Ideas Wanted: “Basketball Math”

I’m hoping I can get some ideas from math teacher types (and others) around an idea I’ve been kicking around for my son Tucker, who, as you might guess by the title of this post, loves basketball. (He loves math, too.) Not that he needs it or has asked for it, but I keep wondering what a “Basketball Math” curriculum might look like for Tucker, one that would combine his serious interest in the sport with his growing interest in math, and one that would also give him opportunities to connect with other basketball and math lovers outside of the classroom. A few basic things seem obvious, even to my English teacher brain, in terms of learning percentages, ordering numbers, reading some blogs on using statistics in basketball, etc. But I’m thinking there’s a lot of other stuff about geometry, physics and more that he might find hidden in the game as well.

So if you have a second, I’m hoping you might post your ideas here. Assuming we could (and would want to) build a K-? math curriculum around the game of basketball that, if possible, takes advantage of these social learning spaces online, what might that look like?

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Hi…

Field goals of the top 40 NBA players!

Bivariate data to understand writing equations of lines and interpreting slope. Plot field goals attempted as the independent variable and field goals made as the dependent variable.

How would the top 20 WNBA players data look in comparison?

How does your team’s data compare to these elite players? What is their practice standard for honing and keeping their skills?

Oh, you might have to explain to your students what a field goal is in basketball; I did!

Also works with free throws.

I have data, graphics, etc. to share if wanted.

Player heights…single variable data. How does the WNBA and your team’s stats compare to the NBA?

Is the ability to dunk dependent on height? gender?

This last is a really great question, and he’s rattling off all the characteristics that are required to dunk.

There are some probability applications. If a free throw shooter has a 75% chance of making a free throw, what are the chances that he or she makes 2 free throws? 1 of 2? 0 of 2?

You could use a spinner to simulate the probability, or even a deck of cards (heart/spade/club = made free throw, diamond = missed free throw).

It is interesting (mathematically) to ask what is the most likely outcome in a 1-1 free-throw situation.

There is the straightforward version: Player X makes P percent of their free-throws. In a 1-1 situation, what is the most likely outcome? The least likely outcome.

There also the backwards version. For which values of P is 2 points the mostly outcome of a 1-1 situation? For which values of P is 1 point the most likely outcome? For which values of P is 0 points the most likely outcome?

Dan Meyer’s dy/dan blog had this on it:

http://blog.mrmeyer.com/?p=4778

I don’t have a huge math background and am trying to stretch myself into that field because I know it’s important, and I really like this post and find his math so interesting. I would think this could be expanded on in many aspects.

Why not set up a fantasy team with a salary cap? Involves almost every type of mathematical equation.

He has fantasy teams on ESPN…is there a place that adds in the $$$ piece?

Check out the bball article in the Encyclopedia of Sports Science (1997, MacMillan/Simon & Schuster). It’s got discussions of arc, force, angles, trajectories, spin, direction, friction, ratios, center of gravity, balance, etc. You could get a LOT of math out of that!

My initial thoughts are just to expound on the things you named. For example, one of my favorite players was Allen Iverson, who could score 30 points on any given night, but did it while shooting about .300 from the field which probably hurt his team in the long run. You can probably set up different metrics – basically giving different weights to things like free throw percentage, scoring, rebounds, steals, etc. – and compare players and be able to claim “I can prove that Kobe is better than Lebron” or whoever else you want to compare. This would also extend to comparing teams and stuff.

We’re liking comparisons like these. Tucker’s talking about how Lebron may not score as much this year since he’s a part of the “Big 3″ so that’s why he may not be “better” than Kobe this year even though he may be a better player. (I’m liking his analysis.)

Could study linear inequalities and look at profits and losses when running managing a basketball team.

Could study quadratic functions and look at the path of the basketball. Force required to obtain correct arc to make basket.

I think you are getting at how we should redesign ALL of our math instruction. Instead of teaching specific curricular outcomes we should take a real world situation and study all parts of it indepth and the math outcomes WILL be covered.

Some other mathematical / physical connections are: Volume of air in ball, volume of the air if it were out of the ball, mass of air in ball, density of air. Design an experiment to determine these. Volume of skin making up ball assuming skin is 1/16 th thick. Mass of skin. Density of skin. Design an experiment to determine skin density. Now recalculate the volume of air in ball taking into account the thickness of skin. What is definition of mass and weight. Does ball have water vapor or liquid water or both? What would this depend on?

