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Unit Rate Worksheets

These free  unit rate worksheets  will help develop mastery of unit rates.  You will learn to work with unit rates in graphs, tables, and word problems. Each math worksheet is accompanied by an answer key, is printable, and can be customized to fit your needs.

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Percents and Rates

New york state common core math module 1, grade 6, lesson 24.

• Students understand that percents are related to part-to-whole ratios and rates where the whole is 100. • Students model percents and write a percent as a fraction over 100 or a decimal to the hundredths place.

• Percent means out of 100. Therefore, percents are fractions with a denominator of 100. We can create models of percents. One example would be to shade a 10 x 10 grid. Each square in a 10 x 10 grid represents 1% or 0.01.

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Math  /  6th Grade  /  Unit 2: Unit Rates and Percent

Unit Rates and Percent

Students investigate rates and percentages by identifying the rates associated with a ratio, defining a percent as a rate per 100, and applying strategies to solve rate and percent problems.

Unit Summary

In Unit 2, 6th grade students continue and extend their study of ratios to investigate rates and percentages. Using their knowledge of ratios, students will learn to identify two rates associated with a ratio and use them as efficient strategies to solve rate problems. Students will draw on their prior knowledge of the two measurement systems, and see unit conversions as applications of ratio and rate problems. Lastly, students will define a percent as a rate per 100, and understand that the strategies you use to solve a rate problem can also be applied to solve a percent problem. Throughout the entire unit, students will draw on their ability to reason abstractly and quantitatively (MP.2). As they work with different unit rates and conversion factors, students will need to attend to the units at hand, what the quantities mean, and how all of the pieces fit together. Calculators are recommended for several lessons in order to provide students with the option to use the tool in their calculations (MP.5).

In 4th grade and 5th grade , students interpreted fractions as division problems and began to make the connection between fractions and decimals. They multiplied fractions by whole numbers and other fractions in context of real-world problems, and they reasoned about what happens to a quantity when you multiply it by a number greater than one or less than one. Students will draw on these prior skills and understandings as they make connections between unit rates and fractions, and between fractions, decimals, and percentages. 

Beyond this unit, students will revisit percentages in Unit 6 when they study equations as another strategy to solve percent problems. In 7th grade , students will solve even more complex ratio, rate, and percent problems involving, for example, tax and percent increase or decrease. Additionally, students will investigate and analyze proportional relationships between quantities, and use more efficient and abstract methods to solve problems. For example, in 7th grade , students will learn to set up and solve proportion equations, using their knowledge of unit rates and equivalent ratios. (Note that using proportions to solve ratio or rate problems is not an expectation in sixth grade).

Pacing: 19 instructional days (14 lessons, 4 flex/review days, 1 assessment day)

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The following assessments accompany Unit 2.

Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.

Pre-Unit Student Self-Assessment

Have students complete the Mid-Unit Assessment after lesson 7.

Use the resources below to assess student understanding of the unit content and action plan for future units.

Post-Unit Assessment

Post-Unit Assessment Answer Key

Post-Unit Student Self-Assessment

Use student data to drive instruction with an expanded suite of assessments. Unlock Pre-Unit and Mid-Unit Assessments, and detailed Assessment Analysis Guides to help assess foundational skills, progress with unit content, and help inform your planning.

Intellectual Prep

Suggestions for how to prepare to teach this unit

Before you teach this unit, unpack the standards, big ideas, and connections to prior and future content through our guided intellectual preparation process. Each Unit Launch includes a series of short videos, targeted readings, and opportunities for action planning to ensure you're prepared to support every student.

Internalization of Standards via the Post-Unit Assessment

• Standards that each question aligns to
• Strategies and representations used in daily lessons
• Relationship to Essential Understandings of unit 
• Lesson(s) that Assessment points to

Internalization of Trajectory of Unit

• Read and annotate the Unit Summary.
• Notice the progression of concepts through the unit using the Lesson Map.

Essential Understandings

• Connection to Post-Unit Assessment questions
• Identify key opportunities to engage students in academic discourse. Read through our Teacher Tool on Academic Discourse and refer back to it throughout the unit.

Unit-Specific Intellectual Prep

• The Progressions for the Common Core State Standards in Mathematics 6-7, Ratios and Proportional Relationships  is valuable to read before the unit.
• UnboundEd also has a great 6th grade content guide on ratios, Ratios: Unbound, A Guide to Grade 6 Mathematics Standards .
• Read the following table that includes models used throughout the unit.

The central mathematical concepts that students will come to understand in this unit

• A rate, associated with a ratio a:b, is a/b or b/a units of one quantity per 1 unit of the other quantity. For example, if a person walks 6 miles in 2 hours, the person is traveling at a rate of 3 miles per hour, or equivalently a rate of 1/3 hour per mile. 
• A percent is a rate per 100; percent problems can be solved using the same strategies that are used for other rate problems.
• There are many applications to rate, including unit price, constant speed, and measurement conversions, that can be solved using several different strategies, such as using double number lines, tables, tape diagrams, and the unit rate. 

