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Understanding Unit Rates: Finding Values in Everyday Situations

ulric-wells avatar
ulric-wells
24 diapositives · 413 Views · Nov 27, 2014

This lesson dives into the concept of rates and unit rates, helping students learn how to find units and compare unit rates like average speed and unit prices. Through various examples—from calculating how many minutes it takes for a Ferris wheel to complete one revolution to determining the amount of ice needed for smoothies—students engage with relatable scenarios. Key vocabulary includes rates and unit rates. By the end, students will have a clear understanding of how to divide quantities to determine unit rates in multiple contexts.

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  1. 5-2 Rates Course 2 Warm Up Problem of the Day Lesson Presentation

  2. 5-2 Rates Course 2 Learn to find units and compare unit rates, such as average speed and unit price.

  3. 5-2 Rates Course 2 Insert Lesson Title Here Vocabulary rate unit rate

  4. 5-2 Rates Course 2 A rate is a ratio that compares two quantities measured in different units. A unit rate is a rate whose denominator is 1. To change a rate to a unit rate, divide both the numerator and denominator by the denominator. We 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.

  5. 1 mile 1 hour On a bicycle you can travel 20 miles in 4 hours. What are the unit rates in this situation, (the distance you can travel in 1 hour and the amount of time required to travel 1 mile)?

  6. 5-2 Rates Course 2 Find the unit rate. A Ferris wheel revolves 35 times in 105 minutes. How many minutes does 1 revolution take? Write a rate that compares minutes and revolutions. 105 minutes 35 revolutions Divide the numerator and denominator by 35. 105 minutes ÷ 35 35 revolutions ÷ 35 3 minutes 1 revolution Simplify. The Ferris wheel revolves 1 time in 3 minutes.

  7. 5-2 Rates Course 2 Find the unit rate. A Ferris wheel revolves 35 times in 105 minutes. How many revolutions does it complete in 1 minute? Write a rate that compares revolutions and minutes. 35 revolutions 105 minutes Divide the numerator and denominator by 105. 35 revolutions ÷ 105 105 minutes ÷ 105 0.333.. revolutions 1 minute Simplify. The Ferris wheel makes 1/3 of a revolution in 1 minute.

  8. 5-2 Rates Course 2 Find the unit rate. To make 12 smoothies, Henry needs 30 cups of ice. How many cups of ice does he need for one smoothie? Write a rate that compares cups of ice and smoothies. 30 cups of ice 12 smoothies Divide the numerator and denominator by 12. 30 cups of ice ÷ 12 12 smoothies ÷ 12 2.5 cups of ice 1 smoothie Simplify. Henry needs 2.5 cups of ice per smoothie.

  9. 5-2 Rates Course 2 Find the unit rate. To make 12 smoothies, Henry needs 30 cups of ice. How many smoothies can he make with one cup of ice? Write a rate that compares smoothies and cups of ice. 12 smoothies 30 cups of ice Divide the numerator and denominator by 30. 12 smoothies÷ 30 30 cups of ice ÷ 30 0.4 smoothies 1 cup of ice Simplify. Henry can make 0.4 smoothies with one cup of ice.

  10. 5-2 Rates Course 2 Find the unit rate. A dog walks 60 steps in 2 minutes. How many steps does he walk in one minute? Write a rate that compares steps and minutes. 60 steps 2 minutes Divide the numerator and denominator by 2. 60 steps ÷ 2 2 minutes ÷ 2 30 steps 1 minute Simplify. The dog walks 30 steps per minute.

  11. 5-2 Rates Course 2 Find the unit rate. A dog walks 60 steps in 2 minutes. How many minutes does it take him to walk 1 step? Write a rate that compares minutes and steps. 2 minutes 60 steps Divide the numerator and denominator by 2. 2 minutes÷ 60 60 steps÷ 60 1/30 minute 1 step Simplify. It takes the dog 1/30 of a minute (or two seconds) to walk a step.

  12. 36 inches in 3 feet Rate 1 Rate 2 How many feet in one inch? • How many inches in one foot?

  13. 5 gallons of gas cost $6.50 Rate 1 Rate 2 How much gas can I get for $1.00? • How much does 1 gallon cost?

  14. In 25 minutes Jenny can run 10 laps Rate 1 Rate 2 How many laps can Jenny run in ONE minute? • How long does it take Jenny to run ONE lap?

  15. The copier makes 120 copies in 5 minutes Rate 1 Rate 2

  16. The copier makes 120 copies in 5 minutes Rate 1 Rate 2 How long does it takes to make ONE copy? • How many copies does it make in ONE minute?

  17. 5-2 Rates Course 2 A 12-ounce sports drink costs $0.99, and a 16-ounce sports drink costs $1.19. Which size is the best buy? Divide the price by the number of ounces (oz) to find the unit price of each size. $0.99 12 oz $1.19 16 oz $0.08 oz $0.07 oz ≈ ≈ Since $0.07 < $0.08, the 16 oz sports drink is the best buy.

  18. 5-2 Rates Course 2 A 1.5 gallon container of milk costs $4.02, and a 3.5 gallon container of milk costs $8.75. Which size is the best buy? Divide the price by the number of grams (g) to find the unit price of each size. $4.02 1.5 gal $8.75 3.5 gal $2.68 gal $2.50 g = = Since $2.50 < $2.68, the 3.5 gallon container is the best buy.

  19. Let’s build a table! The Fall Movie Double Issue of Entertainment Weekly said The Dark Knight Rises earned $354 million in three weeks. Total Recall earned $26 million in its first week. Ice Age: Continental drift earned $132 million in four weeks. Which movie has earned more on average per week? At this rate, how much will each movie earn in five weeks? Let’s set up a table of values to illustrate this information. What should our column headings be? That will tell us how many boxes our table needs.

  20. What about a title for the table?

  21. Top Movie Revenues What goes in the columns?

  22. Top Movie Revenues Which movie earned more on average per week? At this rate, what will each movie earn in 5 weeks? Which movie would you like to own a piece of?

  23. 5-2 Rates Course 2 Insert Lesson Title Here Lesson Quiz 1. Ian earned $96 babysitting for 12 hours. How much did he earn each hour? 2. It takes Mia 49 minutes to complete 14 homework problems. On average, how long did it take to solve each problem? 3. Seth plans to drive 220 miles to his vacation. He would like to complete the drive in 4 hours. What should his average speed be in miles per hour? $8 3.5 minutes 55 4. Abby can buy a 7-pound bag of cat food for $7.40, or she can purchase a 3-pound bag for $5.38. Which size is the best buy? 7 lb bag