# MAFS.6.RP.1.1Archived Standard Export Print
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.”
General Information
Subject Area: Mathematics
Domain-Subdomain: Ratios & Proportional Relationships
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Understand ratio concepts and use ratio reasoning to solve problems. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Whole numbers should be used for the quantities. Ratios can be expressed as fractions, with “:” or with words. Items may involve mixed units within each system (e.g. convert hours/min to seconds). Context itself does not determine the order. Limit use of percent to MAFS.6.RP.1.3c.
• Calculator :

No

• Context :

Allowable

Sample Test Items (2)
• Test Item #: Sample Item 1
• Question: Jordan has 3 blue marbles and 8 red marbles.

What is the ratio of blue marbles to red marbles?

• Difficulty: N/A
• Type: MC: Multiple Choice

• Test Item #: Sample Item 2
• Question: Nora’s fruit stand sold 12 fewer pineapples than bananas last week. The stand sold 48 bananas last week.

Complete the sentences to determine and interpret the ratio of bananas sold to pineapples sold. For each blank, fill in the circle before the word or phrase that is correct.

Last week, the ratio of bananas sold to pineapples sold was:

A. 1:4

B. 3:4

C. 4:1

D. 4:3

E. 4:5

This ratio means that for every

A. 1   banana(s) sold,

B. 3

C. 4

D. 5

the number of pineapples sold was

A. 1

B. 3

C. 4

D. 5

• Difficulty: N/A
• Type: ETC: Editing Task Choice

## 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))
1508000: M/J Fitness - Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1508100: M/J Education Gymnastics/Educational Dance - Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2019 (course terminated))
1508600: M/J Comprehensive - Grades 6/7 (Specifically in versions: 2014 - 2015, 2015 - 2019 (course terminated))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
7912110: Fundamental Explorations in Mathematics 1 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))
1508010: M/J Education Gymnastics/Educational Dance - Grade 6 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
1508060: M/J Comprehensive Physical Education Grade 6/7 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

## Related Resources

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

## Formative Assessments

Writing Ratios:

Students are asked to write part-to-part and part-to-whole ratios using values given in a table.

Type: Formative Assessment

Interpreting Ratios:

Students are asked to explain the meaning of ratios in the context of problems.

Type: Formative Assessment

Comparing Time:

Students are given a scenario involving an additive comparison of two quantities, asked to write a ratio, and explain its meaning.

Type: Formative Assessment

Comparing Rectangles:

Students are asked to determine which of three given comparisons contains a correctly computed ratio in a context involving rectangles.

Type: Formative Assessment

## Lesson Plans

Champion Volleyball Team:

Students will help create a championship volleyball team by selecting 4 volleyball players to be added to open positions on the team. The students will use quantitative (ratios and decimals) and qualitative data to make their decisions.

Type: Lesson Plan

Genetics can be a Monster!:

In this lesson, students will use Punnett squares to calculate the probabilities of different genotypes and phenotypes produced by genetic crosses.

Type: Lesson Plan

All “Tired” Up:

In this lesson students will utilize mathematical computation skills involving percentages and critical thinking skills to select the best tire deals advertised.

Type: Lesson Plan

Selecting a Car for Display/Ratio:

Teacher will use students’ responses to their selection of the most efficient car to create and introduce ratio concepts and reasoning. The activities can be completed as a whole group, a few groups, or individually. The teacher may also alternate so that certain parts of the activities can be whole group, few groups, or individually according to the classrooms functional, behavioral, and academic levels.

Type: Lesson Plan

Best Day Care Center for William:

This MEA requires students to formulate a comparison-based solution to a problem involving choosing the BEST daycare based upon safety, playground equipment, meals, teacher to student ratio, cost, holiday availability and toilet training availability. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client. Students will receive practice on calculating a discount, finding the sum of the discounts, working with ratios and ranking day cares based on the data given.

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.

Type: Lesson Plan

RATIOS: Compare This!:

Students will explore ratios with models; express ratios in fraction form (simplest form), by use of a colon, and with words as a relationship between two quantities.

