In this activity, students use a tape diagram to help them reason about a situation, write an equation that represents it, and solve the equation. Students can use both the diagram and the solution strategy of doing the same to each side and undoing that they saw in the past few lessons. The first two questions provide more scaffolding and the last question provides none.

When students work on the last question, monitor for students who:

• Reason numerically without any diagrams or representations.
• Create a tape diagram and use it to reason numerically.
• Write an equation like and solve it by using the distributive property to find the total amount saved, .
• Write an equation and solve it by first dividing by 6 to find the cost of each discounted ticket.

For the last question, students need to decide how to represent the situation and use their representation to reason about a solution, which requires reasoning abstractly and quantitatively (MP2).

Invite previously selected students to share their strategies for the last problem. Sequence the discussion of the strategies in the order listed in the Activity Narrative. If possible, record and display the students’ work for all to see.

Connect the different responses to the learning goals by asking questions, such as:

• “How are the approaches different, and what do they have in common?”
• “Where do you see the 6 people, the $1.50 coupon, and the $46.50 total in each approach?”
• “Which approach is the fastest? What are some reasons a person might use an approach that takes longer?”

In this activity, students solve one or more word problems using strategies of their choice. The problems increase in difficulty. It is suggested that students create a visual display of one of the problems and do a Gallery Walk or presentation, but if time is short, you may choose to just have students work in their workbooks or devices.

Since these problems are relatively unscaffolded, students make sense of the problems and persevere in problem solving (MP1).

The phrases “9 times as far” and “9 times as many” may lead students to think about multiplying by 9 instead of dividing (or multiplying by ). Encourage students to act out the situations or draw diagrams to help reason about the relationship between the quantities. Remind them to pay careful attention to what or who a comparison refers to. 

The purpose of this discussion is to compare and contrast different solution methods.

If students created a visual display and you opt to conduct a Gallery Walk, ask students to post their solutions. Distribute sticky notes and ask students to read others’ solutions, using the sticky notes to leave questions or comments. Give students a moment to review any questions or comments left on their displays.

Invite any students who chose to draw a diagram to share. Ask the class if they agree or disagree with each diagram and encourage them to suggest any revisions. Next, invite students who did not try to draw a diagram to share strategies. Ask students about any difficulties they had creating the expressions or equations. Did the phrase “9 times as many” suggest an incorrect expression? If yes, how did they catch and correct for this error?