Unit 2, Lesson 10
Comparing Situations by Examining Ratios
Grade 6
Preparation
Lesson Narrative
In this lesson, students compare ratios to see if two situations involve the same rate. For instance:
- Two people run different distances in the same amount of time. Do they run at the same speed?
- Two people pay different amounts for different numbers of items. Do they pay the same cost per item?
- Two recipes for a drink are given. Do they taste the same?
In each case, the numbers are purposely chosen so that reasoning directly with equivalent ratios is a more appealing method than finding how-much-for-one and then scaling. The reason for this is to reinforce the concept that equivalent ratios describe the same rate, before formally introducing the notion of unit rate and methods for calculating it. Students can use any method, however. Regardless of their chosen approach, they need to be able to explain their reasoning (MP3) in the context of the problem.
- Choose and create diagrams to help compare two situations and explain whether they happen at the same rate.
- Justify that two situations do not happen at the same rate by finding a ratio to describe each situation where the two ratios share one value but not the other, that is, $a:b$ and $a:c$, or $x:z$ and $y:z$.
- Recognize that a question asking whether two situations happen “at the same rate” is asking whether the ratios are equivalent.
Let’s use ratios to compare situations.
Required Preparation
None