This is a different problem, but a realistic one that students are more likely to experience in their lives. I don’t know of any cars that have their fuel tank exposed or a cylindrically shaped tank.

Of course my kids said, “Why not just fix the gas gauge?” But that was easily dealt with by saying that if he’s run out of gas twice and had to pay to get towed or have some trucker version of AAA bring him 90 gallons of diesel that maybe he’s strapped for the cash. And it sure didn’t stop them from delving into the problem with sincere fury. It was incredible to watch.

For my geometry class it was an awesome opportunity to use multiple concepts at once:

Trig functions
Area of a circle
Area of a sector of a circle
Area of a triangle

Very well done. Keep picking up those bricks of gold :)

I went a little different direction and created a spreadsheet that gives the gallons for any particular depth (in inches, since he’s old-school), so that he could use any yardstick/meterstick, or for that matter a tape measure, and we didn’t have to worry about deterioration of the stick.

However, it strikes me that creating a dipstick that is marked in regular gallon intervals (say every 10 gallons) would be an interesting question. What would such a dipstick look like, and how could we go about creating it?

The fuel gauge of an 18-wheeler is broken, so the driver decides to check the gas level of his cylindrical gas tank with a dipstick. When the level of the gas measures 20 inches high, the tank is completely full. What will the dipstick measurement be when the gas tank is one-quarter full?

Based on the working definition of pseudocontext, this problem fails on both counts. It completely ignores reality: Why wouldn’t you just fix the gas gauge? Then the problem asks for an irrelevant measurement: Why would we need to know that the tank is one-quarter full? (Personally, I find the Car Talk problem kind of boring and not very mathematically rich.) The only thing that rescues this from the insurmountable depths of end-of-chapter textbook exercise is that it was generated by a real person. Is what divides a WCYDWT problem from a pseudocontext problem is that an actual person generates it from a genuine need? Is it an issue that it is so easy to transform a genuine WCYDWT problem into a textbook-like exercise? While it is certainly true that there are pseudocontext problems that would (probably) not manifest themselves in someone’s actual existence, there are plenty of exercises that were originally born from a genuine situation and have found their way into mass-produced textbooks. Does that make them irrelevant? Or do we need a better filter?

Another word of caution: Mathematics is part utility and part artistry. By limiting mathematical study to problems related to genuine physical phenomena can only serve to retard the growth of mathematics. Many branches of mathematics, especially those pioneered last century, could not survive if physical use for the mathematics were a necessary condition of research. (For example, the cubic formula would never have been developed if Tartaglia and Cardano had not manipulated of square roots of negative numbers without really understanding what they were.) Indeed, sometimes mathematicians describe patterns, not because the patterns are useful but because the patterns are there.

But this is a much better outcome. My post wouldn’t have reached the same readership nor had the same dramatic photos.