Type: Lesson Plan

PROFITS BY PROPORTIONS:

Students will use proportions to determine how much to charge for a ticket to their concert performance. They will justify the price of tickets based upon the cost of facility rental and the number of tickets they anticipate being able to sell.

Type: Lesson Plan

“My Favorite Recipe.” An introduction to ratios and rates.:

This lesson shows how ratios can be indicated in words such as "to", "for every", "out of every." In grade 6, rates mean "for each 1," "for each," and "per." The students will use diagrams and tables to build their ability to use proportional thinking. At the end of the lesson, the students will increase or decrease recipes they find in cookbooks.

Type: Lesson Plan

The Concept of Ratios:

This lesson introduces students to the term ratio, its meaning and use, and the various ways in which a ratio can be presented.

Type: Lesson Plan

Paper Route Logic:

The main problem students will need to solve is helping Lily Rae Wridenhoud find a route that will afford her the quickest time, least distance and highest customer satisfaction rating. Students will be given a map of all the streets leading around the neighborhood and customer rating (smiley faces). Students will need to use a ruler to figure out distances as well as decide elevation numbers on the topographic map. Then they will write out the route they have chosen to give Lily, and write a short explanation as to why this is the quickest and least distance traveled. Students will then be asked to look over their findings and be informed that some of the old clients have canceled the paper delivery and a few new paper clients have signed on. Does their new route still fit their findings?

Type: Lesson Plan

## Original Student Tutorial

Equivalent Ratios:

Help Lily identify and create equivalent ratios in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Professional/Enthusiasts

Mathematical Thinking for Ceramic 3D Printing:

In this video, Matthew Lawrence describes how mathematical thinking is important for 3D printing with ceramic materials.

Type: Perspectives Video: Professional/Enthusiast

The Science and Math Behind Sour Fizzy Candy:

Master candymaker Wes Raley describes the process and science behind making sour fizzy candy.

Type: Perspectives Video: Professional/Enthusiast

Coffee Mathematics: Ratios and Total Dissolvable Solids:

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

Type: Perspectives Video: Professional/Enthusiast

Motorcycle Mathematics: Tuning Compression Ratios for Performance:

Get revved up about math when this motorcycle mechanic explains compression ratios.

Type: Perspectives Video: Professional/Enthusiast

Isotopes and Paleoclimates:

Let this researcher explain how studying fossils and isotopes can help us understand ancient climate conditions!

Type: Perspectives Video: Professional/Enthusiast

Ratios of Horse Feed:

An equestrian describes, nay, explains mathematics principles applied to feeding a horse!

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Ideas

Sling Psychrometers for Measuring Relative Humidity!:

Dave Rodriguez demonstrates the use of a sling psychrometer to compare wet and dry-bulb temperatures to determine relative humidity.

Type: 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.

Type: Perspectives Video: Teaching Idea

The Escalator, Assessment Variation:

Students are provided seven choices and are asked to determine the ratios that are correct for the given context.

Voting for Two, Variation 3:

This problem is the third in a series of tasks set in the context of a class election. Students are given a ratio and total number of voters and are asked to determine the difference between the winning number of votes received and the number of votes needed for victory.

Voting for Two, Variation 1:

This is the first and most basic problem in a series of seven problems, all set in the context of a classroom election. Students are given a ratio and total number of voters and are asked to determine the number of votes received by each candidate.

Voting for Two, Variation 2:

This is the second in a series of tasks that are set in the context of a classroom election. It requires students to understand what ratios are and apply them in a context. The simple version of this question just asked how many votes each gets. This has the extra step of asking for the difference between the votes.

Voting for Two, Variation 4:

This is the fourth in a series of tasks about ratios set in the context of a classroom election. Given only a ratio, students are asked to determine the fractional difference between votes received and votes required.

Games at Recess:

Students are asked to write complete sentences to describe ratios for the context.

