\) inches.

Explanation:
Length of First shortest colored pencil = 4 \(\frac{1}{2}\) inches.
Length of Second shortest colored pencil = 4 \(\frac{3}{4}\) inches.
Difference:
Length of Second shortest colored pencil – Length of First shortest colored pencil
= 4 \(\frac{3}{4}\) – 4 \(\frac{1}{2}\)
= \(\frac{1}{4}\) inches.

 

 

 

Guided Practice
Do You Understand?
Question 1.
The scale of the line plot, Lengths of Serena’s Pencils, goes from 4 to 5 by eighths. Why is this a good scale to use?
Answer:
This is a good scale to use because its easy to plot the measurements on the line and easy to understand the values.

Explanation:
The scale of the line plot, Lengths of Serena’s Pencils, goes from 4 to 5 by eighths. This is a good scale to use because its easy to plot and to understand too.

 

 

Question 2.
Use the table shown at the right to compare the lengths of Sandy’s pencils with the lengths of Serena’s pencils shown on the previous page. Who has more pencils that are the same length, Serena or Sandy? Which set of data was easier to compare? Why?
Answer:
Serena has more more pencils that are the same length of 4 \(\frac{3}{4}\) inches. Both set of data are easier to compare because the values are clear to understand.

Explanation:
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 16Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 18

 

 

 

Do You Know How?
Question 3.
Complete the line plot.
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 18

Answer:
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Lesson 11.2 Make Line Plots-Do You Know How-3

Explanation:
Line plotting for the following data:
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 18

 

 

Independent Practice
Leveled Practice For 4-5, use the table at the right.
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 19
Question 4.
Use the data in the table to make a line plot.
Answer:
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Lesson 11.2 Make Line Plots-Independent Practice-4

Explanation:
Line plotting of data:
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 19

 

 

Question 5.
What is the length of the longest bracelet? What is the shortest length? What is the difference?
Answer:
Difference = 2 inches.

Explanation:
Length of the longest bracelet =  8 \(\frac{1}{2}\) inches.
Length of the shortest bracelet = 6 \(\frac{1}{2}\) inches.
Difference:
Length of the longest bracelet – Length of the shortest bracelet
= 8 \(\frac{1}{2}\) – 6 \(\frac{1}{2}\)
= 2 inches.

 

 

Problem Solving
Question 6.
Nora weighed each of the 7 beefsteak tomatoes she picked from her garden. The total weight of the 7 tomatoes was 10\(\frac{3}{4}\) pounds. Her line plot shows only 6 dots. What was the weight of the missing tomato?
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 20

Answer:
Weight of the missing tomato = 1\(\frac{3}{4}\) pounds.

Explanation:
Total weight of the 7 tomatoes =10 \(\frac{3}{4}\) pounds.
Number of dots shown on line plot = 6.
Total weight of the 7 tomatoes = dots value plotted on line + Weight of the missing tomato
10 \(\frac{3}{4}\)  =  1 + 1 + 1\(\frac{1}{4}\) + 1\(\frac{2}{4}\) + 2 + 2\(\frac{1}{4}\) + Weight of the missing tomato
=> 10 \(\frac{3}{4}\)  = 9 + Weight of the missing tomato
=> 10 \(\frac{3}{4}\) – 9 =  Weight of the missing tomato
=> 1\(\frac{3}{4}\) pounds = Weight of the missing tomato.

 

 

Question 7.
Make Sense and Persevere Alyssa made a pink-and-white-striped blanket for her bed. There are 7 pink stripes and 6 white stripes. Each stripe is 8 inches wide. How wide is Alyssa’s blanket? Explain.
Answer:
Total length of Alyssa’s blanket = 104 inches.

Explanation:
Number of blanket with pink stripes = 7.
Number of blanket with pink stripes = 6.
Length of each stripe = 8 inches.
Total length of Alyssa’s blanket = (Number of blanket with pink stripes + Number of blanket with pink stripes) × Length of each stripe
= (7 + 6) × 8
= 13 × 8
= 104 inches.

 

 

For 8-9, use the table at the right.
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 21

Question 8.
Trisha measured how far her snail moved each day for 5 days. Make a line plot of Trisha’s data.
Answer:
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Lesson 11.2 Make Line Plots-Higher Order Thinking-9

Explanation:
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 21
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Lesson 11.2 Make Line Plots-Higher Order Thinking-9

 

 

Question 9.
Higher Order Thinking Write a question that would require addition or subtraction to solve using Trisha’s data. What is the answer?
Answer:
Total distance Trisha’s snail moved in 5 days = 7 \(\frac{2}{8}\) inches.

Explanation:
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 21
Distance Trisha’s snail moved on Monday = 1\(\frac{4}{8}\)
Distance Trisha’s snail moved on Tuesday =1\(\frac{3}{8}\)
Distance Trisha’s snail moved on Wednesday =1\(\frac{1}{8}\)
Distance Trisha’s snail moved on Thursday = 2\(\frac{1}{8}\)
Distance Trisha’s snail moved on Friday = 1\(\frac{1}{8}\)
Total distance Trisha’s snail moved in 5 days = Distance Trisha’s snail moved on Monday +
Distance Trisha’s snail moved on Tuesday + Distance Trisha’s snail moved on Wednesday  + Distance Trisha’s snail moved on Thursday + Distance Trisha’s snail moved on Friday
= 1\(\frac{4}{8}\) + 1\(\frac{3}{8}\) + 1\(\frac{1}{8}\) + 2\(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 2 \(\frac{7}{8}\) + 1\(\frac{1}{8}\) + 2\(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 4 + 2\(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 6 \(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 7 \(\frac{2}{8}\) inches.

