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 = 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!

We’ve had some fun doing cryptarithms in alternative bases. For example, Brilliant.com yesterday sent this one: XX + YY + ZZ = XYZ

Using standard numerals, there is only one solution in each base. If you allow numerals larger than the base (6 in base 5, for example) then there are more solutions. Like James Tanton’s exploding dots, this seems to help the kids better understand what they are really doing with place value.

## Comments

We’ve had some fun doing cryptarithms in alternative bases. For example, Brilliant.com yesterday sent this one: XX + YY + ZZ = XYZ

Using standard numerals, there is only one solution in each base. If you allow numerals larger than the base (6 in base 5, for example) then there are more solutions. Like James Tanton’s exploding dots, this seems to help the kids better understand what they are really doing with place value.