How well do you understand math concepts? See if you can explain the following 13 statements:
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, .002
5) “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) True or false: .99999.... = 1
13) Explain why a negative times a negative is a positive.
I came across this list in Grant Wiggins blog.