 

 

Assessment Practice
Question 10.
Brianna is making bracelets for her friends and family members. The bracelets have the following lengths in inches:
6, 6\(\frac{3}{4}\), 6\(\frac{1}{4}\), 5\(\frac{3}{4}\), 5, 6, 6\(\frac{2}{4}\), 6\(\frac{1}{4}\), 6, 5\(\frac{3}{4}\)
Use the data set to complete the line plot.
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 22

Answer:
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Lesson 11.2 Make Line Plots-Assessment Practice-10

Explanation:
The bracelets lengths in inches:
6, 6\(\frac{3}{4}\), 6\(\frac{1}{4}\), 5\(\frac{3}{4}\), 5, 6, 6\(\frac{2}{4}\), 6\(\frac{1}{4}\), 6, 5\(\frac{3}{4}\)

 

 

 

Lesson 11.3 Use Line Plots to Solve Problems

Solve & Share
Ms. Earl’s class measured the lengths of 10 caterpillars in the school garden. The caterpillars had the following lengths in inches:
\(\frac{3}{4}\), 1\(\frac{1}{4}\), 1\(\frac{3}{4}\), 1\(\frac{1}{2}\), 1, 1, \(\frac{3}{4}\), 1\(\frac{1}{4}\), 1\(\frac{3}{4}\), 1\(\frac{1}{2}\)
Plot the lengths on the line plot. Write and solve an equation to find the difference in length between the longest and shortest caterpillars.
I can … use line plots to solve problems involving fractions.
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 23

Look Back! How can a line plot be used to find the difference between the greatest and least values?
Answer:
A line plot can be used to find the difference between the greatest and least values by doing the subtraction function between the two numbers.

 

Essential Question
How Can You Use Line Plots to Solve Problems involving Fractions?
Answer:
We can use line plots to Solve Problems involving Fractions by dividing the fractions by fractions to find the required solution to the problem.

 

 

Visual Learning Bridge
Alma and Ben are filling water balloons. The line plots show the weights of their water balloons. Who filled more water balloons? How many more? How much heavier was Alma’s heaviest water balloon than Ben’s heaviest water balloon?
Envision Math Common Core 4th Grade Answers Topic 11 Represent and Interpret Data on Line Plots 24

Who filled more water balloons? How many more?
Each dot in the line plots represents 1 water balloon.
Alma filled 20 water balloons.
Ben filled 15 water balloons.
20 – 15 = 5
Alma filled 5 more water balloons than Ben.

How much heavier was Alma’s heaviest water balloon than Ben’s heaviest water balloon?

The dot farthest to the right in each line plot represents the heaviest water balloon.
Alma’s heaviest water balloon was 2\(\frac{2}{8}\) pounds.
Ben’s heaviest water balloon was 2\(\frac{1}{8}\) pounds.
Subtract.
2\(\frac{2}{8}\) – 2\(\frac{1}{8}\) = \(\frac{1}{8}\)
Alma’s heaviest water balloon was pound heavier than Ben’s heaviest water balloon.

Convince Me! Make Sense and Persevere How much heavier was Alma’s heaviest water balloon than her lightest water balloon? How much heavier was Ben’s heaviest water balloon than his lightest water balloon? Write and solve equations.
Answer:
1\(\frac{1}{8}\) pounds heavier was Alma’s heaviest water balloon than her lightest water balloon.
\(\frac{6}{8}\) pounds heavier was Ben’s heaviest water balloon than her lightest water balloon.

Explanation:
Weight of Alma’s heaviest water balloon = 2\(\frac{2}{8}\) pounds
Weight of Alma’s lightest water balloon = 1\(\frac{1}{8}\) pounds
Difference:
Weight of Alma’s heaviest water balloon – Weight of Alma’s lightest water balloon
= 2\(\frac{2}{8}\) – 1\(\frac{1}{8}\)
= 1\(\frac{1}{8}\) pounds.

Weight of Ben’s heaviest water balloon = 2\(\frac{1}{8}\)pounds
Weight of Ben’s lightest water balloon = 1\(\frac{4}{8}\) pounds
Difference:
Weight of Ben’s heaviest water balloon – Weight of Ben’s lightest water balloon
= 2\(\frac{1}{8}\) – 1\(\frac{4}{8}\)
= \(\frac{6}{8}\) pounds.

Another Example!
Rowan’s class measured the snowfall for 5 days. The line plot shows the heights of snowfall they recorded. How many inches of snow were recorded? What amount of snowfall occurred most often?
Envision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots 25
Find the total number of inches of snowfall recorded.
\(\frac{1}{4}\) + \(\frac{2}{4}\) + \(\frac{2}{4}\) + \(\frac{2}{4}\) + \(\frac{3}{4}\) = 2\(\frac{2}{4}\) inches
The amount of snowfall that occurred most often was \(\frac{2}{4}\) inch.

