Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 Lesson Plans: Introduction Lesson Plan 1: Mathematical Modeling, Circular Movement and Transmission Ratios Lesson Plan 2: Skeeter Populations and Exponential Growth

Lesson Plan 1: Mathematical Modeling, Circular Movement and Transmission Ratios

The questions below dealing with mathematical modeling have been selected from various state and national assessments. Although the lesson above may not fully equip students with the ability 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 New York Regents Exam, Mathematics (August 2002):

In the accompanying diagram, x represents the length of a ladder that is leaning against a wall of a building, and y represents the distance from the foot of the ladder to the base of the wall. The ladder makes a 60° angle with the ground and reaches a point on the wall 17 feet above the ground. Find the number of feet in x and y.

Solution: The triangle formed by the ladder, the wall, and the ground is a 30-60-90 triangle. Consequently, feet,

and feet. Another solution method would

be for students to use right-triangle trigonometry.

The graph below shows the height of Cindy's model rocket during the course of its flight.

Which of these equations can be used to find the height of the rocket at any time during its flight?

A. y = 9x
B. y = x2 - 81
C. y = x2 + 9x
D. y = 9x - x2 (correct answer)
• Taken from the Virginia End of Course Exam, Algebra I (Spring 2001):

Mary published her first book. She was given \$10,000.00 and an additional \$0.10 for each copy of the book that sold. Her earnings, d, in dollars, from the publication of her book are given by:

d = 10,000 + 0.1n

where n is the number of copies sold. During the first year Mary earned \$35,000.00 from the publication and sale of her book. How many copies of her book sold in the first year?

A. 25,000
B. 35,000