Session 5, Part A: Linear Relationships in Patterns

Session 5, Part A:
Linear Relationships in Patterns

In This Part: Finding the Pattern | Spreadsheet Tutorial | Using a Spreadsheet



Problem A4
Open a spreadsheet on your computer and enter your table from Problem A1 into the first two columns. Each cell in the first column will contain the number of squares in a row. The cell next to it in the second column will contain the number of toothpicks needed to build that number of squares. Note 3


Problem A5
Use your spreadsheet program to create a graph of the numbers in these two columns.

If you need more help with this, click here for the spreadsheet tutorial on graphing. Close Tip

Video Segment
In this video segment, Professor Cossey asks whether or not the points on Problem A5's graph should be connected with a line. Watch the segment after you've completed Problem A5.

In what situations should the points on a graph be connected?
What does connecting two points on a line imply about the points in between?

You can find this segment on the session video, approximately 7 minutes and 23 seconds after the Annenberg Media logo.

Different types of function rules can be entered into a spreadsheet. Note 4

Example: Closed-Form Rule
The formula y = 3x + 7 expresses the dependent variable y as a function of the independent variable x. Suppose that the values of x appear in the first column, beginning at cell A2, and the corresponding values of y are placed in the third column, beginning with C2. The formula would first be entered in C2 as "=3*A2+1," and then the fill down command would be used to complete the remaining values of y.

Example: Recursive Rule
Suppose you have a recursive rule that says "The first output is 10; to get any other output, subtract 2 from the output before it." You would enter the first output into cell C2. Then you could enter the formula "=C2-2" in C3, and use the fill down command for the remaining cells.


Problem A6
Enter your formula from Problem A2 into the third column of your spreadsheet. Compare the values computed by the spreadsheet program using your formula with those you entered by hand. Are they the same?


Problem A7
Enter your recursive rule from Problem A3 into the fourth column of your spreadsheet. Are the values computed by the spreadsheet program the same as those you entered by hand?



You can extend your formula to more values by filling down the output column. You will need to either enter the input numbers by hand or enter a formula that increases numbers in that column by one each time. See the spreadsheet tutorial for more information on how to do this.


Problem A8
Use the spreadsheet program to create a graph of the input/output columns for either of your rules.

Next > Part B: Slope

Session 5: Index | Notes | Solutions | Video