Reviewing bases

I asked the boys what they wanted to talk about today and they said base 16 – I’ve got no idea why or even where this idea came from! The structure of the morning was honestly just off the top of my head, but I think it was a fun little project. Here’s what we did:

(1) A quick review of binary, including looking at adding in binary with snap cubes

This section includes a quick review of powers (and why $10^0$ = 1) and a demonstration of why arithmetic is, essentially, the same in different bases.

(2) Converting between related bases

Here we looked at how you could, for example, quickly convert from base 2 to base 4, or from base 2 to base 8

(3) Next we looked at decimals

The example here was writing 1/3 in binary. I think this is a really fun exercise for kids learning about bases – it is a nice example of mathematical thinking and also a nice chance for some fraction practice!

(4) Finally looking at base 16!

We did a few simple arithmetic examples and even say that it was very easy to convert from base 16 back to base 2. I was going to also do base 16 to base 4, but we ran out of time.

Definitely a fun little project. I’ve always thought that playing around with different bases is a great way to help kids learn about basic arithmetic. It is also a nice little topic all by itself!