Lesson 9: Tables of Equivalent Ratios In this lesson we explored the idea that each ratio in a ratio table can be simplified to have the same value. We can use ratio tables to solve problems. Jan 8 8:18 AM
Learning Targets By the end of this lesson, you will be able to answer the following questions: (1) When creating a ratio table, what does each pair of values represent? (2) Where do you find ratio tables in the world outside of school? Why are they there? (3) Are all tables you see ratio tables? How can you decide if a table is or is not a table of equivalent ratios? Jan 8 8:18 AM
Learning Targets Why do you need to know this? Ratios can be used to solve all types of real world problems. We use ratios to decide what items have the best price when we shop, which cars get the best gas mileage, and many other real world problems. Jan 8 8:18 AM
Classwork Example 1 To make Paper Mache, the art teacher mixes water and flour. For every two cups of water, she needs to mix in three cups of flour to make the paste. Find equivalent ratios for the ratio relationship 2 cups of water to 3 cups of flour. Represent the equivalent ratios in the table below: What does this ratio mean? For every two cups of water, there are 3 cups of flour? It means that every time we add two cups of water, we have to add 3 cups of flour. Why is it worded, "for every two cups of water there are 3 cups of flour"? This suggests that we might be doing this action repeatedly. Why would I do it more than once? It depends on how much paste we need to make for the paper mache project. Can we list all of the possible recipes for this mixture in order in a table? Let's start with the ratio that uses the smallest whole numbers. We cannot list ALL of the possible mixtures, since the list would be infinite, but we can list as many as we have time or need to list. Aug 17 10:16 AM
To make Paper Mache, the art teacher mixes water and flour. For every two cups of water, she needs to mix in three cups of flour to make the paste. Find equivalent ratios for the ratio relationship 2 cups of water to 3 cups of flour. Represent the equivalent ratios in the table below: Let's start with the ratio that uses the smallest whole numbers. Is there an equivalent ratio that uses smaller whole numbers than the ratio 2 to 3? No, there is no equivalent ratio with smaller whole numbers we can make. Aug 17 10:16 AM
To make Paper Mache, the art teacher mixes water and flour. For every two cups of water, she needs to mix in three cups of flour to make the paste. Find equivalent ratios for the ratio relationship 2 cups of water to 3 cups of flour. Represent the equivalent ratios in the table below: Let's start with 2 cups of water for every 3 cups of flour as our first entry. What would the next possibility be? If we don't want to skip over any possible entires, how would we fill the table? We repeat the pattern, adding two cups of water and three cups of flour each time. Aug 17 10:16 AM
To make Paper Mache, the art teacher mixes water and flour. For every two cups of water, she needs to mix in three cups of flour to make the paste. Find equivalent ratios for the ratio relationship 2 cups of water to 3 cups of flour. Represent the equivalent ratios in the table below: What is the value of each ratio in the table? The value is 2:3 or 2/3 each time. This is what you get if you simplify the ratio each time. Aug 17 10:16 AM
Example 2 Javier has a new job designing websites. He is paid at a rate of $700 for every 3 pages of web content that he builds. Create a ratio table to show the total amount of money Javier has earned in ratio to the number of pages he has built. Javier is saving up to purchase a used car that costs $4,300. How many web pages will Javier need to build before he can pay for the car? 21 pages Is there an equivalent ratio to 700:3 that still uses smaller whole numbers? No, because there is no whole number (besides 1) that divides evenly into both 700 and 3. Let's build our table without skipping any possible ratios. Aug 17 10:24 AM
Complete Exercises 1 2 in your groups. You have 5 minutes to see how much you can get done in your groups. Then we will share your answers. Aug 17 10:26 AM
Exercise 1 Spraying plants with cornmeal juice is a natural way to prevent fungal growth on the plants. It is made by soaking cornmeal in water, using two cups of cornmeal for every nine gallons of water. Complete the ratio table to answer the questions that follow. a. How many cups of cornmeal should be added to 45 gallons of water? 10 cups of cornmeal b. Paul has only 8 cups of cornmeal. How many gallons of water should he add if he wants to make as much cornmeal juice as he can? 36 gallons of water c. What can you say about the values of the ratios in the table? The values are all 2:9 or 2/9 Aug 17 10:31 AM
Exercise 2 James is setting up a fish tank. He is buying a breed of goldfish that typically grows to be 12 inches long. It is recommended that there be 1 gallon of water for every inch of fish length in the tank. What is the recommended ratio of gallons of water per fully grown goldfish in the tank? Complete the ratio table to help answer the following questions: a. What size tank (in gallons) is needed for James to have 5 full grown goldfish? 60 gallons b. How many fully grown goldfish can go in a 40 gallon tank? 3 goldfish c. What can you say about the values of the ratios in the table? The value is 1:12 or 1/12 Aug 17 10:31 AM
Learning Targets Answer this question: (1) When creating a ratio table, what does each paid of values represent? Each pair of ratios represents an equivalent ratio. Each has the same value. (2) Where do you find ratio tables in the world outside of school? Why are they there? Ratio tables are often found on the back of products used in recipes, like pancake and biscuit mix boxes. (3) Are all tables you see ratio tables? How can you decide if a table is or is not a table of equivalent ratios? Not all tables are ratio tables. To figure out if a table is a ratio table, you can simplify each of the pairs of numbers and see if they have the same value. Jan 8 8:18 AM
Homework Problem Set Lesson 9 Aug 10 6:42 PM