Linear Equation Activity

Symbolic Manipulation
Using Technology


Teachers Notes: Rationale/Level for Lesson

Objective:
Given a "real world" situation students will write an equation which represents the problem stated. The activity will ask students to use estimation to determine the reasonableness of an answer then students will be guided through the symbolic manipualation required to solve the equation using the graphing calculator (dynamic algebra solftware).

Background:
When solving problems involving money, it usually takes more than one step. For example, to find the amount of sales tax to be charged, you first find the sum of the items to be purchased, then multiply the total by the tax rate. Solving multi step problems involves solving multi step equations.

Problem Statement:
Jim wanted to buy six mugs and six glasses. He knew that the cost of one mug is $5.98 and the cost of one glass is $2.99. The salesperson rang up an amount that he thought was too high, $65.78. Help Jim to determine if the salesperson miscalculated.

  1. Estimate the combined cost of one mug and one glass. __________

  2. Estimate the total cost of 6 mugs and 6 glasses. __________

  3. Do you think Jim was overcharged? Explain.



Part I: As Jim watched the salesperson ring up his purchases he thought he saw her correctly charge him for 6 mugs @ $5.98 a piece for a total of $35.98. He wants to know how many glasses he was charged for to reach the total of $65.78.

  1. Write an equation that models this problem using the information stated
    above.

    1. What facts does Jim have?

    2. What information is Jim missing? Identify a variable to represent the unknown value(s).


    3. Write the equation that models this problem.

  2. Jim needs to find the value of the variable assigned to represent the
    unknown information. ( number of glasses)

    1. Isolate the term containing the variable

      1. Using inverse operations, subtract $35.88 from both sides.
      2. What is the next inverse operation to be performed? Do this step next .
      3. What is the value of n?

    2. Is your answer reasonable? How can you check?

    3. When Jim asked the salesperson to check, the register receipt showed that he had been charged for 7 mugs and 8 glasses. How is this possible?

  3. Now let's use NuCalc to solve the original equation from #2.

    1. Display the full keypad. Enter 65.78 = 35.88 + 2.99x
    2. Now solve for x using the same steps as described in #2

      1. Isolate the term containing x by highlighting 2.99x. Next select and click on the isolate key. Write the result below.

      2. ii. Isolate the variable x. Highlight the expression and evaluate if not simplified.

      3. iii. What is the value of x? Is the value from the calculator the same as that worked out by hand.


Part II:Now using the same process with NuCalc or Graphing Calculator 2.0 solve the following equations.

Show each step in the process.

1. 1.80 + 2X = 12.40

2. 5X - 20.5 = 10.75

3. 108.75 = 8X + 6.35

4. 9X + 36 = 396

5. 17x - 25 = 94

     6. 75 + 5x = 140

7. .5x - 85 = 15

8. (1/4)x + 60 = 180

9. (2/3)x + 35 = 75

10. x/5 - 150 = 350

Follow Up:
As we have seen, there is computer software that solve equations like the ones you just used. As equations become more complicated, you can use technology to solve them. However, explain why it is important to know how to write and solve equations without relying on technology.

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1998 Summer Institute || Onsite Participants || Online Participants || Sum98 Staff || Agenda
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Email: Marjorie Ader at mader@k12.colostate.edu

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