The magic of Cuisenaire Rods & Equivalent Fractions, Dance snapshot: An overlapping post for Wednesday through Friday

Some theoretical points from the Cuisenaire rods:

The following items have been taken from the literature that came with the rods.  I wanted to read it before looking at the student responses and moving forward.

Our observations and descriptive feedback:

On another level, check out how the Cuisenaire rods can be used to learn some grammar rules associated with learning English.  It is a method known as "Silent Way."  More information can be found here:  https://en.wikipedia.org/wiki/Silent_Way.

 

Fraction Equivalency:

Hopefully, the idea of equal fractions makes some sense as you have picked and played with the rods. A few weeks ago, when we first were chatting about fractions, we looked at this example:

When I arrive at school today, I will photograph a model of the "chocolate bars" using Cuisenaire rods to show how the idea of equivalency works.  We will then walk through a guided lesson and make some connections to the work you will be responsible for in the textbook. 

An example of Cuisenaire rods in action.  (1/3=6/18)

While the fractions are equivalent, 1/3 is also the simplest form or lowest term of 6/18.  More on the in the lowest term in the video that follows.  By the time you read this, I would have taught you some more about this concept.

In the class is a couple of sets of Fraction Circles that you can play and investigate some of the concepts shared in that video.  

All of these circles, each one being 1.0 are "sliced up" in different ways.

The green portion is still half of a circle at 5/10.  The purple portion is also half but looks like 6/12.

 Before watching the video, look at this last set of fractions.  This fractions that are pictured here can be seen as examples of an equivalent fraction and then being represented in its lowest term.  The Cuisenaire rods help with visualizing these concepts (I hope).  

I am in the process of coming up with a rule for explaining how the lowest term can be expressed for a fraction using the rods.  At this point, I think the reduced fraction must be the same size (length) or rods, but with the least number of rods used.

For example, 6/12 involves the use of 12 cubes, whereas 1/2 only involves the use of 2 rods.
For 3/12, we have 12 cubes, whereas 1/4 only inolves using 4 rods.  

Rob, from Math Antics, take a shot at explaining how fractions are equivalent.  

# 3, 4, 6, 8, 9, 10

In addition to the class lesson, this may also help with understanding how to reduce fractions to the Lowest/Simplest term.

Dance snapshot:

We will begin our presentations next week.  Here is a short look at the various groups at work.