MA.6.AR.3.2

Given a real-world context, determine a rate for a ratio of quantities with different units. Calculate and interpret the corresponding unit rate.

Examples

Tamika can read 500 words in 3 minutes. Her reading rate can be described as begin mathsize 12px style fraction numerator 500 space w o r d s over denominator 3 space m i n u t e s end fraction end style which is equivalent to the unit rate of begin mathsize 12px style 166 2 over 3 end style words per minute.

Clarifications

Clarification 1: Instruction includes using manipulatives, drawings, models and words and making connections between ratios, rates and unit rates.

Clarification 2: Problems will not include conversions between customary and metric systems.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 6
Strand: Algebraic Reasoning
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.AR.3.AP.2: Given a rate, calculate the unit rate for a ratio with different units.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

Unit Rate Length:

Students are asked to write ratios and unit rates from fractional values.

Type: Formative Assessment

Unit Rate Area:

Students are asked to convert a ratio of mixed numbers to a unit rate and explain its contextual meaning.

Type: Formative Assessment

Comparing Unit Rates:

Students are asked to compute unit rates from values that include fractions.

Type: Formative Assessment

Computing Unit Rates:

Students are asked to compute and interpret unit rates in two different ways from values that include fractions and mixed numbers.

Type: Formative Assessment

Writing Unit Rates:

Students are given verbal descriptions of rates and asked to write them as unit rates.

Type: Formative Assessment

Identifying Unit Rates:

Students are asked to decide if given statements express unit rates.

Type: Formative Assessment

Explaining Rates:

Students are asked to explain the meaning of given rates and identify any that are unit rates.

Type: Formative Assessment

Book Rates:

Students write and explain the meaning of a ratio and corresponding unit rate in the context of a word problem.

Type: Formative Assessment

Lesson Plans

Cool Special Effects:

In this MEA, students will apply the concepts of heat transfer, especially convection. Students will analyze factors such as temperature that affect the behavior of fluids as they form convection currents.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Rate Your Local Produce Market:

The students will rank the local produce markets by using qualitative and quantitative data. The students will have to calculate unit rates and compare and order them.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Real Estate Rental Agency:

In this Model Eliciting Activity, MEA, students will choose the best location for a family relocating and will find the monthly costs per month to make the best decision.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

The Best Domestic Car:

In this MEA students will use problem-solving strategies to determine which car to recommend to Americans living in India.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Orange Juice Conversion:

In this MEA, the students will be able to convert measurements within systems and between systems. They will be able to use problem solving skills to create a process for ranking orange juices for a Bed and Breakfast.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Original Student Tutorial

Farmers Market: Ratios, Rates and Unit Rates:

Learn how to identify and calculate unit rates by helping Milo find prices per item at a farmer's market in this interactive tutorial.  

Type: Original Student Tutorial

Perspectives Video: Expert

Statistical Sampling Results in setting Legal Catch Rate :

Fish Ecologist, Dean Grubbs, discusses how using statistical sampling can help determine legal catch rates for fish that may be endangered.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiasts

Unit Rates in Swimming:

In this video, David Fermin demonstrates real-time estimates for monitoring swimming performance and physiology.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Unit Rate: Spring Water Bottling:

Nestle Waters discusses the importance of unit rate in the manufacturing process of bottling spring water.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Unit Rate and Florida Cave Formation:

How long does it take to form speleothems in the caves at Florida Caverns State Parks?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Pizza Pi: Area, Circumference & Unit Rate:

How many times larger is the area of a large pizza compared to a small pizza?  Which pizza is the better deal? Michael McKinnon of Gaines Street Pies talks about how the area, circumference and price per square inch is different depending on the size of the pizza.  

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Amping Up Violin Tuning with Math:

Kyle Dunn, a Tallahassee-based luthier and owner of Stringfest, discusses how math is related to music. 

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Building Scale Models to Solve an Archaeological Mystery:

An archaeologist describes how mathematics can help prove a theory about mysterious prehistoric structures called shell rings.