Incorporate geography…calculating traveling distances/methods to visit arenas and attend games. Ticket prices. NBA Tour 2010-2011.

I’m liking this one. Tucker’s a little overwhelmed by the idea of using the calendar to make sure the teams are actually playing on the nights we visit. ;0)

There’s gotta be an app for that.

How about studying the lines and shapes on the court? A little bit of geometry there.

Of course you could study force, mass, and acceleration which is applied math.

You could throw in something about advertising that is done inside the arenas and money made through selling clothing etc at the souvenir stores (not to mention the cost of drinks and snacks.)

To build off WM’s idea…

using the vernier physics application for iPhone/iPod touch, he could do some data collection, analysis, etc. I wrote a post about this not too long ago: http://middleschoolblog.blogspot.com/2010/09/video-analysison-my-phone.html

one other comment.

Motion Math is a math game targeted to elementary aged students…it was actually developed by a graduate of the stanford learning, design and technology program who interned with, Gabriel Adauto. Not sure where the connection here is, but if he has any interested in coding, this is at least something to consider.

More on motion math at: http://motionmathgames.com/

Will,

As a former three-point killer myself back in the 80′s, I can relate to such a curriculum with profound respect.

My favourites would tend to be around a perfect arced three-pointer/jumper/free throw, where the parabolic trajectory of the ball is definitely ‘find-out-able’ through quadratic functions, or possibly cubics. Huge potential to teach regression analysis, curve-fitting, and possibly even 3-D vectors. (Your son may be a bit too young, but I commented because many of the previous commenters were discussing stats, and this is a different path)…

As always, your blog inspires. Thank you for what you write.

Sincerely,

Ryan Maksymchuk

Swan River, Manitoba, Canada

I would suggest incorporating a video game like EA’s NBA Live 10 into the curriculum and using it both as a data generator and motivational tool. It could be used for lower level math skills for the younger grades to complex statistical analysis for older grades. It can be played in groups to promote collaborative and team-building skills. Off-line exercizes can be created to utilize the data that comes from the game and help define the next set of data the students need to generate (ie, play the game). I teach a course about using entertainment console video games in standards-based curriculum and many math teachers have used sports games in this way.

Tucker likes this idea. Imagine that!

I recently started coaching a girl’s soccer team in an area where math and english scores are consistently low. I would love to find a way to incorporate both into everyday practice. Does anyone have any ideas about this?

Estimation, Rates, and Perimeter:

Discover many high-knees it take to go across one side of the goalie box, then apply that knowledge to how many high-knees it would go around the perimeter of the entire goalie box.

If it takes one player an average of 15 seconds to dribble across the field, how much time would it take for a team of x to finish?

Area, perimeter of the floor. Determine the hypotenuse using the distance from the free throw line to the center of the hoop and the height of the hoop. Compare the diameter and circumference of the hoop and different sized balls.

Create a scale model of a court and engineer a shooting mechanism to launch a ping-pong ball toward the hoop.

Put “basketball math” into NCTM’s search box and you will come up with many other ideas and articles. One NCTM link for math basketball ideas:

http://www.nctm.org/eresources/article_summary.asp?from=B&uri=MTMS2006-03-334a

Basketball is great for physics, and I use it quite a bit when talking about not only the obvious things (projectile motion, parabolic trajectory, freefall, vectors) but also things like energy (potential & kinetic), collisions (dribbling, bank shots), as well as relative vectors (passing lanes, dribbling) and rotational dynamics (why you put backspin on your jump shots).

It’s a really great base for a good physics curriculum.

I have created a Physics Performance Task with this scenario (based on an event that happened in 2006):

“You are the National Basketball Association scientific advisor and you have to evaluate whether or not a new type of ball should be used in the upcoming basketball season.”

The students receive seven different documents (included a biased article) that will help them in validating their decision. The physics concepts are related to friction, conservation of energy, absorbency, bouncing, etc.

The task culminates when the students have to design and conduct their own experiments.

Our athletic department has been very generous donating old basketballs and swatches of different types of balls: leather, synthetic, etc.

Thanks Alex and Dolores…when Tucker gets to the physics stage, I’ll link him back here.

Haven’t had a chance to see any of the comments above, but I’ll throw mine out there just in case.

