*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.*

**Subject Area:**Mathematics

**Grade:**7

**Domain-Subdomain:**Ratios & Proportional Relationships

**Cluster:**Level 2: Basic Application of Skills & Concepts

**Cluster:**Analyze proportional relationships and use them to solve real-world and mathematical 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

**Assessed:**Yes

**Assessment Limits :**

The item stem must include at least one fraction. Ratios may be expressed as fractions, with “:” or with words. Units may be the same or different across the two quantities.**Calculator :**yes

**Context :**allowable

**Test Item #:**Sample Item 1**Question:**A recipe used cup of sugar for every 2 teaspoons of vanilla. How much sugar was used per teaspoon of vanilla?**Difficulty:**N/A**Type:**MC: Multiple Choice

**Test Item #:**Sample Item 2**Question:**A recipe calls for cup of sugar for every 4 teaspoons of vanilla. How much vanilla should be used for every 1 cup of sugar?**Difficulty:**N/A**Type:**MC: Multiple Choice

**Test Item #:**Sample Item 3**Question:**A recipe calls for cup of sugar for every 2 teaspoons of vanilla. What is the unit rate in cups per teaspoon?**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 4**Question:**A recipe calls for cup of sugar for every 4 teaspoons of vanilla. What is the unit rate in teaspoons per cup?**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 5**Question:**A recipe calls for cup of sugar for every teaspoon of vanilla. What is the unit rate of cups per teaspoon?

**Difficulty:**N/A**Type:**EE: Equation Editor

## Related Courses

## Related Access Points

## Related Resources

## Assessments

## Formative Assessments

## Lesson Plans

## Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

## Problem-Solving Tasks

## Teaching Ideas

## Tutorials

## Virtual Manipulative

## STEM Lessons - Model Eliciting Activity

Students at a local middle school are interested in attending a basketball tournament in Orlando. There is an entrance fee and hotel costs to consider. Students must calculate the total cost and the cost per student to attend the tournament. Each hotel has different qualities that could influence the students' choice of which hotel is best for their team.

Students will calculate unit rate & circumference, compare & order decimals, convert metric units, and round decimals. Bubble Burst Corporation has developed some chewing gum prototypes and has requested the students to assist in the selection of which gum prototypes will be mass produced by using both quantitative and qualitative data to rank the prototypes for Bubble Burst Corporation.

This MEA requires students to formulate a comparison-based solution to a problem involving finding the best choice on purchasing cooking ingredients for a family who runs a restaurant considering different aspects. 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 are presented with the task of evaluating several types of fabric based on each of its characteristics. They need to analyze their current uniform needs and decide by choosing which type of fabric will best fit their uniform needs. Then they have to write a report explaining the procedure they used to analyze their choices, reasoning for their ranking and make the requested recommendations.

The principal of Central Middle School is thinking of adding pizza to the lunch menu on Mondays and Fridays but needs help deciding the costs per slice and what students think is important about the pizza. After the students' initial decision about the pizza the principal remembers that there is a delivery charge.The students must revisit their decision and do additional calculations to see if their original process still works.

This MEA requires students to formulate a comparison-based solution to a problem involving choosing the best shipping options for importing machine parts from India to US. 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.

This MEA requires students to formulate a comparison-based solution to a problem involving finding the best plan for installing tile floor considering different aspects. 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.

In this 7^{th} grade MEA Laura Banks requests a consulting firm, JJ Consulting, to help her make a decision on an employer. Students are to use the data table to calculate unit rates (nightly rate and hourly rate) and then rank her choices and write a recommendation with the procedure used to come up with the ranking.

## MFAS Formative Assessments

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

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

## Student Resources

## Problem-Solving Tasks

Students are asked to use proportional reasoning to answer a series of questions in the context of a recipe.

Type: Problem-Solving Task

This task asks students to solve a problem in a context involving constant speed. This task provides a transition from working with ratios involving whole numbers to ratios involving fractions. This problem can be thought of in several ways; in particular, this problem also provides an opportunity for students to work with the "How many in one group?'' interpretation of division.

Type: Problem-Solving Task

Use the information provided to find out how long it will take Molly to run one mile.

Type: Problem-Solving Task

This problem requires a comparison of rates where one is given in terms of unit rates, and the other is not. See "Music Companies, Variation 2" for a task with a very similar setup but is much more involved and so illustrates MAFS.7.RP.1.3.

Type: Problem-Solving Task

This activity asks the student to use unit rate and proportional reasoning to determine which of two runners is the fastest.

Type: Problem-Solving Task

## Tutorials

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

Type: Tutorial

One common application of rate is determining speed. Watch as we solve a rate problem finding speed in meters per second using distance (in meters) and time (in seconds).

Type: Tutorial

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

## Problem-Solving Tasks

Students are asked to use proportional reasoning to answer a series of questions in the context of a recipe.

Type: Problem-Solving Task

This task asks students to solve a problem in a context involving constant speed. This task provides a transition from working with ratios involving whole numbers to ratios involving fractions. This problem can be thought of in several ways; in particular, this problem also provides an opportunity for students to work with the "How many in one group?'' interpretation of division.

Type: Problem-Solving Task

Use the information provided to find out how long it will take Molly to run one mile.

Type: Problem-Solving Task

This problem requires a comparison of rates where one is given in terms of unit rates, and the other is not. See "Music Companies, Variation 2" for a task with a very similar setup but is much more involved and so illustrates MAFS.7.RP.1.3.

Type: Problem-Solving Task

This activity asks the student to use unit rate and proportional reasoning to determine which of two runners is the fastest.

Type: Problem-Solving Task