# Family Math night for grades 4 and 5

This week I’ve been thinking about what to do for the Family Math nights at my younger son’s school. The plan for the K-1 night is here:

K-1 Family Math night

And the plan for Grades 2-3 is here:

Family Math Night for Grades 2 and 3

The plan for the Grade 4-5 night was the most difficult because there were so many things to narrow down! My goodness – how do you choose?

What I’ve settled on for now is the same sort of idea as in the two prior nights – 2 main projects with a 3rd in my back pocket if we have time.

The first project will be looking at the Collatz conjecture. I’m interested to try out this idea because:

(i) it gives them a view into an unsolved problem,
(ii) the problem requires only a little arithmetic, and should be accessible to 4th and 5th graders, and
(iii) John Conway’s extension gives them a fun opportunity for follow up if any of the kids are interested.

Here’s one of the talks we’ve done on the Collatz conjecture:

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and here’s the John Conway extension:

The Collatz conjecture and John Conway’s amusical variation

The second topic for the night will be the Monty Hall problem. This is always a fun problem to talk about in a crowd (and really only in a crowd!) because you get to tally up lots of results. Also, if you have a large number of people playing a small number of trials of the game, the results aren’t really obvious to anyone until all of the numbers are tallied. Oh, and if you want to get people arguing about math, there’s no better problem (though this is good and bad which is another reason why the large crowd helps!).

We’ve done a couple of projects based on this problem – here’s the most recent one:

The Monty Hall Problem

Finally, the project that I’ll keep in my back pocket is the Chaos game. I’ll have to change this one if I don’t have a way to hook up my computer to a projector, but for now I’d like to give the kids a “wow” moment similar to what my kids had here (watch the whole 5 minutes for the set up, or just start at 2:20 for the punch line):

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The whole Chaos game project is here:
Computer Math and the Chaos Game

I’m super excited for these family math nights. Now that I’ve got the simple outline in my mind for the 5 nights it is time to start thinking about how to implement these projects with a large group.

# Some Exponent Practice

My son had two problems from his Mathcounts practice that puzzled him last night. I thought it was best that he puzzled through one of the questions – what is 47 * 53. His question about this problem was simple – why would they even ask this question?

The other question required a little more review since we’ve not talked about exponents in a while:

Evaluate: $( ( \sqrt{2} )^{\sqrt{2}})^{\sqrt{8}}$

Unlike the first problem which really just involves learning a difference of squares trick, this problem actually connects to an interesting puzzle (and one that we’ve studied before):

Can an irrational number to an irrational power be rational?

I didn’t go all the way to exploring that connection last night, but instead we had a nice 10 minute review about exponents.

By luck, today he was working through a few problems from the 2010 AMC 8 and came across this problem:

Problem #24 from the 20010 AMC 8

The problem asks you to arrange these three numbers in increasing order – $10^8 , 5^{12}$, and $2^{24}$. A nice problem to encounter after a review of exponents.

Here’s how he approached it:

After he worked through the problem I wanted to do a quick review just to give a little extra emphasis to last night’s review.

So, a happy coincidence running into this problem today. Nice to be able to put our little exponent review from last night to work today!