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CommunicationSession 02 Overviewtab aTab btab ctab dtab eReference
Part B

Exploring Communication
  Introduction | Problem: Shaded/Unshaded Circles | Solution: Shaded/Unshaded Circles | Talking About the Problem | Representing Fractions with Rods | Other Denominators | Modeling Operations | Try It Yourself: Cuisenaire Rods | Problem Reflection | Summary | Your Journal


We will now explore the model for adding halves and thirds, using dark green to represent "1." Note that all of the rods shorter than dark green have been assigned a fractional value; each rod represents a fraction of the dark-green rod. (The fractional values of the rods would change if we were to change the rod that represents "1.")

Cuisenaire Rods

Using the rods to model addition and subtraction is a simple matter of "making trains."

Think of addition as merging different "cars" of the trains. For example, since red = 1/3 and light green = 1/2, you can model 1/3 + 1/2 by putting a red and a light-green rod together:

Their combined length is equal to a yellow rod, whose value is 5/6. Therefore, 1/3 + 1/2 = 5/6.

Red and Light Green over Yellow Rods

A red rod and a light-green rod are two different lengths, so you won't get an answer that's expressed in terms of either rod. Therefore, you need to find a new rod to illustrate your answer. This is made visually apparent from the model.

When subtracting fractions, you can think in terms of a missing addend (What rod is missing?). For example, you can model 1/2 - 1/3 (a light-green rod minus a red rod) by finding what you would need to add to the red rod to make a train the length of a light-green rod.

The answer is the white rod, whose value is 1/6. In other words, 1/2 - 1/3 = 1/6.

Light Green over Red and White Rods

When subtracting 1/2 - 1/3, we cannot name the resulting length in either halves or thirds because this length is not a whole number of either of those two rods. This shows why we need a common unit to discuss this length. We can call the light green 3/6 instead of 1/2 and the red 2/6 instead of 1/3, and then the difference of 3/6 - 2/6 (or the missing addend of 3/6 and 2/6) is 1/6 (the white rod). This is visually apparent from the model.

The Cuisenaire Rods model illustrates why the algorithms for adding and subtracting fractions work -- namely, that you cannot add or subtract the fractions until they are expressed in the same units.

Cuisenaire Rods can also be used to model multiplication and division with fractions. For examples, see Learning Math: Number and Operations.

Next  Explore communication using the Cuisenaire Rods

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