Cuisenaire Rods:

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
• Assigning Values
• Relationships Study
• Ground Rules for Math Operations
• Beyond Operational Math Activities
• Availability and Cost

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:

1. Make a staircase, using one rod of each color. Make it smallest to largest and largest to smallest.
2. Make a staircase using only white rods.
3. Make a staircase, using each rod of a different color, showing how the next rod is chosen by adding one white rod to the present one.
4. Encourage the students to make forts, people, houses, airplanes and other objects.
5. Learn the modified "Put Away Pattern" in order to know if all the rods are present. This is not necessary if you have the trays to store your rods.
   

• Make white teeth, two rows, between orange lips
• Make two rows of red teeth between dark green lips
• Make one row of purple teeth between dark green lips
• Make a light green cube (three high, long and wide)
• Count 5 yellow rods
• Count 4 each of black, blue and orange rods

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:

1. Place a chart in the front of the room with each numeral from one to ten written in the color of the corresponding rod. That is the numeral one would be written in white, the two in red and so on up to the ten in orange. It is also helpful later on to have the eleven written in orange and white, twelve in orange and red and so on. The chart is removed when no longer needed.
   
2. Have the students close their eyes and picture a staircase. Oral games can be played, like what do you see after yellow, or before blue.
   
3. From three different rods, a student with eyes closed, tactilly identifies the longest and shortest and guesses the name-- yellow or five. A student could also be handed one rod and just by feeling it behind his/her back correctly tell what number it is (+/- 1). With eyes closed, the students can try to find a specified rod from within the carton. The one, two and ten rods are usually the first ones learned.
   
4. The students measure the difference between longer and shorter rods.
   
5. They form equal trains.
   
6. They can make many different trains that equal the orange rod, placing each below the succeeding one. Then take one car off a train and have the student tell which one has been taken away. This is good practice for learning which two numerals make ten.
   
7. Have the students consider staircases in which mistakes have been made. Have them correct the mistakes through oral discussion.
   
8. Worksheets can be made to provide the student with experiences other than oral ones. Students can color rods drawn on paper their appropriate color, and write the corresponding numerical value under a picture of a rod. They can trace around rods to represent a specified numerical value or color shapes or a picture labeled with the numbers 1-10 with the corresponding colors.

Relationships Study

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:

1. Have the student find a rod that is longer than green but shorter than orange. This involves oral work, with the teacher first giving the specifications, and then students can give the whole group or a partner specifications. The color and then the numeral name are used.
   
2. Find a rod which is 3 times as long as the red, green, or white.
   
3. Find a rod longer than light green by the same amount as the purple is longer than the red, and so on.
   
4. Know the relationship of the white and red and light green rods to the others. White is 1/2 of red, 1/3 of green, and 1/4 of purple.
   
5. Match trains of two different colors to the same length.
   
6. Worksheets using greater than, less than and equal symbols are used for independent activities.
   
7. Make number families. For example, show how many different ways there are to make trains which equal 8 or brown. Discuss combinations. Those who are ready to, write equations.

Ground Rules

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:

1. Oral Word Problems: When given an oral word problem the student uses the rods to represent the story elements. For instance, in the story, "I had three pennies and lost one. How many do I have now?" The student can use three white rods to represent the pennies. By removing the lost one from the group, s/he clearly sees that two are left.
   
2. The rods help to build a left to right progression as all work with them moves in a left to right direction.
   
3. Visual sequencing is strengthened as students match patterns with other students' patterns.
   
4. Auditory sequential memory is developed through oral activities. The teacher says 4 + 3 + 7 + 9=? or red + green + black makes how much. The student remembers the order of the numbers called and works from left to right.
   
5. Visual sequential memory can be developed by arranging a pattern, showing the pattern for a length of time, and then the student recreates it without the visual stimulus.
   
6. Chip or Rod Trading: In this game the students roll 2 dice, figure the sum and are given the number (combination) of rods needed to match the number on the dice. Whenever the student gets to ten, the combination of blocks are turned in for an orange or tens rod. The first student with ten orange rods or 100 wins.

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

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