Guided Practice
Do You Understand?
Question 1.
Use Structure How could you use the Commutative and Associative Properties of Addition to make the addition in the Another Example easier?
Answer:
We can use the Commutative and Associative Properties of Addition to make the addition in the Another Example easier by rewriting the values and doing addition because the result is same.

 

 

Do You Know How?
For 2-3, use the example on the previous page.
Question 2.
Who filled more water balloons over 2 pounds?
Answer:
Ben filled more water balloons over 2 pounds.

Explanation:
Ben’s heaviest water balloon was 2\(\frac{1}{8}\) pounds.

 

Question 3.
How much heavier were Alma’s two heaviest water balloons than Ben’s two heaviest?
Answer:
\(\frac{1}{8}\) pounds heavier were Alma’s two heaviest water balloons than Ben’s two heaviest.

Explanation:
Weight of Alma’s two heaviest water balloons = 2 × 2\(\frac{2}{8}\)
Weight of Ben’s two heaviest water balloon = 2 × 2\(\frac{1}{8}\) pounds.
Difference:
Weight of Alma’s two heaviest water balloons – Weight of Ben’s two heaviest water balloon
= 2 × 2\(\frac{2}{8}\) – 2 × 2\(\frac{1}{8}\)
= 4 \(\frac{2}{8}\)  – 4 \(\frac{1}{8}\)
= \(\frac{1}{8}\) pounds.

 

Independent Practice
For 4-5, use the line plot at the right.
Envision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots 26
Question 4.
What is the difference in height between the tallest and shortest patients?
Answer:
1 \(\frac{3}{4}\) feet is the difference in height between the tallest and shortest patients.

Explanation:
Height of the tallest patient = 6 feet.
Height of the shortest patient = 4\(\frac{1}{4}\) feet.
Difference:
Height of the tallest patient – Height of the shortest patient
= 6 – 4\(\frac{1}{4}\)
= 6 – 4.25
= 1 \(\frac{3}{4}\) feet.

 

Question 5.
Oscar says 5 feet is the most common height Dr. Chen measured. Do you agree? Explain.
Answer:
No, 5 feet is not the most common height Dr. Chen measured as Oscar says because 5 \(\frac{2}{4}\) feet is most common height Dr. Chen measured.

Explanation:
Most common height Dr. Chen measured = 5\(\frac{2}{4}\) feet in the given data.

 

Problem Solving
Question 6.
Make Sense and Persevere Marcia measured her dolls and showed the heights using a line plot. How much taller are Marcia’s two tallest dolls combined than her two shortest dolls? Explain.
Envision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots 27
Answer:
2\(\frac{3}{4}\) inches taller are Marcia’s two tallest dolls combined than her two shortest dolls.

Explanation:
Marcia’s two tallest dolls heights = 7 inches and 6\(\frac{3}{4}\) inches.
Marcia’s two tallest dolls combined = 7 inches + 6\(\frac{3}{4}\) inches.
= 13 \(\frac{3}{4}\)  inches.
Marcia’s two shortest dolls heights = 5\(\frac{1}{4}\) inches and 5 \(\frac{3}{4}\) inches.
Marcia’s two shortest dolls combined = 5\(\frac{1}{4}\) inches + 5 \(\frac{3}{4}\) inches.
= 5.25 + 5.75
= 11 inches.
Difference:
Marcia’s two tallest dolls combined – Marcia’s two tallest dolls combined
= 13 \(\frac{3}{4}\) inches – 11 inches
= 2\(\frac{3}{4}\) inches.

 

 

Question 7.
Higher Order Thinking Marlee is knitting a scarf. The line plot shows the length she knits each day. How many more inches does Marlee need to knit so the scarf is 30 inches long?
Envision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots 28
Answer:
2 inches more inches Marlee needs to knit so the scarf is 30 inches long.

Explanation:
The length she knits each day = 2, 2\(\frac{2}{8}\) inches, 2\(\frac{2}{8}\) inches, 2\(\frac{4}{8}\) inches, 2\(\frac{4}{8}\) inches, 2\(\frac{4}{8}\) inches, 2\(\frac{5}{8}\) inches, 2\(\frac{6}{8}\) inches, 2\(\frac{6}{8}\) inches,  2\(\frac{7}{8}\) inches, 3 inches.

Total of the lengths she knits all days = 2 + 2\(\frac{2}{8}\) + 2\(\frac{2}{8}\)  + 2\(\frac{4}{8}\) + 2\(\frac{4}{8}\) + 2\(\frac{4}{8}\) + 2\(\frac{5}{8}\) + 2\(\frac{6}{8}\) + 2\(\frac{6}{8}\)  + 2\(\frac{7}{8}\) + 3 inches
= 28 inches.

More inches Marlee needs to knit so the scarf is 30 inches long = 30 – Total of the lengths she knits all days
= 30 – 28 inches
= 2 inches.