Ratio of Boys to Girls:

Use the information provided to find the ratio of boys to girls. Tasks like these help build appropriate connections between ratios and fractions. Students often write ratios as fractions, but in fact we reserve fractions to represent numbers or quantities rather than relationships between quantities. In some textbooks, a distinction is made between a ratio, which is assumed to have a common unit for both quantities, and a rate, which is defined to be a quotient of two quantities with different units (e.g. a ratio of the number of miles to the number of hours). No such distinction is made in the standards and hence, the two quantities in a ratio may or may not have a common unit.

Space Math - Comparing Planets Orbiting Other Stars:

This NASA lesson utilizes real world data about the size of planets orbiting other stars. Students are asked to use this data to compare the size of the planets to Earth and Jupiter. Lesson includes a visual representation and an answer key.

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Text Resource

This informational text resource is intended to support reading in the content area. Although scientists haven't determined a specific reason why one baseball player's hitting streak improves his whole team's performance, they have observed a very real mathematical pattern. There may be many reasons for the phenomenon, but no one has found them out yet.

Type: Text Resource

## 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

## Video/Audio/Animations

Atlantean Dodge Ball (An entetaining look at appropriate use of ratios and proportions):

Ratio errors confuse one of the coaches as two teams face off in an epic dodgeball tournament. See how mathematical techniques such as tables, graphs, measurements and equations help to find the missing part of a proportion.

Atlantean Dodgeball addresses number and operations standards, the algebra standard, and the process standard, as established by the National Council of Teachers of Mathematics (NCTM). It guides students in:

• Understanding and using ratios and proportions to represent quantitative relationships.
• Relating and comparing different forms of representation for a relationship.
• Developing, analyzing, and explaining methods for solving problems involving proportions, such as scaling and finding equivalent ratios.
• Representing, analyzing, and generalizing a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.

Type: Video/Audio/Animation

Bad Date (A Real World Application of Ratios):

In this video from Math Snacks, a women goes on three dates, after which she analyzes the ratio of how many words she speaks compared to the number of words her date speaks. By attaining a 1:1 ratio of words, she attains her "Happily Ever After." (Apparently, in her eyes, this is the only desirable quality in a man that really matters.) A learner's guide, teachers guide, and transcript of the video is included.

Type: Video/Audio/Animation

## STEM Lessons - Model Eliciting Activity

All “Tired” Up:

In this lesson students will utilize mathematical computation skills involving percentages and critical thinking skills to select the best tire deals advertised.

Best Day Care Center for William:

This MEA requires students to formulate a comparison-based solution to a problem involving choosing the BEST daycare based upon safety, playground equipment, meals, teacher to student ratio, cost, holiday availability and toilet training availability. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client. Students will receive practice on calculating a discount, finding the sum of the discounts, working with ratios and ranking day cares based on the data given.

Champion Volleyball Team:

Students will help create a championship volleyball team by selecting 4 volleyball players to be added to open positions on the team. The students will use quantitative (ratios and decimals) and qualitative data to make their decisions.

Paper Route Logic:

The main problem students will need to solve is helping Lily Rae Wridenhoud find a route that will afford her the quickest time, least distance and highest customer satisfaction rating. Students will be given a map of all the streets leading around the neighborhood and customer rating (smiley faces). Students will need to use a ruler to figure out distances as well as decide elevation numbers on the topographic map. Then they will write out the route they have chosen to give Lily, and write a short explanation as to why this is the quickest and least distance traveled. Students will then be asked to look over their findings and be informed that some of the old clients have canceled the paper delivery and a few new paper clients have signed on. Does their new route still fit their findings?

Selecting a Car for Display/Ratio:

Teacher will use students’ responses to their selection of the most efficient car to create and introduce ratio concepts and reasoning. The activities can be completed as a whole group, a few groups, or individually. The teacher may also alternate so that certain parts of the activities can be whole group, few groups, or individually according to the classrooms functional, behavioral, and academic levels.

The Best Domestic Car:

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

## MFAS Formative Assessments

Comparing Rectangles:

Students are asked to determine which of three given comparisons contains a correctly computed ratio in a context involving rectangles.

