MTT

Sometimes when you are teaching something the first time–or even the second–you want a really concrete way of showing what’s going on. I really love how Carolyn’s lesson on factoring polynomials using fractions tiles worked (go read it right now!).

There are two things I see that made the lesson work really well: one is that she started with numbers, and made the connection that factoring with numbers and factoring with polynomials were really finding the same sorts of things, geometrically as well as algebraically. Then she provided good problems (not all polynomials can be factored easily with algebra tiles), and gave the children a chance to make their own connections between the tiles and the pencil and paper work. I find that one of the most effective things to do when starting out with a new skill like this is to work several problems in parallel: do the tiles, and then do the same thing with symbols.

It’s hard to find the right balance because there’s never enough time for everything, but with foundational skills like factoring, it can really pay off later to make extra practice time so that students feel confident. I homeschooled my daughter for 8th grade, and when we did factoring, and again when we did completing the square, I assigned problems for a couple of days and then asked: should we go on now, or do you feel like you need more practice on this first? And we ended up spending a whole week or more on those topics.