 

Assessment Practice
For 8-9, use the line plot.
Envision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots 29
Question 8.
Which of the following statements are true? Select all that apply.
☐ Most of the players are 6 feet or taller.
☐ Five players are 6 feet tall.
☐ The combined height of two of the shortest players is 1\(\frac{1}{2}\) feet.
☐ The difference between the tallest and the shortest players is \(\frac{3}{4}\) foot.
☐ All of the players are taller than 5\(\frac{3}{4}\) feet.
Answer:
Statements which are true:
Most of the players are 6 feet or taller.
All of the players are taller than 5\(\frac{3}{4}\) feet.

Explanation:
Statements which are true:
☐ Most of the players are 6 feet or taller.
☐ Five players are 6 feet tall.
☐ The combined height of two of the shortest players is 1\(\frac{1}{2}\) feet.
Combined height of two of the shortest players =
5\(\frac{3}{4}\) + 5\(\frac{3}{4}\)
= 11\(\frac{2}{4}\).

☐ The difference between the tallest and the shortest players is \(\frac{3}{4}\) foot.
Tallest player height = 6\(\frac{3}{4}\) feet.
Shortest player height = 5\(\frac{3}{4}\) feet.
Difference:
Tallest player height – Shortest player height
= 6\(\frac{3}{4}\) – 5\(\frac{3}{4}\)
= 1 feet.

☐ All of the players are taller than 5\(\frac{3}{4}\) feet.

 

 

Question 9.
If one of the shortest players grew \(\frac{3}{4}\) foot before the next season started, how tall would the player be?
A. \(\frac{6}{4}\) feet
B. 5\(\frac{3}{4}\) feet
C. 6 feet
D. 6\(\frac{2}{4}\) feet

Answer:
6\(\frac{2}{4}\) feet taller the player would be.

Explanation:
Shortest player height = 5\(\frac{3}{4}\) feet.
If one of the shortest players grew \(\frac{3}{4}\) foot.
=> 5\(\frac{3}{4}\) + \(\frac{3}{4}\)
=> 6\(\frac{2}{4}\) feet.

 

 

Lesson 11.4 Problem Solving

Critique Reasoning
Solve & Share
A class made a line plot showing the amount of snowfall for 10 days. Nathan analyzed the line plot and said, “The difference between the greatest amount of snowfall recorded and the least amount of snowfall recorded is 3 because the first measurement has one dot and the last measurement has 4 dots.” How do you respond to Nathan’s reasoning?
I can … use what I know about line plots to critique the reasoning of others.
Envision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots 30

Thinking Habits
Be a good thinker! These questions can help you.

  • What questions can ask to understand other people’s thinking?
  • Are there mistakes in other people’s thinking?
  • Can I improve other people’s thinking?

Look Back! Critique Reasoning Millie said that the total amount of snowfall for the 5 days above was 10 inches. Is Millie correct?
Answer:
No, Millie is incorrect because Total amount of snowfall for the 5 days is 5 \(\frac{2}{4}\) inches. not 10 inches.

Explanation:
Amount of snowfall for the 5 days = \(\frac{3}{4}\), 1, 1, 1\(\frac{1}{4}\), 1\(\frac{2}{4}\)
Total amount of snowfall for the 5 days = \(\frac{3}{4}\) + 1 + 1 + 1\(\frac{1}{4}\) + 1\(\frac{2}{4}\)
= 5 \(\frac{2}{4}\) inches.

 

 

Essential Question
How Can You Critique the Reasoning of Others?
Answer:
We can Critique the Reasoning of Others by checking the process how the problem is solved and finally tallying their solution.

 

 

Visual Learning Bridge
The line plots show the amount of rainfall for two months.

Val said, “The total rainfall for February was greater than the total rainfall for January because \(\frac{7}{8}\) + \(\frac{7}{8}\) equals \(\frac{14}{8}\), and the highest rainfall in January was \(\frac{5}{8}\)“.
Envision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots 31
What is Val’s reasoning?
Val compared the two highest amounts of rainfall for each month.

How can I critique the reasoning of others?
I can

  • ask questions for clarification.
  • decide if the strategy used makes sense.
  • look for flaws in estimates or calculations.

Here’s my thinking.
Val’s reasoning is not correct.
She compared the days with the greatest amount of rainfall for the two months. The days with the greatest amounts of rainfall are not the total for the months.

Val should have added the amounts for each month. Then she could compare the amounts.
January \(\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{3}{8}+\frac{3}{8}+\frac{3}{8}+\frac{5}{8}=\frac{17}{8}\) inches
February: \(\frac{1}{8}+\frac{1}{8}+\frac{5}{8}+\frac{7}{8}+\frac{7}{8}=\frac{21}{8}\) inches
During February, there was \(\frac{21}{8}-\frac{17}{8}=\frac{4}{8}\) inch more rain than January

Convince Me! Critique Reasoning Bev thought January had more rainfall because it rained on 7 days and February only had rain on 5 days. How do you respond to Bev’s reasoning?
Answer:
Well, Bev’s reasoning is not correct because to find the more rainfall in between January and February months, you should calculate the rainfall not the number of days.

