Activity 5. Applications Utilizing the Concepts

These concepts apply to real life situations. Here is a simple example:

Use the tool SimulateousEqn.xls, which displays the graph for simultaneous equations.

Do This:

NOTE: To complete a change to the tool press the enter key after typing the new value.

Write an equation to express the following situation algebraically:

Magix Pens at Friendly’s Supermarket are sold at $4.00 each.

Example: Write an equation to model the cost in buying Magix Pens at Friendly’s:

y = 4x or C(x) = 4x

At Cheapee’s Store, Magix Pens cost $2.00 each.

a. Write an equation to express the cost of Magix pens at Cheapee’s

b. Using the simultaneous equation tool, insert values for “m” and “b” for both equations located at the top left side above the graph. Explain what you noticed about the differences in the slopes between the two lines and explain the differences in the context of the problem.

c. Suppose that at Cheapee’s Express Store, Magix Pens cost $2.00 each but there is a one-time standing charge of $4.00 for packaging regardless of the number of pens bought. Write an equation to model the cost of Magix Pens at Cheapee’s Express.

d. In the simultaneous equation tool change the equation that represents the cost of Magix Pens at Cheapee’s to reflect the case in part “c”, and study the resulting graphs, using them to assist you in answering these questions.

(1) In terms of cost, when would it not matter from which store the Magix Pens were bought? Give the number of pens and explain why.

(2) When should someone buy at each store, and why?

(3) If Jennifer had exactly $8.00 to spend on Magix Pens, what might be the deciding factor as to which store she buys the pens from? Explain your answer.

(4) Algebraically solve the cost of buying one Magix Pen from each store respectively, and then explain how you can find the answer by simply examining the graph lines

(5) Give the slope and y-intercept in each case and explain how you found them and whether you could have used another method.

(6) In the context of the problem, explain the meaning of the slope and y-intercept. Be specific in relating your answer to the situation at Cheapee’s Express and at Friendly’s.

(7) In the context of the problem, explain the meaning of a negative value for x. Explain if this makes sense for buying pens.

(8) Based on the answer in part “7”, what single quadrant makes sense for the problem?

TEACHER NOTES

This lesson incorporates the following teaching strategies bases on the NCTM standards.

• Technology integration
• Interactive learning
• Concept-building through discovery
• Actively building new knowledge from experience and prior knowledge
• Discourse in mathematics
• Formulate explanations
• Mathematical literacy
• Using modeling to solve problems
• Making connections by investigating various models
• Promoting mathematics as a tool for solving real life problems

In addition the lesson meets the following technology guidelines specified by Garofolo, Drier, Harper, Timmerman, and Shockey (2000):

• Using technology in context
• Applying technology to meaningful problems
• Employing technology to improve pedagogy
• Connect mathematical topics
• Use multiple representations