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Ratios and Rates Warm-Up Problem Lesson

Practice solving real-world ratio and rate problems including finding unit rates and equivalent ratios. Common Core Standards Objective: MAFS.6.RP.1.3. Improve math skills with practical examples. Additional examples for understanding and comparing rates are included.

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Ratios and Rates Warm-Up Problem Lesson

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. Warm Up Find the unit rate. 1. 16 miles in 4 hours 2. 3 oranges for $2.40 3. 3 bottles for $0.93 4. 6 DVDs for $36.60 4 mi/h $0.80 per orange $0.31 per bottle $6.10 per DVD

  3. Common Core Standards Objective- Solve problems in real world context using ratios and rates. MAFS.6.RP.1.3

  4. 3 miles _________ 60 minutes 3 60 3 6 ___ 9 12 ___ ___ ___ The ratios , , , and are equivalent. 60 120 180 240 Additional Example 1B: Finding Equivalent Ratios and Rates Use a table to find three equivalent ratios or rates. B. Samantha walks at a rate of . Original Rate 3 • 2 3 • 3 3 • 4 Multiply the numerator and the denominator by 2 3, and 4. 6 9 12 120 180 240 60 • 2 60 • 3 60 • 4

  5. Find rates equivalent to . $0.25 1 min Additional Example 2: Comparing Rates The cost of each additional minute over 500 minutes on Jill's cell phone plan is . Which person's cell phone plan has the same rate for additional minutes over 500 minutes? $0.25 1 min $3.25 12 min $6.50 24 min $12.00 48 min

  6. Additional Example 2: Comparing Rates The cost of each additional minute over 500 minutes on Jill's cell phone plan is Which person's cell phone plan has the same rate for additional minutes over 500 minutes? $0.25 1 min $0.25 • 12 $0.25 • 24 $0.25 • 48 Original Rate $0.25 $3.00 $6.00 $12.00 48 12 1 24 1 • 12 1 • 24 1 • 48 $12.00 48 min Zach's rate of is equivalent to Jill's rate.

  7. Check It Out Example 2 Plane W traveled at an average speed of . Which plane traveled at the same rate as plane W? 750 miles 1 hour 750 miles 2 hours 2200 miles 3 hours 3250 miles 4 hours

  8. Check It Out Example 2 continued 750 750 . 2 1500 _______ _______ _______ = = 1 1 . 2 2 which is the same as plane X

  9. Additional Example 3: Application Several groups of friends are going to take a shuttle bus to the park. It costs $24 for a group of 12 people to ride the bus. How much will a group of 15 friends pay? Find the unit rate. Divide the bus fare by the number in each group to find the amount paid per person. 24 ÷ 12 = 2 Multiply the unit rate by 15 to find the rate for 15 people. 2 • 15 = 30 A group of 15 friends will pay $30 in bus fare.

  10. Check It Out: Additional Example 3A Several groups of friends are going to take a shuttle bus to the park. It costs $40 for a group of 10 people to ride the bus. How much will a group of 8 friends pay? $40 ÷ 10$4 = 1 10 ÷ 10 $4 • 8 = $32 1

  11. Check It Out: Additional Example 3B Groups of friends are going to ride the Ferris wheel at the county fair. It costs $6.00 for a group of 3 people to ride the Ferris wheel. How much will a group of 8 friends pay? $6 ÷ 3$2 = 1 3 ÷ 3 $2 • 8 = $16 1

  12. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  13. 9 18 27 36 __ __ __ __ 1 2 3 4 __ __ __ __ , , , , 4 8 12 16 3 6 9 12 12 6 2 1 __ __ __ __ , , 60 30 10 5 Lesson Quiz: Part I Use a table to find three equivalent ratios. 1. 2. 3. Possible Answers:

  14. Weeks 4 8 12 Savings 50 100 150 Lesson Quiz: Part II 4.Fred is saving for a new sound system. The table shows some amounts he could save in different numbers of weeks. Predict the amount of his savings after 10 weeks. $125

  15. Lesson Quiz for Student Response Systems 1. Use a table to identify three equivalent ratios of . A. B. C. D.

  16. Lesson Quiz for Student Response Systems 2. Use a table to identify three equivalent ratios of . A. B. C. D.

  17. Lesson Quiz for Student Response Systems 3. Use a table to identify three equivalent ratios of . A. B. C. D.

  18. Lesson Quiz for Student Response Systems 4. A grocery store sells eggs in crates. The following table shows the prices of some crates. Predict how much Lee will pay for a crate of 18 eggs at the rate shown in the table. A. $2.75 B. $3.00 C. $3.25D. $3.50

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