Curriculum / Math / 6th Grade / Unit 6: Equations and Inequalities / Lesson 6
Math
Unit 6
6th Grade
Lesson 6 of 14
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Lesson Notes
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Solve percent problems using equations.
The core standards covered in this lesson
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.
6.RP.A.3.C — Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
The foundational standards covered in this lesson
6.RP.A.1 — Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."
6.RP.A.2 — Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. Expectations for unit rates in this grade are limited to non-complex fractions. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
In Unit 2, students solved percent problems by reasoning about diagrams, double number lines, and tables. Now having learned about equations in the form $${px=q}$$, students revisit percent problems to see how they can be modeled and solved efficiently using an equation (MP.4).
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
What is...
In general, if you’re given a percent and a whole, how can you find the part? Write this as an equation.
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30% of what number is 12?
Solve this problem first by drawing a diagram. Then write and solve an equation to verify your solution.
For each situation below, write and solve an equation to answer the question.
a. There are 6 liters of water in a bucket, which is 20% of the maximum number of liters the bucket can hold. What is the maximum number of liters the bucket can hold?
b. A softball team won 18 games, which was 60% of the games they played this season. How many games did the softball team play this season?
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
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
5-10 minutes
Paula is saving money to buy a tablet. So far, she has saved $54, which is 45% of what she needs to buy the tablet.
Write and solve an equation to find the price of the tablet.
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.
Next
Solve multi-part equations leading to the form $${x+p=q }$$ and $${px=q}$$.
Topic A: Reasoning About and Solving Equations
Represent equations in the form $${ x+p=q }$$ and $${px=q}$$ using tape diagrams and balances.
Standards
6.EE.B.66.EE.B.7
Define and identify solutions to equations.
6.EE.B.5
Write equations for real-world situations.
Solve one-step equations with addition and subtraction.
Solve one-step equations with multiplication and division.
6.EE.B.76.RP.A.3.C
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Topic B: Reasoning About and Solving Inequalities
Define and identify solutions to inequalities.
6.EE.B.56.EE.B.8
Write and graph inequalities for real-world conditions. (Part 1)
6.EE.B.8
Write and graph inequalities for real-world conditions. (Part 2)
Solve one-step inequalities.
6.EE.B.66.EE.B.8
Topic C: Representing and Analyzing Quantitative Relationships
Write equations for and graph ratio situations. Define independent and dependent variables.
6.EE.C.96.RP.A.3.A
Represent the relationship between two quantities in graphs, equations, and tables. (Part 1)
Represent the relationship between two quantities in graphs, equations, and tables. (Part 2)
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