Developing the question means attending to processes that interest normal people before attending to the processes that interest mathematicians.

Too glib perhaps.

Describe the configuration of scales on a snake using 3D transformations.

Given a closed two-dimensional shape, invent a statistic that describes how “round” the shape is. When your statistic is applied to a circle, it should yield the highest possible score.

A tree’s primary branches are those branches that sprout directly from the trunk. Secondary branches are those that sprout from a primary branch. Tertiary branches sprout from secondary ones, etc. What is the ratio of a tree’s trunk circumference to the circumference of it’s thickest primary branch? What about the ratio of the circumference of a tree’s thickest primary branch to the thickest secondary branch? Thickest secondary to tertiary, etc?

How many kisses will happen today?

How close can you get the tip of your right index finger to the tip of your right elbow? What is the farthest distance you can make between that finger and elbow? Answer the same two questions for your right index finger and left elbow.

Imagine two line segments that are connected at one end. What could this be a model of?

How much do the raw materials used to make a single wooden pencil cost?

A lattice point is a point in the coordinate plane with integer coordinates. Is it possible for a line to go through exactly one lattice point?

Think of as many words as you can that are related to geometry and contain the letters c and t.

Make a serious effort to find the best word or phrase to complete the following analogy and explain your choice. Math is to beauty as ___________ is to emotions.

http://cdli.ucla.edu/search/search_results.php?SearchMode=Text&ObjectID=P254438

So yes, students have been doing this sort of “fake world” word problem for upwards of 3,600 years!

(the translation above comes from http://oracc.museum.upenn.edu/).

In my Algebra 1 and Geometry classes I like to pull out and show some of the word problems (with worked-out solutions) found on clay tablets in Old Babylonian excavations. Apart from the base-60 number system, these are pretty much identical to what we might see in a textbook today.

To give one favorite example (I think this one comes from a Sippar in the 9th century BCE but I’d have to check):

“A textile. The length is 48 [rods]. In 1 day she wove 0:20 [rods]. In how many days will she cut [it] off [the loom]?
You solve the reciprocal of 0:20. You will see 3. Multiply 48 by 3. You will see 2:24. She will cut [it] off after 4 months, 24 days.”

(I especially like to show a picture of this tablet because the scribe ran out of room at the bottom of the tablet and the second half of this particular solution is marked along the bottom edge. Students can usually sympathize with this if they have ever run out of room on a page while solving an equation).

Mr. Meyer, I read in a yahoo article that you taught math. For how long did you teach before moving on to advanced studies?