Session 5, Part A:
Linear Relationships in Patterns (35 minutes)

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

A function expresses a relationship between variables. For example, consider the number of toothpicks needed to make a row of squares. The number of toothpicks needed depends on the number of squares we want to make. If we call the number of toothpicks T and the number of squares S, we could say that T is a function of S. S is called the independent variable in this case, and T the dependent variable -- the value of T depends upon whatever we determine the value of S to be. Note 2

In this section, we'll explore the dependence of one variable on another with the help of a spreadsheet program.

Make a row of squares using toothpicks. The squares are joined at the side.

Problem A1

How many toothpicks are needed for one square? For two squares? For five squares? Make a table of these values.

 Squares Toothpicks 1 4 2 3 4 5

 Squares Toothpicks 1 4 2 7 3 10 4 13 5 16 hide answers

 Problem A2 Develop a formula describing the number of toothpicks as a function of the number of squares.

 As in Session 2, try to develop the formula based on the context of the toothpick squares.   Close Tip As in Session 2, try to develop the formula based on the context of the toothpick squares.

 Video Segment In this video segment, Gina explains her solution to Problem A2, including how she generated a rule for the number of toothpicks in each row of squares. Watch the segment after you have completed Problem A2. If you get stuck on the problem, the video segment may help you come up with a solution. Does Gina's work involve a closed-form description or a recursive description for the number of toothpicks in each new row? Refer to Session 2, Part E for more information on these two kinds of descriptions. You can find this segment on the session video, approximately 3 minutes and 9 seconds after the Annenberg Media logo.

 Problem A3 As you add each new square to the row, how many toothpicks are added? This gives you a recursive rule for the number of toothpicks.

 Problems in Part A adapted from IMPACT Mathematics Course 1, developed by Education Development Center, Inc. (New York: Glencoe/McGraw-Hill, 2000), p.32.
 Session 5: Index | Notes | Solutions | Video