Space, Color, and Mathematics
by Carolyn True Ito, T/TAC - Eastern Virginia
The Cuisenaire Rods are an especially valuable tool for any student with math difficulties because they provide a visual, tactile, and concrete approach to abstract math. Color and size characteristics are systematically associated with numbers. Number, then take up a certain space and mathematics begins to take on visible, tactile and colorful meaning.
To use the rods successfully, each student must have a supply of rods, which is stored in a specified place. At a minimum, each student needs 72 rods: 20 white; 12 red; 9 light green; 6 purple; 5 yellow; 4 dark green; and 4 each of black, brown, blue and orange. A large, flat surface is the best and least frustrating one for working on. The floor works well if the students are otherwise confined to small, slant-top desks.
The following areas will be covered:
Becoming Familiar with The Rods
When any student begins to use the rods, whether using them for remediation or as the basis of an instructional program, time getting to know the rods needs to be provided. A week or more is not too long. It is helpful to provide some "play-time" with the rods daily, especially after the students have begun to use them to learn math. Some activities for getting to know the rods are:
This pattern differs from the one suggested by the Teacher's Edition of Opening Doors in Mathematics by Genise and Kunz, Cuisenaire Company of America, Inc. I have found this faster and easier for the little fingers to manage.
Assigning Numerical Value
The next step in using the rods is to assign numerical values to each rod. I again differ from the Cuisenaire philosophy in this area as I do not believe in teaching a letter name for a rod. Rather, I encourage only a numeric value according to these values: white= 1 (not w), red= 2, light green= 3, purple= 4, yellow= 5, dark green= 6, black= 7, brown= 8, blue= 9, and orange= 10. From the beginning, I write and encourage students to write equations with numerals, not letters. We do, however, express relationships by color orally, simultaneously with numeric value. Some suggestions for helping students learn the numeric value for the rods are:
The next area to cover is that of relationships study. The student begins to see and know which rod is bigger than another and by how much. Some activities include:
The next area of instruction is called Ground Rules or knowing the mechanics for placement of rods for their use in adding, subtracting, multiplying, dividing, and in fractions.
Addition: Place the rods end to end, moving left to right to make a train; find a single rod to match the length of the train. The addends are the cars of the train. The sum is the rod placed beneath the addend train. If the addend train is longer than orange, match it with a train made of as many orange rods as will fit and whatever smaller rod will fill out the length of the train.
Subtraction: Place the smaller rod on top of the larger one and see what rod is needed to make a matching train or fill the gap. Place the subtrahend on top of the minuend, and the difference is that rod which fills up the space.
Multiplication: example 2 x 3. Make a cross of the rods with the rod first named 2(or red) vertical on the bottom and the second named or 3 (light green) on the top. Read it as 2 cross 3. The cross represents the number of red rods that would form a floor under the green one. Fit the rods under the green one. Then take these three red rods and form a train. Measure the train.
Towers are more than two rods crossing. They can be any height. This equation 2 x 3 x 4 would be a tower with the red on the bottom, light green crossing on top and the purple on top of the light green. Solve 2 x 3 first equaling 6 and then 6 x 4 equaling 24.
Division: Place the longer rod or the dividend above the shorter one, the divisor. Make a train of equal short rods that equal the one long rod. The number of rods in the matching train is the quotient. If the divisor train is not as long as the dividend, then make as long a train as will fit. End the matching train with a smaller rod. The remainder is the smaller rod.
Fractions: The first rod (when placing two rods vertically side by side) is the numerator; the second rod is the unit or denominator, based upon white as the unit rod. Purple next to yellow is 4/5.
Beyond Operational Mathematics Activities
I have found the use of the rods helpful beyond aids in computing math problems. They can be used as concrete aids in many other ways:
Availability and Cost
Rods are available from the Cuisenaire Company of America, Inc. They are distributed by Dale Seymour Publications, P.O. Box 10888, Palo Alto, CA 94303. The introductory set for Cuisenaire Rods consists of a single set of 74 rods, wall poster, and teacher guide, Learning with Cuisenaire Rods. The cost is $10.95 for wooden rods and $9.95 for plastic rods. The starter set for Cuisenaire Rods includes an idea book for use of Cuisenaire Rods at the primary level, and Learning with Cuisenaire Rods, a teacher's guide. The set is $36.95 for wooden rods and $33.95 for plastic rods. The 800 number for ordering a catalog is 1-800-872-1100. The world wide web address is: http://www.awl.com/www.cuisenaire.com
Much of the information herein contained is found in Using the Cuisenaire Rods- A Photo/Text Guide for Teachers by Jessica Davidson; Cuisenaire Company of America, Inc. ($16.95 as of 1995). I have modified the material according to my experience. Many activities are discussed in the Photo/Text.