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MS After School Intervention Unit 3: Ratios, Rate, and Proportion Theme: Sports Park Day 2 Lesson Objective Students will solve problems involving unit rates. Common Core Standards: 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b 0 , and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is a 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ½/¼ miles per hour, equivalently 2 miles per hour. Materials Computer Chart paper Tape LCD projector Cuisenaire® Rods (one set per group) “What’s Your Rate” resource sheets (one per student) Timers (or clocks) (one per pair) “Food Gallery Walk” resource sheets “Food Gallery Walk: Student Answer Sheet” resource sheets (one per student) “Exit Ticket: Which Snack Do you Want” resource sheets (one per student) Calculators (one per student) Warm-Up: “Exploring with Cuisenaire® Rods” (10 minutes) Divide students into groups and give each group a set of Cuisenaire Rods. Have students build a staircase of ten rods with white being the first rod and orange being the tenth. Assign the number name of “one” to the white rod. Students are to number name the other rods. Ask students to select a purple rod, and place a red rod underneath it. P R This shows a comparison of 4 to 2. Ask students to find other combinations that represent this same comparison. Some examples would be dark green to light green and orange to yellow, and red to white. Have students share their method of exploring the problem. Emphasize that the comparison of red to white, or two to one, models a unit rate. Have students show other combinations for unit rates. Introductory Activity (20 minutes) Read and display the following scenario for students: “Betsy is using the running track at the Sports Park to help her train for the cross country meet and she is keeping a record of the data. On Monday, she ran around the track 5 times in 20 minutes. Betsy thinks it would be easier to compare her progress each day if she knew about how long it takes her to complete each lap.” Tell students that Betsy is trying to find a “unit rate.” Pair up students and have them discuss what the unit rate would be for Monday. (Answer: 4 minutes per lap) Next, pose the following situation and have students pair and then explain to the group how they determined their answers: On Tuesday, Betsy ran around the track 10 times in 30 minutes. Is the unit rate (minutes to times around) the same as the unit rate for Monday? (Answer: No, Tuesday’s unit rate is 3 minutes per lap) Do you think her running time was faster on Monday or Tuesday? (Answer: Tuesday is faster since it only takes 3 minutes to complete one lap.) Think-Pair-Share (15 minutes) Give students 5 minutes to think of and list examples of unit rates. (Sample responses: miles per hour, dollars per ounce, dollar a per pound, etc.) Pair up students and give them 5 minutes to compare lists, looking for similarities and examples that only appeared on one person’s list. With the remaining 5 minutes, have the students share their examples with the class. Make a list on the board/overhead. Solicit answers from each pair. What’s Your Rate? (20 minutes) This is based on NCTM LESSON found at http://illuminations.nctm.org/LessonDetail.aspx?ID=L511 Arrange students in pairs and distribute student answer sheets and timers (clocks can also be used). Students will take turns completing four activities for one minute each: saying their full name, jumping jacks, writing their initials, and hopping on one foot. Their partner should keep time and record the number of complete activities (only use whole numbers). Once the data is collected, students should complete the answer sheet together. Have the pairs record their data on the board to compare unit rates. Discuss reasons for differences in the unit rates. (Sample responses: longer names vs. shorter names, speed, energy level, handwriting, etc.) Post the questions below on the board and have students answer on their papers. 1) Based on your unit rate, how many jumping jacks (or any of the activities) could you do in ten minutes? How many in 30 minutes? (Answers will vary: students should multiply their rate by 10, by 30) 2) Which of your answers is more likely to be accurate? Why? (Answer: Ten minutes because most people would tire and slow down after 30 minutes of the activity Discuss answers as a class. Food Gallery Walk (15 minutes) Display the following using the LCD projector: “Your baseball team will be going to the Sports Park for a tournament. This will last several days. The coach needs to buy food for the team to bring for the tournament. You are going to help the coach find the unit rate of several foods that can be compared at different stores in order to get the best price.” Display the first Food Gallery Walk station using the LCD projector. Distribute calculators for students to utilize. As a class, find the unit rate, cost per ounce, of the Lay’s Potato Chips. (Answer: (using $3 and 11 oz) -- $0.27 per ounce) Ask students to find the unit rate of the