Activity 5. Applications Utilizing the Concepts
These concepts apply to real life situations. Here is asimple example:
Use the tool SimulateousEqn.xls, which displays the graphfor simultaneous equations.
NOTE: To complete a change to the tool press the enter keyafter typing the new value.
Write an equation to express the following situationalgebraically:
Magix Pens at Friendly’s Supermarket are sold at $4.00 each.
Example: Write anequation 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 costof 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 sideabove the graph. Explain what you noticed about the differences in the slopesbetween the two lines and explain the differences in the context of theproblem.
c. Suppose that at Cheapee’s ExpressStore, 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 equationto model the cost of Magix Pens at Cheapee’s Express.
d. In the simultaneous equation toolchange the equation that represents the cost of Magix Pens at Cheapee’s toreflect the case in part “c”, and study the resulting graphs, using them toassist you in answering these questions.
(1) In terms of cost, when would it notmatter from which store the Magix Pens were bought? Give the number of pens andexplain why.
(2) When should someone buy at each store,and why?
(3) If Jennifer had exactly $8.00 to spendon Magix Pens, what might be the deciding factor as to which store she buys thepens from? Explain your answer.
(4) Algebraicallysolve the cost of buying one Magix Pen from each store respectively, and thenexplain how you can find the answer by simply examining the graph lines
(5) Give the slope and y-intercept in eachcase and explain how you found them and whether you could have used anothermethod.
(6) In the context of the problem, explainthe meaning of the slope and y-intercept. Be specific in relating your answerto the situation at Cheapee’s Expressand at Friendly’s.
(7) In the context of the problem, explainthe meaning of a negative value for x. Explain if this makes sense for buyingpens.
(8) Based on the answer in part “7”, whatsingle quadrant makes sense for the problem?
This lesson incorporates the following teaching strategiesbases 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 technologyguidelines 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