Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data

Big Ideas Math Book 3rd Grade Answer Key Chapter 14 Represent and interpret Data answer key is useful for students who are preparing for their examinations and can download this pdf for free of cost. In this chapter, each and every question was explained in detail which helps students to understand easily. Big Ideas Math Book 3rd Grade Answer Key Chapter 14 explains different types of questions on Represent and interpret data.

Big Ideas Math Book 3rd Grade Answer Key Chapter 14 Represent and Interpret Data

This chapter contains different topics like Reading and Interpret Picture Graphs, Make Picture Graphs, Make line plots, make bar graphs, etc. Those topics were being set up by the mathematical professionals as indicated by the most recent release. Look down this page to get the answers for all the inquiries. Tap the connection to look at the subjects shrouded in this chapter Represent and Interpret Data.

Lesson 1 Read and Interpret Picture Graphs

Lesson 2 Make Picture Graphs

Lesson 3 Read and Interpret Bar Graphs

Lesson 4 Make Bar Graphs

 Lesson 5 Make Line Plots

Lesson 6 Measure Lengths: Half Inch

Lesson 7 Measure Lengths: Quarter Inch

Performance Task

Lesson 14.1 Read and Interpret Picture Graphs

Explore and Grow
You survey 14 students about their favorite type of party. The results are shown on the left picture graph. Use the key to represent the same data on the right picture graph.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 1

Answer:
In left side
the bounce house has 6 students
the costume has 2 students
the pool has 4 students
and skating has 2 students.
And on the right side
the bounce house was represented with 6 students as 1×6= 6
the costume was represented with 2 students as 1×2= 2
the pool was represented with 4 students as 1×4= 4
and skating was represented with 2 students as 1×2= 2.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 1
Here, we can see that the left side was given each emoji was equal to 2 students
so bounce house has three emojis which means 3×2= 6 students
the costume has one emoji which means 1×2= 2 students
the pool has two emojis which means 2×2= 4 students
and skating has one emoji which means 1×2= 2 students.
So to represent the same data on the right picture graph
here, we can see that in the right picture graph,
one emoji is equal to 1 student, so
the bounce house has  6 students which means 6×1= 6 emojis will be placed
the costume has 2 students which means 2×1= 2 emojis will be placed
the pool has 4 students which means 4×1= 4 emojis will be placed
and skating has 2 students which means 2×1= 2 emojis will be placed.

Structure
You ask one more student to name his favorite type of party. He chooses a pool party. How can you represent this on each graph? Explain.
Answer:
On the left side, we will add half emoji, and on the right side, we will add one emoji.

Explanation:
On the left side, we will represent the pool party by half emoji as on the left side one emoji is equal to 2 students, so to add one student we will place half emoji. And on the right side, we will represent the pool party by one emoji as on the right side one emoji is equal to 1 student, so to add one student we will place one emoji.

Think and Grow : Read and Interpret Picture Graphs
A picture graph shows data using pictures or symbols. The key of a picture graph gives the value of one picture or symbol. The value of one picture, or symbol, can be greater than 1.
Example
Use the graph to answer the questions.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 2

Answer:
There are 6 national forests in Arizona.
There are 5 national forests in Colorado.

Explanation:
Given that one full tree is equal to two forests, and the half tree is equal to 1 forest.
In Arizona, there are 3 full trees which means 3×2= 6 national forests
and in Colorado, there are 2 full trees which means 2×2= 4 national forests, and a half tree which means 1×1= 1 national forest. So the total number of national forests is 4+1= 5 national forests.

Show and Grow

Question 1.
Use the graph to answer the questions. How many students chose dog? How many students chose fish?
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 3
Answer:
The number of students who chose the dog is 30 students
The number of students who chose the fish is 15 students.

Explanation:
Given one emoji is equal to 10 students,
as we can see three emojis for the dog
so the number of students who chose the dog is
3×10= 30 students.
And we can see one emoji and a half emoji for the fish
so the number of students who chose the fish is
1×10= 10 students and 1×5= 5 students
so the total number of the students who chose fish are
10+5= 15 students.

Question 2.
Use the graph to answer the questions. What does the symbol Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 4 represent?
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 5
How many more students did not choose sledding?
Answer:
The total number of students who didn’t choose sledding is 7+4+6= 17 students.

Explanation:
Here, each emoji represents 2 students, and to find the number of students who didn’t choose sledding
we will add all the students of the other three activities rather than sledding
so in the skiing activity, there are three emojis and half emoji
which is 3×2= 6 students and 1×1= 1 students,
so the total number of students who choose skiing is 6+1= 7 students.
and in the snowboarding activity, there are two emojis which are 2×2= 4 students.
so the total number of students who choose snowboarding is 4 students.
in the sledding activity, there are four emojis and half emoji
which is 4×2= 8 students and 1×1= 1 students,
so the total number of students who choose skiing is 8+1= 9 students.
And in the ice skating activity, there are three emojis,
which is 3×2= 6 students.
So the total number of students who choose skiing is 6 students.
And the total number of students who didn’t choose sledding are 7+4+6= 17 students.

Question 3.
Use the graph to answer the questions. How many mangoes were eaten in June?
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 6
How many total mangoes were eaten in the months shown? Were more mangoes eaten in July or in June and August combined?
Answer:
The number of mangoes eaten in June is 21 mangoes.
The total number of mangoes eaten is 21+42+18= 81 mangoes.
Yes in the month of July more mangoes are eaten.

Explanation:
Given each emoji represents 6 mangoes,
so in the month of June, there are three emojis,
which means 3×6= 18 and a half emoji means 6/2= 3.
So the total number of mangoes eaten in June is 18+3= 21 mangoes.
in the month of July, there are seven emojis
which means 7×6= 42, so the total number of mangoes eaten in July is 42 mangoes.
in the month of August, there are three emojis,
which means 3×6= 18, so the total number of mangoes eaten in august is 18 mangoes.
The total number of mangoes eaten is 21+42+18= 81 mangoes.

Question 4.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 7 on a picture graph, then what value does Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 8 represent? Explain.

Answer:
10.

Explanation:
Let the single ball be 10 and then the half ball will be 5,
so 10+10+5= 25.

Think and Grow: Modeling Real Life

During which two weeks were a total of 52 cans recycled?
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 9
During ___ and ___ 52 cans were recycled.
Answer:
During week 3 and week 4 52 cans were recycled.

Explanation:
In week 1 the number of cans recycled is 8+8+8+4= 28 cans
In week 2 the number of cans recycled is 8+8+8+8= 32 cans
In week 3 the number of cans recycled is 8+4= 12 cans
In week 4 the number of cans recycled is 8+8+8+8+8= 40 cans
so during week 3 and week 4, 52 cans were recycled.

Show and Grow

Question 5.
Which two origami animals did a total of 32 students choose?
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 10
How many more students chose a frog or penguin than swan or butterfly?
Answer:
The two origami animals that did a total of 32 students are Swan and Penguin.

