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Ratios, Rates, and Unit Rates - Understanding Proportional Relationships

This lesson teaches students how to identify rates and unit rates from given ratios, and understand the concept of proportional relationships. Students will practice solving examples and challenges to reinforce their understanding.

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Ratios, Rates, and Unit Rates - Understanding Proportional Relationships

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  1. October 14, 2014 Day A Math English Science LUNCH Social Studieslocker Exploratory Exploratory

  2. Tuesday ~ October 14 [Day A] Activator: • Take out your notebook • Copy this in your notebook. A rate indicates, for a proportional relationship between two quantities, how many units of one quantity there are for every 1 unit of the second quantity. $10 for every 4 packs of diet soda is a rate because it is a ratio of two quantities. Rate The numeric value of the rate. The unit rate is 2.5 because it is the value of the ratio. Unit Rate The rate unit is dollars/packs of diet soda because it costs 2.5 dollars for every 1 pack of diet soda. Rate Unit

  3. Tuesday ~ October 14 [Day A] Today’s Objective(s): SWBAT: Given a ratio, students precisely identify the associated rate. They identify the unit rate and the rate unit. 6.RP.A.2

  4. Tuesday ~ October 14 [Day A] Ratios can be transformed to rates and unit rates.

  5. Tuesday ~ October 14 [Day A] A ratio of two quantities, such as 5 miles per 2 hours, can be written as another quantity called a rate. The numerical part of the rate is called the unit rate and is simply the value of the ratio, in this case 2.5. This means that in 1 hour, the car travels 2.5 miles. The unit for the rate is miles/hour, which is read “miles per hour”.

  6. Tuesday ~ October 14 [Day A] Expressing ratios as rates: • per • for each • for every

  7. Exploratory Challenge (25 minutes) page : S.65-67 • Work in pairs or small groups to discuss different methods of solving the examples. • Show or explain your thinking as much as possible • Different groups present their findings and explain the methods used to solve each problem.

  8. Exploratory Challenge pg. S.65 #1 Teagan went to Gamer Realm to buy new video games. Gamer Realm was having a sale: $65 for 4 video games. He bought 3 games for himself and one game for his friend, Diego, but Teagan does not know how much Diego owes him for the one game. What is the unit price of the video games? What is the rate unit? • The unit price is $16.25 𝟐𝟓 • The rate unit is dollars/video game

  9. Exploratory Challenge pg. S.66 #2 • What two quantities are being compared? • What is the ratio of the two quantities for Andre’s portion of the trip? What is the associated rate? The two quantities being compared are distance and time, which are measured in miles and hours. For each driver in parts (b) and (c), circle the unit rate and put a box around the rate unit.

  10. Exploratory Challenge pg. S.66 #2 • Answer the same two questions in part (b) for the other three drivers. For each driver in parts (b) and (c), circle the unit rate and put a box around the rate unit.

  11. Exploratory Challenge pg. S.67 #3

  12. How do you feel? topic.

  13. Tuesday ~ October 14 [Day A] Today’s Homework Page S.68 Problem Set #1-2

  14. Tuesday ~ October 14 [Day A] Ticket To Leave (Exit Ticket) Answer in agenda or notebook. Angela enjoys swimming and often swims at a steady pace to burn calories. At this pace, Angela can swim 1,700 meters in 40 minutes. a. What is Angela’s unit rate? b. What is the rate unit?

  15. Tuesday ~ October 14 [Day A] Accommodations • Read or reread presentation or activity directions, as needed or after prompting • Use examples to model and act as a guide for emerging learners

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