I often have to tell my students to bring along all of the tools they think they might need BEFORE they begin a problem. In other words, get your formulas, shortcuts, and traps to avoid all ready to go — before you dig in to the problem.
Recently my wife told me that our garbage disposal in our kitchen sink was clogged. So, naturally, I rolled up my sleeves and took a look. There was some food stuck in there, so I scooped that out and threw it away. Then I noticed that the blades weren’t spinning. I took off the rubber gasket and tried to spin them with my hand, but no luck.
Next, I opened the cabinet and knelt down. There’s a hex wrench opening where you can loosen a stuck blade, so I went to the garage and got a hex wrench. I gave it a few twists, but it stayed stuck.
It was time to get a better look inside, so I decided to take down the disposal unit. This required loosening a few of the PVC drain pipes, but they were at an awkward angle. I went to the garage and got a pair of channel locks and loosened the pipes. But the disposal wouldn’t move, until I took off a certain overflow pipe that was held on by a metal cuff. To loosen this cuff, I needed a screwdriver.
So, I went to the garage and grabbed a screwdriver. I loosened the cuff and the unit came loose, spilling water onto the floor of the cabinet. I took off my sweatshirt, which had gotten wet, and grabbed a few towels for cleanup.
Now that the disposal was finally detached and sitting in my lap, I could see that some egg shells had gotten wedged under the blades and jammed them up. I went to the garage and grabbed some needle-nosed pliers and a razor blade. With a little elbow grease, I managed to get the blades loose and spinning freely. I figured I could probably save myself some future trouble if I lubricated the spinning mechanism, so I went to the garage and got some penetrating oil.
After that, all I had to do was put Humpty Dumpty back together again, and we were in business. That thing could have ground up a whole ham with the bone inside.
When I started to pick up my tools to take them back to the garage, I realized just how ridiculous and inefficient I had been. I had taken five trips to the garage (down and back up a flight of steps each time), and one trip to the linen closet for towels. But here’s the thing — I’ve done little plumbing projects before, and I need a bunch of different tools absolutely every single time. Why didn’t I just grab my entire tool bag at the very beginning?
This is what students must do on the SAT. If you see a semicolon in a problem, it is absolutely inevitable that you will need to find subjects and verbs, so you may as well access that part of your toolbox. And while you’re there, you should bring along your colon and comma knowledge as well, because it will definitely come in handy.
Likewise, there is almost zero chance that a question about arithmetic mean won’t use the formula “Sum/number of things = average.” So just write it out at the very beginning, and get ready to use it! The same goes for a percentage problem: you will be setting up a ratio, so you might as well draw two lines separated by an equals sign, and then start filling in the blank spaces. If it’s a circle, prep yourself with C=2𝛑r and A=𝛑r^2. If you are doing a unit conversion, you better go grab your toolbox full of parentheses for the dimensional analysis.
Don’t be like me and take 5 trips to the garage to get the tools you need. Get totally prepared for the job at hand, and then get to work. If you don’t end up needing anything but a screwdriver, who cares? Better to have a tool and not need it than need it and not have it.
And maybe bring a towel for the mess.
