Loquacious Problems

We’ve talked a little bit this week about how math can sometimes seem like a foreign language. Well, this means that sometimes, we need to “translate” English into “math” – this phenomenon is also known as “solving word problems.”
A “word problem” is really just a math problem written in every day English speak (or German, or Italian, you know, depending on what language you speak). We solve word problems all the time. Like when you tell your mom you want five people at your birthday party, and that means you will need three pizzas, because each pizza has eight slices, and if everyone has three slices (you’re a teenage boy, and your friends are teenage boys), and three slices is 18, but two pieces would only be 16 slices, so you better go with three pizzas and you can save the rest for your little brother and sister’s lunch the next day. That is basically just one really long word problem. Or when you want to run a 5K (3.1 miles) and you know you run a 10 minute mile, so you tell your mom to meet you at the finish in about half an hour (10 minutes/mile * 3.1 miles = 31 minutes).
So really our lives are made up of word problems and they happen all the time, and we even write our own word problems without even being aware that we are doing it! Ha – how’s that for knowing more math than you thought you knew?
But for some reason, when we’re sitting in Mr. Hamlin’s math class staring at our pop quiz that is asking something about people washing cars and how fast can they wash the cars together, our brains freeze up and we feel like we have no clue what these people are talking about.
Well, the first thing you should do is stop and take a deep breath! You know how to do this – you’ve been doing it your whole life. Don’t let the fact that you are sitting in math class and not on the football field running laps freak you out. You can do this!
Let’s put together a sample problem so we can work through it together.

Joe, James, and Jessica are all pro car washers. Joe can wash a car in 40 minutes. James can wash a car in 47 minutes, and Jessica takes about an hour to wash a car. If they all work together washing a car, how long would it take them?

Now, it’s always good to read through the problem all the way before you start working on the problem, just to get a feel for what the situation is. Now, this time when you read it, read it as if you’re actually in the problem, and the situation is your situation. It’s much more motivating to solve a problem when it is your problem. Replace one of the characters with yourself – now it’s you, James, and Jessica, instead of Joe.
After you have read through the problem once (without hyperventilating), I want you to think about what you’re actually looking for. Are you trying to find out how many cars you can wash? How long it would take one person if the other two are helping? What is the question asking you to find?
In this particular “word problem”, the question says, “If they all work together washing a car, how long would it take them?” First off, let’s find out what kind of answer we’re looking for. Are we looking for a rate, a number, a distance? It looks like we are looking for an amount of time: “How long would it take them?” So chances are we’re going to come up with a number of minutes or hours. Since most of the rates given were in minutes (40 minutes, 47 minutes) let’s go with minutes. That means we need to change Jessica’s rate into minutes. This one should be pretty easy. How many minutes are in an hour? Sixty.
The next thing we need to do is write down some kind of relationship between what we know, and what we want to find out.
Well, since we’re talking about rates of washing cars, let’s look at the rates of car washing. Let’s call the rates R, and we’ll give subscripts to each person’s rate.

Now, to find their combined rate of washing the car, we need to add them all together.

So, together, you and your friends can wash 71 cars in 1128 minutes. Well, that’s great, but we don’t really want to know how many cars you can wash in a certain amount of time, we want to know how long it will take you to wash ONE car. So, the easiest way to do that would be to divide 1128 minutes by 71 cars (giving you the amount of time it takes to wash ONE car): 15.89 minutes.
So the basic steps for solving word problems are:
1.) Read the problem all the way through (without freaking out), and putting yourself in the problem, or pretending it is your situation, so you’re more motivated to solve the problem.
2.) Write down what you know (in this case, the rates of car washing).
3.) Figure out what you want to know (in this case, how long it would take to wash one car)
4.) Write an expression, using the information you have.
5.) Solve the expression.
I will have another post next week on word problems. Until then, check out this page over at PurpleMath.

If you have questions, you can ask them in the comments, email me, ask on Facebook, or on Twitter. I am on Facebook and Twitter live from 3:00-3:30 pm Mon-Thurs MDT.

you know more math than you think

Do you ever feel like math is a foreign language?

Think about how it feels to learn another language, or to be in a place where people are speaking a language you don’t understand.

Now think about how a child learns to speak their mother tongue (the language their parents speak). If a child is exposed to a language from the time they are born, and if someone interacts with them on a regular basis in that language, the child will eventually learn to speak that language. Are children born speaking a language? Maybe baby talk – but mostly they just cry.

Turns out, the ability to learn math is programmed in us similar to the way the ability to learn a language is programmed in us.

You can read about a study that was done on this subject here.

In the article, they mentioned that a lot of Euclidean Geometry (lines, space, shapes – all that basic stuff) concepts were “innate” in members of a remote tribal community in the Amazon who had no formal training in geometry. They got as many answers right about geometry as formally educated Americans.

Something that was interesting, however, was that younger children (5 and 6 years old) didn’t know the answers. The researchers weren’t sure why, but I have a hypothesis.

Since math is similar to a foreign language, and young children don’t often understand the concepts of grammar, it make sense that they also wouldn’t understand the concepts of math especially if math has not been “spoken” to them regularly. This goes back to the principle of teaching “pre-math” skills by exposing young children to concepts like classifying, sorting, number conservation, counting, etc.

If you want your child to understand math concepts better, speak math with them! Try to make it a point to “speak math” with your child every day. Whether it is by sorting and classifying, or by talking about shapes around you, or multiplying a recipe, or talking about how “steep” the stairs are, speak math with the children in your life!

How do you “speak math” with the children in your life?

If you have questions, you can ask them in the comments, email me, ask on Facebook, or on Twitter. I am on Facebook and Twitter live from 3:00-3:30 pm Mon-Thurs MDT.