Unit 2, Lesson 8: How Much for One?

Transcription

1 Unit 2, Lesson 8: How Much for One? Lesson Goals Use double number lines to find equivalent ratios between prices and quantities. Use the word per to refer to cost of 1 item or unit of purchase. Understand what at this rate means in the context of unit prices. Required Materials rulers tools for creating a visual display 8.1: Number Talk: Remainders in Division (10 minutes) Setup: Display the problem for all to see. 2 minutes of quiet think time, followed by a whole-class discussion. Find the quotient mentally Anticipated misconceptions Students may struggle to interpret the remainder as a decimal or fraction and may instead write r 6. Unit 2: Introducing Ratios, Lesson 8: How Much for One? 1

2 8.2: Grocery Shopping (10 minutes) Setup: Access to rulers. Start with quiet think time, followed by a partner discussion. Unit 2: Introducing Ratios, Lesson 8: How Much for One? 2

3 Answer each question and explain or show your reasoning. If you get stuck, consider drawing a double number line diagram. 1. a. $8 b. $10 1. Eight avocados cost $4. c. $4.50 a. How much do 16 avocados cost? 2. b. How much do 20 avocados cost? a. 4 bottles for $3 c. How much do 9 avocados cost? b. $ Twelve large bottles of water cost $9. c. $5.25 a. How many bottles can you buy for $3? 3. b. What is the cost per bottle of water? a. $32 c. How much would 7 bottles of water cost? b. $ A 10-pound sack of flour costs $8. Anticipated misconceptions a. How much does 40 pounds of flour cost? Some students may have difficulty with the answers not being integers. Either fractions or decimals are acceptable. b. What is the cost per pound of flour? Fractions provide the most direct route, but decimals are common for working Unit 2: Introducing Ratios, Lesson 8: How Much for One? 3

4 with dollars and cents. Also, students may use the larger numbers as the dividend, simply because they are larger. Encourage students to check the reasonableness of their answers. Are you ready for more? Is bigger always better? It is commonly thought that buying larger packages or containers, sometimes called buying in bulk, is a great way to save money. For example, a 6-pack of soda might cost $3 while a 12-pack of the same brand costs $5. Find 3 different cases where it is not true that buying in bulk saves money. You may use the internet or go to a local grocery store and take photographs of the cases you find. Make sure the products are the same brand. For each example that you find, give the quantity or size of each, and describe how you know that the larger size is not a better deal. Possible Responses Answers vary. Unit 2: Introducing Ratios, Lesson 8: How Much for One? 4

5 8.3: More Shopping (15 minutes) Setup: Students in groups of 3 4. Provide tools for creating a visual display and access to rulers. Discuss the meaning of at this rate. Unit 2: Introducing Ratios, Lesson 8: How Much for One? 5

6 1. Four bags of chips cost $6. 1. a. The cost per bag is $1.50. a. What is the cost per bag? b. At this rate, how much will 7 bags of chips cost? 2. At a used book sale, 5 books cost $15. a. What is the cost per book? b. At this rate, how many books can you buy for $21? b. Seven bags cost $ a. The cost per book is $3. b. You can buy 7 books for $ a. The cost per bracelet is 25 cents. 3. Neon bracelets cost $1 for 4. a. What is the cost per bracelet? b. At this rate, how much will 11 neon bracelets cost? Pause here so you teacher can review your work. 4. Your teacher will assign you one of the problems. Create a visual display that shows your solution to the problem. Be prepared to share your solution with the class. b. Eleven bracelets cost $2.75. Anticipated misconceptions The first and third questions involve using decimals to represent cents. If the decimal point is forgotten, remind students that the cost of the bracelet is less than one dollar, and the cost of the chips is in between one and two dollars. Watch for students working in cents instead of dollars for the bracelets. They may come up with an answer of Unit 2: Introducing Ratios, Lesson 8: How Much for One? 6

7 275 cents. For these students, writing 25 cents as $0.25 should help, or consider reminding them of the avocados from a previous activity, which had a unit price of $0.50. Lesson Synthesis (5 minutes) How do I find a unit price? Why is a unit price a useful thing to know? 8.4: Unit Price of Rice (Cool-down, 5 minutes) Setup: None. Here is a double number line showing that it costs $3 to buy 2 bags of rice: 1. 8 bags 2. $ $30 1. At this rate, how many bags of rice can you buy with $12? 2. Find the cost per bag. 3. How much do 20 bags of rice cost? Unit 2: Introducing Ratios, Lesson 8: How Much for One? 7