# MA.6.AR.3.1

Given a real-world context, write and interpret ratios to show the relative sizes of two quantities using appropriate notation: , a to b, or a:b where b ≠ 0.

### Clarifications

Clarification 1: Instruction focuses on the understanding that a ratio can be described as a comparison of two quantities in either the same or different units.

Clarification 2: Instruction includes using manipulatives, drawings, models and words to interpret part-to-part ratios and part-to-whole ratios.

Clarification 3: The values of a and b are limited to whole numbers.

General Information
Subject Area: Mathematics (B.E.S.T.)
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.1: Given a real-world context, write and interpret ratios to show the relative sizes of two quantities using notation: a/b, a to b, or a:b where b ≠ 0 with guidance and support.

## 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

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

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

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

## Teaching Idea

Students communicate mathematical ideas and visually represent ideas by constructing charts, graphs, and scale drawings based on information cards about various marine animals.

Type: Teaching Idea

## 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

## 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

## Parent Resources

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