Christopher Danielson’s square problem

Saw an interesting problem on twitter last night:

with this one extra clarification on the shape:

Seems like a good problem for a kid learning geometry, so I tried it out with my older son tonight. First we looked at the two twitter posts to make sure that he understood the problem and I asked him to come up with a plan for how to solve it:


Next we went to the white board to work out the solution. He did a good job following through on this plan, which was nice. One thing that I thought might give him a little difficult was that the 4th root of 3 appears in his solution. However, he did not simplify the numbers in the problem the way I expected him to, so the 4th root of 3 didn’t appear 🙂


Definitely a fun little problem. One alternate problem that I skipped because I thought it would be too difficult was finding the area of a different square hiding in Danielson’s picture. The “center” of the 4 pointed star is also a square – what area does it have if the kites have area 1?

Fibonacci, Zome, and Patterns of the Universe

The kids wanted to do an other project using Patterns of the Universe today:



Flipping through the book last night I found a neat page featuring golden rectangles, so I turned that into a little half coloring / half zometool project for this morning.

We started by talking about the picture in the book. The kids were interested in the spiral pattern and my older son remembered a few of the properties of “golden” rectangles:


Next we built a golden spiral on the living room floor using our zometool set. We actually did a similar project about a year ago, so the ideas weren’t totally new:

Fibonacci Spirals and Pentagons with our Zometool Set

I liked hearing their description of how the Fibonacci sequence appear in the shape – it was a nice way to get talking and thinking about math ideas:


While I cleaned up the Zometool pieces the kids colored in Patterns of the Universe. Here are their descriptions of their colorings. Here’s the one from my younger son:


and here’s my older son:


So, a fun little project for kids connecting the Fibonacci numbers to some geometric patterns. It is neat to hear how the kids think about these connections. I really love how the coloring ideas in Patterns of the Universe lead so naturally to fun projects!