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Using Clicker Items to Deepen Understanding of Measurement Concepts

Using Clicker Items to Deepen Understanding of Measurement Concepts Foster Desirable Habits of Mind. Logging In Procedure. 1. Turn -on your clicker. 2. Wait until it says “Enter Student ID” (Enter your 5-digit ID). 3. The screen should display “ANS”.

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Using Clicker Items to Deepen Understanding of Measurement Concepts

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  1. Using Clicker Items to • Deepen Understanding of Measurement Concepts • Foster Desirable Habits of Mind

  2. Logging In Procedure • 1. Turn-on your clicker • 2. Wait until it says “Enter Student ID”(Enter your 5-digit ID) • 3. The screen should display “ANS”

  3. Suppose p kilometers is equal to q feet, where p and q are positive numbers. • Which statement is correct? • p > q • p <q • p = q • None of the above Item 1

  4. Suppose p kilometers is equal to q feet, where p and q are positive numbers. • Which statement is correct? • p > q • p <q • p = q • None of the above Revote 1

  5. Suppose p kilometers is equal to q feet, where p and q are positive numbers. • Which statement is correct? • p > q • p <q • p = q • None of the above Fact: 1 km  0.62 mile; 1 mile = 5280 feet Procedure: 1 km  0.62 x 5280 feet = 3273.6 feet HoM: Explore and generalize a pattern

  6. Concept: Conservation (recognizing smaller units will produce larger counts) HoM: Explore and generalize a pattern

  7. Concept: Conservation (recognizing smaller units will produce larger counts) 1 wav ? wavs ? 1 arro ?arros

  8. Concept: Conservation (recognizing smaller units will produce larger counts) 1 wav  3.7 wavs 1 arro  7arros Concept: Measurement involves iterating a unit

  9. Concept: Conservation (recognizing smaller units will produce larger counts) 1 wav  3.7 wavs 1 arro  9.6 arros Concept: Measurement involves iterating a unit Concept: Units must be consistent Concept: Inverse relationship between the size of a unit and the numerical count

  10. True or False: If the volume of a rectangular prism is known, then its surface area can be determined. Item 2

  11. True or False: If the volume of a rectangular prism is known, then its surface area can be determined. Revote 2

  12. True or False: If the volume of a rectangular prism is known, then its surface area can be determined. Concept: Volume = Length  Width  Height HoM: Reasoning with Change and Invariance

  13. “[S]ome students may hold the misconception that if the volume of a three-dimensional shape is known, then its surface area can be determined. • This misunderstanding appears to come from an incorrect over-generalization of the very special relationship that exists for a cube.” • (NCTM, 2000, p. 242)

  14. True or False: If the surface area of a sphere is known, then its volume can be determined. Item 3

  15. True or False: If the surface area of a sphere is known, then its volume can be determined. Revote 3

  16. True or False: If the surface area of a sphere is known, then its volume can be determined. Concept: A = 4 r2 V = 4/3 r3 HoM: Reasoning with Formulas

  17. True or False: If the area of an equilateral triangle is known, then its perimeter can be determined. Item 4

  18. True or False: If the area of an equilateral triangle is known, then its perimeter can be determined. Revote 4

  19. True or False: If the area of an equilateral triangle is known, then its perimeter can be determined. CU: Area = ½LH = ½L [L2 – (L/2)2] 0.5 = ½L (0.75L2)0.5 = ½L (0.75)0.5 L  0.433L2 L L H L/2 L HoM: Reasoning with Relationships

  20. True or False: As we increase the perimeter of a rectangle, the area increases. Item 5

  21. True or False: As we increase the perimeter of a rectangle, the area increases. Revote 5

  22. True or False: As we increase the perimeter of a rectangle, the area increases. HoM: Seeking causality

  23. True or False: As we increase the perimeter of a rectangle, the area increases. 16 m 2 m 4 m 8 m Concept: Perimeter = 2L + 2W ;Area = LW HoM: Seeking counter-example

  24. True or False: As we increase the perimeter of a rectangle, the area increases. 20 m 0.5 m 1 m 2 m 16 m 4 m 12 m 8 m Concept: Perimeter = 2L + 2W ;Area = LW HoM: Reasoning with change and invariance

  25. “While mixing up the terms for area and perimeter does not necessarily indicate a deeper conceptual confusion, it is common for middle-grades students to believe there is a direct relationship between the area and the perimeter of shapes and this belief is more difficult to change. • In fact, increasing the perimeter of a shape can lead to a shape with a larger area, smaller are, or the same area.” • (Driscoll, 2007, p. 83)

  26. Consider this two-dimensional figure: 4 cm 7 cm 10 cm Note: Each corner is a right angle.

  27. Consider this two-dimensional figure: Which measurement can be determined? Area only Perimeter only Both area and perimeter Neither area nor perimeter 4 cm 7 cm 10 cm Note: Each corner is a right angle. Item 6

  28. Consider this two-dimensional figure: Which measurement can be determined? Area only Perimeter only Both area and perimeter Neither area nor perimeter 4 cm 7 cm 10 cm Note: Each corner is a right angle. Revote 6

  29. 4 cm 7 cm 10 cm HoM: Reasoning with Change and Invariance

  30. Consider this two-dimensional figure: 4 m 3 m 10 m Which measurement can be determined? Area only Perimeter only Both area and perimeter Neither area nor perimeter Note: The two horizontal lines are parallel. Item 7

  31. Consider this two-dimensional figure: 4 m 3 m 10 m Which measurement can be determined? Area only Perimeter only Both area and perimeter Neither area nor perimeter Note: The two horizontal lines are parallel. Revote 7

  32. Consider this two-dimensional figure: 4 m 4 m 4 m 4 m 4 m HoM: Reasoning with Change and Invariance Note: The two horizontal lines are parallel.

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