### Examples

Tamika can read 500 words in 3 minutes. Her reading rate can be described as which is equivalent to the unit rate of 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.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**6

**Strand:**Algebraic Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Rate
- Unit Rate

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 5, students represented the division of two whole numbers as a fraction. In doing this, students started to work with a ratio relationship that relates parts to wholes. In grade 6, students extend this concept to include rates, which are ratios between quantities that are most often in different units. Students use ratio relationships to describe unit rates and percentage relationship and use the division of positive rational numbers to calculate unit rates from rates. In grade 7, students learn that a unit rate is the same as a constant of proportionality in a proportional relationship between two variables.- Instruction connects rate and unit rate to student understanding of equivalent fractions from elementary school in both numeric and picture or model forms. Students can use the models to represent the situations in different ways
*(MTR.5.1)*. - Allow student flexibility in accepting both simplified and non-simplified responses for rates unless unit rate is the specified or expected form.

### Common Misconceptions or Errors

- Students may incorrectly identify what is being compared or the order of quantities being compared by the rate.
- Students may have difficulty connecting a unit rate, which is represented by a single number, to a ratio or non-unit rate, which may be represented by two numbers.

### Strategies to Support Tiered Instruction

- Instruction includes the use of manipulatives and models to represent the provided rates and then to use multiplicative reasoning to determine the rate of one unit. Manipulatives and models include snap cubes, marbles, bar models, number lines or rate tables to help visually represent the relationship.
- Instruction includes the use of manipulatives to allow for students to explore the meaning of a unit rate. The teacher should provide two different counters to represent a rate equivalent to a whole number unit rate and then co-model the division of the counters into equal groups to determine how many counters of one color are needed to represent a single counter of the other color.
- For example: At the grocery store, you paid $9.00 for 3 pounds of apples. What is the unit price paid per pound of apples?

- For example: At the grocery store, you paid $9.00 for 3 pounds of apples. What is the unit price paid per pound of apples?

### Instructional Tasks

*Instructional Task 1*In buying ground beef for hamburgers, there are several packages from which to choose as shown in the table below.

**(MTR.6.1, MTR.7.1)**

- Part A. Predict how much it would cost for a pound of beef. Explain why your prediction is reasonable.
- Part B. What is the unit cost of the ground beef? Does the unit cost differ by the package size at this store?

*Instructional Task 2*The Jones family is planning on expanding their garden so that they can plant more vegetables. The ratio of the area of the old garden to the area of the new garden is 4¼:8 ¾. Convert this ratio to a unit rate and explain what it means in this context.

**(MTR.4.1)**

*Instructional Task 3*

**(MTR.2.1, MTR.4.1, MTR.5.1)**- Part A. In your group, use the chart below to determine the rate and unit rate in miles per minute.
- Part B. Which form would be most efficient for this context? Why?

### Instructional Items

*Instructional Item 1*

At the grocery store, you paid $9.87 for 3.3 pounds of apples. What is the unit price paid per pound of apples?

Instructional Item 2

Instructional Item 2

Brenda wants to buy one of the three cereals listed below. Determine which box is the best buy. Show and explain how you determined this.

- 16 ounces of Frosted Flurries for $3.50
- 12.4 ounces of Chocolate O’s for $2.42
- 11.5 ounces of Cinnamon Grahams for $2.35

**The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.*

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

## Perspectives Video: Teaching Idea

## Problem-Solving Tasks

## Tutorials

## STEM Lessons - Model Eliciting Activity

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.

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.

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.

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.

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

## MFAS Formative Assessments

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

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

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

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

## Original Student Tutorials Mathematics - Grades 6-8

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

## Original Student Tutorial

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

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

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

Students are asked to use a given ratio to determine if two different interpretations of the ratio are correct and to determine the maximum quantity that could be purchased within a given context.

Type: Problem-Solving Task

Students are asked apply knowledge of ratios to answer several questions regarding speed, distance and time.

Type: Problem-Solving Task

## Tutorials

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

Type: Tutorial

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

Type: Tutorial

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

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

## Perspectives Video: Professional/Enthusiast

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

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

Students are asked to use a given ratio to determine if two different interpretations of the ratio are correct and to determine the maximum quantity that could be purchased within a given context.

Type: Problem-Solving Task

Students are asked apply knowledge of ratios to answer several questions regarding speed, distance and time.

Type: Problem-Solving Task