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Measurement Session 10: Classroom Case Studies
 
Session 10 Session 10 6-8 Part A Part B Part C Homework
 
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Session 10, Part C:
Problems That Illustrate Measurement Reasoning (55 minutes)

In this part, you'll look at several problems that are appropriate for students in grades 6-8. For each problem, answer the below questions. If time allows, obtain the necessary materials and solve the problems.

 Questions to Answer:

a. 

What is the measurement content in the problem? What are the big ideas that you want students to consider and understand?

b. 

What prior knowledge is required? What later content does it prepare students for?

c. 

How does the content in this problem relate to the mathematical ideas in this course?

d. 

What other questions might extend students' thinking about the problem?

e. 

What other instructional activities or problems might you use in conjunction with this one to further your content goals?

Problem C1

Solution  

Bicycles are equipped with different types of tires. Twenty-six-inch tires have a diameter of 26 in., whereas 28 in. tires have a diameter of 28 in. You are riding a bicycle with 26 in. tires. If one turn of the pedals moves you forward one tire rotation, how many times must you turn the pedals to ride 1 mile?

 

Problem C2

Solution  

Take a unit cube and increase all three dimensions by the scale factor in the table below. For example, to make a new cube that has a scale factor of 2:1, you would double the length, width, and height. The new cube would have dimensions of 2 by 2 by 2, a surface area of 24 square units, and a volume of 8 cubic units. Fill in the chart with the dimensions, surface area, and volume of the new, scaled-up cubes.

Scale Factor

Dimensions

Surface Area

Volume

1:1

2:1

3:1

4:1

5:1

10:1

25:1

Examine the surface-area and the volume columns in your table. What patterns of growth do you notice? Can you determine a general rule?


 

Problem C3

Solution  

Charlene is out surfing and catches the eye of her friend, Dave, who is standing at the top of a vertical cliff. The angle formed by Charlene's line of sight and the horizontal measures 28 degrees. Charlene is 50 m out from the bottom of the cliff. Charlene and Dave are both 1.7 m tall. The surfboard is level with the base of the cliff. How high is the cliff?


 

Problem C2 adapted from Mathscape: Gulliver's Worlds. p. 31. © 1988 by Glencoe/McGraw Hill. www.glencoe.com/sec/math

Problem C3 adapted from Fendel, D.; Resek, D.; Alper, L.; Fraser, S. Interactive Mathematics Program Year 1: Shadows. p. 181. © 1997 by Key Curriculum Press, 1150 65th Street, Emeryville, CA 94608. 1-800-995-MATH. www.keypress.com

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