So Part 2 was supposed to be about the big ideas in K-7 mathematics that students will need for high school. But that’ll have to wait for Part 3. Instead, more on times tables.

Three oft-used arguments for the importance of memorizing times tables:

- When learning higher levels of math, there just isn’t
**time**to use calculators or strategies to determine basic facts. - Besides, thinking taxes
**working memory**which means by the time you’ve worked out the first part of the question, you will have forgotten the…*Where am I?* - Because
**factoring**.

1 & 2 are gospel. Well, so is 3; nevertheless, it’s the focus of this post. I have a couple of thoughts on times tables and factoring trinomials.

The reason some students struggle with factoring trinomials is *not* because they haven’t memorized products to 10 × 10. I can get away with this if we’re talkin’ Pythagoras. But factoring?! I mean, that’s all it is, right? To factor *x*² + 7*x* + 10, you just have to ask yourself, “What two numbers multiply to 10 and add to 7?”

HS math teachers, try this: give your students a quiz on factoring. Include both *x*² + 10*x* + 24 and *x*² + 25*x* + 24. Get back to me. For extra credit (yours, not theirs), throw *x*² + 6*x* + 5 in there. If your students are anything like mine, I bet *x*² + 25*x* + 24 gives them at least as much difficulty as *x*² + 10*x* + 24. What does this mean for these students? More practice multiplying by one?!

Of course, 1 × 24 falls outside *most* times tables. Recall of products to 10 × 10 gets us the factors of *x*² + *b**x* + 60 – if *b* = 16. But *x*² + 17*x* + 60, *x*² + 19*x* + 60, *x*² + 23*x* + 60, and *x*² + 32*x* + 60 are fair game, right? Try *c* = 48. Or 72. Or 96. Or 100. What role does memorizing times tables play? What role does being flexible with numbers play?

My point, I think, is that these are different, albeit related, skills. In other words, the “it” they’ll need for factoring (trinomials) is factoring (numbers). And number sense. This has some implications for K-7: not necessarily more “What’s 4 × 6?” but more “A rectangle has an area of about 24 square units. What could its length and width be?” or even “The answer is 24. What’s the question?”; not thinking digits/standard algorithm but thinking – and talking! – factors/mental math strategies, e.g. 16 × 25 = (4 × 4) × 25 = 4 × (4 × 25) = 4 × 100 = 400 (via Sherry Parrish).

Say you’re still asking, “How am I supposed to teach them factoring when they don’t even know their multiplication facts?” When I introduced polynomial division in Math 10, some of my high school students didn’t even know long division. So I taught division of numbers and polynomials side-by-side, highlighting connections. Can the same *miiindset* (channeling my inner Leinwand) be applied to factoring trinomials and times tables?

And what about something like *x*² − 2*x* − 24? If that – asking yourself, “What two numbers multiply to -24 and add to -2?” – is all it is, why not factoring trinomials to teach multiplication (and addition) of integers?