Objective
By the end of this lesson, Noah will understand the concepts of ratios and unit rates, and he will be able to use ratio language to describe relationships between two quantities. He will also apply these concepts to solve real-world problems.
Materials and Prep
- Paper and pencil
- Whiteboard (if available) or a large sheet of paper
- Timer (for timed activities)
- Access to a calculator (optional)
Before the lesson, it would be helpful to review basic multiplication and division, as these skills will be useful when working with ratios and rates.
Activities
- Ratio Scavenger Hunt:
Noah will go around the house or yard to find items that can be compared in ratios. For example, he could find 4 apples and 2 oranges and express the ratio of apples to oranges. He will write down the ratios he finds and describe them using ratio language.
- Unit Rate Challenge:
Set a timer for 10 minutes and challenge Noah to calculate unit rates for different scenarios, such as how many miles he can run in one hour if he runs 3 miles in 15 minutes. This will help him understand how to simplify ratios into unit rates.
- Real-World Ratio Problems:
Create a few real-world problems that require Noah to use ratios and rates to solve. For example, "If a recipe calls for 2 cups of flour and 3 cups of sugar, what is the ratio of flour to sugar?" or "If a car travels 150 miles on 5 gallons of gas, what is the unit rate of miles per gallon?"
Talking Points
- "A ratio is a way to compare two quantities. For example, if I have 2 apples and 3 oranges, the ratio of apples to oranges is 2 to 3."
- "We can express ratios in different ways, like using the word 'to' or with a colon. So, we can say the ratio of apples to oranges is 2 to 3 or write it as 2:3."
- "A unit rate tells us how much of one thing there is for every one unit of another thing. For example, if you can run 4 miles in 2 hours, the unit rate is 2 miles per hour."
- "When we solve problems with ratios, we often need to think about how the quantities relate to each other. For example, if a recipe is doubled, how does that change the ratio of ingredients?"
- "Ratios and rates are everywhere in real life! We use them when shopping, cooking, and even when planning trips. Can you think of a time you used a ratio or rate today?"