Explanation:
Given each emoji represents 4 students
The two origami animals did a total of 32 students are
Swan has three emojis and half emoji
which means 3×4= 12 and a half emoji means 4/2= 2
so the total number of students is 12+2= 14 students.
and Penguin has four emojis and half emoji
which means 4×4= 16 and a half emoji means 4/2= 2
so the total number of students is 16+2= 18 students.
The two origami animals that did a total of 32 students are Swan and Penguin.
How many more students chose frog or penguin than swan or butterfly
Butterfly has two emojis and half emoji
which means 2×4= 8 and a half emoji means 4/2= 2
so the total number of students is 8+2= 10 students.
and Frog has six emojis, which means 6×4= 24 students.
so the total number of students is 10+24= 34 students.
so there are 34-32= 2 more students who choose frog or penguin than Swan or Butterfly.

Read and Interpret Picture Graphs Homework & Practice 14.1

Question 1.
Use the graph to answer the questions. What value does the symbol Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 11 represent?
How many students chose pterodactyl?
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 12
How many students chose stegosaurus or velociraptor?
How many students did choose tyrannosaur?
Answer:
The value of half emoji represents 5 students.
The total number of students who choose pterodactyl is 45 students.
The total number of students who chose stegosaurus or velociraptor is 60 students.
the total number of students who choose tyrannosaur is 20 students.

Explanation:
Given each emoji represent 10 students, and
In pterodactyl, there are four emojis and half emoji which means
4×10= 40 and a half emoji represents 10/2= 5
the total number of students who choose pterodactyl is 40+5= 45 students.
In stegosaurus, there are two emojis and half emoji which means
2×10= 20 and a half emoji represents 10/2= 5
the total number of students who choose stegosaurus is 20+5= 25 students.
In velociraptor, there are three emojis and half emoji which means
3×10= 30 and a half emoji represents 10/2= 5
the total number of students who choose velociraptor is 30+5= 35 students.
The total number of students who chose stegosaurus or velociraptor is 60 students.
In tyrannosaur, there are five emojis which means
2×10= 20 and the total number of students who choose tyrannosaur is 20 students.

Question 2.
Use the graph to answer the questions.
How many dogs participated in the survey?
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 13
Which dog treat has more votes than biscuits, but fewer votes than peanut butter? How many dogs chose this treat?
Answer:
The total number of dogs that participated in the survey are 30 dogs.
Dog bone dog treat has more votes than biscuits and fewer votes than peanut butter. And 8 dogs choose this treat.

Explanation:
Given each emoji represent two dogs
so dog bone has four emojis which means 4×2= 8 dogs
Peanut butter has five emojis which means 5×2= 10 dogs
Cheese has two emojis and half emoji which means
2×2= 4 and a half emoji represents 1 dog
so the total number of dogs is 4+1= 5 dogs.
Biscuits have three emojis and half emoji which means
3×2= 6 and a half emoji represents 1 dog
so the total number of dogs is 6+1= 7 dogs.
So the total number of dogs who participated in the survey are
8+10+5+7= 30 dogs.
Dog bone dog treat has more votes than biscuits and fewer votes than peanut butter.
And 8 dogs choose this treat.

DIG DEEPER!
Why would it be difficult to use a key where the value of one symbol represents an odd number of dogs?
Answer:
It would be difficult to use a key where the value of one symbol represents an odd number of dogs because if the symbol is half then the value will be in decimals and we cannot divide the dog into decimals, so it’s difficult to represent an odd number.

YOU BE THE TEACHER
Newton says that one more dog likes peanut butter than dog bones. Is he correct? Explain.
Answer:
Yes, Newton is correct

Explanation:
Yes, Newton is correct. We can see in the table that the number of dogs who likes peanut butter is more than the dogs who like a dog bone. So Newton is correct.

Question 3.
Modeling Real Life
Which creature has 3 more eyes than the squid?
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 14
Answer:
The creature which has 3 more eye images than the squid is the spider which has four eye images.

Explanation:
Given each eye image represents 2 eyes
as we can see squid contains one eye image, which means 2 eyes
the spider has four eye images, which means 4×2= 8 eyes
Praying mantis has three eye images and half eye image, which means
3×2= 6 eyes and half eye image represents 1 eye
so the total number of eyes is 6+1= 7 eyes.
Starfish has three eye images, which means
3×2= 6 eyes.
So the creature which has 3 more eye images than the squid is the spider which has four eye images
and the creature has 3 more eyes than the squid is the spid=r, praying mantis, and starfish.

Review & Refresh

Find the area of the shape.

Question 4.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 15
Area = ___
Answer:
The area of the shape is 20 square centimeters.

Explanation:
To find the area of the shape, we will divide the shape into parts, and then we will find the area of the shape.
So we will divide the shape into two rectangles,
the length of rectangle 1 is 7 cm, and
the breadth of rectangle 1 is 2 cm
so the area of rectangle 1 is
area= length×breadth
= 7×2
= 14 square centimeters.
the length of rectangle 2 is 3 cm, and
the breadth of rectangle 2 is 2 cm
so the area of rectangle 2 is
area= length×breadth
= 3×2
= 6 square centimeters.
So the total area of the shape is
14+6= 20 square centimeters.

Question 5.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 16
Area = ___
Answer:
The area of the rectangle is 15 square meters.

Explanation:
The length of the rectangle is 5 m, and
the breadth of the rectangle is 3 m
so the area of the rectangle is
area= length×breadth
= 5×3
= 15 square meters.
The area of the rectangle is 15 square meters.

Lesson 14.2 Make Picture Graphs

Explore and Grow

Flip a two-color counter 10 times. Record the results. Then complete the picture graph.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 17
Reasoning
Why might you change the key if you flip the counter 100 times?
Answer:

Think and Grow: Make Picture Graphs

A frequency table is a table that gives the number of times something occurs.
Example
You survey students about their favorite planet. The frequency table shows the results. Use the table to complete the picture graph.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 18
Step 1: Write the title at the top of the picture graph. Label a row for each category.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 19
Step 2: Look at the numbers Saturn in the table. Choose a value for the key.
Step 3: Use the key to decide how many symbols you need for each planet. Then draw the symbols.
Answer:
Earth needs five symbols,
Mars needs three symbols,
Saturn needs six symbols, and
Jupiter needs four symbols.

Explanation:
The number of students who chooses Saturn is 30 students and the value for the key is six symbols.
By using the key the planet Earth needs five symbols,
Mars needs three symbols,
Saturn needs six symbols, and
Jupiter needs four symbols.

Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 2

Show and Grow

Question 1.
Use the frequency table to complete the picture graph.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 20
Answer:
Each circle represents three books

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 3
Each circle represents three books
To represent in a picture graph
June will be represented with two circles,
July will be represented with one circle,
August will be represented in three circles.

Apply and Grow: Practice

Question 2.
Use the frequency table to complete the picture graph.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 21
How many symbols did you draw to represent 10 inches of snowfall in March?
How many inches do you think April would receive?
Answer:
Each circle represents 5 inches

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 4
Each circle represents 5 inches
To represent in a picture graph
January will be represented with six circles,
February will be represented with five circles,
March will be represented with two circles.

Question 3.
Use the frequency table to complete the picture graph.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 22
Structure
Choose a different value for the key. How would the picture graph change?
Answer:
Each emoji represents 4 students.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 5
Each emoji represents 4 students
To represent in a picture graph
Flying will be represented with eight emojis,
Time travel will be represented with eight emojis,
Super strength will be represented with three emojis,
Invisibility will be represented with six emojis,
Super speed will be represented with seven emojis.

