Unit 3, Lesson 4
Comparing Speeds and Prices
Grade 6
Preparation
Lesson Narrative
In this lesson, students continue to work with ratios in context and reason about rates per 1. They consider situations and questions about speed and prices, such as:
- A runner ran 4,200 meters in 30 minutes. Another runner ran 6,300 meters in 45 minutes. Did they run at the same speed?
- Which shopping deal, 2 for \$3 or 8 for \$6, is better?
Students see that expressing ratios as rates per 1 is an effective way to compare them. For instance:
- Calculating the distance run in 1 hour (or 1 minute) shows that both runners ran at a rate of 8,400 meters per hour (or 140 meters per minute).
- Calculating the price for 1 item shows that it costs \$1.50 per item in the first deal and \$0.75 per item in the second deal.
Students work toward the general understanding that when two ratios have the same rate per 1, they are equivalent ratios. They also notice that dividing one quantity in a ratio by the other is an efficient way to find a rate per 1.
As students reason about ratios in situations, find rates per 1, and interpret the meanings of numbers in context, they practice reasoning abstractly and quantitatively (MP2).
- Explain (orally and in writing) that if two ratios have the same rate per 1, they are equivalent ratios.
- Justify (orally and in writing) comparisons of speeds or prices.
- Recognize that calculating how much for 1 of the same unit is a useful strategy for comparing rates. Express these rates (in spoken and written language) using the word “per” and specifying the unit.
Let’s compare some speeds and some prices.
Required Preparation
If possible, gather some examples of grocery store advertisements from newspapers or weekly fliers for deals like “3 for \$5.”