 

Guided Practice
Critique Reasoning At a dog show, a judge wrote down the heights of 12 dogs. Cole made a line plot of the heights, shown to the right. He concluded, “The height with the most dots is 1\(\frac{1}{4}\) feet, so that is the greatest height of the dogs at the dog show.”
Envision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots 32
Question 1.
What is Cole’s conclusion? How did he reach this conclusion?
Answer:
Cole concluded, “The height with the most dots is 1\(\frac{1}{4}\) feet, so that is the greatest height of the dogs at the dog show.” He reached this conclusion by marking most dots on 1\(\frac{1}{4}\) feet in the line plot chart.

 

 

Question 2.
Is Cole’s conclusion correct? Explain.
Answer:
No, Cole’s conclusion incorrect because what he marked as the highest height of dog is the most common height of dogs and highest height of dog is 3 feet not 1\(\frac{1}{4}\) feet.

 

 

Independent Practice
Critique Reasoning
Natasha keeps a log of the total amount of time her students practiced on their violins outside of their weekly lesson. She creates the line plot shown. Each dot represents one student who practices a specific amount of time in one week. Natasha says that 5 of her students’ practice times combined is 1\(\frac{1}{4}\) hours because there are 5 dots above 1\(\frac{1}{4}\).
Envision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots 33
Question 3.
What is Natasha’s argument? How does she support it?
Answer:
Natasha’s argument is that 5 of her students’ practice times combined is 1\(\frac{1}{4}\) hours. She supports it because there are 5 dots above 1\(\frac{1}{4}\).

 

Question 4.
Critique Natasha’s reasoning.
Answer:
Natasha’s reasoning says that 5 of her students’ practice times combined is 1\(\frac{1}{4}\) hours because there are 5 dots above 1\(\frac{1}{4}\). She thinks its correct but she is saying about more common hours the students who practiced a specific amount of time in one week.

 

 

Problem Solving
Performance Task

Taking Inventory
Mr. Pally is building a desk using screws of different lengths. The instructions show how many screws of each length he will need to use. Mr. Pally concludes he will use more of the shortest screws than the longest screws.
Question 5.
Model with Math Draw a line plot to show the screw lengths Mr. Pally will use to build the desk.
Envision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots 34
Answer:
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Lesson 11.4 Problem Solving-Problem Solving-Performance Task-5

Explanation:
Envision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots 34

 

 

Question 6.
Reasoning How can you use the line plot to find which length of screw Mr. Pally will need the most?
Answer:
We use the line plot to find which length of screw Mr. Pally will needs the most by counting the dots potted on the line, which occurred many times.

 

 

Question 7.
Critique Reasoning is Mr. Pally’s conclusion correct? How did you decide? If not, what can you do to improve his reasoning?
Envision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots 35
Answer:
Yes, Mr. Pally conclusion he will use more of the shortest screws than the longest screws is correct because in the line plotted shows many dots on shorter screws than the longest screws.

Explanation:
Mr. Pally concludes he will use more of the shortest screws than the longest screws.

 

 

Topic 11 Fluency Practice Activity

Find a Match
Work with a partner. Point to a clue.
Read the clue.
Look below the clues to find a match. Write the clue letter in the box next to the match.
Find a match for every clue.
I can …add and subtract multi-digit whole numbers.

Clues
A. The sum is between 3,510 and 3,520.
B. The difference is exactly 3,515.
C. The sum is between 3,560 and 3,570.
D. The difference is between 3,530 and 3,540.
E. The sum is exactly 3,584.
F. The difference is between 3,590 and 3,600.
G. The sum is exactly 3,987.
H. The difference is between 1,000 and 2,000.
Envision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots 36
Answer:
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Lesson 11.4 Problem Solving-Topic 11 Fluency Practice Activity-Find a Match

Explanation:
Clues
A. The sum is between 3,510 and 3,520.
B. The difference is exactly 3,515.
C. The sum is between 3,560 and 3,570.
D. The difference is between 3,530 and 3,540.
E. The sum is exactly 3,584.
F. The difference is between 3,590 and 3,600.
G. The sum is exactly 3,987.
H. The difference is between 1,000 and 2,000.
Envision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots 36

 

 

 

 

Topic 11 Vocabulary Review

Understand Vocabulary
Word List

  • data set
  • graph
  • line plot
  • number line
  • scale
  • table

Write T for true and F for false.
Question 1.
________ Graphs are used to display and represent data.
Answer:
__True______ Graphs are used to display and represent data.

 

Question 2.
_________ A data set is a collection of pieces of information.
Answer:
____True_____ A data set is a collection of pieces of information.

 

Question 3.
__________ A table is never used to display data.
Answer:
___False_______ A table is never used to display data.

 

Question 4.
__________ A line plot shows data along a number line.
Answer:
___True_______ A line plot shows data along a number line.

 

Question 5.
_________ A line plot may have more points than there are numbers in the data set.
Answer:
___False______ A line plot may have more points than there are numbers in the data set.

 

Write always, sometimes, or never.
Question 6.
A line plot _________ displays data.
Answer:
A line plot ___always______ displays data.

 

Question 7.
The scale on a line plot is ________ numbered using fractions.
Answer:
The scale on a line plot is ___sometimes_____ numbered using fractions.

