The purpose of this activity is for students to use their understanding of bar graphs to make sense of tape diagrams. Students physically create a tape diagram from a bar graph and compare two of the categories. Students recognize that even without a given scale, they can use this visual structure to compare amounts and reason about the difference between the two (MP2).

Students revisit the meaning of a diagram—a drawing or picture that represents quantities.

• Display a student’s completed tape diagram.
• “How does your diagram make it easy to see which food received the most votes?” (We wrote labels to show which bar matches which food.)
• “What do you need to add to the bars to answer questions like ‘How many more students chose hot dogs than burgers?’” (Label what number the bar represents.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share responses.
• As needed, draw a diagram that resembles the tape diagram in the warm-up.
• “Diagrams can help represent Compare problems. You can use rectangles like the bars in a bar graph to represent the bigger amount, the smaller amount, and the difference.”

The purpose of this activity is for students to complete a tape diagram and describe the features of tape diagrams. Throughout the activity, students use what they know about bar graphs to make sense of what each number in a tape diagram represents and the role of the question mark. They also connect the structure of the tape diagram to equations that represent a comparison of two quantities (MP2). As students connect the labels on the tape diagram to the question, the features on the graph, and the context, they attend to precision and reason abstractly and quantitatively (MP6).

If the student assigns the larger value to the smaller part or places the question mark in a place other than the difference, consider asking:

• “Can you explain your representation to me?”
• “How can you use the bar graph to help you label the diagram?”

• “How did you figure out what food was being compared to pizza?” (We looked for the food that was picked by 14 students.)
• “What does the question mark represent in the diagram?” (It shows the difference between hot dogs and pizza. It shows how many more students would need to pick hot dogs to be the same as the number of students who picked pizza.)
• Point out the dashes representing the difference, but not an actual quantity.
• “What equation could we write to represent this difference?” (, ) 
• Record responses.
• “How do you see each number represented in the diagram?” (19 shows how many picked pizza, 14 shows how many picked hot dogs. The question mark shows the difference.)