Terms and notation that students learn or use in the unit

conversion rate

customary system

equivalent ratio

metric system

percent/ percentage

To see all the vocabulary for Unit 2, view our 6th Grade Vocabulary Glossary .

The materials, representations, and tools teachers and students will need for this unit

• Calculators (1 per student) — It is recommended that students use calculators in this lesson since some of the problems involve decimals. Students have experience with calculating with decimals from fifth grade, but they will study them more in depth and with fluency in Unit 3. Calculators will ensure the focus of the lesson is on the concepts and reasoning, rather than calculations (MP.5).
• 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.

To see all the materials needed for this course, view our 6th Grade Course Material Overview .

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.

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

Solve challenging problems involving unit rate.

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

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Topic B: Measurement Unit Conversions

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

Solve measurement unit conversion problems.

Topic C: Percent

Define percent as a rate per 100. Find percentages of 100 and 1.

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

Common Core Standards

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

The content standards covered in this unit

Ratios and Proportional Relationships

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?

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.

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

Foundational Standards

Standards covered in previous units or grades that are important background for the current unit

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 — 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 — 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.

Number and Operations in Base Ten

5.NBT.B.6 — Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Number and Operations—Fractions

4.NF.B.4.B — Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

4.NF.B.4.C — Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

4.NF.C.6 — Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

5.NF.B.3 — Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

5.NF.B.4.A — Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

5.NF.B.5 — Interpret multiplication as scaling (resizing), by:

5.NF.B.5.A — Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

5.NF.B.5.B — Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.

5.NF.B.6 — Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

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."

Future Standards

Standards in future grades or units that connect to the content in this unit

Expressions and Equations

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.EE.C.9 — Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

7.RP.A.1 — Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ^1/2/_1/4 miles per hour, equivalently 2 miles per hour.

7.RP.A.2 — Recognize and represent proportional relationships between quantities.

7.RP.A.3 — Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Standards for Mathematical Practice

CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6 — Attend to precision.

CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.

Understanding and Representing Ratios

Multi-Digit and Fraction Computation

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Unit 3: Rates and percentages

About this unit.

Rates and percentages are a new and exciting real world application of arithmetic! They come up frequently in everyday life—from figuring out sale prices to calculating tips at restaurants. These are concepts you can actually use every day!

Intro to rates

• Intro to rates (Opens a modal)
• Solving unit rate problem (Opens a modal)
• Solving unit price problem (Opens a modal)
• Rate problems (Opens a modal)
• Comparing rates example (Opens a modal)
• Rate review (Opens a modal)
• Unit rates Get 5 of 7 questions to level up!
• Rate problems Get 3 of 4 questions to level up!
• Comparing rates Get 3 of 4 questions to level up!

Intro to percents

• The meaning of percent (Opens a modal)
• Meaning of 109% (Opens a modal)
• Percents from fraction models (Opens a modal)
• Intro to percents Get 5 of 7 questions to level up!
• Percents from fraction models Get 3 of 4 questions to level up!

Visualize percents

• Finding percentages with a double number line (Opens a modal)
• Finding the whole with a tape diagram (Opens a modal)
• Find percents visually Get 5 of 7 questions to level up!

Equivalent representations of percent problems

• Fraction, decimal, and percent from visual model (Opens a modal)
• Converting percents to decimals & fractions example (Opens a modal)
• Percent of a whole number (Opens a modal)
• Ways to rewrite a percentage (Opens a modal)
• Converting between percents, fractions, & decimals (Opens a modal)
• Finding common percentages (Opens a modal)
• Converting percents and fractions review (Opens a modal)
• Converting decimals and percents review (Opens a modal)
• Equivalent representations of percent problems Get 3 of 4 questions to level up!
• Benchmark percents Get 5 of 7 questions to level up!

Percent problems

• Finding a percent (Opens a modal)
• Finding percents Get 5 of 7 questions to level up!

Percent word problems

• Percent word problem: recycling cans (Opens a modal)
• Rates and percentages FAQ (Opens a modal)
• Percent word problems Get 5 of 7 questions to level up!

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Unit Percents Homework 1

Displaying top 8 worksheets found for - Unit Percents Homework 1 .

Some of the worksheets for this concept are Percents homework 1, Handouts on percents 2 percent word problems, Unit 1 fractions decimals and percents homework unit 1, Ratio proportion and percent work, Unit 2 fractions decimals percents and scientific notation home, Percents homework 4, Percents homework 3, Fractions decimals and percents.

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1. Percents Homework #1

2. handouts on percentspage 2 percent word problems ..., 3. unit 1: fractions, decimals, and percents homework page unit 1 ..., 4. ratio, proportion and percent worksheet, 5. unit 2: fractions, decimals, percents, and scientific notation home ..., 6. percents homework #4, 7. percents homework #3, 8. fractions, decimals, and percents.

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