# I’m loving talking about basic statistics to my son

We’ve only been at it a week, but the new chapter we are studying – “Basic Statistics” – has been super fun. For now our talks have been limited to averages mostly, but the problems we’ve been doing have allowed him to pull a lot of different mathematical ideas together. Honestly, I never would have expected relatively straightforward basic statistics problems to bring together so many different ideas in the mind of a kid – I even skipped this chapter with my older son! But watching him work though these problems has been great.

The first problem from yesterday was this: The average of your first 7 test scores was 82. If you want to raise your average to 84 after the 8th test, what score do you need to get?

His first instinct is to assume that all of the first 7 scores were 82, but he gets a little stuck after that. He decides to see what happens if your 8th test score was 84. He sees that 84 doesn’t work, but makes a pretty cool observation – if the 8th test score is 2 higher than the previous 7, the average goes up by 1/4, so you’ll have to raise the score by 16 to raise the average by 2.

A nice observation that involves a little bit of thinking about fractions and a fairly good understanding of averages considering we’ve only been talking about them for a week. Nice solution!

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Today’s problem was a problem from an old AMC 8 and involved thinking about the mean and the median of a set of 5 numbers. Here’s the problem: The mean of a set of 5 positive integers is 15 and the median is 18. What is the largest possible value of the largest integer in this set?

His first instinct is to make lots of numbers equal to 1, but that turns the median into 1 unfortunately. After noticing that only two of the numbers can be 1 and the 4th number has to be 18, he goes through a pretty clever calculation to find the 5th number.

His idea was to compare the list of numbers to the list 15, 15, 15, 15, 15, and look at the differences. If the mean is going to be 15, the sum of the differences has to be 0. If he first four numbers are 1, 1, 18, and 18, the differences are -14, -14, 3, and 3 which add to -22. That forces the largest number to be higher than 15 by 22. Again, great reasoning for a kid seeing averages for the first time!

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So, never having going through this section before, I’m pleasantly surprised at the way the problems have gotten my son to think about many different ideas in math. Who knew that going through basic statistics could be so fun!!

# A nice game for kids tweeted by Max Ray-Riek

Saw this tweet earlier this evening:

I had about a minute to look at it before running out the door, but thought it would make for a fun 20 minute exercise with the boys tonight before they went to bed. Turned out to be really fun.

Here’s the unboxing of the game, I guess.

Right off the bat I love that the kids have to figure out how the game works (hopefully that’s part of the game and not me just missing the directions – ha!). Having to figure out what’s going on got them talking about math right away, and then they talked and solved their way through the first 5 puzzles.

Once we finished the first 5 puzzles, I asked them what they thought they were learning.

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We did the next 10 puzzles with the camera off and came in on some slightly more challenging puzzles.

My younger son noticed that you could “cancel the moons” on the second problem, so that was kind of surprising connection he made ðŸ™‚

Even if the puzzles here were still on the basic side, I do like the way that each puzzle immediately got them thinking and talking about solving equations.

They both really seemed to enjoy solving the puzzles and I even had to restrict each kid to solving every other one when the camera was off to stop them from talking over each other. While we were talking at the end of this part my younger son told me that he noticed there were more challenging levels, so we decided to take a shot at the more difficult levels.

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So we clicked on the “master” level and immediately got a surprise – the sum of the weights was zero!

In the next puzzle we solved for some “weights” that were negative.

I was happy that the zero weights and the negative weights didn’t bother them. It was also sort of interesting to hear the difference between what my older son thought the math in the game was – basic algebra – and what my younger son thought the math was – math about weights.

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Anyway, after just playing around for 20 minutes, I’d say that this is a great math game for kids. I’m sure there’s much more to it than we stumbled on, but even just the basic puzzles we did were fun and engaging for the kids. Can’t wait for the boys to try out a few more puzzles tomorrow.