Module 1 lesson 9
- 1. Module 1 Lesson 9 Tables of Equivalent Ratios.notebook 1 September 23, 2014 Lesson 8 Homework Review 1. The ratio of the number of shaded sections to the number of unshaded sections is 4 to 2. What is the value of the ratio of the number of shaded pieces to the number of unshaded pieces? or 2 2. Use the value of the ratio to determine which ratio(s) is equivalent to 7:15. a. 21:45 b. 14:45 c. 3:5 d. 63:135 Both a and d are equivalent to 7:15. 3. Sean was at batting practice. He swung 25 times but only hit the ball 15 times. a. Describe and write more than one ratio related to this situation. Ratio of the number of hits to the total number of swings is 15:25. Ratio of the number hits to the number of misses is 15:10. Ratio of the number of misses to the number of hits is 10:15. Ratio of the number of misses to the total number of swings is 10:25.
- 2. Module 1 Lesson 9 Tables of Equivalent Ratios.notebook 2 September 23, 2014 b. For each ratio you created, use the value of the ratio to express one quantity as a fraction of the other quantity. c. Make up a word problem that a student can solve using one of the ratios and its value. If Sean estimates he will take 10 swings in his next game, how many hits would he expect to get, assuming his ratio of hits–to–swings does not change.
- 3. Module 1 Lesson 9 Tables of Equivalent Ratios.notebook 3 September 23, 2014 13 3. Your middle school has 900 students. of the students bring their lunch instead of buying lunch at school. What is the value of the ratio of the number of students who do bring their lunch to the number of students who do not? 13 First, I created a tape diagram. In the tape diagram, of the students bring their lunch instead of buying lunch at school. I determined that 300 students bring their lunch, leaving 600 students who buy their lunch. One unit of the tape diagram represents 300, and 2 units of the tape diagram represent 600 This creates a ratio of 1:2 As such, the value of the ratio of the number of students who bring their lunch to the number of students who buy their lunch is 12
- 4. Module 1 Lesson 9 Tables of Equivalent Ratios.notebook 4 September 23, 2014 Module 1 Ratios and Unit Rates Topic B: Collections of Equivalent Ratios Lesson 9: Tables of Equivalent Ratios Student Outcomes § Students understand that a ratio is often used to describe the relationship between the amount of one quantity and the amount of another quantity as in the cases of mixtures or constant rates. § Students understand that a ratio table is a table of equivalent ratios. Students use ratio tables to solve problems.
- 5. Module 1 Lesson 9 Tables of Equivalent Ratios.notebook 5 September 23, 2014
- 6. Module 1 Lesson 9 Tables of Equivalent Ratios.notebook 6 September 23, 2014 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? · Why is it worded, “for every 2 cups of water there are 3 cups of flour”? · 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. · Is there an equivalent ratio that uses smaller whole numbers than the ratio 2 to 3? · What would the next possibility be? I don’t want to skip over any of my options here.
- 7. Module 1 Lesson 9 Tables of Equivalent Ratios.notebook 7 September 23, 2014 · What is the value of each ratio in the table? · Is that what we expected? Should the value of all of these ratios be equal to each other? · What we have created here is a ratio table, a table in which all of the values of the ratios are equivalent to one another. · What kinds of questions could we answer with the data in our table? Can anyone think of a question we might have had at the start of this problem that this table could help us answer?
- 8. Module 1 Lesson 9 Tables of Equivalent Ratios.notebook 8 September 23, 2014 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. Is there an equivalent ratio to 700:3 that still uses smaller whole numbers? Go ahead and fill in the table without skipping over any possible ratios 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?
- 9. Module 1 Lesson 9 Tables of Equivalent Ratios.notebook 9 September 23, 2014 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.
- 10. Module 1 Lesson 9 Tables of Equivalent Ratios.notebook 10 September 23, 2014 a. How many cups of cornmeal should be added to 45 gallons of water? 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? c. What can you say about the values of the ratios in the table?
- 11. Module 1 Lesson 9 Tables of Equivalent Ratios.notebook 11 September 23, 2014 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:
- 12. Module 1 Lesson 9 Tables of Equivalent Ratios.notebook 12 September 23, 2014 a. What size tank (in gallons) is needed for James to have 5 full‐grown goldfish? b. How many fully‐grown goldfish can go in a 40‐gallon tank? c. What can you say about the values of the ratios in the table?
- 13. Module 1 Lesson 9 Tables of Equivalent Ratios.notebook 13 September 23, 2014 Closing · When creating a ratio table, what does each pair of values represent? Each pair of values represents a ratio that is equivalent to all the other ratios in the table and that describes the ratio relationship of two quantities. · Can anyone think of a situation where you have seen a ratio table other than here in class? · Can you think of an example of a table of numbers you’ve seen that was not a ratio table? If you can’t think of one that you’ve seen, see if you can make one up to match a realworld situation. Please take out your exit ticket for Lesson 9, close your binder, and complete the exit ticket. This will be collected.