Warm-up: Notice and Wonder: Bar Graph Scales (10 minutes)
The purpose of this warm-up is to elicit the idea that adjusting the scale changes the size of the bars in a bar graph and can make it easier or more difficult to interpret. While students may notice and wonder many things about these graphs, the different scales in the bar graphs are the most important discussion points.
- Groups of 2
- Display the graphs.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
What do you notice? What do you wonder?
- “How are the three graphs different?” (They show the same data, but the bars are different heights. They have different scales.)
Activity 1: Represent Pattern Blocks (20 minutes)
The purpose of this activity is for students to analyze a scale and create a scaled bar graph. Students consider a large collection of pattern blocks and decide which scale will work best to represent the categorical data. They consider three students’ ideas, choose a scale of 2, 5, or 10, and create a scaled bar graph to represent the categorical data. Students must justify why they agree that a particular scale would be best. During the activity and whole-class discussion, students share their thinking and have opportunities to listen to and critique the reasoning of their peers (MP3). Providing a variety of scales for students to choose from allows for discussion about the benefits of using larger scales for larger groups of objects and the effect of a scale on how easy it may be to read and interpret data in a graph.
Supports accessibility for: Organization, Visual-Spatial Processing
- Groups of 2
- Display the image.
- “Take a minute to consider these pattern blocks and think about how you could represent them in a scaled bar graph.”
- 30 seconds: quiet think time
- “Now answer the questions about organizing and representing the pattern blocks in a bar graph with your partner. Be prepared to justify your choice of scale.”
- 12 minutes: partner work
- Monitor for students who used each of the scales to create their bar graph.
Here is a collection of pattern blocks.
Mai, Noah, and Priya want to make a bar graph to represent the number of triangles, squares, trapezoids, and hexagons in the collection.
- Mai says the scale of the bar graph should be 2.
- Noah says the scale of the bar graph should be 5.
- Priya says the scale of the bar graph should be 10.
- Who do you agree with? Explain your reasoning.
Use the scale that you chose to create a scaled bar graph to represent the collection of pattern blocks.
Advancing Student Thinking
If students use a scale of 2, consider asking:
- “How did you decide on the scale to use in your graph?”
- “How would using a scale of 5 or 10 affect your graph?”
- Display selected student work showing each of the scales.
- “What scale did you use for your bar graph? Why did you choose that scale?” (I used a scale of 5 because each amount can be counted by 5. I used a scale of 10 so I don’t have to make as many marks on the scale.)
Activity 2: Represent More Data in a Scaled Bar Graph (15 minutes)
The purpose of this activity is for students to represent data in a scaled bar graph. In this activity, the categorical data is presented in a table. Students choose a scale and make a scaled bar graph of the categorical data. Students have prior experience with scales of 2, 5, and 10, and are not directed to a specific scale in this activity. However, due to the larger numbers, it is likely that students choose a scale of 5 or 10. If students struggle to get started, you could suggest a scale of 5 or 10. In the whole-class discussion, students share how their choice of scale affected their graph.
Students will use their scaled bar graphs again in the next lesson.
Advances: Listening, Speaking
- Groups of 4
- “What is your favorite time of the year?”
- 30 seconds: quiet think time
- Share responses.
- “We are going to make a scaled bar graph to represent some 3rd grade students’ favorite times of the year.”
- “Represent the data shown in the table in a scaled bar graph. Think about a scale that makes sense with the number of students.”
- 5–7 minutes: independent work time
- “Share your graphs with your small-group. Discuss the scales you chose to use.”
- 2–3 minutes: small-group discussion
All the third-grade students at school were asked, “What is your favorite time of the year?” Their responses are shown in this table:
|favorite time of the year||number of students|
Use the data from this table to create a scaled bar graph.
- “How did the scale you chose for your graph affect how your graph looked in the end?” (Certain scales make it easier or more difficult to read the data. For example, with a scale of 10, it might be more difficult to read the exact values from the graph.)
Display the bar graphs from today’s lesson.
“What did you learn today that will help you make decisions about how to create scaled graphs in the future?” (You can pick scales that match the data. If there's mostly larger numbers, you might pick a scale like 5 or 10. The scale can help make the graph easier to read.)
After the cool-down, ask students to individually reflect on the following question: “Which one of the norms did you feel was most important in your work today, and why?” Students can write their responses on the bottom of their cool-down paper, on a separate sheet of paper, or in a math journal.
Tell students that as their math community works together over the course of the year, the group will continually add to and revise its “Doing Math” and “Norms” actions and expectations.