Think and Grow: Modeling Real Life

You survey 90 students about their favorite type of field trip. 35 students choose science center, 10 choose theater, and 20 choose zoo. The rest of the students choose museum. Complete the picture graph.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 23
Answer:
Each emoji represents 5 students.
The total number of students who choose the Museum is 25 students.

Explanation:
Let’s take each emoji represents 5 students,
As the Science center was chosen by 35 students, which means we can represent with 35/5= 7 emojis,
The theater was chosen by 10 students, which means we can represent with 10/5= 2 emojis,
Zoo was chosen by 20 students, which means we can represent with 20/5= 4 emojis,
so to know how many students choose Museum, we will add all the three field students and then subtract from the total number of the students, so
The number of students from the three fields is 35+10+20= 65 students
and the number of students who choose the Museum is 90-65= 25 students.
And the Museum was chosen by 25 students, which means we can represent with 25/5= 5 emojis.

Show and Grow

Question 4.
You survey 48 students about their favorite type of movie. 8 students choose cartoon, 12 choose action, and 24 choose comedy. The rest of the students choose musical. Complete the picture graph.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 24
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 25
All of the students who chose the musical go to see a movie. Each ticket costs $9.The students use two $20 bills to pay for all of the tickets. What is the change?
Answer:
Each emoji represent 4 students.
The remaining change will be $4.

Explanation:
Let’s take that each emoji represent 4 students.
The total number of students who participated in the survey are 48 students,
and in that eight students chooses cartoon, which means we can represent with 8/4= 2 emojis,
and 12 students choose an action, which means we can represent with 12/4= 3 emojis,
and 24 students choose comedy, which means we can represent with 24/4= 6 emojis,
so to know how many students choose Musical, we will add all the three type of movie students and then subtract from the total number of the students, so
The number of students from three types of movies is 8+12+24= 44 students
and the number of students who choose the Musical are 48-44= 4 students.
And the Musical was chosen by 4 students, which means we can represent with 4/4= 1 emoji.

Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 7
The total number of students who choose a musical type of movie is 4 students and each ticket costs $9. So for a total of 4 students, it will cost 4×$9= $36. As two students use $20 bills and four students, it will take $40 bill for all of the tickets. So the remaining change will be $40-$36= $4.

Make Picture Graphs Homework & Practice 14.2

Question 1.
Use the frequency table to complete the picture graph.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 27
Which type of art has more votes than painting, but fewer votes than crafts? How many students chose that type of art?
Answer:
Ceramic has more votes than painting and fewer votes than Crafts. So the total number of students who choose Ceramic is 25 students.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 8
Each emoji represents 5 students
To represent in a picture graph
Drawing will be represented with two emojis,
Ceramics will be represented with five emojis,
The painting will be represented with three emojis,
Crafts will be represented with six emojis.
Ceramic has more votes than painting and fewer votes than Crafts. So the total number of students who choose Ceramic is 25 students.

Question 2.
Use the frequency table to complete the picture graph.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 28
Answer:
Each circle represents 3 insects.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 9
Each circle represents 3 insects.
To represent in a picture graph
Ant will be represented with eight circles,
Bee will be represented with one circle,
Ladybug will be represented with four circles.
DIG DEEPER!
You see 1 more bee and 4 more ladybugs. How might you change the key?
Answer:
We might change the key by each circle with 4 insects

Explanation:
In the above, we can see Bee has three insects and if we add one more bee then the number of insects will be
3+1= 4 insects.
And in the above, we can see ladybugs have 12 insects and if we add four more ladybugs then the number of insects will be 12+4= 16 insects.
So we might change the key by each circle with 4 insects,
so that bee will be represented with one circle,
and the ladybug will be represented with 16/4= 4 circles.

Question 3.
Modeling Real Life
You survey 72 students about their favorite carnival ride. 12 choose Ferris wheel, 24 choose swings, and 6 choose bumper cars. The rest of the students choose roller coaster. Complete the picture graph.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 29

Answer:
Let’s take that each emoji represent 6 students.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 10
Let’s take that each emoji represent 6 students.
The total number of students who participated in the favorite carnival ride survey are 72 students,
and in that twelve students chooses Ferris wheel, which means we can represent with 12/6= 2 emojis,
and 24 students choose swings, which means we can represent with 24/6= 4 emojis,
and 6 students choose bumper cars, which means we can represent with 6/6= 1 emoji,
so to know how many students choose roller coaster, we will add all the three types of carnival ride students and then subtract from the total number of the students, so
The number of students from three types of carnival rides is 12+24+6= 42 students
and the number of students who choose the roller coaster is 72-42= 30 students.
And the roller coaster was chosen by 30 students, which means we can represent with 30/6= 5 emojis.

Modeling Real Life
All of the students who chose roller coaster want to ride together. Each ride ticket costs $2. The students have three $10 bills and four $5 bills. Will they have enough to ride the roller coaster together?
Answer:
No. they don’t have enough money.

Explanation:
As there are a total number of students who choose roller coaster ride are 30 students, so ride ticket costs for 30 students is 30×$2= $60. As three students have a $10 bill which means $10×3= $30 and four students have a $5 bill which means $5×4= $20. So together the students have $30+$20= $50, and they need $60. So they don’t have enough money.

Review & Refresh

Question 4.
532 + 54 = ___
Answer:
532 + 54 = 586.

Explanation:
On adding 532 and 54 we will get 586.

Question 5.
718 + 226 = ___
Answer:
718+226= 944.

Explanation:
On adding 718 and 226 we will get 944.

Question 6.
81 + 647 = ___
Answer:
81+647= 728.

Explanation:
On adding 81 and 647 we will get 728.

Lesson 14.3 Name Read and Interpret Graphs

Explore and Grow

You survey 12 students about their favorite school club. The results are shown on the picture graph. Represent the same data on the bar graph.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 30

Answer:
The drama was chosen by 4 students,
Math was chosen by 2 students,
Robotics was chosen by 6 students.

Explanation:
Given each emoji represents two students,
To represent in a bar graph
Drama is represented with two emojis, which is 2×2= 4 students
Math is represented with one emoji, which is 1×2= 2 students
Robotics is represented with three emojis, which is 3×2= 6 students.
and represented in the graph as shown below.

Structure
How would you change the scale of the bar graph to match the picture graph?
Answer:
The number of students will be represented with 2,4,6,8, etc., and change the scale of the bar graph to match the picture graph.

Think and Grow:
A bar graph shows data using bars. The scale of a bar graph is the group of labels that shows the values at equally spaced grid lines.
Example
Use the graph to answer the questions.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 31
How many gold medals did Jamaica win?
Jamaica won ___ gold medals.
Which country won the fewest gold medals?
__ won the fewest gold medals.
Answer:
Jamaica won 6 gold medals.
Sweden won the fewest gold medals.

Explanation:
In the above graph, we can see Jamaica won 6 gold medals and Sweden won the fewest gold medals.

