Fractions, Sam Loyd, and a MArTH Journal

I was looking for some interesting and fun MaRTh for some fourth to sixth graders I have the pleasure of working with. As I was digging around the interwebs, I found one of my favorite haunts, MathMunch.org, had just what I needed. I will be using this article to have some fun and I’ll see what happens. Look back here soon for results from this activity….oh, and I think I know an extension of this for some very bright seventh graders I work with, I bet they will love this.

Math Munch

Welcome to this week’s Math Munch!

Check out this awesome graph:

What is it?  It’s a graph of the Farey Fractions, with the denominator of the (simplified) fraction on the vertical axis and the value of the fraction on the horizontal axis, made by mathematician and professor at Wheelock College Debra K. Borkovitz (previously).  Now, I’d never heard of Farey Fractions before I saw this image – but the graph was so cool that I wanted to learn all about them!

So, what are Farey Fractions, you ask?  Debra writes all about them and the cool visual patterns they make in this post.  To make a list of Farey Fractions you first pick a number – say, 5.  Then, you list all of the fractions between 0 and 1 whose denominators are less than or equal to the number you picked.  So, as Debra writes in…

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