Comparing Time:

Students are given a scenario involving an additive comparison of two quantities, asked to write a ratio, and explain its meaning.

Interpreting Ratios:

Students are asked to explain the meaning of ratios in the context of problems.

Writing Ratios:

Students are asked to write part-to-part and part-to-whole ratios using values given in a table.

## Original Student Tutorials Mathematics - Grades 6-8

Equivalent Ratios:

Help Lily identify and create equivalent ratios in this interactive tutorial.

## Student Resources

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

## Original Student Tutorial

Equivalent Ratios:

Help Lily identify and create equivalent ratios in this interactive tutorial.

Type: Original Student Tutorial

Voting for Two, Variation 3:

This problem is the third in a series of tasks set in the context of a class election. Students are given a ratio and total number of voters and are asked to determine the difference between the winning number of votes received and the number of votes needed for victory.

Voting for Two, Variation 1:

This is the first and most basic problem in a series of seven problems, all set in the context of a classroom election. Students are given a ratio and total number of voters and are asked to determine the number of votes received by each candidate.

Voting for Two, Variation 2:

This is the second in a series of tasks that are set in the context of a classroom election. It requires students to understand what ratios are and apply them in a context. The simple version of this question just asked how many votes each gets. This has the extra step of asking for the difference between the votes.

Voting for Two, Variation 4:

This is the fourth in a series of tasks about ratios set in the context of a classroom election. Given only a ratio, students are asked to determine the fractional difference between votes received and votes required.

Games at Recess:

Students are asked to write complete sentences to describe ratios for the context.

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## 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

## Video/Audio/Animation

Atlantean Dodge Ball (An entetaining look at appropriate use of ratios and proportions):

Ratio errors confuse one of the coaches as two teams face off in an epic dodgeball tournament. See how mathematical techniques such as tables, graphs, measurements and equations help to find the missing part of a proportion.

Atlantean Dodgeball addresses number and operations standards, the algebra standard, and the process standard, as established by the National Council of Teachers of Mathematics (NCTM). It guides students in:

• Understanding and using ratios and proportions to represent quantitative relationships.
• Relating and comparing different forms of representation for a relationship.
• Developing, analyzing, and explaining methods for solving problems involving proportions, such as scaling and finding equivalent ratios.
• Representing, analyzing, and generalizing a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.

Type: Video/Audio/Animation

## Parent Resources

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

Voting for Two, Variation 3:

This problem is the third in a series of tasks set in the context of a class election. Students are given a ratio and total number of voters and are asked to determine the difference between the winning number of votes received and the number of votes needed for victory.

Voting for Two, Variation 1:

This is the first and most basic problem in a series of seven problems, all set in the context of a classroom election. Students are given a ratio and total number of voters and are asked to determine the number of votes received by each candidate.

Voting for Two, Variation 2:

This is the second in a series of tasks that are set in the context of a classroom election. It requires students to understand what ratios are and apply them in a context. The simple version of this question just asked how many votes each gets. This has the extra step of asking for the difference between the votes.

Voting for Two, Variation 4:

This is the fourth in a series of tasks about ratios set in the context of a classroom election. Given only a ratio, students are asked to determine the fractional difference between votes received and votes required.

Games at Recess:

Students are asked to write complete sentences to describe ratios for the context.

## Video/Audio/Animation

Atlantean Dodge Ball (An entetaining look at appropriate use of ratios and proportions):

Ratio errors confuse one of the coaches as two teams face off in an epic dodgeball tournament. See how mathematical techniques such as tables, graphs, measurements and equations help to find the missing part of a proportion.

Atlantean Dodgeball addresses number and operations standards, the algebra standard, and the process standard, as established by the National Council of Teachers of Mathematics (NCTM). It guides students in:

• Understanding and using ratios and proportions to represent quantitative relationships.
• Relating and comparing different forms of representation for a relationship.
• Developing, analyzing, and explaining methods for solving problems involving proportions, such as scaling and finding equivalent ratios.
• Representing, analyzing, and generalizing a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.

Type: Video/Audio/Animation