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Course: 3rd grade (Eureka Math/EngageNY) > Unit 6

Lesson 1: Topic A: Generate and analyze categorical data
Math
3rd grade (Eureka Math/EngageNY)
Module 6: Collecting and displaying data
Topic A: Generate and analyze categorical data
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Reading bar graphs: multi-step

Google Classroom
​Interpret bar graphs to answer multi-step questions about a context.

Reading bar graphs (multi-step)

In a bar graph each bar represents a number.
The following bar graph shows the number of seconds that different rides last at the fair. We can tell how long each ride lasts by matching the bar for that ride to the number it lines up with on the left.
The spinning cups are the shortest ride. They last only 120 seconds. The Ferris wheel is the longest ride. It lasts 240 seconds.
Sometimes to answer questions about bar graphs we will need to look at several of the bars. Let's break this next question into smaller steps.
Which rides last longer than the spinning cups but not as long as the roller coaster?
Here are the steps.
Problem 1, Part A
How many seconds does the spinning cups ride last?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
seconds

Problem 1, Part B
How many seconds does the roller coaster ride last?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
seconds

Now we know we are looking for rides that last between 120 and 210 seconds. We are ready to answer the original question:
Problem 1, Part C
Which rides last longer than the spinning cups but not as long as the roller coaster?
Choose all answers that apply:

Understanding bar graphs

The following bar graph shows the prizes given away one day at the Ring Toss game at the fair.
The number of rubber ducks that were given away is equal to which other two categories combined?
This is another question that we can break into smaller steps.
Problem 2, Part A
How many rubber ducks were given away?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
rubber ducks

Problem 2, Part B
Fill in the blanks.
There were
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
beach balls,
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
stuffed frogs, and
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
stuffed pigs given away.

Now we are ready to answer the original question:
Problem 2, Part C
The number of rubber ducks that were given away is equal to which other two categories combined?
Choose all answers that apply:

Sometimes we will need to look at all the bars to answer a question.
Practice Problem 3
62 of the prizes were given to kids who were 14 and younger. How many of the prizes were given to people older than 14?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
prizes

Combining bar graphs with other information

We can also combine the information from a bar graph with other information to answer a question.
The following graph shows the number of different foods that were sold one afternoon at the fair's Snack Shack.
The cost of funnel cake is $6 and the cost of chili fries is $8.
In this question we need to combine information from the bar graph about the number of foods sold with the information about the cost of those foods.
How much more was spent on funnel cakes than on chili fries?
Let's break this down into several steps.
Problem 4, Part A
Fill in the blanks.
The Snack Shack sold
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
funnel cakes and
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
chili fries.

To figure out how much was spent on each food we need to multiply the number of the food that was sold by the cost for that food.
Problem 4, Part B
$
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
was spent on funnel cakes and $
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
was spent on chili fries.

Now we have the information we need to answer the original question:
Problem 4, Part C
How much more was spent on funnel cakes than on chili fries?
$
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Let's try another question about this graph. We will still need to take multiple steps, but this time the steps haven't been broken down for us.
Practice Problem 5
The cost of a corn dog is $5, and the cost of cotton candy is $4.
What was the total amount spent on corn dogs and cotton candy?
$
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Comparing two bar graphs

Hui and Theo went to the fair. They each kept track of how much time they spent waiting in line for three different rides. When they got home they each made their own bar graph to show their waiting times.
Practice Problem 6A
What is the longest time either Hui or Theo spent waiting for a ride?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
minutes

Practice Problem 6B
What is the shortest time either Hui or Theo spent waiting for a ride?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
minutes

Practice Problem 6C
Which two rides had the same waiting time?
Choose all answers that apply:

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