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).

The last question is challenging to represent with a tape diagram, because part of the diagram would need to be divided into 30 equal pieces. This is intentional, and can be used to make the point that we are trying to develop ways to solve problems that are more efficient than drawing a diagram every time.

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.

The purpose of this discussion is to understand how each situation is represented by a tape diagram. 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.)
• “How is the last situation different from the others?” (It’s the only one where 30 is the coefficient of rather than the total.)
• “Why was it tough to draw a diagram for the last question?” (You would have to divide part of the diagram into 30 equal pieces.)

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 subtracted the 9 extra markers and then divided the remaining 21 markers by 7,” 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.