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27.2

Activity

35 mins

Cycling, Fundraising, Working, and ___?

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

MLR8: Discussion Supports

Materials

To Gather

Tools for creating a visual display

Activity Narrative

In this activity, students reason about situations involving two different relationships between the same two quantities. Then they invent their own problem of the same type. Although students are encouraged by the language of the activity to use a system of equations to solve the problems, they may elect to use a different representation to explain their thinking (MP1, MP3).

As students work through the first three problems, notice the ways in which students reason about the problems with and without systems of equations. Identify some groups with particularly compelling or clear reasoning, and ask them to share later.

Launch

Arrange students in groups of 2. Provide tools for creating a visual display.

After students have completed the first three problems, select previously identified groups to share their solutions. Bring out why these solutions are particularly good (for example, greater clarity or efficiency), and discuss the connections between them, particularly the connections between groups that did and did not use systems of equations where possible. Next, have students begin the second part of the activity, in which they write their own problem to trade with another group.

Representation: Access for Perception. Provide appropriate reading accommodations and supports to ensure student access to written directions, word problems, and other text-based content.
Supports accessibility for: Language

MLR8 Discussion Supports. During group presentations, invite the student(s) who are not speaking to follow along and point to the corresponding parts of the display.
Advances: Speaking, Representing

Activity

None

Student Task Statement

Solve each problem. Explain or show your reasoning.

Two friends live 7 miles apart. One Saturday, the two friends set out on their bikes at 8 a.m. and started riding toward each other. One rides at 0.2 miles per minute, and the other rides at 0.15 miles per minute. At what time will the two friends meet?
Students are selling school spirit gear for a fundraiser. Bracelets with the school mascot on them cost $1 each, and shirts with the school crest cost $10 each. They sold 100 items and made $307. How many bracelets did they sell?
Jada earns $7 per hour mowing her neighbors’ lawns. Andre gets paid $5 per hour for the first hour of babysitting and $8 per hour for any additional hours he babysits. What is the number of hours they both can work so that they get paid the same amount?
Pause here so your teacher can review your work. Then, invent another problem that is like one of these, but with different numbers. Solve your problem.
Create a visual display that includes:
- The new problem you wrote, without the solution.
- Enough work space for someone to show a solution.
Trade your display with another group, and solve each other's new problem. Make sure that you explain your solution carefully. Be prepared to share this solution with the class.
When the group who got the problem that you invented shares their solution, check that their answer is correct.

Activity Synthesis

Most of the discussions happen within and between groups, but the last question requires a whole-class discussion. Have each group share the peer-generated question that they were assigned and its solution. Although the group that wrote the question will be responsible for confirming the answer, encourage all students to listen to the reasoning that each group used.

Alternatively, after groups have checked the work of the group that solved their problem, have students complete a gallery walk to see all the created problems. Ask students to look for situations similar to theirs and to identify the most common solution methods used. After the gallery walk, select a few groups to share a problem and how they solved it.

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Lesson 27

Solving Problems with Systems of Equations

Warm-up

Are We There Yet?

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Student Response

Building on Student Thinking

Are You Ready for More?

Activity Synthesis

Activity

Cycling, Fundraising, Working, and ___?

Standards Alignment

8.EE.8.c

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Activity Synthesis

Have feedback on the curriculum?

Standards Alignment

6.EE.9

Student Response

Building on Student Thinking

Are You Ready for More?