More Algebra I/II topics…

How many times will a ball bounce before it stops (exponential decay)

How long will a ball bounce before it stops (sequences and series)

After observing a ball bounce 5 times, determine how high you would have to throw it from half court for it to bounce and make it in the basket (that one might be made more clear with a diagram, but it’s math [quadratics] and physics)

I see some great ideas from the physics people out there! I home-schooled a “b-baller” as well. I’ve been in your shoes! It sounds like some of those ideas are for the future. (?) Not sure how old your son is now.

I remember early on having my son count shots from this angle and that, keep stats, etc. Also, the league we joined kept stats posted on their web site – he would scour through that site (reading!) and compare everyone’s stats.

But I do have a little “warning” – Eventually backyard b-ball became his dreamy alone time (I think probably pretending to be M. Jordan though he won’t admit it.) So, I’m sure you’ve thought of this, but you don’t want him to reject you, math, and b-ball if he gets in a tizzy at some point!

Our son is in high school advanced math now. It is by far his favorite subject.

So, the main thing I can tell you from my past experience is don’t panic and enjoy this precious time!

Cooking (recipe manipulation), yahtzee, “Math 24″ all helped along the way – esp. the latter as both our sons loved beating their parents at a math game.

I think their confidence is helped if they feel like they are “discovering” a concept vs. being taught – so in a way (err), maybe a little acting from Mom and Dad comes in handy at times too. And chatting casually about shopping, politics, etc. and being as “nerdy” as possible demonstrates how life can be viewed quantitatively. It calms me to think of all the prior math that humans have done throughout time and place – so we must be wired for it. And, not to be too gender-bender, but I’m in an all male clan now (‘cept me) and competition, numbers, and systemization just ooze about in every corner.

Anyway, do you know how to you make classic literature a blast?

Oops! I think I thought I was in a different forum! Sorry if I offended!

To summarize a little better: we believe that math (well, school actually) is a game, and learning to teach yourself is the match point.

We’ve had our kids in and out of public school – private not really a financial option – but when they go back to public school, they are given the option.

Everything that helps put them in the driver’s seat seems to help.

My father in law – a med school proff – told me that in some classes in med school in Canada, they had to throw out grades or nobody could learn it. And little guys are supposed to be more mature than that?

Play fantasy basketball. Means, standard deviation, and z-scores become extremely important in comparing the relative strengths of players in the various statistical categories. Later in the season the player makes judgments about how many opponents are still within striking distance in each statistical category. The team owner also needs a system to evaluate players when offering or making trades.

Will, my brother-in-law is a huge Strat-o-matic baseball player. I just checked their website, and it looks like there is a Strat-o-matic basketball, too: http://www.strat-o-matic.com/products/basketball.

I have no idea if this is what you’re thinking of, but I do know that the game involves heavy stats.

Too funny…I used to play Strat o Matic baseball as a kid! Thanks, Diana.

Karen Bruce, math teacher, over at Sine of Times has a great post about seeing math everywhere with an example of basketball. May be worth a peek. Check out the post: I see math

~ punya

At Tutor.com, we had a series of blog posts about math in sports. I hope this helps!

How Math Can Lead to a Career in Basketball

Using Math to Calculate Baseball Statistics

Hi,

Thought I’d weigh in on this one — if I’m not too late. In the spirit of thinking ‘globally’, consider expanding to other sports as well. I participated in a wonderful training this summer (at Patriot’s Place in Foxborough, MA) where teachers learned about ‘sports materials’. The training was given by CASE (Center for the Advancement of STEM Education) trainers who used the Materials World Module — Sports Materials, (http://materialsworldmodules.org/modules/sports.shtml)

Middle and high school teachers explored a large vaiety of sports materials (basketballs, golf balls, soccer balls, tennis balls — you get the picture). The training comes with a kit of sports materials (balls) cut in half so one experience is seeing what’s inside and thinking about how the inside impacts the performance of the sports ball. It was an engaging inquiry experience that really looked at the practical connections between math and science.

This leads me to my established belief that ALL ideas should be presented outside the vacuum of single content/concept teaching. We are such isolationists when we present new material. We force students to think that everything stands by itself — yet in truth everything (and I DO mean EVERYTHING!) has a relationship to something (usually many things) else. No wonder our students cannot grasp the essence of an idea — there are no references that allow them to appreciate some or all the connections.

Brain research has acknowledged that long term memory needs those connections. So if we MUST teach to the test we need to help student recall by creating obvious connections for our students. Let’s provide them with ‘memorable’ experiences that make sense (using real world experiences).

I’ve enjoyed all of the creative ideas. They do seem like they could be incorporated into a basketball math “curriculum”.