 

Question 8.
A number line is __________ numbered out of order.
Answer:
A number line is ___never_______ numbered out of order.

 

 

Use Vocabulary in Writing
Question 9.
Use at least 3 terms from the Word List to describe another way Patrick can display his data.
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 37
Answer:
Graph, Line plot and Number line are the 3 terms from the Word List to describe another way Patrick can display his data.

Explanation:
Word List given:

  • data set
  • graph
  • line plot
  • number line
  • scale
  • table

 

 

Topic 11 Reteaching

Set A pages 417-420

The line plot shows the number of hours Mrs. Mack was at the gym each day, during a two week period.
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 38

Remember each dot above the line plot represents one value in the data set.

Question 1.
How many days did Mrs. Mack go to the gym?
Answer:
Mrs. Mack went to the gym for 11 days.

Question 2.
What is the least amount of time Mrs. Mack spent at the gym?
Answer:
1\(\frac{1}{4}\) hours is the least amount of time Mrs. Mack spent at the gym.

Question 3.
How many hours was Mrs. Mack at the the gym during the two weeks?
Answer:
25\(\frac{3}{4}\) hours Mrs. Mack was at the the gym during the two weeks.

Explanation:
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 38
Number of hours Mrs. Mack was at the the gym during the two weeks:
1, 1\(\frac{1}{4}\) , 1\(\frac{2}{4}\) ,2 , 2 , 2\(\frac{1}{4}\) , 2 \(\frac{1}{4}\) , 2\(\frac{1}{4}\) ,2 \(\frac{2}{4}\) , 2\(\frac{3}{4}\) ,3 , 3.
Total number of hours Mrs. Mack was at the the gym during the two weeks = 1 + 1\(\frac{1}{4}\) + 1\(\frac{2}{4}\) + 2 + 2 + 2\(\frac{1}{4}\) + 2 \(\frac{1}{4}\) + 2\(\frac{1}{4}\) + 2 \(\frac{2}{4}\) + 2\(\frac{3}{4}\) + 3 + 3
= 25\(\frac{3}{4}\) hours.

Set B pages 421-424

Lilly measured the lengths of the ribbons in her craft kit and drew a line plot.
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 39
The number line shows the lengths from least to greatest. The labels show what the dots represent.

Remember to choose a reasonable scale for your number line.

A zoo in Australia studied platypuses. Their masses are recorded below.
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 40
Question 1.
Draw a line plot for the data set.
Answer:
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Lesson 11.4 Problem Solving-Set B pages 421-424-1
Explanation:
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 40

 

 

 

Question 2.
What is the difference in mass of the platypus with the greatest mass and the platypus with the least mass?
Answer:
1\(\frac{1}{8}\) kg is the difference in mass of the platypus with the greatest mass and the platypus with the least mass.

Explanation:
The greatest mass of the platypus = 2\(\frac{6}{8}\) kg.
The least mass of the platypus = 1\(\frac{5}{8}\) kg.
Difference:
The greatest mass of the platypus – The least mass of the platypus
= 2\(\frac{6}{8}\)  – 1\(\frac{5}{8}\)
= 1\(\frac{1}{8}\) kg.

 

Set C pages 425-428

Carly and Freddie pick up trash. The line plots show how much they picked up each day for 14 days. What is the difference between the greatest and least amounts Carly picked up?
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 41
The greatest amount of trash Carly picked up was 3 pounds. The least amount was \(\frac{1}{2}\) pound.
Subtract. 3 – \(\frac{1}{2}\) = 2\(\frac{1}{2}\) pounds

Remember you can use equations to help solve problems with data from line plots.

For 1-3, use the line plots at the left.
Question 1.
Explain how to find the total weight of the trash Freddie picked up.
Answer:
We can find the total weight of the trash Freddie picked up in 14 days by adding the every day trash he collected.

Explanation:
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 41

Question 2.
Write and solve an equation to find , the difference between the greatest amount Freddie collected and the least amount he collected.
Answer:
2 pounds is the difference between the greatest amount Freddie collected and the least amount he collected.

Explanation:
The greatest amount Freddie collected = 2\(\frac{1}{2}\) pounds.
The least amount he collected = \(\frac{1}{2}\) pounds.
Difference:
The greatest amount Freddie collected – The least amount he collected
= 2\(\frac{1}{2}\) pounds – \(\frac{1}{2}\) pounds
= 2 pounds.

Question 3.
What is the sum of Carly’s most frequent weight and Freddie’s most frequent weight? Explain.
Answer:
5 pounds is the sum of Carly’s most frequent weight and Freddie’s most frequent weight.

Explanation:
Carly’s most frequent weight = 2\(\frac{1}{2}\) pounds.
Freddie’s most frequent weight = 1\(\frac{1}{2}\) pounds.
Sum:
Carly’s most frequent weight + Freddie’s most frequent weight
= 2\(\frac{1}{2}\) pounds + 1\(\frac{1}{2}\) pounds
= 5 pounds.

 

 

Set D pages 429-432

Think about these questions to help you critique the reasoning of others.
Thinking Habits!

