Lesson 6 | Unit Rates and Percent | 6th Grade Mathematics

Objective

Reason with measurement units and solve unit conversion problems using different strategies.

Common Core Standards

Core Standards

The core standards covered in this lesson

6.RP.A.3.D — Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Ratios and Proportional Relationships

6.RP.A.3.D — Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Foundational Standards

The foundational standards covered in this lesson

4.MD.A.1

Measurement and Data

4.MD.A.1 — Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …
4.MD.A.2

Measurement and Data

4.MD.A.2 — Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
5.MD.A.1

Measurement and Data

5.MD.A.1 — Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Recall common measurement units for length, volume, and weight and know the relative sizes of units within the same system.
Understand that when converting between units of different sizes, the number of the smaller units will be greater and the number of the larger units will be fewer.
Use ratio reasoning to solve simple unit conversion problems, attending to the relationship of the units in the problem (MP.2).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Lessons 6 and 7 engage students in using ratio reasoning to solve unit conversion problems. In Lesson 6, students re-engage in 4.MD.1, 4.MD.2, and 5.MD.1 to make sense of units and their relative sizes. They also solve straight forward conversion problems using strategies they’ve learned so far in the unit. In Lesson 7, students encounter additional unit conversion problem where the need for or direction of conversion is not explicitly stated.

Lesson Materials

Calculators (1 per student) — See note from lesson 1.
Massachusetts Comprehensive Assessment System Grade 6 Mathematics Reference Sheet (1 per student) — We recommend the MCAS reference sheet, however, other reference sheets may suffice as well.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Reason about the size of each measurement unit to determine if you would have more or less of each unit described below.

a. You have 5 feet of ribbon. Do you have more or less than 5 cm of ribbon?

b. You have 3 cups of milk. Do you have more or less than 3 liters of milk?

c. You have 6 kilograms of corn. Do you have more or less than 6 grams of corn?

d. You are traveling 30 miles per hour. Is that faster or slower than 30 meters per hour?

Guiding Questions

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Problem 2

There are approximately 2.54 cm in every inch. A book measures 7 inches tall. How tall is the book in centimeters?

Guiding Questions

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Problem 3

There are 4 cups in a quart.

a. A recipe for lemonade calls for 2 ½ quarts of water. How many cups of water should you use for the recipe?

b. You measure out 15 cups of water. How many quarts is this?

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

The conversion rates between kilograms and pounds are:

1 kg $$\approx$$ 2.2 lbs

1 lb $$\approx$$ 0.454 kg

a. How many kilograms is a backpack that weighs 6 pounds? Show how you arrive at your answer.

b. How many pounds is a cat that weighs 11 kilograms? Show how you arrive at your answer.

Student Response

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Additional Practice

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.

Include problems where students reason about the relative sizes of units, such as true/false problems or error analysis.

EngageNY Mathematics Grade 6 Mathematics > Module 1 > Topic C > Lesson 21 — Examples, Exercises, Problem Set
Estimation 180 Days 1-220 — Good problems to engage students in estimation; for example, Days 1 - 5 all involve estimating height.

Lesson 5

Lesson 7

Lesson Map

Topic A: Defining Rate & Solving Rate Problems

Investigate and use rate in real-world situations.

6.RP.A.3 6.RP.A.3.B

Define rate and unit rate, and find rates from situations involving ratios.

6.RP.A.2 6.RP.A.3.B

Find unit rates and use them to solve problems.

6.RP.A.2 6.RP.A.3.B

Compare situations using unit rates, including speed, price, and work problems.

6.RP.A.3.B

Solve challenging problems involving unit rate.

6.RP.A.2 6.RP.A.3 6.RP.A.3.B

Topic B: Measurement Unit Conversions

Reason with measurement units and solve unit conversion problems using different strategies.

6.RP.A.3.D

Solve measurement unit conversion problems.

6.RP.A.3.D

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.

6.RP.A.3.C

Convert between fractions, percent, and decimals.

6.RP.A.3.C

Find a percent of a quantity.

6.RP.A.3.C

Find the whole quantity, given a part and percent.

6.RP.A.3.C

Solve percent problems, including finding percent when given a part and a whole.

6.RP.A.3.C

Solve multi-step problems involving rate and percent.

6.RP.A.2 6.RP.A.3 6.RP.A.3.C 6.RP.A.3.D

Unit Rates and Percent

Objective

Common Core Standards

Core Standards

Ratios and Proportional Relationships

Foundational Standards

Measurement and Data

Measurement and Data

Measurement and Data

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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