Warm-up: What Do You Know About Bar Graphs? (10 minutes)
- “What do you know about bar graphs?”
- 1 minute: quiet think time
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
What do you know about bar graphs?
- "What is an example of how we might use a bar graph?" (You can use it to show data that you collected after asking a question or counting things. You could show favorite ice cream flavors or how many of each kind of animal we saw at the zoo.)
- "What are other ways you can represent data?" (picture graphs, lists, tallies, tables)
Activity 1: Classroom Survey and Graph (30 minutes)
The purpose of this activity is for students to create a survey, collect and organize their data, and represent their data as a picture or bar graph.
To add movement to this activity, consider a gallery walk for students to see and compare the different representations of their data.
Advances: Reading, Representing
Supports accessibility for: Attention, Organization
Materials to Gather
Materials to Copy
- Picture and Bar Graph Template
- Groups of 2.
- “These are some topics we explored in previous lessons.”
- Display list of topics:
- How we get to school
- Favorite sport
- Favorite season
- Field trip choice
- Recess activity
- Favorite pet
- Food for a party
- Fruits we love
- Veggies we love
- “With your partner, brainstorm other ideas for things you want to learn about your classmates.”
- 2 minutes: partner discussion.
- Invite a few students to share and record responses.
- “Look through both lists of possible topics for surveying our classmates. With your partner, pick one topic and write a survey question. Decide on 3 or 4 possible responses for your survey question.”
- “Take turns asking your survey question to your partner and record both of your responses in your workbook.”
- "Now you will ask other students in our class your survey question and record the data you collect."
- 5 minutes: partner work time
- Monitor to ensure students have collected sufficient data.
- While students survey, give each student the graph template and access to colored pencils.
- “Use your data to create a picture or bar graph. “
- 10 minutes: partner work time.
- Monitor for students who create:
- a picture graph that use pictures that represent each category (for example, drawing each kind of animal for a survey about pets)
- a picture graph that uses the same abstract picture for each category (for example, drawing a circle to represent each pet in a survey about pets)
- a bar graph with a clear title, scale, and category labels
- What is your survey question?
What are your categories?
- Category 1: __________________________________
- Category 2: __________________________________
- Category 3: __________________________________
- Category 4: ___________________________________
- Record the data.
- Organize and represent the data in a picture graph or bar graph.
- Invite previously selected students to share their graphs.
- “How are these graphs the same? How are they different?” (The bar graph has numbers on it, but the picture graphs don’t. Some have 3 and some have 4 different responses. Some are up and down and some are side-to-side.)
- “What choices did these mathematicians make with their graphs?” (They had to decide what kind of graph to make, a title, which direction to show the bars in how to represent their data so it is clear with a title, labels, or pictures.)
Activity 2: I Ask, then You Ask (15 minutes)
- Combine pairs into groups of 4
- “Switch graphs. Use the sentence stems or create your own questions about the other group’s graphs.”
- 1–2 minutes: independent work time
- 4 minutes: partner work time.
- “Take turns to ask each other the questions you came up with and use your own graph to answer.”
- “When possible, write down an equation to show your reasoning.”
- 5 minutes: group discussion.
- Monitor for students who write equations to show the categories they combine or compare when answering their peers' questions.
- Trade graphs. Create questions about the other group’s graph.
How many students picked ___________ and __________ all together?
How many more students picked _______ than _______?
- Take turns asking and answering questions.
Advancing Student Thinking
- Invite previously selected students to share.
- “Where do we see the equations in their graph? What does the equation mean?”
- “What’s the difference between answering the questions from a bar graph and answering them from a picture graph?”
Activity 3: Analyze the Data with Diagrams (15 minutes)
The purpose of this activity is for students to analyze what they have learned from the data and representations in the previous activities and to share their findings. In this activity, students select two things they learned and illustrate them using a tape diagram.
Monitor for tape diagrams that can be displayed during the lesson synthesis and compared to the bar graph selected in a previous activity. While the graph and diagram do not have to be from the same pair, it would be helpful for students to see data from the same survey displayed with different representations.
To add movement to this activity, consider a gallery walk. Students can make their diagrams on poster paper. As students walk around the room, they select a few diagrams and determine what information they learn about their class based on the diagram and equation.
- Groups of 2
- “You and your partner are going to draw a diagram. Your diagram should compare two facts you learned from your survey.”
- “Decide with your partner which 2 facts you want to share with the class and how you will compare the two facts.”
- 1 minute: partner discussion.
- 5 minutes: independent work time
- Students check in with their partners to be sure their representations make sense and are accurate.
- 3 minutes: partner discussion
- Monitor for a few examples of accurate tape diagrams and equations.
- Draw a diagram. Your diagram should compare two facts you learned from your survey.
- Write an equation that represents the comparison.
- Display selected student work.
- “What information does this diagram or equation tell us about our classmates?”
- “Where do you see this equation in the diagram?”
"Today we had a chance to learn more about each other by collecting data and representing it in multiple ways.”
Display a student generated bar or picture graph and the tape diagram side by side.
- “How are these representations the same?” (They are from the same survey.)
- “What information can we see in the picture/bar graph that we don’t see in the diagram?” (All of the people that were surveyed.)
- “What information can we see in the diagram that we don’t see in the picture/bar graph?” (It’s easier to compare two of the groups in the diagram than in the graph.)