  • What questions can ask to understand other people’s thinking?
  • Are there mistakes in other people’s thinking?
  • Can I improve other people’s thinking?
    Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 42

Remember you can use math to identify mistakes in people’s thinking.
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 43
Question 1.
Spencer says 2\(\frac{3}{8}\) miles is the most common delivery distance. Do you agree? Explain.
Answer:
No, I disagree with what Spencer says 2\(\frac{3}{8}\) miles is the most common delivery distance because the most common delivery distance is \(\frac{6}{8}[/Latex] miles.

 

 

 

Topic 11 Assessment Practice

Question 1.
What is the difference between the heaviest and lightest weights?
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 44
Answer:
1 pounds is the difference between the heaviest and lightest weights.

Explanation:
The heaviest weight = 3[latex]\frac{2}{4}\) pounds.
The lightest weight = 2\(\frac{2}{4}\) pounds.
Difference:
The heaviest weight – The lightest weight
= 3\(\frac{2}{4}\)  – 2\(\frac{2}{4}\)
= 1 pounds.

Question 2.
How many dots would be placed above 1\(\frac{3}{4}\) in a line plot of these data?
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 45
A. 3 dots
B. 2 dots
C. 1 dot
D. 0 dots
Answer:
3 dots dots would be placed above 1\(\frac{3}{4}\) in a line plot of these data.
A. 3 dots.

Explanation:
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 45
Dots would be placed above 1\(\frac{3}{4}\) in a line plot of these data:
3 dots.

 

 

Question 3.
Which is the most common length of snail Fred has in his backyard?
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 46
Answer:
3 inches is the most common length of snail Fred has in his backyard.

Explanation:
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 46
3 inches is the most common length of snail Fred has in his backyard.

 

Question 4.
During a sleep study, the number of hours 15 people slept was recorded in the table below.
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 47
A. Use the data in the table to draw a line plot.
Answer:
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Lesson 11.4 Problem Solving-Topic 11 Assessment Practice-4

Explanation:
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 47

B. How many more hours did the person who slept the greatest number of hours sleep than the person who slept the least number of hours? Explain.
Answer:
3\(\frac{1}{2}\) more hours the person who slept the greatest number of hours sleep than the person who slept the least number of hours.

Explanation:
The person who slept the greatest number of hours = 9 .
The person who slept the least number of hours = 5\(\frac{1}{2}\).
Difference:
The person who slept the greatest number of hours – The person who slept the least number of hours
= 9 – 5\(\frac{1}{2}\)
= 3\(\frac{1}{2}\).

Question 5.
Use the line plot below. Select all the true statements.
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 48
☐ The greatest height is 2\(\frac{1}{2}\) inches.
☐ More plants have a height of 2 inches than 1\(\frac{1}{2}\) inches.
☐ There are 3 plants with a height of 1 inch.
☐ There are 3 plants with a height of 2 inches and 3 plants with a height of 2\(\frac{1}{2}\) inches.
☐ The tallest plant is 1\(\frac{1}{2}\) inches taller than the shortest plant.
Answer:
All the true statements:
The greatest height is 2\(\frac{1}{2}\) inches.
There are 3 plants with a height of 2 inches and 3 plants with a height of 2\(\frac{1}{2}\) inches.
The tallest plant is 1\(\frac{1}{2}\) inches taller than the shortest plant.

Explanation:
Select all the true statements:
☐ The greatest height is 2\(\frac{1}{2}\) inches. (True)
☐ More plants have a height of 2 inches than 1\(\frac{1}{2}\) inches. (False)
☐ There are 3 plants with a height of 1 inch. (False)
No, There are 2 plants with a height of 1 inch.
☐ There are 3 plants with a height of 2 inches and 3 plants with a height of 2\(\frac{1}{2}\) inches. (True)
☐ The tallest plant is 1\(\frac{1}{2}\) inches taller than the shortest plant. (True)
=> Tallest plant height = 2\(\frac{1}{2}\) inches.
Shortest plant height = 1inches.
Difference:
Tallest plant height – Shortest plant height
= 2\(\frac{1}{2}\) – 1
= 1\(\frac{1}{2}\).

 

Question 6.
Mr. Tricorn’s class measured the lengths of crayons. How many crayons did they measure? Use the line plot.
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 49
Answer:
Total number of crayons they measured = 10.

Explanation:
Number of crayons of length 1\(\frac{1}{2}\) inches = 1.
Number of crayons of length 2\(\frac{1}{2}\) inches = 4.
Number of crayons of length 3\(\frac{1}{2}\) inches = 2.
Number of crayons of length 4\(\frac{1}{2}\) inches = 3.
Total number of crayons measured = Number of crayons of length 1\(\frac{1}{2}\) inches + Number of crayons of length 2\(\frac{1}{2}\) inches + Number of crayons of length 3\(\frac{1}{2}\) inches + Number of crayons of length 4\(\frac{1}{2}\) inches
= 1 + 4 + 2 + 3
= 10.

 

 

Question 7.
Use the line plot from Exercise 6. How many crayons were greater than 3 inches long?
A. 9
B. 5
C. 6
D. 3
Answer:
Number of crayons greater than 3 inches long = 5.
B. 5.

