# Unit Rate Problems (Grade 6)

Examples, solutions, and lessons to help Grade 6 students learn how 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.3b

### Suggested Learning Targets

• I can solve problems involving unit pricing and speed.
• I can find a percent of a given quantity involving finding the whole, given a part and the percent.

 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. 6.RP.3a 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.
How to solve for missing values in a rate problem by setting up a table?
Solving a ratio word problem using a ratio table. How to find the unit rate, and then find equivalent ratios.
Example:
Dasia typed 84 words in 2 minutes. Assuming that she types at a constant rate, use a ratio table to find out how many words she would type in 1 minute, 3 minutes, and 9 minutes.

How to solve for missing values in a rate problem by setting up a double number line?
1. Find the unit rate - a ratio with a denominator of 1.
2. Use the unit rate to calculate an equivalent rate using multiplication.
Example:
Oranges were on super sale at the store. Juan bought 12 oranges for \$4. At this rate, how many oranges could he buy with \$1? How many could he buy with \$10? Finding A Unit Rate
1) Using a ratio table
2) Using division
Example:
It took Valerie 80 minutes to drive 120 miles. How many miles per hour is this? 6.RP.3.b - Solve Unit Rate Problems with a Double Number Line Diagram (Singapore Math)
This video explains how to solve unit rate problems using a double number line diagram. This is a pictorial method for solving rate problems in the Singapore math curriculum when you are dealing with only 2 different units. This addresses 6.RP.3b in the Grade 6 Common Core Standards for Mathematics.
Example:
If James earned \$72 in 8 hours, how much money would he earn in 3 hours at that rate? Find unit rates using division Examples:
1. If a box of wheat crackers contains 6 servings and has a total of 420 calories. Find the number of calories in 1 serving.
2. Two sizes of sports drink bottles are 32 oz. and 24 oz. If the 32 oz. drink costs \$1.39 and the 24 oz. drink costs \$1.20, which is the better buy? Round each unit cost to the nearest cent.
3. A car travels about 25 miles on 1 gallon of gas. About how far can the car travel on 8 gallons of gas? Find unit rates using division

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