Mathematics Grade 6
Strand: RATIOS AND PROPORTIONAL RELATIONSHIPS (6.RP)
Understand ratio concepts and use ratio reasoning to solve problems (Standards 6.RP.1–3)
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. The following are examples of rate language: "This recipe has a ratio of four cups of flour to two cups of sugar, so the rate is two cups of flour for each cup of sugar." “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (In sixth grade, unit rates are limited to non-complex 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.
Equivalent Ratios and Unit Rates
This task should come after students have done extensive work with representing equivalent ratios and understand that for any ratio a:b, the ratio sa:sb is equivalent to it for any s>0. The purpose of this task is to make explicit the fact that equivalent ratios have the same unit rate.
Grade 6 Mathematics 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.
Hippos Love Pumpkins
The purpose of this task is for students to find unit rates in different situations involving unusual units. Most students are familiar with miles per hour, but students are unlikely to have encountered the idea of pumpkins per hippo or goats per pizza. By working with unusual (even silly) units, students must reason abstractly and quantitatively in order to answer the questions because they can't rely on their experience with the situation to guide them through it.
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.
Mangos for Sale
The purpose of this task is to generate a classroom discussion about ratios and unit rates in context.
Price per pound and pounds per dollar
This task could be used by teachers to help students develop the concept of unit rates. Its purpose is to help students see that when you have a context that can be modeled with a ratio and associated unit rate, there is almost always another ratio with its associated unit rate (the only exception is when one of the quantities is zero), and to encourage students to flexibly choose either unit rate depending on the question at hand.
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.
Riding at a Constant Speed, Assessment Variation
Riding at a Constant Speed addresses aspects of 6.RP.2 "Understand the concept of a unit rate a/b associated with a ratio a:b" and 6.RP.3 "Use ratio and rate reasoning to solve real-world and mathematical problems." The numbers are chosen so that it would be easy to implement this task as a fill-in-the-blank item.
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.
The goal of this task is to compare unit rates in a real world context. In addition to solving the problem by finding unit rates, students could also make a ratio table.
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