The Math That Saved Apollo 13

Two hours after a service module’s oxygen tank explosion on Apollo 13, Commander James Lovell did calculations that helped put the ship back on course so that they could return back to Earth. They needed to establish the right course to use the Moon’s gravity to get back home. Check out the article on Gizmodo from November 2011.

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Khan Academy

If you haven’t heard about Khan Academy, then you probably aren’t in the field of education. There has been tremendous criticism of Khan Academy by educators because it ultimately just lectures to students and many educators – at least the ones I keep up with – prefer having students approach math in a different way. Math is often seen as something that you learn and then practice. With more practice, you’re supposed to – with the traditional thought behind mathematics education – get better at math but I don’t think the point of math is to be able to memorize and practice problems over and over until you’ve mastered the skill. Although this can be one way people learn math, I don’t think they’ll truly understand it this way. Many other teachers really like Khan Academy because it does the lecturing for them. The program does have its benefits as it does allow students to work and learn at their own pace. Unfortunately, I’ve witnessed teachers just have their entire class watch a lesson in lieu of them teaching it, then pass out a worksheet for them to practice this new concept that they have just “learned.” While I may not be its biggest fan, I know Khan Academy does help some students. So for those of you that may get some benefit from it, check it out. Here’s a sample of what the videos are like:

Show Your Work

Teachers love to force students to show their work. It’s not only a way to see if the student actually knows what they’re doing; it’s also a way to see exactly what a student doesn’t know. A wrong answer tells nothing about what the student knows or doesn’t know. Partial credit is usually the incentive for students to show their work – but you shouldn’t force students to show everything if the reaction is negative because you don’t want to have your students feel annoyed by you. As a teacher, you need to motivate, inspire, encourage, and enlighten. If you focus on the wrong parts of math, you’ll lose your students.

With that said, here’s a fun comic to remind us to lighten up sometimes. Don’t forget to use PEMDAS to get the correct answer!

thanks DOGHOUSEDIARIES

NASA Has Space Math

Here’s just a quick heads up on the awesomeness that is NASA. They have a page dedicated to math! My favorite are the “Problem Archives” where teachers can present real data, pictures, graphs, etc. from NASA to their students in an already lesson-friendly PDF. There’s nothing better than supplementing a textbook with this kind of stuff!

Space Math @ NASA

Please Excuse My Dear Aunt Sally

The reason your math teacher made you (most likely) remember PEMDAS, or “Please Excuse My Dear Aunt Sally,” is because without it we wouldn’t be able to properly read mathematics. For example, you can read the sentence, “The quick brown fox jumps over the lazy dog,” and picture what it is trying to convey. There’s a dog, he or she is lazy, maybe laying down. A fox, which is the color brown, jumps over the dog and is doing this at a fast speed. Everyone reads this sentence and understands it in the exact same way. We know which adjectives describe which nouns and what the verb is referring to. We know the fox jumped, not the dog. We know that the word “brown” describes the color of the fox. We learned the rules of English in order to be able to read, write, and communicate so that everyone knows exactly what we are trying to say. The order of operations is the equivalent of this, but for mathematics.

Without the order of operations, everyone would do calculations however he or she wanted and everyone could get different answers. If I say to you, “First add two and eight, then divide your sum by five,” I could write it out as: (2+8)÷5 or (2+8)/5. If you follow the order of operations properly, you will get the solution I was referring to. If you don’t, you don’t understand what I’m trying to say. I also use the knowledge of the order of operations to write those expressions. I couldn’t write 2+8÷5 because the answer you would get, following the correct procedures according to the order of operations, would not be the one I was referring to. The order of operations allows everyone to be able to communicate mathematics correctly, without further explanation or confusion.

PEMDAS stands for: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction and that’s the order you’re supposed to do the mathematics (sort of). You’d think math teachers would love PEMDAS, and I’m sure you thought they did, but most math teachers have a huge problem with it. It makes their students think that multiplication comes before division and addition before subtraction when in fact multiplication and division are essentially the same operation, as is addition and subtraction. With two small examples, let me explain. 2-1 (two minus one) is mathematically equivalent to 2+(-1) (two plus negative one). 4×2 (four times two) is mathematically equivalent to 4÷½ (four divided by one half). If we have a longer expression for which we will use PEMDAS to simplify, like 4÷½-2+4×2, and we don’t use PEMDAS correctly, then when I rewrite the expression but keep it mathematically equivalent, like 4×2+(-2)+4÷½, you’d get a different solution even though both expressions are mathematically equivalent and give you the same solution if you follow the order of operations correctly.

Ok, that was a lot of boring math stuff and I apologize, so here’s an awesome graphic design I found on shirt.woot! to lighten up this post a little. Enjoy!

You can use the order of operations to read this expression!

Why You Can’t Divide By Zero

There are two ways to think about division.

1. You can divide a certain number of things into groups of a certain size. For example, 6 ÷ 3 can be thought of as: 6 things divided into groups of size 3. The answer of course is two, so you have two groups, 3 things in each group.2. You can divide a certain number of things into a certain number of groups. For example, 6 ÷ 3 can be thought of as: 6 things divided into 3 groups. The answer two refers to how many things are in each group.

Now let’s use this to think about dividing by zero.

1. Can you divide a certain number of things into groups of size zero? Let’s use the example 5 ÷ 0.

2. Can you divide a certain number of things into zero number of groups? Use the example 5 ÷ 0 above.

This is why the calculator screams “ERROR” when you try to divide by zero.

More Math “Magic”

Take any three-digit number and write it down twice to make a six-digit number.

(For example, the three-digit number 123 would be the six-digit number 123,123).

No matter what three-digit number you choose to start with, your six-digit number will be divisible by 7, 11, and 13.

Fancy stuff.