## Objective

Solve equations in the forms $${px+q=r }$$and $${p(x+q)=r}$$algebraically.

## Common Core Standards

### Core Standards

The core standards covered in this lesson

7.EE.B.4.A— Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

*For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?*### Expressions and Equations

7.EE.B.4.A— Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

*For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?*

### Foundational Standards

The foundational standards covered in this lesson

6.EE.B.7

### Expressions and Equations

6.EE.B.7— Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

## Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

- Understand that an equation is a statement of balance, and in solving the equation, the balance must be maintained.
- Understand solving an equation as a process of undoing operations using inverse operations that adhere to arithmetic properties.
- Solve equations in the forms $$px+q=r$$ and $$p(x+q)=r$$.

## Tips for Teachers

Suggestions for teachers to help them teach this lesson

In this lesson, students learn the concepts behind the mechanics of solving an equation. In the next two lessons, students will have further opportunities to practice solving equations in contextual situations. Solving equations in these two forms is a fluency expectation in 7th grade. See our Guide to Procedural Skill and Fluency for ideas of activities to use throughout the lesson and remaining part of the unit.

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## Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

25-30 minutes

### Problem 1

A balance is shown below.

a.Describe how you can use the balance to find the value of $$x$$.

b.Write an equation to represent the situation shown in the balance.

c.Use the equation to model the actions you did in part A with the balance.

d.Repeat parts A–C using the balance shown below.

#### Guiding Questions

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### Problem 2

Yoshiro has a new puppy. She decides to create an enclosure for her puppy in her backyard. The enclosure is in the shape of a hexagon, with one pair of opposite sides running the same distance along the length of two parallel flowerbeds. A sketch of the enclosure is shown below.

If the perimeter of the enclosure is 137 feet, what is the length of each side that runs along the flowerbed, labeled $$n$$ in the diagram? Write an equation to represent the situation, and solve using algebraic properties.

#### Guiding Questions

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#### References

EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic C > Lesson 22—Example 1

Grade 7 Mathematics > Module 2 > Topic C > Lesson 22 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

### Problem 3

Solve the equations:

a.$${12(x-2)=72}$$

b.$${- {1\over3}x+4=-2}$$

c.$${5.6-2p=13}$$

#### Guiding Questions

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## Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

15-20 minutes

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## Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

5-10 minutes

Solve each equation for the variable. Show every step in your work that maintains the balance in each equation.

a.$${{1\over2}(x+8)=-10}$$

b.$${-5x+12=20}$$

c.

#### Student Response

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## Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

- Open Up Resources
*Grade 7 Unit 6 Practice Problems*—Lessons 7 and 8, skip review questions - EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic C > Lesson 22—Exercises 1-5, Problem Set
- Kuta Software Free Pre-Algebra Worksheets
*Two-Step Equations Containing Integers* - Kuta Software Free Algebra 1 Worksheets
*Two-Step Equations* - Algebra By Example
*3.1 Solving 1 and 2 Step Equations* *SolveMe Mobiles*—These can be done on the computer, or screen shots can be taken and added to a problem set; stick to one-variable mobiles. Also find good challenges here.

Lesson 3

Lesson 5