Strand: RATIOS AND PROPORTIONAL RELATIONSHIPS (6.RP)

Understand ratio concepts and use ratio reasoning to solve problems (Standards 6.RP.1–3).

Standard 6.RP.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. The following are examples of ratio language: “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.”

• Apples to Apples
The purpose of this task is to connect students' understanding of multiplicative relationships to their understanding of equivalent ratios.
• Bag of Marbles
The purpose of this task is to help students develop fluency in their understanding of the relationship between fractions and ratios. It provides an opportunity to translate from fractions to ratios and then back again to fractions.
• Chapter 1 - Mathematical Foundations (UMSMP)
This is Chapter 1 of the Utah Middle School Math: Grade 6 textbook. It provides a Mathematical Foundation for Ratio Relations.
• Chapter 1 - Student Workbook (UMSMP)
This is Chapter 1 of the Utah Middle School Math: Grade 6 student workbook. It covers the following topics: Ratio Relations.
• Evaluating Ratio Statements
The goal of this task is to assess student understanding of ratios. The task offers five questions, some of which can be addressed using ony the given ratio, whereas others require knowledge of the total number of students.
• Games at Recess
In this task, given the scenario of students playing games at recess, students are asked to compare different aspects of the games using ratios and then writing sentences to express those ratios.
• Grade 6 Math Module 1: Ratios and Unit Rates (EngageNY)
Students begin their sixth grade year investigating the concepts of ratio and rate. They use multiple forms of ratio language and ratio notation, and formalize understanding of equivalent ratios. Students apply reasoning when solving collections of ratio problems in real world contexts using various tools (e.g., tape diagrams, double number line diagrams, tables, equations and graphs). Students bridge their understanding of ratios to the value of a ratio, and then to rate and unit rate, discovering that a percent of a quantity is a rate per 100. The 35 day module concludes with students expressing a fraction as a percent and finding a percent of a quantity in real world concepts, supporting their reasoning with familiar representations they used previously in the module.
• Grade 6 Unit 2: Rate, Ratio, and Proportional Reasoning Using Equivalent Fractions (Georgia Standard
In this unit, students will gain a deeper understanding of proportional reasoning through instruction and practice, develop and use multiplicative thinking, develop a sense of proportional reasoning, develop the understanding that ratio is a comparison of two numbers or quantities, find percents using the same processes for solving rates and proportions and solve real-life problems involving measurement units that need to be converted.
• Gross Domestic Product: Unit Rates in the Real World
Using interactive maps from KQED students will examine the economic divide in European countries by looking at GDP. In the activity data from the maps is used to compare GDP among other countries. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Life Expectancy: Finding Ratio Relationships
This lesson using infographics examines how health factors such as obesity and hypertension have changed in the U.S. over the past decades. The classroom activity has students work with the mathematical concept of statistical analysis as they compare the life expectancy of men and women. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Many Ways to Say It
The purpose of this task is to help students understand and use ratio language.
• Mixtures
This activity will help students understand percentages and mixture problems by working with two piles of colored chips.
• One-Dimensional Scaling To Find Unknown Heights
An interactive activity helps students understand real-world application of ratios and asks them to scale a model of a T-Rex for a diorama. In the classroom activity students are asked to draw scale models. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Ratios and Proportional Relationships (6.RP) - 6th Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 6 - Ratios and Proportional Relationships
• Real World Ratio and Rate Problem: Bianca's Fifty Percent Solution
Viewers follow Bianca as she's drawn into a store by the discounts advertised in this video from Cyberchase. While shopping she understands that while discounts are nice they still can add up when shopping. The classroom activity asks students to calculate the savings on an item when various discounts are applied. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Representing a Context with a Ratio
The purpose of this task is to introduce students to ratios and ratio language.
• Scaling Up Rectangles in the Real World
By looking at murals in this video students see how artists use proportion and measurement to create them. The class then does an activity where they enlarge a drawing by using scale and then create a classroom mural. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Scaling Up Rectangles Using Simulations
This interactive allows students to create murals in different sizes by understanding two-dimensional scaling. The activity for the classroom has students use graph paper to draw and compare squares with different proportional dimensions and record the data as they change. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Similar Figures and Unknown Heights in Practice
Students will learn about proportional reasoning in this interactive and how it can help find an unknown height as well as exploring proportional relationships among similar triangles. The classroom activity uses the interactive as a catalyst into a discussion of these math concepts. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Similar Figures in the Real World
A visit to the Louisville Slugger Museum and Factory shows students how measurement and engineering are involved in the creation of new baseball bats. The math skills of proportional reasoning and equivalent ratios are used in the classroom activity involving an oversized bat and a player. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• The Escalator, Assessment Variation
This task presents a scenario about someone riding an escalator. Students are then given a series of statements such as "He traveled 2 meters every 5 seconds" and then asked to determine which of the statements are true.

http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer Throndsen .

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.