Solving One-Variable Equations
Lesson 4
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.
Foundational Standards
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7.EE.B.4
Criteria for Success
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- Write expressions for unknowns in terms of other unknowns.
- Use expressions and equations to model situations with unknowns.
- 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.
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?
Guiding Questions
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
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
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
Problem Set
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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.
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EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic A > Lesson 5
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Examples, Exercises, and Problem Set; choose only the problems with variables on one side of the equation.
- RDA Performance Task Bank SBAC Item MAT.08.CR.1.0000G.G.129 C1 TG — Geometry application
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Algebra By Example 3.6 Writing Expressions and Equations from Words
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Note, these are very basic.
Target Task
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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
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 cost $15 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. $${15(0.7x-10)=150}$$
Mastery Response
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