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3rd grade

Course: 3rd grade > Unit 14

Lesson 2: Bar graphs
Math
3rd grade
Represent and interpret data
Bar graphs
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Reading bar graphs: multi-step

CCSS.Math:
3.MD.B.3
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.
A bar graph shows the horizontal axis labeled Ride and the vertical axis labeled Time in seconds. The horizontal axis is labeled, from left to right: Swinging ship, Bumper cars, Roller coaster, Spinning cups, and Ferris wheel. The vertical axis is labeled from the bottom of the axis to the top of the axis as follows: 0, 30, 60, 90, 120, 150, 180, 210, 240, and 270. The bar line for each ride shows the following: Swinging ship bar line extends to 150, Bumper cars bar line extends to 180, Roller coaster bar line extends to 210, Spinning cups bar line extends to 120, and Ferris wheel bar line extends to 240.
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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
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.
A bar graph shows the horizontal axis labeled Prize and the vertical axis labeled Number. The horizontal axis is labeled, from left to right: Rubber duck, Beach ball, Stuffed frog, and Stuffed pig. The vertical axis is labeled from the bottom of the axis to the top of the axis as follows: 0, 5, 10, 15, 20, 25, 30, 35, 40, and 45. The bar line for each prize shows the following: Rubber duck bar line extends to 40, Beach ball bar line extends to 25, Stuffed frog bar line extends to 15, and Stuffed pig bar line extends to 5.
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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
beach balls,
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
stuffed frogs, and
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
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.
A bar graph shows the horizontal axis labeled Food and the vertical axis labeled Number Sold. The horizontal axis is labeled, from left to right: Corn dog, Funnel cake, Popcorn, Chili fries, and Cotton candy. The vertical axis is labeled from the bottom of the axis to the top of the axis as follows: 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, and 110. The bar line for each food shows the following: Corn dog bar line extends to 80, Funnel cake bar line extends to 100, Popcorn bar line extends to 50, Chili fries bar line extends to 70, and Cotton candy bar line extends to 30.
The cost of funnel cake is dollar sign, 6 and the cost of chili fries is dollar sign, 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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
funnel cakes and
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
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
dollar sign
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
was spent on funnel cakes and dollar sign
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
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?
dollar sign
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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 dollar sign, 5, and the cost of cotton candy is dollar sign, 4.
What was the total amount spent on corn dogs and cotton candy?
dollar sign
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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.
A bar graph shows the horizontal axis labeled Hui's Rides and the vertical axis labeled Waiting Time in minutes. The horizontal axis is labeled, from left to right: Tilt-A-Whirl, Spinning swings, and Giant slide. The vertical axis is labeled from the bottom of the axis to the top of the axis as follows: 0, 3, 6, 9, 12, 15, 18, and 21. The bar line for each Hui’s Ride shows the following: Tilt-A-Whirl bar line extends to 12, Spinning swings bar line extends to 3, and Giant slide bar line extends to 6.
A bar graph shows the horizontal axis labeled Theo’s Rides and the vertical axis labeled Waiting Time in minutes. The horizontal axis is labeled, from left to right: Haunted house, Octopus, and Merry-go-round. The vertical axis is labeled from the bottom of the axis to the top of the axis as follows: 0, 2, 4, 6, 8, 10, and 12. The bar line for each Theo’s Ride shows the following: Haunted house bar line extends to 6, Octopus bar line extends to 10, and Merry-go-round bar line extends to 2.
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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
minutes

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

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