I wonder, however, if it might not be better to let the student(s) brainstorm and come up with ideas for projects that they may want to pursue. The ideas in the replies could be used as a brainstorming aid if necessary.

Keep up the great great posts!

[...] Will Richardson: I keep wondering what a â€œBasketball Mathâ€ curriculum might look like for Tucker, one that would combine his serious interest in the sport with his growing interest in math. [...]

There’s someone in one of the districts near here working on a sports statistics book, with questions like ‘Is it possible to go on a shooting “hot streak”?’ and ‘Did LeBron James choke during the NBA Finals?’

I’m not sure how close the book is to publication, though.

Plot the relationship between ball pressure and bounce height.

Find which shoe allows the quickest pivot.

After you do the path of the ball through flight. Use http://www.addictinggames.com/gimmefrictionbaby.html to explore how the ball bounces off the backboard. That leads to the reason for the square on the backboard. Why a square and not a rectangle, and even why the basket is set away from the backboard.

Then there’s also why the big backboard if most shots off the backboard won’t go in? What’s the proportion of the area of the square to the backboard? Proportion of lengths. There’s probably some human perception issue there that leads to an ideal size.

From an 8th grade math class I taught once a week:

Start with who’s the better team: Celtics or Lakers? Justify. Eventually, it gets down to Kobe versus the trio of Pierce, Allen and Garnett.

Alright, so what makes a good team a good team? Star players or the strength of the whole team? Check out the stats (PPG), what’s the distance between Kobe and the second best player on the Lakers? How about between each member of the Celtics top trio? Or even the lowest of the Celtics three to the fourth best player on their team? OR even the distance between the first and last ranked players on both teams. Let your son figure out all the ways to compare the two teams using the Points Per Game stats. We’re hitting decimal subtraction, comparison, and range. We could even check out average PPG of the entire team for both sides(hitting decimal addition and division) and you could intro different measures of central tendency by comparing the average PG with the median PPG for each team.

Heck, we could illustrate it for people who don’t want to get bogged into the details and would rather see a visual. Graph the distribution of PPG for each team’s players. Do a bar graph, a line graph, even a box and whisker…you can still see the distribution of PPG among all the players really clearly with any of those. Maybe do ‘em all and have him choose which is clearest and have him explain why.

And finally, it all comes back to the original question: which team is “better”? He’ll be able to speak his mind with authority and back it up with data. As often as you can, make sure you always bring the context of basketball scores to the data analysis, so he has a stable link to the reality of the points on the graph or the whisker of the box and whisker; that way they won’t get lost in the theoretical.

I have the lesson plan somewhere on my other computer, if you want me to fire it up for further info. Sorry for any confusion in this transcript of my memory.

Yeah…these are the types of questions that he’s most interested in right now. And I’m thinking there is a lot of useful math he could learn in the context of defending his choice of the Lakers over the Heat. (Even though he’s wrong, of course.)

I’m going to suggest this type of an exercise to his math teacher. We’ll see.

Not sure what grade level you’re thinking about, but here are some basketball lessons that you might find helpful:

Basketball IQ (shooting distance vs. percent, or

Is a 3-pointer ever a good idea)Mad Hops & Super Strength (do NBA players really jump that high?)

I’ve created a 3 variable system of equations problem by printing out a Celtics box score and then blacking out a few of the statistics. Say you block out all of Ray Allen’s shooting statistics, and Paul Pierce’s point totals, and the 3-pt statistics for everyone but Pierce. Maybe the question is how many 3-pointers did Ray Allen make…In order to find it you have to find Pierce’s point total by adding up his made 2′s and 3′s, and then from that and the team total points, you’ve got Allen’s point total, and, well, you can take it from there.

I would suggest downloading a free copy of Alice, the 3-D virtual world simulator from http://www.alice.org. It includes 3-d basketball models that can be manipulated through a simple drag & drop programming interface. He could actually create a fairly complex basketball game using Alice.

I have posted a brief introduction to Alice on my blog and it includes resources such as a basic Alice programming PDF. To make a successful simulation, you’ll have to get into some physics math, which I haven’t written about yet, but I do know you can do a pretty good model of projectile motion in Alice. Maybe I should write something up on that topic? I do have an Alice project (but not basketball) I did a while ago that uses projectile physics. Let me know if you would like a copy you could play with and modify if you decide to try this idea out.

Figuring out the math needed to model the physical world is a great way to connect these ideas together, and using Alice software would be a good way to do it.