Type: Perspectives Video: Professional/Enthusiast

Coffee Mathematics: Ratios and Total Dissolvable Solids:

Math - the secret ingredient for an excellent cup of coffee!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Bicycle Mathematics: Selecting Gear Ratios for Performance:

Don't let math derail you. Learn how bicycle gears use ratios to help you ride comfortably on all kinds of terrain.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

KROS Pacific Ocean Kayak Journey: Calories, Distance, and Rowing Rates:

Food is fuel, especially important when your body is powering a boat across the ocean.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

KROS Pacific Ocean Kayak Journey: Calories, Exercise, and Metabolism Rates:

How much food do you need to cross the Pacific in a kayak? Get a calculator and a bag of almonds before you watch this.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Type: Perspectives Video: Professional/Enthusiast

Perspectives Video: Teaching Idea

Bicycle Mathematics: Speed and Distance Calculations:

Cycling involves a lot of real-time math when you use an on-board computer. Learn about lesson ideas and how computers help with understanding performance.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Tutorials

Determining Rates with Fractions:

This video demonstrates finding a unit rate from a rate containing fractions.

Type: Tutorial

Rate Problem With Fractions:

Watch as we solve a rate problem finding speed in meters per second using distance (in meters) and time (in seconds).

Type: Tutorial

Solving Unit Rate Problem:

This video demonstrates solving a unit rate problem using equivalent ratios.

Type: Tutorial

Solving Unit Price Problem:

This video demonstrates solving a unit price problem using equivalent ratios.

Type: Tutorial

Converting Speed Units:

In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.

Type: Tutorial

STEM Lessons - Model Eliciting Activity

Cool Special Effects:

In this MEA, students will apply the concepts of heat transfer, especially convection. Students will analyze factors such as temperature that affect the behavior of fluids as they form convection currents.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Orange Juice Conversion:

In this MEA, the students will be able to convert measurements within systems and between systems. They will be able to use problem solving skills to create a process for ranking orange juices for a Bed and Breakfast.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Rate Your Local Produce Market:

The students will rank the local produce markets by using qualitative and quantitative data. The students will have to calculate unit rates and compare and order them.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Real Estate Rental Agency:

In this Model Eliciting Activity, MEA, students will choose the best location for a family relocating and will find the monthly costs per month to make the best decision.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

The Best Domestic Car:

In this MEA students will use problem-solving strategies to determine which car to recommend to Americans living in India.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

MFAS Formative Assessments

Book Rates:

Students write and explain the meaning of a ratio and corresponding unit rate in the context of a word problem.

Comparing Unit Rates:

Students are asked to compute unit rates from values that include fractions.

Computing Unit Rates:

Students are asked to compute and interpret unit rates in two different ways from values that include fractions and mixed numbers.

Explaining Rates:

Students are asked to explain the meaning of given rates and identify any that are unit rates.

Identifying Unit Rates:

Students are asked to decide if given statements express unit rates.

Unit Rate Area:

Students are asked to convert a ratio of mixed numbers to a unit rate and explain its contextual meaning.

Unit Rate Length:

Students are asked to write ratios and unit rates from fractional values.

Writing Unit Rates:

Students are given verbal descriptions of rates and asked to write them as unit rates.

Original Student Tutorials Mathematics - Grades 6-8

Farmers Market: Ratios, Rates and Unit Rates:

Learn how to identify and calculate unit rates by helping Milo find prices per item at a farmer's market in this interactive tutorial.  

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorial

Farmers Market: Ratios, Rates and Unit Rates:

Learn how to identify and calculate unit rates by helping Milo find prices per item at a farmer's market in this interactive tutorial.  

Type: Original Student Tutorial

Perspectives Video: Professional/Enthusiast

Building Scale Models to Solve an Archaeological Mystery:

An archaeologist describes how mathematics can help prove a theory about mysterious prehistoric structures called shell rings.

Type: Perspectives Video: Professional/Enthusiast

Tutorials

Determining Rates with Fractions:

This video demonstrates finding a unit rate from a rate containing fractions.

Type: Tutorial

Rate Problem With Fractions:

Watch as we solve a rate problem finding speed in meters per second using distance (in meters) and time (in seconds).

Type: Tutorial

Solving Unit Price Problem:

This video demonstrates solving a unit price problem using equivalent ratios.

Type: Tutorial

Converting Speed Units:

In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.

Type: Tutorial

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Perspectives Video: Professional/Enthusiast

Building Scale Models to Solve an Archaeological Mystery:

An archaeologist describes how mathematics can help prove a theory about mysterious prehistoric structures called shell rings.

Type: Perspectives Video: Professional/Enthusiast