Basketball Golf Task

The other day, a future teacher asked what one piece of advice I would give to a soon-to-be mathematics teacher. I immediately had several. I settled on one that I felt encapsulated my belief both in and out of class:

Honour curiosity. 

In class, this finds me wandering through student suggestions and constantly posing new problems that create relevant challenges. Curiosity (both student and teacher) keeps a vibrant ecology going, and I would argue that the intellectual tension so often provided through curiosity is necessary for a positive ecology to thrive.

Outside of class, this has me interacting with my curios online and with others. The purpose of this blog was to document and elaborate on my educational (specifically mathematical) creativity. This is such an instance where a simple problem popped into my head and I forced myself to see it through. Who knows, it may become an important piece of a student's learning someday.

For no apparent reason I became curious whether it was easier (mathematically speaking) for a basketball to go through a hoop or a golf ball to fall into the cup. It was an innocent enough question--a starting point.

From a scale point of view, which is easier: sinking a basketball through a standard hoop, or a putt in a standard cup? #mathchat
— Nat Banting (@NatBanting) June 4, 2014

I shared it with a couple colleagues and we began to discuss strategy. We immediately placed it within our neat boxes of curricular units. I said that it would be a great example of scale. I would find the diameters of the large items (basketball), the diameters of the small item (golf), and then find the scale factors between the balls and holes respectively.

She said it would be a great idea for area and percent. She wanted to find all four areas and then find the percentage of the hole that each respective ball would cover. We both thought this was a great start and took to Google.

My strategy
Basketball - 9.07" diameter
Hoop - 18" diameter

Golf Ball - 1.680" diameter
Hole - 4.25" diameter

SF = Basketball / Hoop = 9.07 / 18 = .50 (two significant digits)
SF = Golf Ball / Hole = 1.680 / 4.25 = .40 (two significant digits)

This told me that the basketball diameter was approximately a one-half scale model of the basketball hoop while the golf ball was approximately a four-tenths scale model. Thus, it is easier to sink a golf ball.

Her strategy
Area Basketball = 64.61 (units omitted)
Area Hoop = 254.47 (units omitted)

Area Golf Ball = 2.22 (units omitted)
Area Hole - 14.19 (units omitted)

Ball / Hoop = 64.61 / 254.47 = .25 = 25%
Ball / Hole = 2.22 / 14.19 = .16 = 16%

This told her that the golf ball took up less of the hole than the basketball did of the hoop.

Regardless of strategy, this question poses some interesting extensions if you are willing to search for them. Enabling this curiosity is the critical piece to effective mathematics teaching. I'm curious about a men's basketball. The stats above are for a female ball, the men's ball is an additional inch in diameter. How much harder is it to sink a guy's ball? 

What if we combined the strategies and took the scale factors of the areas or percentages of the diameters? Would our answers be any different?

Two basketballs will squeeze into a hoop simultaneously How small would the golf hole need to be to create this exact phenomenon? How wide would the hoop have to be to create the same ratio that exists in golf? The PGA is wondering about expanding the golf hole, is this a good idea? why or why not? How wide would a basketball hoop need to be to  match the new 15 inch golf hole? 

I could see this task fitting nicely into a unit on area in the middle years. (I like how the relationship between 1/2 diameter and 1/4 area can be explored). That is beside the point of this post. The goal is to encourage teachers to view themselves as creative beings. Follow your queries and develop them. Don't be embarrassed to share; this blog is filled with posts I am sheepish about.

My favourite teacher once told me that he was having trouble with curricular reform because he wasn't creative. This was coming from one of the most creative men I had ever learned from. I think this is more common than we think. Share, collaborate, critique, and honour your curiosities. They just might make the difference.

NatBanting