Using Clicker Items to Deepen Understanding of Measurement Concepts
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Transcript of Using Clicker Items to Deepen Understanding of Measurement Concepts
Using Clicker Items to
i. Deepen Understanding of Measurement Concepts
ii. 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”
Suppose p kilometers is equal to q feet, where p and q are positive numbers.
Which statement is correct?a. p > q b. p < qc. p = qd. None of the above
Item 1
Suppose p kilometers is equal to q feet, where p and q are positive numbers.
Which statement is correct?a. p > q b. p < qc. p = qd. None of the above
Revote 1
Suppose p kilometers is equal to q feet, where p and q are positive numbers.
Which statement is correct?a. p > q b. p < qc. p = qd. None of the above
Fact: 1 km 0.62 mile; 1 mile = 5280 feet
HoM: Explore and generalize a pattern
p q1 3273.6
2 6547.2
10 32736
Procedure: 1 km 0.62 x 5280 feet = 3273.6 feet
Concept: Conservation (recognizing smaller units will produce larger counts)
p q1 3273.6
2 6547.2
10 32736
HoM: Explore and generalize a pattern
?
1 wav
1 arro
? wavs
? arros
Concept: Conservation (recognizing smaller units will produce larger counts)
1 wav
1 arro
3.7 wavs
7 arros
Concept: Conservation (recognizing smaller units will produce larger counts)
Concept: Measurement involves iterating a unit
1 wav
1 arro
3.7 wavs
9.6 arros
Concept: Units must be consistent
Concept: Inverse relationship between the size of a unit and the numerical count
Concept: Measurement involves iterating a unit
Concept: Conservation (recognizing smaller units will produce larger counts)
True or False:
If the volume of a rectangular prism is known, then its surface area can be determined.
Item 2
True or False:
If the volume of a rectangular prism is known, then its surface area can be determined.
Revote 2
True or False:
If the volume of a rectangular prism is known, then its surface area can be determined.
HoM: Reasoning with Change and Invariance
Concept: Volume = Length Width Height
This misunderstanding appears to come from an incorrect over-generalization of the very special relationship that exists for a cube.”
(NCTM, 2000, p. 242)
“[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.
True or False:
If the surface area of a sphere is known, then its volume can be determined.
Item 3
True or False:
If the surface area of a sphere is known, then its volume can be determined.
Revote 3
True or False:
HoM: Reasoning with Formulas
Concept: A = 4 r 2
V = 4/3 r 3
If the surface area of a sphere is known, then its volume can be determined.
True or False:
If the area of an equilateral triangle is known, then its perimeter can be determined.
Item 4
True or False:
If the area of an equilateral triangle is known, then its perimeter can be determined.
Revote 4
L/2
L
True or False:
If the area of an equilateral triangle is known, then its perimeter can be determined.
HoM: Reasoning with Relationships
CU: Area = ½LH
HL
L
= ½L [L2 – (L/2)2] 0.5
= ½L (0.75L2)0.5
= ½L (0.75)0.5 L
0.433L2
True or False:
As we increase the perimeter of a rectangle, the area increases.
Item 5
True or False:
As we increase the perimeter of a rectangle, the area increases.
Revote 5
True or False:
As we increase the perimeter of a rectangle, the area increases.
HoM: Seeking causality
True or False:
As we increase the perimeter of a rectangle, the area increases.
8 m
4 m
Concept:Perimeter = 2L + 2W ; Area = LW
16 m
2 m
HoM: Seeking counter-example
True or False:
As we increase the perimeter of a rectangle, the area increases.
8 m
4 m12 m
2 m16 m
1 m
20 m0.5 m
HoM: Reasoning with change and invariance
Concept:Perimeter = 2L + 2W ; Area = LW
“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)
Consider this two-dimensional figure:
4 cm
10 cm
7 cm
Note: Each corner is a right angle.
Consider this two-dimensional figure:
Item 6
4 cm
10 cm
7 cm
Which measurement can be determined?
(A) Area only
(B) Perimeter only
(C) Both area and perimeter
(D) Neither area nor perimeter
Note: Each corner is a right angle.
Revote 6
Consider this two-dimensional figure:
4 cm
10 cm
7 cm
Which measurement can be determined?
(A) Area only
(B) Perimeter only
(C) Both area and perimeter
(D) Neither area nor perimeter
Note: Each corner is a right angle.
4 cm
10 cm
7 cm
HoM: Reasoning with Change and Invariance
Consider this two-dimensional figure:
Item 7
Which measurement can be determined?
(A) Area only
(B) Perimeter only
(C) Both area and perimeter
(D) Neither area nor perimeter
4 m
10 m
3 m
Note: The two horizontal lines are parallel.
Revote 7
Consider this two-dimensional figure:
Which measurement can be determined?
(A) Area only
(B) Perimeter only
(C) Both area and perimeter
(D) Neither area nor perimeter
4 m
10 m
3 m
Note: The two horizontal lines are parallel.
Consider this two-dimensional figure:
HoM: Reasoning with Change and Invariance
4 m4 m4 m4 m 4 m
Note: The two horizontal lines are parallel.