Pascal's Triangle Guided Discovery thru Permutations with Math Rods

Grade Levels
PDF (1 MB|8 pages)


Pascal's triangle along with the Fibonacci sequence is founded in this guided discovery activity. In this activity, students find all the ways to build the numbers 1 to 8 using ten base blocks like Cuisenaire rods. There are three versions which include a blank to modify with your own rod name colors for whichever ten base system you use. Nine and ten are left off to allow students the opportunity to make predictions on the corresponding page.

The interactive pyramid is designed to help students discover interesting patterns that manifest in this permutation activity, patterns including Pascal's triangle.

Students will begin by building trains, that is a line of rods. The circled numbers help guide students on where to record the number of trains for each color.

For example, the number of 3 car trains for the five rod would be recorded on the five rod line next to the box that has a circled 3. The number of 6 car trains for six rod would be recorded on the six rod line next to the box that has a circled 6.

This particular activity is an extensive project that you may want to do as a class over a week or more. How does a student know when they have found all the 3 car trains for the four rod? Students will need to work together to verify and discover if they indeed found all the trains. It is a great opportunity to verbalize and organize thought.

If they are finding all the trains for each rod, patterns will emerge and they can use those patterns to verify their answers. Answers are found in a picture on one of the picture samples. The answers are hard to see. WARNING: I am not providing a formal answer sheet, but you can google Pascal's triangle if you need to. There is also a photo that you can examine closely to find the answer.

Happy Pattern Hunting!
Total Pages
8 pages
Answer Key
Teaching Duration
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