In this activity, students draw a tape diagram to represent each situation. The purpose is to show students that some situations can be represented by an equation of the form (or equivalent).

For each question, monitor for one student with a correct diagram. Encourage students to explain what any variables used to label the diagram represent in the situation.

Since students have not been shown how to represent situations like these with a tape diagram, they have to do a notable amount of sense-making to complete the task (MP1).

In the digital version of the activity, students use an applet to create their tape diagrams. The applet allows students to divide the tape into parts and label the parts and total. The digital version may be helpful for students who struggle with drawing their own diagrams. However, even if the class is using the digital version, some students may prefer to draw the diagrams in their notebooks or on scratch paper.

Select one student for each situation to present their correct diagram. Ensure that students explain the meaning of any variables used to label their diagram.

Possible questions for discussion:

• “For the situations with no , how did you decide what quantity to represent with a variable?” (Think about which amount is unknown but has a relationship to one or more other amounts in the story.)
• “What does the variable you used to label the diagram represent in the story?”
• “Did any situations have the same diagrams? How can you tell from the story that the diagrams would be the same?” (Same number of equal parts, same amount for the total.)

This activity is a continuation of the previous one. Students match each situation from the previous activity with an equation, solve the equation by any method that makes sense to them, and interpret the meaning of the solution. Students are still using any method that makes sense to them to reason about a solution.

For each equation, monitor for a student using their diagram to reason about the solution and a student using the structure of the equation to reason about the solution.

Students reason abstractly and quantitatively when they attend to the meaning of the equation’s solution in the context (MP2).

The purpose of this discussion is to connect solving moves on the tape diagram with solving moves on the equation.

Display the first situation next to its matching diagram and equation. Ask  one student who reasoned with the diagram and one who reasoned only about the equation to explain their solutions. Point out or demonstrate connections between the two representations and solving moves. For example, “I divided the number of gift bags by 5, leaving me with 4 pencils per gift bag. Since Tyler added 3 pencils to each gift bag, there must have been 1 pencil in each gift bag to start,” can be shown on a tape diagram and on a corresponding equation. It is not necessary to invoke the more abstract language of “doing the same thing to each side” of an equation yet.