Show and Grow

Question 1.
Use the graph to answer the questions.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 32
How many students chose grapes? Which fruit is the most favorite?
Answer:
Grapes were chosen by 10 students and the most favorite fruit is Apples.

Explanation:
In the above bar graph, we can see the number of students who chosen grapes are 10 students, and the most favorite fruit apples and the number of students who choose are 45 students.

Apply and Grow: Practice

Question 2.
Use the graph to answer the questions.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 33
How many students does each grid line represent? How many students chose fall? Which season is the least favorite?
Answer:
Each grid line represents four students and the fall was chosen by 18 students and the least favorite season is winter.

Explanation:
In the above bar graph, we can see that each grid line represents four students and we can see that the fall was chosen by 18 students. And the least favorite season is winter because winter was chosen by 10 students.

Question 3.
Use the graph to answer the questions.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 34
How many vegetable seeds did the farmer plant in all? The farmer wants to plant green bean seeds. She plants more green bean seeds than zucchini seeds, but fewer than carrot seeds. How many green bean seeds could the farmer have planted? The farmer plants 30 more potato seeds. Will the farmer have more potatoes or more corn?
Answer:
The number of vegetable seeds did the farmer plant in all is four vegetables.
The number of green bean seeds that the farmer can plant is between 61 to 79 seeds.
The farmer will have more corn seeds than potato seeds.

Explanation:
As we can see in the bar graph the number of vegetable seeds is four. As we can see the number of zucchini seeds planted is 60 seeds and the number of carrot seeds planted is 80 seeds. As she planted more green bean seeds than zucchini seeds and fewer than carrot seeds, so the green bean seeds can be in between 61 to 79 seeds.
As we can see in the bar graph, the corn seeds are 95 seeds and the potato seeds are 45 seeds, so if 30 more seeds are added then the total potato seeds will be 45+30= 75 seeds. So farmers will have more corn seeds than potato seeds.

Question 4.
Writing
Do you think a bar graph or a picture graph is easier to read? Explain.
Answer:
A picture graph is easier to read than a Bar graph.

Explanation:
A picture graph was represented using pictures or symbols and a bar graph was represented using bars and compares the data in each category using bars. So the picture graph is easier than a bar graph because in a picture graph we can easily calculate the values than in the bar graph.

Think and Grow: Modeling Real Life

How many more students need to choose the strategy app so that strategy is the most favorite?
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 35
Understand the problem:
Make a plan:
Solve:
___ more students need to choose the strategy app so it is the most favorite.
Answer:
22 more students need to choose the strategy app so it is the most favorite.

Explanation:
As we can see in the above bar graph the strategy app was chosen by 20 numbers and if this strategy app needs to be the most favorite, then 22 more students needed to be chosen.

Show and Grow

Question 5.
Each grade needs to plant 20 trees. How many more trees does second grade need to plant to complete the goal?
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 36
How many more trees did fourth-grade plant than first grade and third grade combined?
Answer:
Second grade needs 6 more trees to plant to complete the goal.
The number of more trees that fourth-grade plant than first grade and third grade are 2 trees.

Explanation:
As we can see in the above bar graph, the second-grade students planted 14 trees and each grade needs to plant 20 trees. So second-grade needs 20-14= 6 more trees to plant to complete the goal.
The fourth grade planted 20 trees and first grade planted 8 trees and the third grade planted 10 plants,
so the total combined trees of first grade and third grade are 8+10= 18 trees. So the number of more trees that fourth-grade plant than first grade and third grade are 20-18= 2 trees.

Name Read and Interpret Graphs Homework & Practice 14.3

Question 1.
Use the graph to answer the questions.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 37
How many students does each grid line represent? Which type of exercise is the least favorite? How many fewer students chose running than swimming? How many students chose walking or biking?
Answer:
Each grid line represents 10 students.
The 5 fewer students choose running than swimming.
Walking was chosen by 15 students and biking was chosen by 45 students.

Explanation:
As we can see in the bar graph that each grid line represents 10 students. And in the bar graph, we can see the skating contains 10 number of students which is the least favorite. The number of students who choose running is 30 students and the number of students who choose swimming is 35 students. So the 5 fewer students choose running than swimming. In the bar graph, we can see that walking was chosen by the 15 number of students, and biking was chosen by 45 students.

Question 2.
Use the graph to answer the questions.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 38
Which sunflowers are taller than 11 feet? Sunflower E has a height of 15 feet. How much taller is Sunflower A than Sunflower E?
Writing
Which sunflower is the shortest? Explain.
Answer:
The sunflowers which are taller than 11 feet are Sunflower A and Sunflower D.
Sunflower A is 11 feet taller than Sunflower E.
Sunflower C is the shortest.

Explanation:
As we can see in the bar graph that the Sunflower A is 26 feet and Sunflower D is 16 feet, and Sunflower B is 10 feet, Sunflower C is 10 feet. So Sunflower A and Sunflower D are taller than 11 feet. Sunflower A is 26 feet and Sunflower E is 15 feet. So the Sunflower A is 26-15= 11 feet taller than Sunflower E. Sunflower C is the shortest, because Sunflower C has the least number of feet.

Question 3.
Modeling Real Life
Use the graph to answer the questions.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 40
How many more students need to choose chameleon so that chameleon is the most favorite? You survey 10 more students and they all choose snake. What is the new total number of students who chose snake? How many more students chose turtle than bearded dragon and lizard combined?
Answer:
There must be 9 more number of students needed to choose Chameleon to be the most favorite.
The new total number of students who choose the snake is 19 students.
There are 3 students more students who choose turtle than bearded dragon and lizard.

Explanation:
As we can see in the bar graph that the total number of students is 30 and in that Chameleon was chosen by 21 number of students. So to choose chameleon as a most favorite then the total number should choose are 30-21=9 students. As we can see in the bar graph the total number of students who choose a snake is 9 students and if 10 more students choose a snake, then the total number of students who choose a snake will be 9+10=19 students. As we can see in the bar graph that the turtle was chosen by 27 students and the bearded dragon was chosen by 18 students and the lizard was chosen by 6 students. So the total number of students who choose bearded dragon and lizard are 18+6= 24 students and the turtle was chosen by 27 students, so there are 27-24= 3 students more students chooses turtle than bearded dragon and lizard.

Review & Refresh

Estimate the difference.

Question 4.
96 – 47 = __
Answer:
96-47= 49.
Explanation:
The difference between 96 and 47 is 49.

Question 5.
678 – 142 = ___
Answer:
678-142= 536.
Explanation:
The difference between 678 and 142 is 536.

Lesson 14.4 Make Bar Graphs

Explore and Grow

Spin the Color Spinner 10 times. Record the results. Then complete the bar graph.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 41
Answer:
Reasoning
Explain how you would change the scale if you spin the spinner 100 times.
Answer:

Think and Grow: Make Bar Graphs

Example
You record the number of times each baseball team wins. The frequency table shows the results. Use the table to complete the bar graph.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 42
Step 1: Write the title at the top of the bar graph. Label a row for each category. Label the categories.
Step 2: Look at the numbers in the table. Use a scale so that most of the bars end on a grid line. Label the scale.
Step 3: Draw and shade a bar for each team.
Answer:
Each grid line represents three wins.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 13
As given the values of the number of wins are the multiples of 3, so we will represent the number of wins with the multiples of 3. To represent these values in a bar graph, we will represent those data with rectangular bars with proper heights and lengths by the given values. And those bars are plotted vertically or horizontally. In the above bar graph, we can see each grid line represents three wins.

