Kenneth W.'s Blog at WyzAnt.com

Math and Metal

posted by WyzAnt tutor: Kenneth W.

My current day job is a sheet metal tech. Every day, I slice slabs of metal into thinner slabs and bend them to specific instructions. The average person might call it necessary blue-collar drudgery. I see opportunity to re-explain different aspects of knowledge.

For instance, the average slab of metal comes in a 10-foot by 4-foot sheet. Commonly, we're tasked to slice along the length to either 4 inches, 6 inches, or 9 inches of length. The excess metal is scrapped.

Now, /ideally/, if I'm given an order for 6-inch pieces the 4 feet (48 inches) should be sliced into 8 equal pieces. Unfortunately, our slicer is not ideal; it cuts at a slight angle such that when it is set to 6 inches, the final piece is almost always an eighth of an inch short on one end and long on the longer. Knowing that I've made 7 cuts, I can calculate the angle the blade actually cuts.

We know that the sheet is ten feet long, and has a difference of half an inch in height after 7 cuts. I can rewrite that as a triangle with length 120 and height .5. If you're decimal or fraction-averse, it's the same as having a triangle with length 240 and height of 1. The ratio between the distances remains the same, so the angles won't change. (Side note: angles can also be described as ratios between length and height, though it's uncommon.) Since we only have the length and height of a triangle to go on, the tangent is the only tool immediately available. Sure, you could calculate the hypotenuse to use sine/cosine, but it's extra unnecessary work. Plus, you'd probably end up with enough rounding error to make it not worth your while.

So the tangent of the angle is 1/40. Thankfully, we have computers now that will do the number-crunching in order to find what that angle is. Plug it into Wolfram Alpha and I get an angle of about 1.4 degrees. Which, mind you, is the result of seven cuts. Divide by 7, and we find out that the actual blade is only off by 0.2 degrees. Such a small difference, but such a large effect of making the last sheet unusable!

Chemistry: molality, lowering the density of water, and perhaps a problem that ignores reality.

posted by WyzAnt tutor: Kenneth W.

So I was working with a college student in her 2nd year of chemistry. We were attempting to find the molality (moles of solute per kilograms of solvent) of a solution when given the molarity (moles of solute per liter of solvent) and the density (grams per milliliter).

Here's the general process of how the problem is supposed to be done. You look at the molarity of the solution, and from that we can figure out the mass of the solute in that solution. And from there, you can calculate the mass of the solvent with basic subtraction, and BOOM! there's your molality.

And it turns out there's a wrong way to do the problem, which I discovered the hard way. Turns out, even when working with an aqueous solution (salt water, for instance), we cannot assume that water's density will remain roughly 1 kg/L. For the purposes of the problem we did this week, water's density was calculated to be roughly 750 g/L. That's not a density I'd expect to see in the natural world. Even at 80 degrees Centigrade, water's density is roughly 970 g/L.

Now, I'm trying to visualise how one might lower the density of water to that point. Perhaps larger molecules (like potassium iodide, or anything else with a high molar mass) would displace the much-smaller water molecules to the point where water's density would be seriously affected. That's the only way I can see it happening.

I may update with an experiment to test whether or not we can successfully lower the density of water by 25% or so. That might be a challenge.

Technology that tests and tracks.

posted by WyzAnt tutor: Kenneth W.

Earlier this week, I began sessions with a young man who needed to shore up his math and reading skills for the military placement exam (ASVAB). I decided I'd change my normal methods a little to see if new methods have a better impact.

This time, I've decided to use two websites with built-in social media functions. KhanAcademy has a battery of K-12 math/geometry/calculus tests. FreeRice has English vocabulary and grammar quizzes. I can sign my students up with a free account and place them on my team. They can work on problems on their own time, and I can see their progress (or lack thereof) on my own time as well.

I'd be interested to find more websites like these that both test knowledge and build groups of people that tutors like myself, teachers, and/or parents can monitor and review. If you have any other useful websites in this vein, feel free to share them.

Parents, sit in on a session!

posted by WyzAnt tutor: Kenneth W.

I woke up this morning to a wonderful email. One of my recent students wrote a very positive review for me. Here it is, uncensored:

"Kenneth knows his math and can explain it in a simple manner. He is easy to understand. He is polite and personable. My son ran through 2 tutors before Kenneth, so I was crossing my fingers that Kenneth could get the job done without drama. My son responded in a very positive manner."

A bit of background: Her son wants to test out of high school at 16. I was asked to review the GED math section with him for this session. This kid is capable of passing the section now, and he's only a freshman. Her mother and I have already discussed him reviewing the SAT/ACT as well, given that it's necessary for most colleges to look at those scores as well.

It helps that I understand where her son is coming from. I was in a very similar mindset when I was in high school. If I wasn't socializing or in math class, I was bored stiff. Not to mention his extra-curricular activities matched mine (gaming). So it's no surprise that connecting with him was a little easier than usual.

Her mother also sat in on the session, which is the first time that's happened in Denver. I sincerely appreciate parents who make the time to show up and watch the tutoring process happen. Parents who work odd hours, I understand where you're coming from. But if you have the time, please watch as your kid is led to understanding. When done right, it's a sight to behold.

Tutors, are you moving soon?

posted by WyzAnt tutor: Kenneth W.

Don't forget to change your account information if you're moving. Here are the two places you need to go:

1) My Account > Change Information. Here, you change your mailing address. This is very necessary to do before tax season hits!

2) My Account > My Profile > ZIP Code. You must also change your profile to reflect where you are now tutoring.

If you do not change *both* of these, it will reflect your browsing experience. Searching for students will default to your mailing address, not the ZIP code in your profile. If your profile still lists you in your old town, it'll be hard to get new business in your new town.