Curriculum / Math / 8th Grade / Unit 2: Solving One-Variable Equations / Lesson 4
Math
Unit 2
8th Grade
Lesson 4 of 12
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Write and solve multi-step equations to represent situations, with variables on one side of the equation.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
7.EE.B.4 — Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
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?
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?
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?
Solve the equations.
a. $${{{2(x-4)}\over9}={{3-7}\over6}}$$
b. $${x-0.8(3x)+14.12=0.75(8)}$$
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
The average household uses 1400kWh of electricity per month. In one household, air conditioning uses 300kWh per month. Twice as much electricity is used to heat water as to run a refrigerator. 50% of total electricity used goes to miscellaneous uses (like lighting, dishwashers, and TVs).
Assuming this household uses the average amount of electricity per month, how much electricity is used to heat water per month?
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?
An example response to the Target Task at the level of detail expected of the students.
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.
Lesson 3
Lesson 5
Topic A: Simplifying Expressions and Verifying Solutions
Write equivalent expressions using properties of operations and verify equivalence using substitution.
8.EE.C.7
Define a solution to an equation. Solve and check solutions to 1 and 2 step equations.
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Topic B: Analyzing and Solving Equations in One Variable
Justify each step in solving a multi-step equation with variables on one side of the equation.
8.EE.C.7.A 8.EE.C.7.B
8.EE.C.7.B
Model with equations using a three-act task.
Solve equations with variables on both sides of the equal sign.
Write and solve multi-step equations to represent situations, including variables on both sides of the equation.
Understand that equations can have no solutions, infinite solutions, or a unique solution; classify equations by their solution.
8.EE.C.7.A
Solve and reason with equations with three types of solutions.
Use equations to model a business plan and determine the break-even point.
Topic C: Analyzing and Solving Inequalities in One Variable
Solve and graph inequalities with variables on one side of the inequality (optional).
A.REI.B.3
Solve and graph inequalities with variables on both sides of the inequality (optional).
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