Explanation:
Number of crayons of length 1\(\frac{1}{2}\) inches = 1.
Number of crayons of length 2\(\frac{1}{2}\) inches = 4.
Number of crayons of length 3\(\frac{1}{2}\) inches = 2.
Number of crayons of length 4\(\frac{1}{2}\) inches = 3.
Number of crayons greater than 3 inches long = Number of crayons of length 3\(\frac{1}{2}\) inches + Number of crayons of length 4\(\frac{1}{2}\) inches
= 2 + 3
= 5.

 

Question 8.
Ms. Garcia measured the heights of her students.
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 50
A. Use the data in the table to draw a line plot.
Answer:
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Lesson 11.4 Problem Solving-Topic 11 Assessment Practice-8A

Explanation:
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 50

 

 

B. Use the data in Exercise 8. Select all of the statements that are true.
☐ The tallest student is 4 feet tall.
☐ The tallest student is 4\(\frac{2}{4}\) feet tall.
☐ The shortest student is 3\(\frac{3}{4}\) feet tall.
☐ The tallest student is 1 foot taller than the shortest student.
☐ The most common height of the students was 4 feet tall.
Answer:
All of the statements that are true:
The tallest student is 4\(\frac{2}{4}\) feet tall.
The tallest student is 1 foot taller than the shortest student.
The most common height of the students was 4 feet tall.

Explanation:
Select all of the statements that are true.
☐ The tallest student is 4 feet tall. (False)
☐ The tallest student is 4\(\frac{2}{4}\) feet tall. (True)
☐ The shortest student is 3\(\frac{3}{4}\) feet tall. (False)
☐ The tallest student is 1 foot taller than the shortest student. (True)
=> Tallest student = 4\(\frac{2}{4}\) feet.
Shortest student = 3\(\frac{2}{4}\) feet.
Difference:
Tallest student – Shortest student
= 4\(\frac{2}{4}\) feet  – 3\(\frac{2}{4}\) feet
= 1 feet.
☐ The most common height of the students was 4 feet tall. (True)
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Lesson 11.4 Problem Solving-Topic 11 Assessment Practice-8A

 

 

Topic 11 Performance Task

Measuring Pumpkins Mr. Chan’s class picked small pumpkins from the pumpkin patch and then weighed their pumpkins.
Question 1.
The class made the Pumpkin Weights line plot of the data.
Envision Math Common Core Grade 4 Answers Topic 11 Represent and Interpret Data on Line Plots 51
Part A
What is the most common weight of the pumpkins?
Answer:
The most common weight of the pumpkins = 4\(\frac{1}{4}\) pounds.

Part B
Write and solve an equation to find, how much more the heaviest pumpkin weighs than the lightest pumpkin.
Answer:
1\(\frac{3}{4}\) pounds more the heaviest pumpkin weighs than the lightest pumpkin.

Explanation:
The heaviest pumpkin weight = 5pounds.
The lightest pumpkin weight = 3\(\frac{1}{4}\) pounds.
Difference:
The heaviest pumpkin weight – The lightest pumpkin weight
= 5 – 3\(\frac{1}{4}\)
= 1\(\frac{3}{4}\) pounds.

Part C
Ayana said 3 pumpkins weigh 4\(\frac{2}{4}\) pounds. Critique Ayana’s reasoning. Is she correct?
Answer:
Yes, she is correct because there are three pumpkins weigh 4\(\frac{2}{4}\) pounds.

 

Question 2.
The class also measures the distance around their pumpkins to the nearest half-inch. They recorded their data in the Pumpkin Size list. Pumpkin Size: 19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 19\(\frac{1}{2}\), 20, 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 20, 21, 22, 19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 21, 21, 21\(\frac{1}{2}\), 20\(\frac{1}{2}\)

Part A
Draw a line plot of Pumpkin Size data.
Answer:
Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-11-Represent-and-Interpret-Data-on-Line-Plots-Lesson 11.4 Problem Solving-Topic 11 Performance Task-2-Part A

Explanation:
Pumpkin Size:
19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 19\(\frac{1}{2}\), 20, 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 20, 21, 22, 19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 21, 21, 21\(\frac{1}{2}\), 20\(\frac{1}{2}\)

 

 

Part B
Drew says 1 more pumpkin was 20\(\frac{1}{2}\) inches around than was 19\(\frac{1}{2}\) inches because 20\(\frac{1}{2}\) – 19\(\frac{1}{2}\) = 1. Critique Drew’s reasoning.
Answer:
No, he is incorrect because pumpkin size of 20\(\frac{1}{2}\) – pumpkin size of 19\(\frac{1}{2}\) = 1 is the difference between two different sized pumpkins but not 1 more pumpkins added to the count.

Explanation:
20\(\frac{1}{2}\) – 19\(\frac{1}{2}\) = 1. Difference between different pumpkins.

 

Part C
What is  the difference between the longest distance and the shortest distance ? Write and solve an equation.
Answer:
3 inches is the difference between the longest distance and the shortest distance

Explanation:
The longest pumpkin sized = 22 inches.
The shortest pumpkin sized = 19 inches.
Difference:
The longest pumpkin sized – The shortest pumpkin sized
= 22 – 19
= 3 inches.

enVision Math Common Core Grade 4 Answer Key

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