## Archive for November, 2016

### NBA, Discovery, and the Math of Basketball

Last week, Discovery Education and the National Basketball Association (NBA) announced a partnership in which real-time data from stats.nba.com will flow into Math Techbook, and students will use that data to solve problems.

How cool is that?

Eighty students from John Hayden Johnson Middle School in Washington, DC, participated in the event, which was emceed by Hall-of-Famer “Big” Bob Lanier and made silly by Washington Wizards mascot G-Wiz.

The event received a lot of press coverage, and as you may have heard, **there’s no such thing as bad publicity**. But one of the articles quoted me as saying:

It’s not like a beautiful, traditional math problem.

That is **not** what I said. I am absolutely certain that I have never used the words *beautiful* and *traditional* in the same sentence. Well, perhaps when referring to a wedding dress or an Irish cottage, maybe, but certainly not when referring to a math problem.

I was also quoted as saying:

It’s going to be messy, for sure.

That is, in fact, one of the things I did say. Because by definition, good math problems are messy. For this project, our writing team created problems that don’t have one right answer. For instance, one problem asks students to **generate a formula to predict which players should be on the All‑NBA 1st Team**. Should they use points and rebounds as part of their formula? If so, how much weight should they give to each? And should there be a deduction for the number of turnovers a player has? All of that is up to the student, and it’s certainly possible that more than one formula would give reasonable results. (If you don’t believe me, do a search for NBA Efficiency, TENDEX, Thibodeau, VORP, or New SPM to get a sense of some formulas currently used by professional statisticians.)

A microsite with a four sample problems is available at **www.discoveryeducation.com/nbamath**. To see all 16 problems and to experience the NBA Math Tool, you’ll need to login to Math Techbook; sign up for a 60‑day trial at **www.discoveryeducation.com/mathtechbook**.

I’m ecstatic about the problems that our writing team — which includes folks who love both math and basketball, like Brenan Bardige, Ellen Clay, Chris Shore, Shauna Hedgepeth, Katie Rhee, Jen Silverman, and Jason Slowbe — has created. One of the simpler problems they’ve written, meant for middle school students, is to **determine which player should take a technical free throw**. It’s not a hard problem, but students get to choose which team(s) to examine and how to use free-throw data to make their choice. With the NBA Math Tool that we’ve created, which includes FTM and FTA but not FT%, one possible formula is **=ROUND(100*FTM/FTA,1)**, which will display the free-throw percentage to one decimal place of accuracy — though there are certainly less sophisticated formulas that will get the job done, too, and students could bypass formulas entirely by using equivalent fractions.

But a different article said that the “questions may look something like” this:

Andrew Wiggins is making 49.1% of his two-point shots and 52.3% of his threes. Which shot is he more likely to make?

Actually, we would **never** ask a question like this in Math Techbook, either as part of this NBA project or otherwise. By the time students start working with percentages in middle school (6.RPA.3.C), we expect that they already understand how to compare decimals (4.NF.C.7). Though basic exercises are included in the service, most problems — and especially those based on NBA data — exist at a greater depth of knowledge.

But what we might do is ask students to use proportions to make a prediction.

As you know, basketball announcers and sportswriters make predictions all the time. They talk about players being “on pace” to score some number of points or to grab a certain number of rebounds. In fact, the Washington Post recently prophesied that Steph Curry will hold the NBA’s all-time three-point record before the next presidential election.

During the first part of the event at Johnson Middle School, the students set out to make a prediction:

How many assists will John Wall finish the season with?

John Wall recently set the Wizards franchise record for assists, so the context was timely.

To solve this problem, students explored the **NBA Math Tool**, which now resides inside Math Techbook. This tool allows students to analyze both NBA and WNBA stats. Students considered data for the Washington Wizards:

Row 6 shows that John Wall had 98 assists through 11 games. Good information, to be sure, but it led to more questions from students than answers:

- Some players on the Wizards have played 13 games. How many games have the Wizards played so far this year?
- How many games will John Wall play this year?
- How many games are in an NBA season?

Looking at team data in the NBA Math Tool, students learned that the Wizards have played 13 games so far this year. And one student knew that every NBA team plays 82 games in a season. Good info… but now what?

One approach is to set up a proportion with the equation

which yields the number of games (*g*) that we can expect John to play this year (69), and then the equation

can be used to find the number of assists (*a*) that we can expect John to record (602).

But the eighty students in the gym were sixth- and seventh-graders, and they weren’t ready for algebraic equations. Instead, they attacked the problem by noting that Wall had 98 assists through the first 13 games, so they estimated:

- He should have about 200 assists through 25 games.
- He’d have about 400 assists through 50 games.
- He’d have about 600 assists through 75 games.
- That’s 7 games shy of a full 82‑game season, and Wall should have about 50 assists in 7 games.
- So, we can expect him to finish the season with about 650 assists.

My role at the event was to lead students through the solution as a group-problem solving activity; and then, to work with them in the media center on the free-throw problem described above. It was an incredible day! I got to co-teach with Ivory Latta, point guard for the Washington Mystics:

I got to meet some incredible people, including current players, former players, and NBA executives:

But most importantly, I was finally able to let the world know about this amazing project, which my team has been working on for a year.

The NBA slogan is,** This is why we play**. But today I say, **this is why we work**: to develop rich curriculum resources that are fun, relevant, and powerful in teaching kids math.

### Fractional Fun

It’s well known that **5 out of 4 people have trouble with fractions**, but even the mathematically advanced may have a little trouble with this puzzle. Your challenge is simple…

Find the sum of all items in the following table.

A hint is below the table, and the answers are below that. Good luck!

Hmm… it seems that you scrolled down here a little too quickly for the hint. Try harder. To put some distance between you and the hint, here are some fraction jokes:

How is sex like a fraction?

It’s improper for the larger one to be on top.Which king invented fractions?

Henry the Eighth.There’s a fine line between the numerator and denominator.

(And it’s called avinculum.)

Okay, you’ve waited long enough. Here’s your hint. The items in the table are a fird (fish + bird), wooden forts, bottles of whiskey, the Sith lord Darth Maul, wraiths, and tents. (By the way, thanks to www.HikingArtist.com for the cool drawing of the fird!) Hope that helps.

To put some space between the hint and the answer, here are some more fraction jokes:

A student once told me, “To prove to you that I understand equivalent fractions, I only did three-sevenths of my homework.”

I was scared half to death… twice.

What is one-fifth of a foot?

A toe.

Okay, you’ve waited (and endured) enough. Without further adieu, the answer is **2.5**. The images in the table are:

- one fird
- two forts
- four fifths
- one Sith
- four wraiths
- two tents

the sum of which is

.

You’re welcome.

Thanks for stopping by. Have a great day!