I. Number Ideas
A. Number Trains
Have students build all the ways to make a rod of a given color. For
example, what are all the ways to build the white rod, the red rod,
the purple rod, and so forth. Have students write number sentences for
each piece of their train. Look for patterns. Predict how many ways
there are to create a rod of length n.
Literature Connections: Read The King's Chessboard, The Rajah's Rice,
and Two of Everything. Have students complete the mathematics
in the book (a nice way to use calculators). With Two of Everything
you could have students create a table that shows the number of coins
they would have after n times in the pot if they start with 5 coins.
After how many times will they have over 1000 coins? What if the pot
were a Three Pot? What if you started with 500 coins and had a Half
Pot? After how many times would you have less than 50 coins?
B. Commutative and associative
Use the rods to illustrate in a concrete manner the commutative and
associative properties. (Another idea is to use human manipulatives
for this -- have several students go the front of the room. Have students
switch places or switch groupings to illustrate these properties.)
C. Fraction representation
Arrange the rods in order; there are 10 different colors. Assign the
value of 1 to the orange rod. Identify the values of the other rods.
Adjust the value of 1 -- that is redefine which rod is equivalent to
1. Find the values of the other rods.
(Notice that you can work on different denominators with the Cuisenaire
rods than with the pattern blocks.)
D. Fraction operations
Let the orange rod represent 1 unit. Use the rods to develop ideas related
Now consider using the rods to develop rules and procedures for adding
and subtracting fractions.
Use the rods to help give meaning to division of fractions similar as
discussed in the section on pattern blocks.
E. Pattern Ideas
Use only the white cubes. Create a pattern that can be extended in a
natural way. Build the first, second, and third figures in the pattern.
For each, determine the number of white rods needed to build the figure.
How many white rods would be needed to build the next figure in the
pattern? What about the next? Test your predictions by actually building
the figures. Describe a pattern that would make it easy to determine
the number of white rods needed to build the 100th figure in the pattern.
Literature connection: Read Anno's Magic Seeds. Have students
keep track of the patterns in the story and determine the number of
seeds that are buried, then produced, and then eaten in any given year.
A. Measuring Lengths
The length of one edge of the white rod is 1 centimeter. Find the lengths
of the longer edges in the other rods. Use the rods to measure the lengths
of objects in the room, such as a table.
B. Perimeter and area
Because perimeter and area deal with issues in two dimensions and the
rods are three-dimensional, it is important that students realize that
area and perimeter issues are related to the two-dimensional space covered
up by the rods.
Have students build figures using the black, the red, and the dark green
rods. Make different figures using the same three rods. Find the perimeter
of each figure. Find its area.
Use the white rod to introduce the concept of volume. Identify the volume
of the white rod as 1 cubic unit. Have the students build figures of
their own choosing or following a specific pattern you provide. Have
them find the volume of each figure by determining the number of cubic
units it holds.
D. Surface Area
Identify the face of one of the white cubes as 1 square unit. Have students
build figures using a variety of rods. Have students determine the surface
area of the figure as well as its volume.
E. Formula for the volume of a box
Have students use the white cubes to build boxes (rectangular prisms)
of given dimensions. Determine the volume of each. Have students record
the data and then look for patterns to develop the formula for finding
the volume of a box.
Charles, Linda Holden and Micaelia Randolph Brummett. Connections:
Linking Mathematics with Manipulatives. Sunnyvale, CA: Creative
Marilyn Burns Manipulative Videos (Cuisenaire Rods)
Learning with Cuisenaire Rods by Cuisenaire
Addenda books from NCTM (There is one book for each grade K-6,
as well as books by strand: Patterns, Making Sense of Data, Number
Sense and Operations, Geometry and Spatial Sense.)