Cuisenaire Rod Questions
Each C-rod (C stands for the company who makes the rods, Cuisenaire) typically represents one
of the first 10 counting numbers. Here is a sample of the kinds of higher order thinking
questions, in order of level of difficulty, that one can ask with the C-rods
Note: A train of rods is a set of rods which are laid end to end in a line. There is a front and a
back to the train, so the order in which the rods are laid end to end is important.
1. How many different trains are there of length 1?
How many different trains are there of length 2?
.
.
.
How many different trains are there of length 10?
2. Suppose you have an extended set of C-rods, which contains rods of all positive integer
lengths where the white rod is considered = 1. How many trains are there of length N?
Justify your answer.
3. What is the total length of rods needed to build a "staircase" of rods (a staircase rods begins
with the white rod, then the red rod - standing on its end, then the light green rod - standing
on its end, and so on) with 1 stair, 2 stairs, 3 stairs,..., and N stairs. Justify your solution.
4. How many different trains of white (1 x 1) and/or red (1 x 2) rods are there of a given length
N?
5. If you have a solution to #4, find at least 2 ways to justify your solution.
6. Can you find a recursion equation to express the number of trains of length N that can be
formed using white, red and/or green (1 x 3) rods?
7. How many ways can you fill a 2 x n rectangle using only red (1 x 2) rods? Two horizontally
placed rods are considered different than two vertical ones.
8. How many ways can you fill a 2 x n rectangle using only red (1 x 2) and white (1 x 1) rods?