Show and Grow

Question 1.
Use the frequency table to complete the bar graph.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 43
Answer:
Each grid line represents two number of students.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 12
In the given frequency table, we can see most of the values are multiplies of 2. So we represent the number of students by the multiplies of 2. To represent these values in a bar graph, we will represent those data with rectangular bars with proper heights and lengths by the given values. And those bars are plotted vertically or horizontally. In the above bar graph, we can see each grid line represents two number of students.

Apply and Grow: Practice

Question 2.
Use the frequency table to complete the bar graph.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 44
How would you use the graph to decide which type of fingerprint is the most common?
Answer:
To decide which type of fingerprint is used most commonly, we will compare the heights of the bars, and then we will choose the most common fingerprint.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 14
In the given frequency table, we can see most of the values are multiplied by 25. So we represent the number of students by the multiplies of 25. To represent these values in a bar graph, we will represent those data with rectangular bars with proper heights and lengths by the given values. And those bars are plotted vertically or horizontally. In the above bar graph, we can see each grid line represents twenty-five number of students.

Question 3.
Use the frequency table to complete the bar graph.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 45
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 46
How many fewer students chose the least favorite type of food than the most favorite type of food?
Answer:
The least favorite type of food chosen by vegetarians and the most favorite type of food was chosen by Mexican.
And each grid line represents four number of students.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 15

In the given frequency table, we can see most of the values are multiplies of 4. So we represent the number of students by the multiplies of 4. To represent these values in a bar graph, we will represent those data with rectangular bars with proper heights and lengths by the given values. And those bars are plotted vertically or horizontally. In the above bar graph, we can see each grid line represents four number of students.

Think and Grow: Modeling Real Life

You survey 27 students about their favorite subject. Nine students choose science. Six fewer students choose English than science. The rest of the students choose math. Complete the bar graph.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 47
Answer:
Each grid line represents three number of students.
The total number of students who choose math is 15 students.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 16
In the given frequency table, we can see most of the values are multiplies of 3. So we represent the number of students by the multiplies of 3. To represent these values in a bar graph, we will represent those data with rectangular bars with proper heights and lengths by the given values. And those bars are plotted vertically or horizontally. In the above bar graph, we can see each grid line represents three number of students.
As the total number of students for the survey is 27 students in that nine students choose science, and six fewer students choose English than Science, which means 9-6= 3. So 3 students choose Science. And the rest of the students chooses math, which means we add the two subjects and then subtract from the total number of students, then we can get the value of the students who choose math. So the total number of students who choose English and Science are 9+3= 12 and then subtract with the total number of students, which means 27-12= 15. So the total number of students who choose math is 15 students.

Show and Grow

Question 4.
You survey 22 students about their favorite camp activity. Eight students choose archery. Four more students choose swimming than archery. The rest of the students choose hiking. Complete the bar graph.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 48
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 49
How many fewer students chose archery than swimming and hiking combined?
Answer:
Six fewer students chose archery than swimming and hiking combined.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 17
In the given frequency table, we can see most of the values are multiplies of 2. So we represent the number of students by the multiplies of 2. To represent these values in a bar graph, we will represent those data with rectangular bars with proper heights and lengths by the given values. And those bars are plotted vertically or horizontally. In the above bar graph, we can see each grid line represents three number of students.
The number of students who choose archery is eight students and in that four more students choose swimming than archery, which means 8+4= 12 students choose swimming. And the rest choose hiking, which means we will add the number of students who choose archery and swimming and then subtract the value with the total number of students. So the number of students who choose archery and swimming is 8+12= 20, and the number of students who choose hiking is 22-20= 2. The total number of students who choose swimming and hiking combined is 12+2= 14 students, and archery was chosen by 8 students. So 14-8= 6 fewer students choose archery than swimming and hiking combined.

Make Bar Graphs Homework & Practice 14.4

Question 1.
Use the frequency table to complete the bar graph.
Big Ideas Math Answers 3rd Grade Chapter 14 Represent and Interpret Data 50
How many students does each grid line represent? How would you use the graph to find the most favorite type of music?
Answer:
Each grid line represents five number of students. By using the graph, we will compare the heights of the graphs and pick the most favorite music.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 18

As given the values of the number of students are the multiples of 5, so we will represent the number of students with the multiples of 5. To represent these values in a bar graph, we will represent those data with rectangular bars with proper heights and lengths by the given values. And those bars are plotted vertically or horizontally. In the above bar graph, we can see each grid line represents five number of students. By using the graph, we will compare the heights of the graphs and pick the most favorite music.

Question 2.
Use the frequency table to complete the bar graph.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 51
Structure
On the last day of school, each backpack weighs less than 5 pounds. How could the scale of the bar graph change?
Answer:
We will subtract the given values by 5 pounds and then we will represent those values in a graph.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 19

As given the values of the number of pounds are the multiples of 4, so we will represent the number of pounds with the multiples of 4. To represent these values in a bar graph, we will represent those data with rectangular bars with proper heights and lengths by the given values. And those bars are plotted vertically or horizontally. In the above bar graph, we can see each grid line represents four pounds. As on the last day, each backpack weighs less than 5 pounds, which means we will subtract the given values by 5, and then we will represent those values in a graph.

Question 3.
Modeling Real Life
You survey 26 teachers about their favorite vacation spot. Six teachers choose amusement park. Two more teachers choose camping than amusement park. The rest of the teachers choose beach. Complete the bar graph.
How many fewer teachers chose camping than amusement park and beach combined?
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 52
Answer:
The beaches were chosen by 12 teachers.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 20
As given the values of the number of teachers are most of them are multiples of 2, so we will represent the number of teachers with the multiples of 2. To represent these values in a bar graph, we will represent those data with rectangular bars with proper heights and lengths by the given values. And those bars are plotted vertically or horizontally. In the above bar graph, we can see each grid line represents five number of students. By using the graph, we will compare the heights of the graphs and pick the most favorite music. As amusement park was chosen by six teachers and two more teachers choose camping than the amusement park, so camping was chosen by 6+2= 8 teachers. And the rest of the teachers choose the beach, which means we will add both the vacation amusement park and camping and then subtract by the total number of teachers. So the total number of teachers who choose both amusement parks and camping is 6+8= 14 teachers, so the teachers who choose the beach are 26-14= 12 teachers.

Review & Refresh

Find the difference.

Question 4.
474 – 19 = ___
Answer:
474 – 19 = 455.

Explanation:
The difference between 474 and 19 is 455.

Question 5.
615 – 204 = ___
Answer:
615 – 204 = 411.

Explanation:
The difference between 615 and 204 is 411.

Question 6.
232 – 53 = ___
Answer:
232 – 53 =179.

Explanation:
The difference between 232 and 53 is 179.

