*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.”*

**Subject Area:**Mathematics

**Grade:**6

**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 Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved - Archived

**Assessed:**Yes

**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

**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

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Perspectives Video: Professional/Enthusiasts

## Perspectives Video: Teaching Ideas

## Problem-Solving Tasks

## Student Center Activity

## Text Resource

## Tutorial

## Video/Audio/Animations

## STEM Lessons - Model Eliciting Activity

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

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.

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.

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.

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 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?

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.

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.

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

## MFAS Formative Assessments

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

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

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

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

## Student Resources

## Original Student Tutorial

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

Type: Original Student Tutorial

## Problem-Solving Tasks

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

## 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

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

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

## Problem-Solving Tasks

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

## Video/Audio/Animation

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