Unit 3, Lesson 10

Using Equations to Solve Problems

Accelerated 7

10.1

Warm-up

5 mins

Remember Tape Diagrams

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

In this Warm-up, students write a story and an equation that could be represented by a tape diagram. The purpose is to reactivate students’ understanding of tape diagrams to make it more likely that tape diagrams are accessible as a representation for them to choose in this lesson. The diagram was deliberately constructed to encourage some students to write an equation like and others like . Monitor for one student who writes each type of equation.

Launch

Arrange students in groups of 2. Give 5 minutes of quiet think time and time to share their work with a partner followed by a whole-class discussion.

Activity

None

Student Task Statement

Tape diagram, 6 parts, a, 2, a, 2, a, 2, total 24. Across the top, brackets above an a and 2 indicate a + 2.

Write a story that could be represented by this tape diagram.
Write an equation that could be represented by this tape diagram.

Student Response

Activity Synthesis

The purpose of this discussion is to help students see that an equation representing the diagram can be written in either form, or . After students have had a chance to share their work with their partner, select a few students to share their stories. Then select one student to share each type of equation and explain its structure.

10.2

Activity

20 mins

At the Community Festival

Instructional Routines

5 Practices

Materials

None

Activity Narrative

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).

10.3

Activity

Optional

10 mins

Running Around

Instructional Routines

None

Materials

To Gather

Sticky notes Tools for creating a visual display

Activity Narrative

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).

Launch

Keep students in the same groups. Instruct all groups to solve the first problem. If time allows, then assign one of the other problems for each group to solve. If opting to have students do presentations or a Gallery Walk, distribute tools for making a visual display.

Give students 5–6 minutes quiet work time and a partner discussion followed by a whole-class discussion or gallery walk.

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

Lesson Synthesis

Ask students to reflect on the work done in this unit so far. Ask:

“What strategies have you learned?”
“What kinds of problems can you solve that you weren’t able to, previously?”

Ask students to write down or share with a partner one new thing they have learned and one thing they still have questions or confusion about.

Student Lesson Summary

Many problems can be solved by writing and solving an equation. Here is an example:

Clare ran 4 miles on Monday. Then for the next 6 days, she ran the same distance each day. Clare ran a total of 22 miles during the week. How many miles did she run on each of the 6 days?

One way to solve the problem is to represent the situation with an equation, , where represents the distance, in miles, Clare ran on each of the 6 days. Solving the equation gives the solution to this problem.

Clare ran 3 miles each day.

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Unit 3, Lesson 10

Using Equations to Solve Problems

Accelerated 7

10.1

Warm-up

5 mins

Remember Tape Diagrams

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

Launch

Arrange students in groups of 2. Give 5 minutes of quiet think time and time to share their work with a partner followed by a whole-class discussion.

Activity

None

Student Task Statement

Write a story that could be represented by this tape diagram.
Write an equation that could be represented by this tape diagram.

Student Response

to access Student Response.

Activity Synthesis

10.2

Activity

20 mins

At the Community Festival

Instructional Routines

5 Practices

Materials

None

Activity Narrative

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).

10.3

Activity

Optional

10 mins

Running Around

Instructional Routines

None

Materials

To Gather

Sticky notes Tools for creating a visual display

Activity Narrative

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

Launch

Give students 5–6 minutes quiet work time and a partner discussion followed by a whole-class discussion or gallery walk.

Lesson Synthesis

Ask students to reflect on the work done in this unit so far. Ask:

“What strategies have you learned?”
“What kinds of problems can you solve that you weren’t able to, previously?”

Ask students to write down or share with a partner one new thing they have learned and one thing they still have questions or confusion about.

to access Cool-down.

Student Lesson Summary

Many problems can be solved by writing and solving an equation. Here is an example:

Clare ran 4 miles on Monday. Then for the next 6 days, she ran the same distance each day. Clare ran a total of 22 miles during the week. How many miles did she run on each of the 6 days?

Clare ran 3 miles each day.

Have feedback on the curriculum?

Help us improve by sharing suggestions or reporting issues.

Submit Feedback

Lesson 10

Using Equations to Solve Problems

Warm-up

Remember Tape Diagrams

Standards Alignment

Building On

Addressing

7.EE.4.a

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Student Response

Activity Synthesis

Activity

At the Community Festival

Instructional Routines

Materials

Activity Narrative

Activity

Running Around

Instructional Routines

Materials

To Gather

Activity Narrative

Launch

Lesson Synthesis

Student Lesson Summary

Have feedback on the curriculum?

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Settings

Audience

Assessment Access

Lesson 10

Using Equations to Solve Problems

Warm-up

Remember Tape Diagrams

Standards Alignment

Building On

Addressing

7.EE.4.a

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Student Response

Activity Synthesis

Activity

At the Community Festival

Instructional Routines

Materials

Activity Narrative

Activity

Running Around

Instructional Routines

Materials

To Gather

Activity Narrative

Launch

Lesson Synthesis

Student Lesson Summary

Have feedback on the curriculum?

Building on Student Thinking

Are You Ready for More?

Launch

Activity

Student Task Statement

Student Response

Building on Student Thinking

Are You Ready for More?

Activity Synthesis

Activity

Student Task Statement

Student Response