Lesson Plans: Introduction Lesson Plan 1: Miles of Tiles - The Pool Border Problem Lesson Plan 2: Cups and Chips - Solving Linear Equations Using Manipulatives

Lesson Plan 1: Miles of Tiles - The Pool Border Problem

The questions below dealing with translating words into symbols 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 standardized assessment questions.

• Taken from the Maine Educational Assessment, Mathematics, Grade 11 (2002):
Carl needed to rent a car for one week. He collected the following information.
• Hillbrook Car Rentals charges \$230/week plus 20¢ per mile.
• Bridge Car Rentals charges \$210/week plus 25¢ per mile.
a. Write an equation for the cost, c, to rent from Hillbrook Car Rentals if Carl drives the car x miles.

b. Write an equation for the cost, c, to rent from Bridge Car Rentals if Carl drives the car x miles.

c. For what number of miles will it cost the same to rent a car from the two companies? Show or explain how you found your answer.

Solution: For Hillbrook Rentals, c = 230 + 0.2x. For Bridge Car Rentals, c = 210 + 0.25x. The cost will be the same when the value of c is equal for both companies, which occurs when
230 + 0.2x = 210 + 0.25x, or when x = 400 miles.

• Taken from the Maryland High School Algebra Exam (2002):

Lydia has \$200 in her bank account at the beginning of the year. Each month, she deposits \$40 into her account. She does not withdraw any money from her account, and the account pays no interest. Which of these equations could Lydia use to find the total amount (T) in her bank account at the end of m months?

A. T = 40m
B. T = 240m
C. T = 200m + 40
D. T = 40m + 200 (correct answer)

• Taken from the New York Regents High School Examination (January 2003):
The equation P = 2L + 2W is equivalent to

 A. (correct answer) B. C. D.
• Taken from the Mississippi Algebra I Test, Version 2 (2003):

Jan took a taxi to visit the Petrified Forest northwest of Jackson, Mississippi. The taxi fare for the trip was \$14.80, based on a fixed charge of \$2.00 plus a charge of \$0.80 for each mile. Which of these could be used to determine m, the number of miles that Jan rode in the taxi?

A. 14.80 = 2 + 0.80m (correct answer)
B. 14.80 = 2m + 0.80
C. 14.80m = 2 + 0.80m
D. 14.80m = 2m + 0.80