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17.2

Activity

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

MLR2: Collect and Display

Materials

To Copy (from Blackline Masters)

Creating and Representing Situations Handout

To Gather

Tools for creating a visual display

Activity Narrative

In this activity, students create their own proportional and nonproportional relationships. This is a significant change from previous activities where students were always given two quantities and asked to decide if they were proportional or not. This new step gives students the opportunity to think about how quantities are related, which is an important step of modeling with mathematics (MP4).

Next, students make a visual display of their scenarios. The posters are displayed around the room so students can view each other's work, give feedback, and critique the reasoning of others (MP3).

Launch

Arrange students in groups of 2. Explain that students are going to come up with relationships that represent things in their daily lives.

Give students 1–2 minutes to brainstorm situations that involve proportional relationships. Invite students to share their ideas. Record the general gist of each idea that is shared and display for all to see. For example, if a student says, “At my favorite arcade, it takes 4 tokens per game of pinball,” you could record this idea as “how many tokens for an arcade game.”

Give students 8–10 minutes of partner work time to invent a relationship and answer the questions. If students struggle to think of situations that involve proportional relationships, consider providing them with copies of the first page of the blackline master, which lists some examples of proportional relationships that they have seen during this unit. Make sure students understand that the examples on the blackline master are just samples and they can still choose to write a different type of relationship.

MLR2 Collect and Display. Direct attention to words collected and displayed from the previous lessons. Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading

Engagement: Provide Access by Recruiting Interest. Invite students to generate a list of additional examples of proportional and nonproportional relationships that connect to their personal backgrounds and interests. Ask students in advance of the lesson to provide time for students to think about it and make more authentic connections to their everyday life.
Supports accessibility for: Conceptual Processing, Attention

Activity

None

Make up a situation where there is a proportional relationship between two quantities.
1. Write one or more sentences describing the relationship.
2. Make a table with at least 5 pairs of numbers relating the two quantities.
3. Graph the relationship and label the axes.
4. Write an equation showing the relationship. Explain in your own words what each number and letter in your equation represents.
If you have time, make up another situation where there is a relationship between two quantities, but the relationship is not proportional.
1. Write one or more sentences describing the relationship.
2. Make a table with at least 5 pairs of numbers relating the two quantities.
3. Graph the relationship and label the axes.
4. If possible, write an equation showing the relationship and explain in your own words what each number and letter in your equation represents.
For each of your situations, explain how you know whether the relationship is proportional or not. Give as many reasons as you can.

Student Response

to access Student Response.

Building on Student Thinking

As students work, pay attention to the numbers they use in their tables. Students can be haphazard when choosing values, and their numbers may end up being unfriendly. Prompt them to reason about what numbers would be more conducive to the situation or easier to calculate.

Some students may struggle to think of a nonproportional situation. Consider providing them with copies of the second page of the blackline master, which lists some examples of nonproportional relationships that they have seen during this unit. However, it is not necessary for every group to come up with a nonproportional relationship, as long as there are a few examples for students to contrast during the discussion.

Activity Synthesis

Give students 5 minutes to trade their work with another group to give feedback about their analysis. Tell them that they should incorporate the feedback they received when making their posters.

Ask students to create a visual display of the relationship they came up with that includes all four of the different types of representations (sentences, table, graph, equation). When the posters are complete, display them around the room. Provide students with these sentence starters, and give them an opportunity to view their classmates’ work and write their responses. This provides a structured way for students to critique the reasoning of others (MP3).

“The most interesting (or surprising) relationship was ____, because . . . .”
“The group ____ should check their work where they . . . .”
“I really liked when the group ____ did this ____ because . . . .”

Conclude with a brief whole-class discussion where students can share similarities they noticed about the different relationships and representations.

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Settings

Audience

Assessment Access

Lesson 17

Four Representations (Optional)

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Activity

Standards Alignment

Building On

Addressing

7.RP.A.2

Building Toward

Instructional Routines

Materials

To Copy (from Blackline Masters)

To Gather

Activity Narrative

Launch

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Lesson Synthesis

Student Lesson Summary

Standards Alignment

Building On

6.RP.A.3

Addressing

7.RP.A.2

Building Toward