Using Cuisenaire Rods for Decimal Calculation

Did you know that Cuisenaire rods can be used for decimal calculations? Read on to see how they provide a concrete tool for adding and subtracting decimals. Teachers often use base-ten blocks to introduce decimals by changing the value of the hundred flat to one.

The ten rod in a Cuisenaire set is the same size as the ten block so they are interchangeable. To avoid having all those little unit cubes to work with, use the Cuisenaire rods to represent the hundredths.

Since students are typically around 4th or 5th grade when they begin working with decimals, they can usually understand the shift from the flat representing 100 to  1.

While you can use base-ten rods to add and subtract decimals (the hundred flat would equal 1, the ten rod would have a value of one-tenth and the unit cubes would now be worth one-hundredth) I chose to use Cuisenaire rods when working with 5th graders who were beginning to add and subtract tenths. I gave the ten rod a value of one. That made the unit rod a value of one-tenth.

Students can discover this on their own by using  unit cubes to create a same-sized train and then using what they know about fractions to determine the value.

Once students identify that there are ten equal-sized pieces that make the whole (1), they should be able to transfer their understanding of fractions to label these as 1/10 and finally rename as 0.1. Allow time for students to repeat this process of using the unit rod (one-tenth) to find the value of the remaining rods.

Having shifted from whole numbers to tenths, students can now begin to use the rods for computation. Placing the 3-tenths rod together with the 5-tenths rod, for example, provides students with a concrete model to solve 0.3 + 0.5.

You can also use this model when the addends total more than 1.

As with subtracting whole numbers, students can use this manipulative to subtract tenths by finding the difference between the two lengths. 

Without a smaller unit in the Cuisenaire rod set, assigning a value of 1 to the ten rod would not be a good visual model for multiplying decimals.

You could, however, bring back the hundred flat from the base-ten blocks and assign a value of one to it. Then the ten rod would be worth one-tenth and the unit cubes would have a value of one-hundredth. 

We need to think of a problem like 0.3 x 0.3 as three-tenths of three-tenths. It’s easier to show this on a representation of a hundred flat ( which is now worth one) than with the actual blocks.

Start by shading in three-tenths of the whole. You can also use slanted lines.

Next, use another color, to shade in or add lines to three-tenths in the other direction. 

The product of the two numbers is the part where the two colors overlap.

In this case, that area is nine-hundredths. Students can visually see this with this model. They are taking three-tenths of three-tenths. In this example, students have broken each tenth into ten parts, hundredths and then they have taken three-tenths (three parts) of each tenth.

Using base-ten blocks with the hundred flat representing one also works for division. In order to find 0.8 ÷ 0.2, students should draw a border around the total that is to be divided, in this case, 0.8. Next, determine how many 0.2s make up the total. Here, you can see that there are 4 two-tenths in eight-tenths, so 0.8 ÷ 0.2 = 4.

The next image shows how to apply this process to larger numbers, such as 1.75 ÷ 0.35. With the dividend marked, students can color in 0.35 sections. It takes five 0.35 sections to make 1.75.

I hope you have found these suggestions for decimal calculations helpful. They are an important steps in the Concrete-Representational-Abstract sequence before jumping into algorithms.

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