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. When students come up with mathematical questions and collect data, they model with mathematics (MP4).

To add movement to this activity, consider a Gallery Walk for students to see and compare the different representations of their data.

• 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, and how to represent their data so it is clear with a title, labels, or pictures.)

The purpose of this activity is for students to analyze what they have learned from the data and representations in the previous activity and to share their findings. In this activity, students select two things they learned and illustrate them using a tape diagram. When students report on conclusions and reasoning, they model with mathematics (MP4). 

Monitor for tape diagrams that can be displayed during the Lesson Synthesis and can be compared to the bar graph selected in the previous activity. Although 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.

• Display selected student work.
• “What information does this diagram or equation tell us about our classmates?” (More people like beans than carrots. Four more people like beans than carrots. Fewer people like carrots than beans.)
• “Where do you see this equation in the diagram?” (The top of the diagram is the 7 in the equation. The bottom is the 3 in the equation. The difference between them is the 4.)