Fresh Express Salad Bags. (Answer: students will need to find the cost per bag 1st -- $0.50 per ounce) Address any problems students may have had with the extra step. Hang the Food Gallery Walk ads around the room. Distribute Student Answer sheets. Instruct students to browse the grocery items and calculate the unit rates for the next 5 minutes using their calculators. Students should complete as many of the items as they can in the time allotted. You may want to suggest rounding on some items. Discuss answers as a class. Solutions: $4.00 $0.25 per ounce 16 ounces $1.80 Ketchup: $0.05 per ounce 36 ounces $3.00 Ice Cream: $0.20 per ounce 15 ounces $3.00 Sugar Snap Peas: about $0.38 per ounce 8 ounces $2.50 Chips: Tortilla about $0.42 per ounce 6 ounces $0.70 Tuna: Bumblebee $0.14 per ounce 5 ounces $1.00 Gatorade: about $0.03 per ounce 32 ounces $0.80 Macaroni& Cheese: about $0.13 per ounce , 6 ounces $0.80 about $0.11 per ounce 7.25 ounces $2.50 Cranberry Drink: about $0.04 per ounce 64 ounces $4.50 Orange Juice: $0.05 per ounce 90 ounces Beef Franks: Closure – Exit Ticket (10 minutes) Pose the following closure questions: 1. What is the difference between a unit rate and a ratio? (Sample answer: A unit rate has a denominator of 1 where a ratio can have any denominator.) 2. Give two examples of unit rates in the real world. (Sample answer: mph, mpg, $ per lb., jumps per minute, etc.) 3. Why is it good to know unit rates for foods? (Sample answer: to know if you are getting a good deal, saving $, etc.) Distribute “Exit Ticket: Which Snack Do You Want?” exit tickets to students. Answers: 1. items per ounce 2. 5 bears/ounce, 5.5 pieces/ounce, 4.5 fish/ounce 3. The fruit snacks give the most per ounce. What’s Your Rate? NAME ___________________________ 1. Tally/count how many times you are able to complete the following activities in one minute. (Only count the whole number of times each activity is completed. Do not count half a jumping jack or a partial letter.) Saying your full name ____________________ Doing jumping jacks _______________ Writing your initials _____________________ Hopping on one foot ________________ 2. Record your answers below as a unit rate – don’t forget the unit! Saying your full name __________________________ Doing jumping jacks ___________________________ Writing your initials ____________________________ Hopping on one foot ___________________________ What’s Your Rate? NAME ___________________________ 1. Tally/count how many times you are able to complete the following activities in one minute. (Only count the whole number of times each activity is completed. Do not count half a jumping jack or a partial letter.) Saying your full name ____________________ Doing jumping jacks _______________ Writing your initials _____________________ Hopping on one foot ________________ 2. Record your answers below as a unit rate – don’t forget the unit! Saying your full name __________________________ Doing jumping jacks ___________________________ Writing your initials ____________________________ Hopping on one foot ___________________________ Food Gallery Walk Page 1 Food Gallery Walk Page 2 Food Gallery Walk Page 3 Food Gallery Walk Page 4 Food Gallery Walk Page 5 Food Gallery Walk Page 6 Food Gallery Walk Page 7 Food Gallery Walk Page 8 Food Gallery Walk Page 9 Food Gallery Walk Page 10 Food Gallery Walk Page 11 Name: ________________ Food Gallery Walk-Student Answer Sheet Calculate the unit rate for each of the following food items. Beef Franks ___________________________ Ketchup ______________________________ Ice Cream ____________________________ Sugar Snap Peas _______________________ Tortilla Chips __________________________ Bumblebee Tuna _______________________ Gatorade _____________________________ Macaroni & Cheese _____________________ Cranberry Drink ________________________ Orange Juice __________________________ Exit Ticket: Which snack do you want? You can eat one ounce of any of the three snacks listed below. Teddy Grahams: 45 bears in a 9 ounce package Fruit Snacks: 55 pieces in a 10 ounce package Goldfish: 54 fish in a 12 ounce package 1. What unit rate must be found? ____________________________ 2. Find the unit rate for each snack ___________ ___________ __________ 3. If you are only allowed one ounce for a snack, which should you eat? Why? _______________________________________________________________________ _______________________________________________________________________ Exit Ticket: Which snack do you want? You can eat one ounce of any of the three snacks listed below. Teddy Grahams: 45 bears in a 9 ounce package Fruit Snacks: 55 pieces in a 10 ounce package Goldfish: 54 fish in a 12 ounce package 1. What unit rate must be found? ____________________________ 2. Find the unit rate for each snack ___________ ___________ __________ 3. If you are only allowed one ounce for a snack, which should you eat? Why? _______________________________________________________________________ _______________________________________________________________________