Lesson 14.5 Make Line Plots

Explore and Grow

A teacher asks students to line up according to the number of siblings they have. The results are shown. Create a Line Plot for the number of siblings the students in your class have.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 53
Answer:
Big-Ideas-Math-Answers-Grade-3-Chapter-14-Represent-and-Interpret-Data-55

Explanation:
The students that have 0 siblings in the line plot 1 is 2,
The students that have 1 sibling in the line plot 1 is 11,
The students that have 2 siblings in the line plot 1 is 5,
The students that have 3 siblings in the line plot 1 is 2,
The students that have 0 siblings in the line plot 2 is 1,
The students that have 1 sibling in the line plot 2 is 6,
The students that have 2 siblings in the line plot 2 is 3,
The students that have 3 siblings in the line plot 2 is 2.
Structure
Compare the two line plots. How are the line plots the same? How are they different?
Answer:
The line plots are the same in that each class has a maximum of 3 siblings and varies in the count of siblings.

Explanation:
Comparing the two-line plots we can see the count of siblings varies and the two number line plots are the same that the class has the maximum number of siblings is 3.

Think and Grow: Make Line Plots
A lion plot uses marks above a number line to show data values.
Example
The table shows the weights of 15 bald eagles. Use the table to complete the line plot.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 54
Step 1: write the title at the top of the line plot.
_____________
Step 2 : Look at the numbers in the table. Use a scale that shows all of the data values. Draw a number line using the scale. Label the scale.
Step 3 : Mark an X for each data value.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 55
Answer:
A line plot can be defined as a graph that displays the given data as a point above a number line.

Explanation:
Big-Ideas-Math-Answers-Grade-3-Chapter-14-Represent-and-Interpret-Data-55
The eagles that weigh 3kgs are 2,
The eagles that weigh 4kgs are 6,
The eagles that weigh 5kgs are 4,
The eagles that weigh 6kgs are 2.

Show and Grow

Question 1.
Use the table to complete the line plot.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 56
Answer:
A line plot can be defined as a graph that displays the given data as a point above a number line.

Explanation:

Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 21
A line plot can be defined as a graph that displays the given data as a point above a number line. As the given values are mostly are multiples of 3, so we will represent the number of inches by multiples of 3. And now we will place the check marks on the given values.

Apply and Grow: Practice

Question 2.
Use the table to complete the line plot.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 57
How many waves were 26 feet tall or taller?
Answer:
There are 11 waves that were 26 feet tall or taller.

Explanation:

Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 28

A line plot can be defined as a graph that displays the given data as a point above a number line. As the given values are mostly a series of numbers from 25 to 30, so we will represent the number of feet by a series of numbers from 25 to 30. And now we will place the check marks on the given values.

Question 3.
Use the table to complete the line plot.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 58
Which giraffe tongue length is the most common?
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 59
Answer:
The most common giraffe tongue lengths are 20 inches.

Explanation:

Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 29

A line plot can be defined as a graph that displays the given data as a point above a number line. As the given values are mostly a series of numbers from 17 to 21, so we will represent the number of feet by a series of numbers from 17 to 21. And now we will place the check marks on the given values. The most common giraffe tongue lengths are 20 inches.

Precision
How many giraffe tongues are 19 inches long?
Answer:
The 19 inches long giraffe tongues are 3.

Think and Grow: Modeling Real Life

What is the difference in height of the tallest student and the shortest student?
Subtraction equation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 60
The difference in height is ___ inches.
Answer:
The difference in height is 6 inches.

Explanation:
As we can see in the above number plot, the height of the tallest student is 56 inches, and the height of the shortest student is 50 inches. And the difference between them is 56-50= 6 inches.

Show and Grow

Question 4.
What is the difference between the greatest number of floors and the least number of floors?
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 61
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 62
How many fewer skyscrapers are there with over 50 floors than skyscrapers with under 50 floors?
Answer:
The fewer skyscrapers are there with over 50 floors than skyscrapers with under 50 floors are 11.

Explanation:
The greatest number of floors is 8 floors and the least number of floors are 2,
so the difference between the greatest number of floors and the least number of floors is 8-2= 6.
The skyscrapers over 50 floors are 32 and the skyscrapers with under 50 floors are 21,
The fewer skyscrapers are there with over 50 floors than skyscrapers with under 50 floors are 32-21= 11.

Make Line Plots Homework & Practice 14.5

Question 1.
Use the table to complete the line plot.
____
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 63
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 64
How many snakes are longer than 10 feet?
Which snake length is the most common?
Answer:
The snakes which are longer than 10 feet are 1.

Explanation:
Big-Ideas-Math-Answers-Grade-3-Chapter-14-Represent-and-Interpret-Data-55
The number of snakes which are 5 feet are 1,
The number of snakes which are 6 feet are 3,
The number of snakes which are 7 feet are 3,
The number of snakes which are 8 feet are 0,
The number of snakes which are 9 feet are 2,
The number of snakes which are 10 feet are 4,
The number of snakes which are 11 feet is 1.

Question 2.
Use the table to complete the line plot.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 66
Reasoning
Are most of the students able to complete 30 sit-ups? Explain.

Answer:
No, the students who completed 30 sit-ups are 1 student.

Explanation:
Big-Ideas-Math-Answers-Grade-3-Chapter-14-Represent-and-Interpret-Data-55
The number of students who completed 27 sit-ups is 6 students.
The number of students who completed 28 sit-ups is 1 student.
The number of students who completed 29 sit-ups is 3 students.
The number of students who completed 30 sit-ups is 1 student.
The number of students who completed 32 sit-ups is 3 students.

DIG DEEPER!
Student H completed more sit-ups than Student F, but fewer sit-ups than Student B. How many sit-ups could Student H have completed?
Answer:

Explanation:

Question 3.
Modeling Real Life
What is the difference of the most number of miles biked and the least number of miles biked?
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 67
Answer:
The most number of miles biked and the least number of miles biked 5.

Explanation:
The most number of miles biked are 6 bikes and the least number of miles biked is 1 bike,
so the difference between the most number of miles biked and the least number of miles biked is 6-1= 5.

Review & Refresh

Find the sum or difference. Use the inverse operation to check.

Question 4.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 68
Answer:
760

Explanation:
On adding 523 and 237 we will get 760. Here, we will subtract 237 with 760 to check the inverse operation, so 760-237= 523.

Question 5.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 69
Answer:
151.

Explanation:
The difference between 403 and 252 is 151. Here we will add 151 and 252 to check the inverse operation, so 252+151= 403.

Question 6.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 70
Answer:
999.

Explanation:
On adding 612 and 387 we will get 999. Here, we will subtract 387 with 999 to check the inverse operation, so 999-387= 612.

Lesson 14.6 Measure Lengths: Half Inch

Explore and Grow

How much longer is the green ribbon than the yellow ribbon? How do you know?
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 71

Answer:
The green ribbon is 1 inch longer than the yellow ribbon.

Explanation:
The green ribbon is 1 inch longer than the yellow ribbon. By measuring the ribbons using a ruler we can know that the green ribbon is longer than the yellow ribbon.

How much longer is the purple ribbon than the orange ribbon? How do you know?
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 72

Answer:
The purple ribbon is 1 inch longer than the orange ribbon.

