1510 Divisible Numbers

Who says you can't teach an old dog new tricks? With the amount of math classes I've taken over the years, I've never been taught some of the shortcuts that are out there for testing number divisibility. I was blown away by how easy this process is. Any textbook out there will refer to them as rules of divisibility, but I still like to call them shortcuts because of how easy it just made my life...too bad it took 30+ years.


The "rules" state, a number is divisible when you can divide one number by another and the result is a whole number. Now, for every number 1-12, there is a special rule that follows it and I encourage you to take a look at these tricks. It's almost freaky how this works out and it makes you wonder how someone figured this out. Knowing these tricks, rules, or shortcuts can really make reducing numbers or fractions a breeze. I can't tell you how long I would spend punching each number into the calculator to see if it was divisible or not. Now, I've made a little cheat sheet with all the rules on it that I keep with my math work and just refer to it when I need it.

Students will be able to memorize 2, 5, and 10 with no problems because they are easily recognizable, but what about 3 or 9? Here is a video that might help them out.

I aspire to be this teacher in a couple of years. If I can rap, I can get my students to learn the divisibility rules, or shortcuts!

1512 Geometry and Tessellations

I've always enjoyed doing geometry and I'm amazed by how geometry surrounds us everywhere. I really enjoy the process of figuring out an answer rather than just plugging in numbers into something. One thing that has sparked my interest, that I wasn't really aware of before, are tessellations. I've never really put much thought into them, but I think they are really neat on how they work out.

Think of the last puzzle you put together, that is a tessellation. A tessellation is when you put together geometric shapes, so that when you are finished there are no gaps in between each shape. Now, that is a very basic definition and not too mathematical so, we must have some rules for a regular mathematical tessellations to exist.
1. Tessellations must be a geometric figure that fits together without gaps or overlaps and covers an infinite plane.

2. The geometric figures must be regular polygons and the same.

3. The vertex must look the same.

Equilateral triangles, squares, and hexagons are all great examples of regular tessellations, but you can combine different regular tessellation shapes to make a semi-regular tessellation.

Wait a second, I've seen this before. This looks like when you tile a floor or a shower. Who knew this was a tessellation? Now that I'm aware of them, I started noticing them more and more in everyday life, like on this McDonald's commercial. Again, geometry surrounds us in so many ways. I found a great educational website that allows students to create their own semi-tessellations.