Ender’s Game

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My school starts the day with 20 minutes of reading, in lots of different groups. The group that reads in my room is reading Ender’s Game. While sitting around after school, I had an idea for a fun task, which starts in 6th ratios and proportions, has a great opportunity for some 7th statistics and probability, and could be extended for standard deviation and z-scores.

How many words are in Ender’s Game?

Start off with estimates. Hold up the book and let students flip through. Hand out a class set if you have one.

Then, what would you need to know to solve it? There are a few ways to approach it, but I feel like students will gravitate toward three pieces of information
Pages in the book
Lines per page
Words per line

Have students name the key information and how they might measure it, and then what they will do with that information when they get it.

Ender’s Game is a book with a ton of dialogue, so these numbers are pretty variable. Here you can stick with 6th grade proportions and calculate it out, either with numbers students generate or numbers you provide. The sequel, which I think is much more interesting, is how long do you think it took Orson Scott Card to write the book? Lots of ways to approach it. There’s a lot of mileage in getting an estimate for words per minute, and then minutes of writing per day, and use those numbers to estimate how long the writing took, but other approaches are also great.

The first extension is for a 7th grade unit on statistical sampling: have students sample lines per page and words per line. There are some funky results here: the lines per page is bimodal, between full pages (most pages) and pages at the beginning of a chapter, with end of chapter pages in between. It’s an interesting data set to work with. The words per line is highly variable, and here is where the quality of the sampling will make a big difference. Use these numbers to calculate an estimate, and look at the variability in sampling methods. For students who finish early, dive into the same sequel: how long would it have taken Orson Scott Card to write the book?

Finally, standard deviation. If kids are putting in the effort to sample pages and lines themselves, we should do something with that data. Collect estimates of the word count, and find the mean and standard deviation. Ask students how good their estimates were. Motivates the idea of standard deviation — which estimates were high? How high were they? Which estimate were low? How low? What were the reasons for the error?

There’s a ton of great stuff here — plenty to run with for a full class or two. Also, if you’re curious about the answer, it’s here.

Question: How should the question be framed? Is this an opportunity to have students notice and wonder, and generate their own questions? Are there other questions that are more interesting to sample from a book? This isn’t too different from my “how big is your vocabulary” task I posted about a while back, and I’m not sure the best way to motivate either.

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