Explanation:
The purple ribbon is 1 inch longer than the orange ribbon. By measuring the ribbons using a ruler we can know that the purple ribbon is longer than the orange ribbon.
Structure
How can you use a ruler to measure an object to the nearest half inch?
Answer:
If the object is closer to the half-inch mark than the zero inches then it’s half-inch is measured.

Explanation:
We will use the ruler by marking the objects it’s starting pointing and ending point and then measure the length of that object. If the object is closer to the half-inch mark than the zero inches then it’s half-inch is measured.

Think and Grow: Measure Lengths: Half Inch

Not all objects are whole numbers of inches long. You can use a ruler to measure length to the nearest half inch. Remember to line up the end of the object with 0.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 73
Example
Measure the length of each string to the nearest half inch. The string is \(\frac{3}{2}\) inches long. You can also represent the length as 1 whole inch and one \(\frac{1}{2}\) inch, or 1\(\frac{1}{2}\) inches.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 74
The string is between \(\frac{1}{2}\) inch and 1 inch long. The half-inch marking that is closest to end of the string is \(\frac{3}{2}\). So, the string is about \(\frac{3}{2}\) inch long.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 75

Example
Measure the length of each line to the nearest half inch. Then record each length on the line plot.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 76
Answer:
The number of strings with half-inch length is 1.

Explanation:
Big-Ideas-Math-Answers-Grade-3-Chapter-14-Represent-and-Interpret-Data-55
The number of strings with half-inch length is 1,
The number of strings with one and half-inch length  is 1,
The number of strings with two-inch length  is 2,

Show and Grow

Question 1.
Measure the length of each line to the nearest half-inch. Then record each length on the line plot above.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 77
Answer:

Explanation:

Apply and Grow: Practice

Question 2.
Measure the length of each line to the nearest half inch. Record each length on the line plot.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 78
How might the scale change if the length of the line below is recorded on the line plot?
___________
Answer:

Question 3.
Measure the length of each toy to the nearest half inch. Then record each length on the line plot.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 79
Answer:

Think and Grow: Modeling Real Life

Measure the lengths of 10 crayons to the nearest half inch. Record each length on the line plot.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data 80
Answer:

Show and Grow

Question 4.
Measure the lengths of 10 shoes to the nearest half inch. Record each length on the line plot.
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 81
What is the length of the longest shoe? What is the length of the shortest shoe?
Answer:

Measure Lengths: Half Inch Homework & Practice 14.6

Question 1.
Measure the length of each ribbon to the nearest half inch. Record each length on the line plot.
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 82
How many pretzel sticks are 1 inch?
Answer:

Question 2.
YOU BE THE TEACHER
Descartes says the pencil is 3\(\frac{1}{2}\) inches long. Is he correct? Explain.
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 83
Answer:

Question 3.
Reasoning
Your friend’s wrist measures \(\frac{13}{2}\) inches around. His friendship bracelet is 6\(\frac{1}{2}\) inches. Will the bracelet fit around his wrist?
Answer:

Question 4.
Modeling Real Life
Measure the lengths of 10 plant leaves to the nearest half inch. Record each length on the line plot.
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 84
What is the length of the longest leaf? What is the length of the shortest leaf? What leaf length is the most common?
Answer:

Review & Refresh

Find the product.

Question 5.
5 × 30 = ___
Answer:
150.

Explanation:
The product of 5×30 is 150.

Question 6.
9 × 50 = ___
Answer:
450.

Explanation:
The product of 9×50 is 450.

Question 7.
6 × 70 = ___
Answer:
420.

Explanation:
The product of 6×70= 420.

Lesson 14.7 Measure Lengths: Quarter Inch

Explore and Grow

How much longer is the green ribbon than the yellow ribbon? How do you know?
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 85
How much longer is the purple ribbon than the orange ribbon? How do you know?
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 86

Reasoning
Measure the line to the nearest half inch and the nearest quarter inch. Which measurement is better? Why?
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 87
Answer:

Think and Grow : Measure Lengths: Quarter Inch

You know how to use a ruler to measure lengths to the nearest half inch. You can also use a ruler to measure lengths to the nearest quarter-inch.
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 88
Example
Measure the length of each string to the nearest quarter inch. The string is \(\frac{7}{4}\) inches long. You can also represent the length as 1 whole inch and three \(\frac{1}{4}\) inches or 1\(\frac{1}{3}\) inches.
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 89

The string is between 1 inch and 1\(\frac{1}{4}\) inches long. The quarter-inch marking that is closest to the end of the string is 1\(\frac{1}{4}\). So, the string is about 1\(\frac{1}{4}\) inches long.
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 90

Example
Measure the length of each line to the nearest quarter inch. Then record each length on the line plot
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 91
Answer:

Show and Grow

Question 1.
Measure the length of each line to the nearest quarter inch. Then record each length on the line plot above.
____ ______ ______
Answer:

Apply and Grow: Practice

Question 2.
Measure the length of each line to the nearest quarter inch. Record each length on the line plot.
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 92
How might the scale change if the two lines below are recorded in the line plot?
___________
____
Answer:

Question 3.
Measure the length of each eraser to the nearest quarter inch. Then record each length on the line plot.
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 94
Answer:

Question 4.
Precision
Draw a line that measures 5\(\frac{3}{4}\) inches long.
Answer:

Think and Grow: Modeling Real Life

Measure the lengths of 10 pencils to the nearest quarter inch. Record each length on the line plot.
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 95
Answer:

Show and Grow

Question 5.
Measure the heights of 10 books to the nearest quarter inch. Record each length on the line plot.
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 96
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 97
Write and answer a question about your line plot.
Answer:

Measure Lengths: Quarter Inch Homework & Practice 14.7

Question 1.
Measure the length of each celery stick to the nearest quarter inch. Record each length on the line plot.
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 98
Which celery stick length is the most common?
Answer:

Question 2.
Which One Doesn’t Belong? Which does not belong with the other three ?
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 99
Answer:

Question 3.
Precision
Find the length of the caterpillar to the nearest quarter inch. Explain.
Big Ideas Math Solutions Grade 3 Chapter 14 Represent and Interpret Data 100
Answer:

Question 4.
Modeling Real Life
Measure the lengths of your 10 fingers to the nearest quarter inch. Record each length on the line plot.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 101
Write and answer a question about your line plot.
Answer:

Review & Refresh

What fraction of the whole is shaded?

Question 5.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 102
Answer:
5/6 is shaded.

Explanation:
As we can see in the above image the circle was divided into 6 parts and in that 5 parts are shaded. So the fraction of the whole shaded part is 5/6 part was shaded.

Question 6.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 103
Answer:
2/4= 1/2 part was shaded.

Explanation:
As we can see in the rectangle was divided into four parts, and in that two parts are shaded. So the fraction of the whole shaded part is 2/4= 1/2 part was shaded.

Represent and Interpret Data Performance Task

Question 1.
You plant 3 bamboo seeds during the first week. You measure and record the growth of your bamboo plants for the next 3 weeks.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 104
a. Find the height of each plant after the fourth week. Make a bar graph of the plant heights.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 105

Explanation:
The height of each plant after the fourth week is
Plant A 4 in,
Plant B 4 in,
Plant C 5 in.
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 26
b. Do you think any of the plants will be taller than 15 inches after 5 weeks? Explain.
Answer:
No, I think that no plant will be taller than 15 inches after 5 weeks.

