Unit 3, Lesson 1: How Well Can You Measure?

Transcription

1 Unit 3, Lesson 1: How Well Can You Measure? Lesson Goals Decide whether a relationship is proportional using a graph and a quotient. Understand that due to measurement error, if a graph of two associated quantities is close to a line through the origin, or quotients are close to each other, there might be a proportional relationship. Understand that if a graph of two associated quantities is clearly not close to a line through the origin, or quotients are clearly not close to each other, this is enough to conclude there is not a proportional relationship. Required Materials copies of blackline master four-function calculators rulers marked with centimeters 1.1: Estimating a Percentage (5 minutes) Setup: Instruct students to find a method of estimation other than performing long division. Student task statement A student got 16 out of 21 questions correct on a quiz. Use mental estimation to answer these questions. Possible responses 1. Less than 80% 1. Did the student answer less than or more than 80% of the questions correctly? 2. More than 75% 2. Did the student answer less than or more than 75% of the questions correctly? Unit 3: Measuring Circles, Lesson 1: How Well Can You Measure? 1

2 1.2: Perimeter of a Square (15 minutes) Setup: Students in groups of 3. Copies of blackline master and rulers. Assign 3 squares to each group. Unit 3: Measuring Circles, Lesson 1: How Well Can You Measure? 2

3 Student task statement Here are nine squares. Possible responses 1. Answers vary, but each group should have 3 rows of the table filled in. In each case the number in the right column is a little less than 3 times the number in the left column. 2. Answers vary, but each group should have 3 points on the graph that almost lie on a straight line through the origin. 3. Answers vary. Your teacher will assign your group three of these squares to examine more closely. Unit 3: Measuring Circles, Lesson 1: How Well Can You Measure? 3

4 1. For each of your assigned squares, measure the length of the diagonal and the perimeter of the square in centimeters. Check your measurements with your group. After you come to an agreement, record your measurements in the table. square A square B square C square D square E diagonal (cm) perimeter (cm) square F square G square H square I 2. Plot the diagonal and perimeter values from the table on the coordinate plane. Unit 3: Measuring Circles, Lesson 1: How Well Can You Measure? 4

5 3. What do you notice about the points on the graph? Unit 3: Measuring Circles, Lesson 1: How Well Can You Measure? 5

6 1.3: Area of a Square (15 minutes) Setup: Students in same groups, working with same squares. 4 minutes of group work time, pause to construct a class graph, 2 3 minutes more group work time followed by whole-class discussion. Unit 3: Measuring Circles, Lesson 1: How Well Can You Measure? 6

7 Student task statement 1. In the table, record the length of the diagonal for each of your assigned squares from the previous activity. Next, calculate the area of each of your squares. Possible responses 1. See lesson plan. square A square B diagonal (cm) area (cm 2 ) 2. Answers vary. Sample responses: The graph appears to curve upward. The relationship is not proportional. square C square D square E square F square G square H square I Pause here so your teacher can review your work. Be prepared to share your values with the class. 2. Examine the class graph of these values. What do you notice? 3. How is the relationship between the diagonal and area of a square the same as the relationship between the diagonal and perimeter of a square from the previous activity? How is it different? 3. As the diagonal of a square increases, both perimeter and area increase. Perimeter is proportional to the length of the diagonal but area is not. Anticipated misconceptions Some students may struggle to calculate the area of the squares, or may use the length of the diagonal as if it were the side length. Prompt them with questions like How can you calculate the area of a rectangle? What is the length and width of your square? Some students may measure the side Unit 3: Measuring Circles, Lesson 1: How Well Can You Measure? 7

8 length of each square again, instead of dividing the perimeter from the previous activity by 4. This strategy is allowable, although you can also prompt them to consider if they no longer had access to a ruler, is there a way they could use the information they already recorded to find this measurement. Are you ready for more? Here is a rough map of a neighborhood. Some students may struggle to organize the information. Prompt them to add a column to the table in the previous activity to record the side length of the squares. There are 4 mail routes during the week. On Monday, the mail truck follows the route A-B-E-F-G-H-A, which is 14 miles long. On Tuesday, the mail truck follows the route B-C-D-E-F-G-B, which is 22 miles long. On Wednesday, the truck follows the route A-B-C-D-E-F-G-H-A, which is 24 miles long. On Thursday, the mail truck follows the route B-E-F-G-B. How long is the route on Thursdays? Possible Responses Thursday s route is 12 miles long. Unit 3: Measuring Circles, Lesson 1: How Well Can You Measure? 8

9 Lesson Synthesis (5 minutes) How can we tell, using a graph, if two quantities are in a proportional relationship? Why is measurement error important when decide if two quantities are in a proportional relationship? 1.4: Examining Relationships (Cool-down, 5 minutes) Setup: None. Unit 3: Measuring Circles, Lesson 1: How Well Can You Measure? 9

10 Student task statement 1. The graph shows the height of a plant after a certain amount of time measured in days. Possible responses 1. Maybe yes. Maybe no. Do you think that there may be a proportional relationship between the number of days and the height of the plant? Explain your reasoning. 2. Definitely no. 2. The graph shows how much snow fell after a certain amount of time measured in hours. Unit 3: Measuring Circles, Lesson 1: How Well Can You Measure? 10

11 Do you think that there may be a proportional relationship between the number of hours and the amount of snow that fell? Explain your reasoning. Unit 3: Measuring Circles, Lesson 1: How Well Can You Measure? 11