Mathematics 6 (Grade 6)
Unit 2: Ratios and Proportional Relationships (6.RP)
During this unit, students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rate.
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What will my child learn?
Students will:
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
6.RP.A.2
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.
6.RP.A.3
Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
6.RP.A.3.A
Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
6.RP.A.3.B
Solve unit rate problems including those involving unit pricing and constant speed.
6.RP.A.3.C
Find a percent of a quantity as a rate per 100 (e.g. 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Note: Include finding percent of any number and converting between forms of a number (fraction, decimal, percent).
6.RP.A.3.D
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities (SAT® Content  PSDA.02).
Students will:
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
 Background Info. & Guided Practice
 Check for Understanding: Representing Ratios
 Review/Rewind: Introduction of Ratios
 Enrichment Tasks: Games at Recess*  The Escalator*
6.RP.A.2
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.
 Check for Understanding: Rate Problems
 Review/Rewind: Introduction of Rates
 Enrichment Tasks: Mangos for Sale  Price Per Pound & Pounds Per Dollar  Hippos Love Pumpkins
6.RP.A.3
Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
 Background Info.  Videos: Understanding Ratios with Tape Diagrams  Introduction to Ratio Tables  Application with Ratio Tables  Tape Diagrams and MultiStep Problems
 Check for Understanding: Ratio Word Problems
 Review/Rewind: Solving Ratio Problems with Tables Example 1
 Enrichment Tasks: Voting for Three, Variation 1  ... Variation 2  ... Variation 3  Converting Square Units  Currency Exchange  Painting a Barn  Jim and Jesse's Money  Fruit Salad
6.RP.A.3.A
Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
 Background Info.
 Check for Understanding: Solving Ratio Problems with Tables
 Review/Rewind: Solving Ratio Problems with Tables Example 2
 Enrichment Tasks: Walkathon 1*  Gianna's Job
6.RP.A.3.B
Solve unit rate problems including those involving unit pricing and constant speed.
 Background Info. & Guided Practice
 Review/Rewind: Solving Unit Price Problem
 Enrichment Tasks: Friends Meeting on Bicycles*  Data Transfer
6.RP.A.3.C
Find a percent of a quantity as a rate per 100 (e.g. 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Note: Include finding percent of any number and converting between forms of a number (fraction, decimal, percent).
 Background Info. & Guided Practice
 Check for Understanding: Finding Percents  Percentage Word Problems 1
 Review/Rewind: Finding a Percent
 Enrichment Tasks: Overlapping Squares*  Shirt Sale*  Anna in D.C.
6.RP.A.3.D
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities (SAT® Content  PSDA.02).
 Check for Understanding: Units
 Review/Rewind: Convert Yards into Inches
What are some signs of student mastery?
Source: GreatSchools, Understanding Ratios in 6th Grade (Oct. 8, 2015)