Explanation:
No plant will be taller than 15 inches after 5 weeks, because we can see that the growth of each plant takes a minimum of 1 or 2 weeks.

Question 2.
a. Measure and record the height of each bamboo plant on Bamboo Growth to the nearest quarter inch.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 106
b. Which height occurs the most?
Answer:

Roll and Graph

Directions:
1. Players take turns rolling a die.
2. Record each of your rolls on your line plot.
3. The first player to get 10 rolls of one number wins!
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 107
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 108
Answer:

Represent and Interpret Data Chapter Practice

14.1 Read and Interpret Picture Graphs

Question 1.
Use the graph to answer the questions. How many tickets were sold in August?
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 109
How many more tickets were sold in July or August than in May, June, or September?
Which month had more ticket sales than June, but fewer ticket sales than July? How many tickets were sold this month?
Answer:
The number of tickets sold in August is 80+10= 90 tickets.
50 tickets more were sold in July or August than in May, June, or September.
In the month of August the ticket sale is more than June, but fewer ticket sales than July. The total number of tickets sold in the month of August is 90 tickets.

Explanation:
As each ticket image represents 20 tickets and the half ticket represents 10 tickets so
The number of tickets sold in August is 4×20= 80 and one-half ticket represents 10
the number of tickets sold in August is 80+10= 90 tickets.
The tickets sold in July are 5×20= 100 and tickets sold in august are 90,
so the total number of tickets sold in July and August is 100+90= 190 tickets.
And the tickets sold in the month of May are 2×20= 40 tickets,
the tickets sold in the month of June are 3×20= 60 tickets and one half ticket image which is 10 tickets,
so the total number of tickets sold is 60+10= 70 tickets.
the tickets sold in the month of September are 1×20= 20tickets and one half ticket image which is 10 tickets,
so the total number of tickets sold is 20+10= 30 tickets.
The total tickets sold in the month of May, June, or September is 40+70+30=140,
So the tickets were sold in July or August than in May, June or September is 190-140= 50.
In the month of August the ticket sale is more than June, but fewer ticket sales than July. The total number of tickets sold in the month of August is 90 tickets.

14.2 Make Picture Graphs

Question 2.
You collect supplies for an animal shelter. You receive 4 collars, 20 tennis balls, 18 dog bones, and 12 cat toys. Complete the picture graph.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 110
Answer:
Each circle is 2 supplies.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 25

Let each circle be 2 supplies,
As there are 4 collars, so we will represent them with two circles,
and 20 tennis balls, so we will represent them with ten circles,
and  18 dog bones, so we will represent them with nine circles,
and 12 cat toys we will represent them with six circles.

Question 3.
A zookeeper takes care of 30 animals. There are 6 monkeys, 12 flamingos, and 9 kangaroos. The rest of the animals are giraffes. Complete the picture graph.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 111
Answer:
The number of giraffes is 3.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 24
Let each circle be 3 animals,
The total number of animals is 30,
As there are 6 monkeys, so we will represent them with two circles,
and the Flamingos is 12, so we will represent them with four circles,
the kangaroos are 9, so we will represent them with three circles,
so to find giraffes we will add all the three types of animals and then subtract them with the total number of animals, so 6+12+9= 27, and the total number of animals are 30.
So the number of giraffes is 30-27= 3 we will represent them with one circle.

14.3 Read and Interpret Bar Graphs

Question 4.
Use the graph to answer the questions. How many more fireflies does your friend catch on Thursday than on Monday?
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 112
Patterns
What do you notice about the number of fireflies caught from Monday to Thursday?

On which two days did your friend catch 10 fireflies combined?
You catch 5 fireflies on Monday, 4 fireflies on Tuesday, 8 fireflies on Wednesday, and 7 fireflies on Thursday. Who caught more fireflies at camp?
Answer: 24
The number of fireflies does my friend catch on Thursday than on Monday is 8.
We can observe that the increase in the graph from Monday to Thursday.
My friend caught more fireflies at camp than I.

Explanation:
The fireflies caught on Monday are 3 and the fireflies caught on Thursday are 11, so
the number of fireflies does my friend catch on Thursday than on Monday are 11-3= 8 fireflies.
We can observe that the increase in the graph from Monday to Thursday.
The fireflies caught by me are 5+4+8+7= 24 and the fireflies caught by my friend is 3+4+7+11= 25 files,
so my friend caught more fireflies at camp than I.

14.4 Make Bar Graphs

Question 5.
Use the frequency table to complete the bar graph.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 113
Another student, Student E, has 45 trading cards. How would the bar graph change?

Answer:
The bar of student E will be the highest.

Explanation:
As student E has 45 trading cards, then the bar of student E will be the highest.

Modeling Real Life
Including the number of trading cards of Student E, order the numbers of cards from least to greatest.
Answer:
The number of trading cards of Student E, order the numbers of cards from least to greatest are
Student C, Student B, Student D, Student A, and the student E.

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 23
The order of the number of cards from least to greatest are
Students C who has 10 cards,
Student B who has 15 cards,
Student D who has 15 cards,
Student A who has 30 cards,
and Student E who has 45 cards.

14.5 Make Line Plots

Question 6.
Use the table to complete the line plot.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 114

Explanation:
Big Ideas Math Answers Grade 3 Chapter 14 Represent and Interpret Data img 22

The number of  trees with 19 meters is 4 trees,
The number of  trees with 21 meters is 3 trees,
The number of  trees with 22 meters is 1 tree,
The number of  trees with 23 meters is 1 tree,
The number of  trees with 24 meters is 3 trees,

14.6 Measure Lengths: Half Inch

Question 7.
Measure the length of each snail trail from a snail race to the nearest half inch. Record each length on the line plot.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 115

Explanation:
The lengths of each snail trail from a snail race to the nearest half-inch are
Big-Ideas-Math-Answers-Grade-3-Chapter-14-Represent-and-Interpret-Data-55

Modeling Real Life
What is the length of the longest snail trail? What is the length of the shortest snail trail?
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 116
Answer:
The longest snail trail is 6 inches and the shortest is 1/2 inch.

Explanation:
The length of the longest snail trail is 6 inches and the length of the shortest snail trail 1/2 inch.

14.7 Measure the Lengths: Quarter Inch

Question 8.
Measure the length of each feather to the nearest quarter inch. Then record each length on the line plot.
Big Ideas Math Answer Key Grade 3 Chapter 14 Represent and Interpret Data 117
Answer:
To measure the feathers to the nearest quarter inch, we will label the marks and then measure the length to the nearest quarter inch.

Explanation:

Big-Ideas-Math-Answers-Grade-3-Chapter-14-Represent-and-Interpret-Data-55
To measure the feathers to the nearest quarter inch, we will label the marks and then measure the length to the nearest quarter inch.
The length of feather 1 is 4 1/4 inch,
The length of feather 2 is 1/4 inch,
The length of feather 3 is 2 2/4 inch,
The length of feather 4 is 1/4 inch,
The length of feather 5 is 2 3/4 inch.

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