This section introduces the relationship between ratio and rate.
The mini-lesson shows the two ways that we can express a ratio. Additionally, students can see that a ratio can show both a comparison of amounts (15 girls:16 boys) or a comparison with a total (15 girls:31 students).
You probably know this old trick:
(Show panel: "Shapes") If you said one is a square and one is a rectangle, you’re right. And if you said they are both rectangles, you’re also right! That’s true even though the shape on the left is also a square. A square is a special kind of rectangle—one with equal side lengths.
Continue to show and discuss remaining panels (categories, ratios, rates, speed):
What is the gender ratio in our class?
Note: it is also correct to use a total in the comparison instead of the way it’s done above. For example: In Ms. Litton’s class there are 15 girls to 31 total students. It’s more like a simple fraction this way, but it’s still correct.
A rate is a special type of ratio that uses two different kinds of units together to give information. In Ms. Litton’s class, we compared the number of girls to boys—all the same unit (students). But consider a different situation: You just got a job that pays $75,000 a year. In this case, you are putting together an amount of money and an amount of time. Two totally different units. This is a rate.
In a rate, the kinds of units are different. For example, $75,000/year. One unit is money; the other unit is a period of time. Students will all recognize a speed limit and be able to identify the two different units used in this rate.
You also use rates when you talk about speed.
Speed is always a rate.