Good math-based, sports-related investigations for middle schoolers?

June 11, 2023 12:32 PM

I'm looking for some sports-related ways to approach math for kids (middle school to early high school). Ideally, looking for high-concept approaches (e.g. "How can knowing about math help me to win at sports?") that could become long-form projects/investigations rather than short one-off activities.
posted by cincinnatus c to Education (11 answers total)

Which kinds of math? Statistics (like sabermetrics for baseball) lends itself well to this, and can also let you incorporate some scientific method (you define your questions, make hypotheses, figure out how to prove or falsify the hypotheses, etc.)
posted by trig at 1:11 PM on June 11, 2023 [1 favorite]

Calculating difficulty/start value in gymnastics.
posted by fluttering hellfire at 2:07 PM on June 11, 2023

Football has some questions regarding punting vs going for it vs field goals on fourth down, but I don't know where data can be gotten to make the analysis.

I'm also unclear what mathematical concepts are being taught
posted by I paid money to offer this... insight? at 2:42 PM on June 11, 2023

Is poker close enough to a sport?
posted by saladin at 2:56 PM on June 11, 2023 [1 favorite]

Best answer: Remember the old Gorillas Basic game? great way to teach trajectory. wind, velocity, angles. Playable at the Archive.
posted by theora55 at 3:06 PM on June 11, 2023

Best answer: I seem to recall a boy from my childhood who went to the regional science fair with a project where he took videos of himself attempting free throws and tried to figure out the ideal height to hold the ball and angle of release to consistently make the shot. I have no memory of whether he was successful in his stated goal, but it definitely lent itself to lots of "drawings where he superimposed a parabola on himself and the basket and then wrote a bunch of equations" which is basically science fair catnip.
posted by potrzebie at 3:34 PM on June 11, 2023 [2 favorites]

Best answer: Something like what was done at Moneyball? Like trying to snipe a player who's undervalued, in order to field a team that is better than its budget?
posted by kschang at 3:38 PM on June 11, 2023

Best answer: I would think sports like track and field and swimming, with a combination of individual events and relays of varying distances, would be good for creating problems of various types. Card games teach odds/percentages. Baseball has a truly ludicrous number of statistics about everything that could be used to teach any number of things.
posted by epj at 4:19 PM on June 11, 2023

Best answer: I just saw this youtube looking at the probability of making a basket shot based on distance to basket and then adjusting to figure out the expected probability of points (just multiple shots that go in by the points - either 2 or 3). You don't have to use the actual NBA data, students could it as their own experiment - making lots of shots from different distances, recording and graphing the results.
posted by metahawk at 7:58 PM on June 11, 2023

Best answer: Perfect goal kicking angle recently on Numberphile.

There are several life-useful lessons in sports around standard errors, allowable accuracy and winner-takes-gold. The specs for Olympic swimming pools require the lanes to be 50m +/- 3cm long. Swimmers correctly reckon that it is therefore silly to measure speeds to thousandths of a second because at champion swimming speed 0.001s = 2.4mm: a distance far smaller than the potential difference in lane lengths. So Olympic swimmers are deemed to have tied if their clocked speed is equal to the nearest 1/100th of a second. For track-and-field, it might be more sporting if Gold invited Silver to share the top tier of the podium when they were separated by a shirt's-thickness at the line. Also reproducibility of such wins.

Also: advantage wrt speed of sound and distance from starter's pistol.

I used to teach intro biology to first year college sporty people. We had a number of neat exercises to measure reaction time. One requires stopping a falling 30cm rule with finger and thumb: hypothesis to test whether arm length affects reaction time. Whether dominant [L/R] hand has better reaction time than the minor hand.
posted by BobTheScientist at 12:16 AM on June 12, 2023 [1 favorite]

Best answer: Perhaps a sideways approach to the 'help me win at sports' part of your question, but there's some _very_ approachably introduced maths-and-physics stuff in this video about rock climbing (well, falling) from user HardIsEasy which might kindle a flame.

The question at stake: when a climber is about to take a fall, should the person holding their rope (the belayer) take the rope very tight, or should they pay out a bit of extra rope so that it's slack? If the rope is kept tight, the climber won't fall very far, but does this mean that at the bottom of their swing they will accelerate quite fast horizontally towards the wall? If the rope is slack, the climber might fall a long way, but does this mean the bottom of their swing towards the wall will be 'softer'?

In the video there are lots of video recordings of a climber taking some pretty impressive falls beneath a bridge on a very slack rope, with lots of curves being drawn over their trajectory and put on a graph.

The inquiry is intended to encourage better belaying practices, to get people to understand that they don't always need to take the rope incredibly tight and that in doing so they may end up scaring their climbing partner. If people get used to having comfortable (not unpleasant, or dangerous) falls, they are more likely to climb in a relaxed and efficient manner.

There are lots of discussions in climbing communities about 'fall factors' and other bits of the maths and physics involved in moving masses up and down, and knowing some of this stuff can definitely help improve peoples' climbing. HardIsEasy has some other videos on some of this stuff on their channel.
posted by Joeruckus at 1:34 AM on June 12, 2023