[sorry for the hasty write up – I had some problems downloading the video from the camera, and the rest of my day is a little busy. Just wanted to get this one out the door because it is so fun.]

Saw this wonderful problem posted on Twitter by Tina Cardone yesterday:

We may be out of PCMI problem sets, but I'm taking a grad class which posed this problem: pic.twitter.com/6YZFKhuNP7

For clarity, here’s the picture rotated so it is easier to read:

I thought it would be fun to try out the problem for our Family Math project today, but I didn’t really think through the problem before getting started. That laziness on my part led to a huge surprise – this is an amazing problem to talk through with kids! There are so many opportunities to talk about arithmetic, patterns, and why the sequences evolve in the way that they do.

We started by talking through the problem and making sure that the kids understood the way the pay evolved over time:

Next up – after choosing Lego figures to represent some of the participants in this problem – we began to look more carefully at the patterns. One of the ideas that begins to emerge in this video is that this problem provides a great opportunity to talk a little bit about arithmetic and rounding with kids.

We continued looking at the initial patterns in this video, but then my younger son noticed something interesting about the numbers in the first column – they were related to powers of 5. We then talked a little bit about how those same numbers were also decimal representations of powers of 2. This conversation went a little longer than usual, but there were some fun observations about the numbers from the boys.

Now we moved on to the middle column – this is where the payment amounts are rounded up. Turns out the pattern here is fairly simple (eventually), but it gives us a great opportunity to talk a little bit about how that pattern relates to the original payment formula.

Finally we look at the last column – where the pay is rounded down. This part of the project provides a great opportunity to talk about arithmetic and rounding with negative numbers. A great way to finish this project.

So, a super project for kids – one of my favorites ever. Thanks so much to Tina for sharing this problem!