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1. Objective: I can solve real world problems involving rate and ratio using diagrams. Ratio Tables Tape Diagrams Double number Line diagrams Equivalent Unit pricing Constant speed Percent Units of measure Coordinate Plane Equations Word Problems What is a ratio? How can it help you convert between units? What is rate reasoning? How can it help us calculate for missing values?
2. Students Approaches. There are several strategies that students could use to determine the solution to this problem. oAdd quantities from the table to total 24 feet (9 feet and 15 feet); therefore the number of yards must be 8 yards (3 yards and 5 yards). oUse multiplication to find 24 feet: 1) 3 feet x 8 = 24 feet; therefore 1 yard x 8 = 8 yards, or 2) 6 feet x 4 = 24 feet; therefore 2 yards x 4 = 8 yards. Performance Task / Model Product Example Examples: A. Using the information in the table, find the number of yards in 24 feet. B. Compare the number of black to white circles. If the ratio remains the same, how many black circles will you have if you have 60 white circles? Pull Pull C. If 6 is 30% of a value, what is that value? (Solution: 20)
3. D. A credit card company charges 17% interest on any charges not paid at the end of the month. Make a ratio table to show how much the interest would be for several amounts. If your bill totals $450 for this month, how much interest would you have to pay if you let the balance carry to the next month? Show the relationship on a graph and use the graph to predict the interest charges for a $300 balance.
4. 1. What is the value of 40% of $ 300.00? 2. Use the table below to determine the number of beaded bracelets Emma can make in 12 hours. 8 4 2 6 Hours 6 12 24 18 Bracelets 3. The chart below illustrates how much water accumulates from a dripping faucet over time. Determine how much water would be lost by 9:45 am change on assessment 4. At a summer music camp, there are three teachers per twenty-four students. At that rate, how many teachers would be needed for forty eight students? Find the unit rate and set up an equation that solve the problem. Next, create a tape diagram to check the relationship between the number of teachers and the number of students beginning with just one teacher and ending with sixty-four students. Write your answer in a complete sentence. 5. The US History exam had a total of sixty questions. Gabbie got 80% of the questions correct. How many of the sixty questions did Gabbie get incorrect? Solve the problem and demonstrate the steps taken to come up with your final answer. Feel free to create a tape diagram or double line diagram to illustrate and prove your reasoning.
5. RATIOS AND RATES A ratio can be expressed three ways: • Using the fraction bar as in 23 • Using a colon symbol as in 2:3 • Using the word “to” as in 2 to 3. Write each ratio using the other two ways: 1. The ratio of 3 inches to 20 feet. 2. The ratio of 26 students: 1 class 3. The ratio of 2 𝑏𝑜𝑦𝑠3 𝑔𝑖𝑟𝑙𝑠
6. When the denominator of a rate is 1, we call the rate a unit rate. We usually use the key word per or the division symbol ( / )to indicate a unit rate. For example: If a student earns $7.65 per hour, it is the same as $7.65/hour, and means $7.65 for every hour of work. Find the unit rate for the following: 4. 120 eggs from 20 chickens 5. $55 for 20 people 6. 250 miles in 4 hours 7. 60 feet in 4 minutes 8. 48 books for 16 students 9. 56 children from 14 families
7. Unit rates can also be used to solve problems. 10. Which is the better deal: 8 ounces of shampoo for $0.89 or 12 ounces for $1.47 11. Which is the better deal: 3 cans of soda for $1.27 or 5 cans of soda for $1.79 12. Which is the better deal: 10 pounds of hamburger for $4.99 or 5 pounds of hamburger for $2.69 13. Which is traveling faster: Traveling 300 miles in 5 hours or traveling 250 miles in 4 hours 14. Which is traveling faster: Traveling 75 miles in 1 hour or traveling 280 miles in 3.5 hours 15. Which is traveling faster: Traveling 150 yards in 40 seconds or traveling 406 feet in 35 seconds
8. Suppose you survey all the students at your school to find out whether they like ice cream or cake better as a dessert, and you record your results in the contingency table below. a) What percentage of students at your school prefers ice cream over cake? b) At your school, are those preferring ice cream more likely to be boys or girls? c) At your school, are girls more likely to choose ice cream over cake than boys are?