 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum                                 Lesson Plans:    Introduction   Lesson Plan 1: Overrun by Skeeters - Exponential Growth   Lesson Plan 2: Bigger and Smaller - Exponent Rules     Download the Workshop 6 Guide          Lesson Plan 2: Bigger and Smaller - Exponent Rules

The questions below dealing with concepts related to exponents have been selected from various state and national assessments. Although the lesson above may not fully equip students to answer all such test questions successfully, students who participate in active lessons like this one will eventually develop the conceptual understanding needed to succeed on these and other state assessment questions.

• Taken from the Massachusetts Comprehensive Assessment, Grade 10 (Spring 2002):
What is the simplest form of the expression
2x4y2 / x2y2, x 0, y 0?

Solution: 2x4y2 / x2y2 = 2(x4 - 2)(y2 - 2) = 2x2
• Taken from the Massachusetts Comprehensive Assessment, Grade 10 (Spring 2002):

On January 1, 2000, a car had a value of \$15,000. Each year after that, the car's value will decrease by 20 percent of the previous year's value. Which expression represents the car's value on January 1, 2003?

A. 15,000(0.8)3 (Correct Answer)
B. 15,000(0.8)4
C. 15,000(0.2)3
D. 15,000(0.2)4

• Taken from the Colorado State Assessment Program, Grade 10 (2002):
Number cubes are the basis for many games. Each face of a number cube is identified by a number from 1 to 6. Some games use one number cube and some games use multiple number cubes.

Part C - Complete the table below to show the number of possible outcomes when 2, 3, 4, and 5 number cubes are used.

 Number of Cubes 1 2 3 4 5 Number of possible outcomes 6

Solution: There are 62 = 36 outcomes when two cubes are used, 63 = 216 outcomes for three cubes, 64 = 1296 outcomes for four cubes, and 65 = 7776 outcomes for five cubes. In general, there are 6n outcomes for n cubes.
• Taken from the Virginia Standards of Learning Assessment, Algebra I (Spring 2001):
Which is equivalent to: A. 1/b3

B. b3

C. b4 (Correct Answer)

D. b8

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