Equivalent Ratios (Grade 6)

Examples, solutions, videos, and lessons to help Grade 6 students learn to use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

A. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios

B. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

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.

D. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Common Core: 6.RP.3a

Suggested Learning Targets

• I can make a table of equivalent ratios using whole numbers.
• I can find the missing values in a table of equivalent ratios.
• I can plot pairs of values that represent equivalent ratios on the coordinate plane.
• I can use tables to compare proportional quantities.
• I can solve real-world and mathematical problems involving ratio and rate, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Component Skills from Previous Grades

6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

6.RP.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.

Solving ratio problems using tables and the coordinate plane (CCSS: 6.RP.3a)
Find the missing values in a table of equivalent ratios.
Multiplying or dividing two related quantities by the same number is called scaling. Sometimes you may need to scale back and then scale forward to find an equivalent ratio.
Examples:

1. Cans of corn are on sale at 10 for $4. Find the cost of 15 cans.
2. Joe mows lawns during his summer vacation to earn money. He took 14 hours last week to mow 8 lawns. At this rate, how many lawns could he mow in 49 hours?
3. A child’s height measures 105 centimeters. Estimate her height in inches.

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6.RP.3a - rates and ratios word problems
Examples:

1. An arcade sold game tokens individually or in package. They are having a sale on token packages.
   a) How many token packages can you buy with $20? $25?. Explain.
   b) What is the unit price?
   c) How much would it cost to buy 6 token packages? d) The arcade sells individual tokens for $0.25 each. If a token package contains 25 tokens, how much would you save by buying a package of 25 tokens instead of 25 individual tokens? Explain.
2. Heritage Middle School has 150 students. Two out of three students in Mrs. Mason’s class prefer gel toothpaste. Use this ratio to predict how many students in the entire middle school prefer gel toothpaste.
   Method 1: Use a bar diagram.
   Method 2: Use equivalent fractions.
3. The ratio of the number of text messages sent by Lucas to the number of text messages sent by his sister is 3 to 4. Lucas sent 18 messages. How many text messages did his sister send?
4. In a survey, four out of five people preferred creamy over chunky peanut butter. There are 120 people shopping at the grocery store. Use the survey to predict how many people in the store would prefer creamy peanut butter.
5. A survey found that 12 out of every 15 people in the United States prefer eating at a restaurant over cooking at home. If 400 people selected eating at a restaurant on the survey, how many people took the survey?
6. The Millers drove 105 miles on 4 gallons of gas. At this rate, how many miles can they drive on 6 gallons of gas?
7. There are 810 calories in 3 scoops of vanilla ice cream. How many calories are there in 7 scoops of ice cream?

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