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Finding Least Common Denominators

Objectives:
1. The teacher will explore using Cuisenaire Rods to determine the Least common Denominator of two unlike fractions .
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TOPIC: FINDING THE LEAST COMMON DENOMINATOR [FINDING LCMs]
Materials: CUISENAIRE RODS

1. As a group , use Cuisenaire Rods and work through these steps to find the LCM (6, 8).

Our Goal:
We wish to find the LCM (6, 8). We need to find a Cuisenaire Rod train that is:
i. A multiple of 6
ii
. A multiple of 8
Iii. The smallest (shortest) train that will work.

It turns out that finding the LCM is extremely easy to model with Cuisenaire Rods using the numbering with the white rod as 1:

a. If the Dark Green Rod is 6, then all trains made of Dark Green Rods represent numbers that are :
____________________ of 6

Starting Sketch:

b. If the Brown Rod is 8, then all trains made of Brown Rods represent numbers that are :
____________________ of 8

Starting Sketch:

c. If the Dark Green Rod is 6 and the Brown Rod is 8, then ALL same-length trains that can be made of all Dark Green OR all Brown Rods represent numbers that are :

Starting Sketch:

d. If the Dark Green Rod is 6 and the Brown Rod is 8, then THE SHORTEST same-length trains that can be made of all Dark Green OR all Brown Rods represent the number that is :

Sketch:

e. This train is _____ whites long, therefore _____ is the LCM of 6 and 8.
At this point you should have trains that look like this on your table .

DARK GREEN RODS DG
BROWN RODS BR

• Since the white rod is 1, these trains are both 24 whites long and they both represent 24 = LCM (6, 8)

2. As a group , use Cuisenaire Rods and determine the LCM (16, 24). Step out your work and draw well-labeled sketches. What’s One?

3. Suppose that you wish to explain how to find the LEAST COMMON MULTIPLE of two numbers to a student. Using the above steps as a general guide, explain how you would share finding the LCM(4, 6) with a student. Discuss this with your group members and show all of the (completed) steps here.

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