Section B: Practice Problems Ways to Represent Data

Section Summary


In this section we represented data in picture graphs and bar graphs and used them to answer questions.

Picture Graph. Favorite Pets. Key, picture of animal represents one pet. Cat, 6. Dog, 10. Fish, 5. Lizard, 3 .
Bar graph. Horizontal axis labeled cat, dog, fish, lizard. Vertical axis from 0 to 10 by ones. Height of bar at each category: Cat, 6. Dog, 10. Fish, 5. Lizard, 3.

A picture graph is an organized way to share data using pictures of the objects.

A bar graph is an organized way to share data using the height or length of rectangles to show how many in each category or group.

We can use these graphs to answer the questions below.

  1. How many students chose a dog?

  2. How many more students chose cats than chose lizards?

  3. How many students voted for their favorite pet?

Problem 1 (Lesson 7)

Here is how Diego recorded his classmates’ favorite colors:

  • yellow

  • red

  • red

  • blue

  • red

  • blue

  • purple

  • yellow

  • red

  • red

  • blue

  • purple

  • red

  • blue

  • blue

  • yellow

  • red

  • red

Create a representation to show Diego’s data.

Problem 2 (Lesson 8)

The picture graph shows the favorite colors of some students.

Picture Graph. Favorite Color. Key: one circle represents one student response. Yellow, 5 circles. Orange, 6 circles. Blue, 4 circles. Green, 7 circles.

Select 3 statements that are true about the data recorded in the graph.

  1. More students like green than any of the other colors.

  2. 5 students chose blue as their favorite color.

  3. 2 more students chose blue than orange.

  4. 22 students voted in all.

  5. 3 fewer students chose blue than green.

Problem 3 (Lesson 8)

The picture graph shows the pattern blocks that were used to create a pattern.

Picture Graph. Pattern Blocks by Shape. Key. 1 pattern block represents 1 pattern block to create the pattern. Triangles, 8. Squares, 6. Trapezoid, 5. Rhombuses, 6.

Select 3 questions that you can answer with the graph.

  1. Are there more trapezoids than squares?

  2. Are all of the triangles together in the pattern?

  3. How many hexagons are there?

  4. How many more triangles are there than rhombuses?

  5. How many squares and trapezoids are there in the shape altogether?

Problem 4 (Lesson 9)

Use the bar graph to answer the questions about the trees in the park.

Bar graph. Trees in the Park. Horizontal axis labeled maple, oak, elm, willow. Vertical axis from 0 to 12 by ones. Height of bar: Maple, 11. Oak, 3. Elm, 9. Willow, 5.
  1. How many trees are there altogether?

  2. How many more maple trees are there than willow trees?

  3. Which kind of tree has the smallest number?

Problem 5 (Lesson 10)

The table shows the fish in a tank.





angle fish


Make a bar graph showing the data from the table.

Bar graph. title, Blank. Horizontal axis labeled goldfish, guppy, angelfish, molly. Vertical axis from 0 to 10 by ones

Problem 6 (Lesson 11)

The bar graph shows the favorite seasons of some students.

Bar graph. Favorite Seasons. Horizontal axis labeled summer, fall, winter, spring. Vertical axis from 0 to 10 by ones. Height of bar: summer, 8, fall, 6, winter, 3. spring, 7.
  1. Write two questions that you can answer using the graph.

  2. Answer your questions.

Problem 7 (Exploration)

The data display about some shapes in a bag is not finished. It shows the kinds of shapes, but not how many of each are in the bag.




Create a set of data about how many shapes are in the bag that makes all of these statements true:

  1. There are more than 15 shapes altogether, but less than 25 shapes.

  2. There are 6 more squares than circles.

  3. There are 7 fewer circles than triangles.

Problem 8 (Exploration)

  1. Gather data at school or at home and make a graph showing the data.

  2. Ask a math question that can be answered with the data.

  3. Trade with a partner and answer each other’s questions.

Problem 9 (Exploration)

Han made this bar graph showing the number of songs Elena and Noah listened to on Saturday.

Bar graph. Horizontal axis labeled Elena, Noah. Vertical axis unlabeled. Height of bar: Elena greater than Noah. 
  1. How could Han improve the diagram?

  2. If Noah listened to 7 songs, how many songs do you think Elena listened to? Explain your reasoning.