I will make a friendly wager: I predict that no student will get all the questions correct. Prove me wrong and I’ll give the teacher and student(s) a big shout-out.1) “You can’t divide by zero.” Explain why not, (even though, of course, you can multiply by zero.)2) “Solving problems typically requires finding equivalent statements that simplify the problem” Explain – and in so doing, define the meaning of the = sign.3) You are told to “invert and multiply” to solve division problems with fractions. But why does it work? Prove it.4) Place these numbers in order of largest to smallest: .00156, 1/60, .0015, .001, .0025) “Multiplication is just repeated addition.” Explain why this statement is false, giving examples.6) A catering company rents out tables for big parties. 8 people can sit around a table. A school is giving a party for parents, siblings, students and teachers. The guest list totals 243. How many tables should the school rent?7) Most teachers assign final grades by using the mathematical mean (the “average”) to determine them. Give at least 2 reasons why the mean may not be the best measure of achievement by explaining what the mean hides.8) Construct a mathematical equation that describes the mathematical relationship between feet and yards. HINT: all you need as parts of the equation are F, Y, =, and 3.9) As you know, PEMDAS is shorthand for the order of operations for evaluating complex expressions (Parentheses, then Exponents, etc.). The order of operations is a convention. X(A + B) = XA + XB is the distributive property. It is a law. What is the difference between a convention and a law, then? Give another example of each.10) Why were imaginary numbers invented? [EXTRA CREDIT for 12th graders: Why was the calculus invented?]11) What’s the difference between an “accurate” answer and “an appropriately precise” answer? (HINT: when is the answer on your calculator inappropriate?)12) “In geometry, we begin with undefined terms.” Here’s what’s odd, though: every Geometry textbook always draw points, lines, and planes in exactly the same familiar and obvious way – as if we CAN define them, at least visually. So: define “undefined term” and explain why it doesn’t mean that points and lines have to be drawn the way we draw them; nor does it mean, on the other hand, that math chaos will ensue if there are no definitions or familiar images for the basic elements.13) “In geometry we assume many axioms.” What’s the difference between valid and goofy axioms – in other words, what gives us the right to assume the axioms we do in Euclidean geometry?Let us know how your kids did – and which questions tripped up the most kids – and why, if you discussed it with them.
So they decided to take him up on the challenge. I will share a modified version with my PreCalc students (I removed some of the verbosity and added lots of white space, it's a word doc via scribd). In the meantime some teachers have already started answering them and so I've declared it a matheme. Can you answer all 13 in a way a kid could understand? Can your kids answer them in a way that shows understanding? If you write a blog post about either please submit it under the category Grant Wiggins Challenge.
p.s. I posted two days in a row because I'm taking Anne's 30 day blogging challenge! Join us? #MTBoS30