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 2: Cups and Chips - Solving Linear Equations Using Manipulatives

The questions below dealing with solving linear equations 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 Maine Educational Assessment, Mathematics, Grade 11 (2002:
Clem's balloon is 200 feet off the ground and rising at a rate of 5 feet per second. Mary's balloon is 100 feet off the ground and rising at a rate of 9 feet per second. In how many seconds will the two balloons be at the same height? Show how you found your answer.

Solution: The height of Clem's balloon can be represented as 200 + 5t, and the height of Mary's balloon can be represented as 100 + 9t, where t is the number of seconds from now. The balloons will be at the same height when 200 + 5t = 100 + 9t, or when t = 25 seconds.
• Taken from the Massachusetts Comprehensive Assessment, Grade 10 (Spring 2002):
Solve the following equation for x.
3x - (2x - 3) = 2x - 9

Solution:
3x - (2x - 3) = 2x - 9
3x - 2x + 3 = 2x - 9
x + 3 = 2x - 9
x = 12
• Taken from the Maryland High School Algebra Exam (2002):
Terry is going to the county fair. She has two choices for purchasing tickets, as shown in the table below.

 Ticket Choices Admission Price Cost per Ride A \$6.00 \$0.50 B \$2.00 \$0.75

• Write an equation for Terry's total cost (y) for ticket
Choice A. Then write an equation for Terry's total cost (y) for ticket Choice B. Let x represent the number of rides she plans to go on.

• How many rides would Terry have to go on for the total cost of ticket A and ticket B to be equal? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

• Terry plans to go on 14 rides. To spend the least amount of money, which ticket choice should Terry choose? Use mathematics to justify your answer.

Solution:
For Choice A, the equation is y = 6 + 0.5x; for Choice B, y = 2 + 0.75x.

For the total costs to be equal, 6 + 0.5x = 2 + 0.75x, or x = 16; therefore, Terry would have to go on 16 rides.

For 14 rides, Choice A would cost 6 + 0.5(14) = \$13. Choice B would cost 2 + 0.75(14) = \$12.50. Terry should choose ticket B.
• Taken from the California High School Exit Examination (2002):

Solve for x:

2x - 3 = 7

A. -5
B. -2
C. 2