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# Solving One-Variable Equations

## Objective

Write and solve multi-step equations to represent situations, with variables on one side of the equation.

## Common Core Standards

### Core Standards

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• 8.EE.C.7.B — Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

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• 7.EE.B.4

## Criteria for Success

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1. Write expressions for unknowns in terms of other unknowns.
2. Use expressions and equations to model situations with unknowns.
3. Decontextualize a situation to represent it algebraically, and re-contextualize to interpret the solution in context of the problem (MP.2).

## Tips for Teachers

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• There are various applications that can be modeled and solved with multi-step equations. This lesson covers a variety of examples including ages, money, geometry applications, consecutive integers, etc. It is more important for students to develop general strategies for tackling problems like these, rather than mastering specific examples (MP.4).
• In terms of pacing, this lesson may be split over more than one day.
• The following tools may be useful for this lesson: calculators.

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problems 1 and 4 (benefit from worked examples). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

The length of a rectangle is 3 cm less than twice the width of the rectangle. If the perimeter is 75 cm, what are the dimensions of the rectangle?

### Problem 2

After collecting coins for a month, you count them to see how much money you have. You determine that you have 12 fewer quarters than you have nickels, and you have twice as many dimes as you have quarters. Altogether, the dimes, nickels, and quarters add up to 10.60. How many of each coin do you have? #### Guiding Questions Create a free account or sign in to access the Guiding Questions for this Anchor Problem. ### Problem 3 Todd and Jason are brothers. Todd says, “I am twice as old as Jason was two years ago.” The sum of the brother’s ages is 38. How old is each brother? #### Guiding Questions Create a free account or sign in to access the Guiding Questions for this Anchor Problem. ### Problem 4 Solve the equations. a. ${{{2(x-4)}\over9}={{3-7}\over6}}$ b. ${x-0.8x(3)+14.12=0.75(8)}$ #### Guiding Questions Create a free account or sign in to access the Guiding Questions for this Anchor Problem. ## Problem Set ? With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set. • Additional procedural practice with solving multi-step equations • Include consecutive integer problems and applications with percents. ## Target Task ? ### Problem 1 Given a right triangle, find the measures of all the angles, in degrees, if one angle is a right angle and the measure of the second angle is six less than seven times the measure of the third angle. #### References EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic A > Lesson 5Exit Ticket Grade 8 Mathematics > Module 4 > Topic A > Lesson 5 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 US license. Accessed Dec. 2, 2016, 5:15 p.m.. ### Problem 2 School uniform shirts normally cost15 each but are on sale for 30% off the original price. You also have a coupon for $10 off the cost before you take the percent discount. If you have$150 to spend, which of the following equations will help you to determine how many shirts, ${ x}$, you can buy?

a.   ${0.7(15x)-10=150}$

b.   ${0.7(15x-10)=150}$

c.   ${15x-0.7(10)=150}$

d.   ${15(0.7x-10)=150}$

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