Sports provides teachers will a tremendous opportunity to bring statistics to life for students. This is an area of mathematics that is sorely lacking in our schools. Whether students are picking their own all-star lineup and using stats to justify their decisions or engaged in a fantasy sports league, sports and stats are a natural route to engage students in math who would otherwise be disengaged. In general, we need to move statistical mathematics up the hierarchy of math topics, as data and data-based decision-making become more common in the workplace.

There are some really interesting possibilities here. If you are targetting algebra students, you could have problems or lessons concerning the parabolic path of the ball. If you could measure the initial upward velocity of the ball when shot you could determine the vertex of the shot (the max height) which could be interesting if you were Spud Webb trying to shoot over Manute Bol…I know that I am dating myself.

You could also do something with the magic number when the end of the season is drawing close. The magic number is the number of wins by the 1st place team or losses by the second place team or combination of both that the 1st place team needs to clinch the division. For example, if the magic number was 5, then any combination of wins by the 1st place team and losses by the second place team that totals five ensures that the first place team will win the division.

One other thought is to have the students explore what happens to the score when the other team steals the ball and scores…is it a 2 pt difference or a 4 pt difference (your team didnt get the 2 pts they were trying to and the other team did). Might make for interesting discussions.

Download a copy of Alice and build a simulation of the physics. I built a projectile simulation a few years ago. It uses an outlaw and a revolver, but the same ideas should work. You can download the simulation here, and see how the math programming works. Please let me know if you try this idea. I’d like to see what you come up with.

For a short overview & resources on getting started with Alice, visit this page</a?.

[...] Richardson asks for suggestions for a developing a basketball-based math curriculum. Some awesome [...]

Excellent request, and, as always — Teachers respond with some terrific ideas! I just did a search on the WeAreTeachers “IDEAS” tab for Basketball and found lots of great ideas here as well. http://www.weareteachers.com/ideas

Full disclosure- – I am a former teacher, and the CEO of WeAreTeachers — Wanted to let you know we have about 10,000 teaching ideas on our site, and we find corporate sponsors to award grants to support many of them — THanks for great blog post, and for getting such great teacher response. I’m always amazed — Teachers are always so willing to share their best ideas and strategies with one another.

Have you considered how the max. cross-sectional area of a BB compares to the area inside the rim? How would a ball of smaller/larger cross-sectional area affect shot percentages. Isn’t the WNBA ball smaller than the men’s? Consider a do-it-yourself experiment with different basketballs. Shoot 25 free-throws with each and compare results with conjecture.

First part.

You’re the basketball coach. Your team is down by 1 point, there are 5 seconds left, and you have to decide who you’re going to throw the ball into. That person will either have to make the shot or get fouled and make free his free throws. How would you pick the first and second targets for the throw in.

Second part.

You’re the coach. Your team is up by 1 point, there are 5 seconds left, and the other team took a time out and is going to throw the ball in. Will you double team any of the players? Will you foul the player who gets the ball? How are you going to decide?

For both parts, assume you can have access to the numbers of shots that each player has made, the number of attempts, the number of free throws made, and the number of attempts (this year and in this game). The class can use the Internet to look these up for a real team if you are teaching this live.

I have read some articles purporting to prove (or disprove) the notion that baseball and basketball players get “hot” or “in a zone”.

Is there such a phenomenon?

Try the Basketball Math curriculum. It is fantasy basketball and I have used it with 3-8 graders and they have all loved it. Also baseball, football, soccer, hockey books available. They come with a free code to the fantasy scoreboard site.

You could have him listen to/watch games and evaluate the comments as fact or opinion.

He could also research to find out if questionable statements could be supported factually.

[...] Which of Will’s commenters has suggested a pseudocontextual [...]

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Here are a couple of fun bball simulations:

http://www.fearofphysics.com/Proj/proj.html

http://www.onlinegames.com/basketball/

Just let your son play and see what conclusions he draws from the games.

You should look at the approach on my colleague Brian Mark’s website, Yummy Math, and particularly his recent post on Fantasy Football:

http://www.yummymath.com/ready-for-football.php

Hi Will,

I think this is a great conceptual idea. So many educators seem to get wrapped up in the idea of curriculum being rigid and only about the subject at hand. So many other lessons can be taught by allowing children to do what they enjoy. This provides inspiration for future teachers to dig deeper than the surface lesson to allow students to have fun while learning the stated curriculum.

Thank you,

Brittany Schneider