Curriculum / Math / 6th Grade / Unit 2: Unit Rates and Percent / Lesson 5
Math
Unit 2
6th Grade
Lesson 5 of 14
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Lesson Notes
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Solve challenging problems involving unit rate.
The core standards covered in this lesson
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."
6.RP.A.3 — Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
6.RP.A.3.B — Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Students have a variety of strategies at their hands to model and solve complex problems involving rate. The problems are open to students taking different approaches; students should clearly organize and explain their strategies so that others, who may have taken a different approach, can follow their line of thinking (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
Chris and David run along a bike path toward a pond. Chris can run 3 miles in 30 minutes, and David can run 5 miles in 60 minutes. They both start running at the same time at the start of the bike path, shown below.
a. If both Chris and David run at their current rates, how long will it take each one to get to the pond?
b. Who will be closer to the pond after 90 minutes? How much farther ahead will this person be in front of the other person?
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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
Market Place is selling chicken for $4.50 per pound. Stop and Buy is selling 5 pounds of chicken for $23.75. You need to buy 8 pounds of chicken. At these rates, which store is cheaper? How much cheaper is it?
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.
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Reason with measurement units and solve unit conversion problems using different strategies.
Topic A: Defining Rate & Solving Rate Problems
Investigate and use rate in real-world situations.
Standards
6.RP.A.36.RP.A.3.B
Define rate and unit rate, and find rates from situations involving ratios.
6.RP.A.26.RP.A.3.B
Find unit rates and use them to solve problems.
Compare situations using unit rates, including speed, price, and work problems.
6.RP.A.3.B
6.RP.A.26.RP.A.36.RP.A.3.B
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Topic B: Measurement Unit Conversions
6.RP.A.3.D
Solve measurement unit conversion problems.
Topic C: Percent
Define percent as a rate per 100. Find percentages of 100 and 1.
6.RP.A.3.C
Solve percent problems using benchmark fractions and percentages, with and without written work.
Convert between fractions, percent, and decimals.
Find a percent of a quantity.
Find the whole quantity, given a part and percent.
Solve percent problems, including finding percent when given a part and a whole.
Solve multi-step problems involving rate and percent.
6.RP.A.26.RP.A.36.RP.A.3.C6.RP.A.3.D
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