Lesson 9
Solving Rate Problems
Lesson Narrative
In previous lessons, students have used tables of equivalent ratios to reason about unit rates. In this lesson, students gain fluency working with unit rates without scaffolding (MP1). They choose what unit rate they want to use to solve a problem, divide to find the desired unit rate, and multiply or divide by the unit rate to answer questions. They may choose to create diagrams to represent the situations, but the problems do not prompt students to do so. The activity about which animal ran the farthest requires students to use multiple unit rates in a sequence to be able to convert all the measurements to the same unit.
Learning Goals
Teacher Facing
 Apply reasoning about ratios and rates to convert and compare (in writing) distances expressed in different units.
 Apply reasoning about ratios and rates to justify (orally) whether a given price is a good deal.
 Practice grade 5 arithmetic with fractions and decimals.
Student Facing
Let's use unit rates like a pro.
Required Materials
Required Preparation
Print and cut the blackline master so that each group of two students gets five cards A–E (or six cards A–F if you expect students to tackle the extension problem).
Optionally, purchase a fourpack of drinks for demonstration purposes in the Deal or No Deal activity.
Providing access to calculators is optional. All of the calculations in this lesson can be done using grade 5 techniques. If you would like students to practice arithmetic, don't offer calculators. If you think the calculations will present too much of a barrier to gradelevel work, make them available.
Learning Targets
Student Facing
 I can choose how to use unit rates to solve problems.
CCSS Standards
Glossary Entries

pace
Pace is one way to describe how fast something is moving. Pace tells how much time it takes the object to travel a certain distance.
For example, Diego walks at a pace of 10 minutes per mile. Elena walks at a pace of 11 minutes per mile. Elena walks slower than Diego, because it takes her more time to travel the same distance.

speed
Speed is one way to describe how fast something is moving. Speed tells how much distance the object travels in a certain amount of time.
For example, Tyler walks at a speed of 4 miles per hour. Priya walks at a speed of 5 miles per hour. Priya walks faster than Tyler, because she travels more distance in the same amount of time.

unit price
The unit price is the cost for one item or for one unit of measure. For example, if 10 feet of chain link fencing cost $150, then the unit price is \(150 \div 10\), or $15 per foot.

unit rate
A unit rate is a rate per 1.
For example, 12 people share 2 pies equally. One unit rate is 6 people per pie, because \(12 \div 2 = 6\). The other unit rate is \(\frac16\) of a pie per person, because \(2 \div 12 = \frac16\).
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