Toothpicks and towers

Mary Beth Weier

Subject: Geometry

Time: One class period

Objectives:  Students will determine the next term in a sequence of numbers.
                    Students will determine the next figure in a visual pattern and answer
                    questions about the pattern.
                    Students will write a rule describing a pattern that allows them to make
                    accurate predictions.

Materials:  “Toothpick Square” activity sheet.
                  “Towering Numbers” activity sheet.

1. Explain inductive reasoning as looking for patterns and making conjectures. Go through number patterns.

            Example:  1, 4, 16, 64,…

2.  Give the students the “Toothpick Squares” activity sheet. Each student should spend about 5-10 minutes reading through the activity sheet and answer as many questions as they can on their own.

3.  In groups of two or three, students work through the activity sheet together comparing their answers and discussing their results.

4.  Go through the activity sheet with the entire class and discuss how they came up with their answers.
5.  Give the students the “Towering Numbers” activity sheet and have them work in groups of two or three on answering the questions.

Notes:  I gave the students the first worksheet and had them try and answer the questions on their own because I wanted to see how many of these questions they could answer on their own.  I had not done an activity like this before and so I was curious as to how well the students could answer the questions.  Some students had quite a bit of trouble at first not understanding what the activity was all about.  When I let them work in groups, they were able to help each other.

We then went through the activity as a class, I could see that most students were able to come up with the concrete answers, but some were still not able to see how to come up with a rule.  I showed them how to make a table to see the pattern and that helped a lot.  Some students found it easier to describe in words the pattern rather than to write it algebraically.

When I gave them the second activity worksheet, they were able to answer the parts of the first two questions rather quickly now that they understood how these kinds of problems are to be done. The last question was rather difficult for most students to answer and those that did found it easier to describe the pattern in words.

After I did these activities, I found the “Marcy’s Dots” activity in our packet. It is a shorter and simpler activity and one that would make a good introductory example to go through, since it seems to me the students are not very familiar with these types of activities. Next time, I plan to do the “Marcy’s Dots” activity first.