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Released Items. NSF REC #0337595 Knowledge of Mathematics for Teaching Algebra Project (2004 – 2007). © 2005 Division of Science and Mathematics Education Michigan State University. Sample Item 1: Identifying an Exponential Function (School Knowledge).

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released items

Released Items

NSF REC #0337595

Knowledge of Mathematics for Teaching Algebra Project

(2004 – 2007)

© 2005 Division of Science and Mathematics Education

Michigan State University

NSF REC #0337595 Released Items

sample item 1 identifying an exponential function school knowledge
Sample Item 1: Identifying an Exponential Function(School Knowledge)

Which of the following situations can be modeled using an exponential function?

i. The height h of a ball t seconds after it is thrown into the air.

ii. The population P of a community after t years with an increase of n people annually.

iii. The value V of a car after t years if it depreciates d% per year.

A. i only

B. ii only

C. iii only

D. i and ii only

E. ii and iii only

NSF REC #0337595 Released Items

results identifying an exponential function
Results: Identifying an Exponential Function

NSF REC #0337595 Released Items

sample item 2 properties of number systems advanced mathematical knowledge
Sample Item 2: Properties of Number Systems(Advanced Mathematical Knowledge)

For which of the following sets S is the following statement true?

For all a and b in S, if ab = 0, then either a = 0 or b = 0.

i. the set of real numbers

i. the set of complex numbers

iii. the set of integers mod 6

iv. the set of integers mod 5

v. the set of 2x2 matrices with real number entries

A. i only D. i, ii, iii and iv only

B. i and ii only E. i, ii, iii, iv, and v

C. i, ii and iv only

NSF REC #0337595 Released Items

results properties of number systems
Results: Properties of Number Systems

NSF REC #0337595 Released Items

sample item 3 identifying student s error in solving a linear equation teaching knowledge
Sample Item 3: Identifying Student’s Error in Solving a Linear Equation(Teaching Knowledge)

A student solved the equation

3(n - 7) = 4 - n

and obtained the solution n = 2.75.

What might the student have done wrong?

NSF REC #0337595 Released Items

results identifying student s error
Results: Identifying Student’s Error

NSF REC #0337595 Released Items

sample item 4 interpreting and relating equivalent expressions teaching knowledge
Hot tubs and swimming pools are sometimes surrounded by borders of tiles. The drawing at the right shows a square hot tub with sides of length s feet. This tub is surrounded by a border of 1 foot by 1 foot square tiles.

s

Sample Item 4: Interpreting and Relating Equivalent Expressions(Teaching Knowledge)

How many 1-foot square tiles will be needed for the border of this pool?

a. Paul wrote the following expression: 2s + 2(s+2)

Explain how Paul might have come up with his expression.

b. Bill found the following expression: (s+2)2 - s2

Explain how Bill might have found his expression.

c. How would you convince the students in your class that the two expressions

above are equivalent?

NSF REC #0337595 Released Items

slide9

Results: Equivalent Expressions

NSF REC #0337595 Released Items