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Modeling Situations With Linear Equations
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  • Improve Individual Solutions to the Assessment Task (10 minutes)
      • Give students back their work on assessment task The Guitar Class, along with a fresh copy of that task sheet.
        • Work on your own for ten minutes.
        • Remember the work you did on The Guitar Class.
        • I'm giving you your own answers, and a new sheet to work on.
        • Read through your original solution and think about what you learned in the last lesson.
        • I want you to use what you have learned to improve your solution for The Guitar Class. Then compare your answers to see what progress you have made.
  • Solutions: The Guitar Class
      1. p = 70n - 400
      2. The point where the graph crosses the horizontal axis is helpful in identifying the number of students that must attend before the music teacher will break even. Thus 5 students will make a loss, but 6 students will make a profit.
      3. p = nf - c
      4. f = p + c
  • Solutions: Making Candles
      1. The student may give a description such as "You find how much money is made by selling them then take off the cost of the kit", a formula such as p = ns - k , or a written calculation such as p = 60 x 4 - 50.

        The calculation method stays the same: you always subtract the costs from the revenue to find profit.

      2. For example: s = p + k  or s = 190 + 50
        n 60

        As in Question 2, the method stays the same whatever values are substituted.

      3. Look for a table of values with an appropriate range of values for n, including cases when p is negative. Check that the graph shows values in equal increments along the axes, is plotted accurately, shows the intercepts, and that the points fit a straight line. The x-intercept is (12.5,0): since you cannot sell half a candle (n is a discrete variable) this means that at least 13 candles must be sold in order to make a profit. You could discuss whether or not it is correct to draw a line joining the points.

      4. p = ns - k

        k = ns - p

        s = p + k
        n = p + k
  • Solutions: Rescue Helicopter
    • The formulas are:

      t = d + w

      d = s(t - w)

      s = d
      t - w
      w = t - d

      Stress that t is the total duration, not the time taken to cover the distance.

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