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Spreadsheet and Graphing Calculator

  • Spreadsheet and Graphing Calculator

    Grade: 6th to 8th, High School

    This tool can be used to investigate rational functions, like those in the lesson plan, Whelk-Come to Mathematics, or the exponential functions lesson plans, as found in Shedding the Light or Trout Pond. It can also be used to investigate any other functions that can be explored with a graphing calculator or spreadsheet software.

    Activity

    Instructions

    Click on the Y= or Plots tab. In this section, you can choose which of three types of relationships to graph.

    Relationships to Graph

    Y=In Y1 through Y5, you can enter an algebraic function to be graphed. Use + for addition, - for subtraction, * for multiplication, / for division, and ^ to raise an expression to a power. For instance, to represent the equation y = 3(x – 2)3 + 4, you would enter 3 * (n ‑ 2) ^ 3 + 4. In addition, the constants a, b, and c can be used within these functions to allow further investigation. For instance, if the equation for Y1= is entered as 3*a, then the graph of the function can be adjusted using the slide for a on the Graph tab.
     Next= For each Next equation, you can enter a Now-Next function to be graphed. These are recursive functions such as Next = Now + 5, which means that the Next value is equal to five more than the current (Now) value. (If you do not enter a value for "Starting At" the first value is assumed to be 0.)
    PlotBy checking the boxes for Plot1 through Plot5, you can indicate that columns from the Data tab should be graphed against one another.

      How to Use

      • The Data tab can be used to access the spreadsheet. Data in columns 1‑4 can be graphed by choosing the Plots in the Y= or Plots tab.
      • Select the Graph tab to see a graph of the functions selected under the Y= or Plots tab. (The sliders for a, b, and c can be adjusted to investigate various functions, if these constants have been used in the Y= or Plots tab. For instance the function Y1 = a*x+b can be entered, and the sliders can then be used to investigate linear functions of the form y = ax + b.)
      • The Window tab can be used to adjust which portion of the graph is displayed.
      • Highlighting the "Show Legend" box will label each function.

      Exploration

      Select the Y= or Plots tab, and enter the following function:
      Y1 = a * x + b

      This is the general form of a linear equation, where a is the slope of the line and b is the y‑intercept.

      Click on the Graph tab, and adjust the values for a and b using the sliders at the bottom of the screen.

      • How does the value of a affect the graph of the line? How does the line change when a is positive or negative?
      • How does the value of b affect the graph of the line? How does the line change when b is positive or negative?
      • Predict what the line for y = ‑3x + 8 will look like. Test your conjecture using the sliders to make a = ‑3 and b = 8.
       

      Objectives and Standards

      NCTM Standards and Expectations
      • Probability / Data Analysis and Statistics
      • 6-8
      • High School (9-12)
      • Data Analysis and Probability