 I'm really excited today to talk about a new and accessible environment for learning mathematics. You're probably thinking about quantity and number every single day of your life, which is different from how you might have thought about number in math class. We were moving from a culture that was okay to say, oh, I don't do math. Enumeracy is not acceptable anymore. We would never sit around and boldly confess, hey, I don't read. Hey, I don't know how to write a sentence. I can't think about anything. We don't do that. And it's no longer okay to brag about not doing mathematics. Really, mathematics comes from a Greek word, which means that which is to be learned. It's simply about learning. It's not about a stack of formulas in the math class that my teacher makes look easy, but gives me a panic attack. That's not what mathematics is. It's about learning and navigating within your environment, having a relationship with the quantity that you deal with every day. We're going to talk today a little bit about how you can bring that into the lab. An example is proportional reasoning. Proportional reasoning is simply how do these quantities relate to each other? How do they compare? Is this a very big number? Is this a very small number? Well, that depends. What are we comparing it to? One example might be, oh, I saved $5 on my purchase. Well, is that big? Well, that depends. Was I purchasing a meal or a pair of shoes or a TV or a car or a new house? The relative size of that $5 gets smaller and smaller as the ticket item price gets bigger and bigger. That's one way to think about proportional reasoning. Or here's another example. I was cooking breakfast the other day and I was making grits. This is a true story. I had boiled one and a half cups of water and the recipe for the grits box had one cup of water or directions for two cups of water and I had boiled one and a half cups of water. For one cup of water the directions read use one fourth cup of grits. Well, to solve my problem I did not set up a formula, set up an equation, find a common denominator. I simply thought about it in a way that made sense to me. I thought about it this way. One and a half cups of water is half again that amount of water from the directions on the box. So what is half of one fourth cups of grits? Well, it's one eighth. So I'm going to add that one eighth to the one fourth cup of grits. I got out my one half cup measure and filled it three forceful and successfully made a pot of grits. Now, I didn't set up, I didn't think about, this was an approximation. In the lab we're probably going to be a little more, we will be a little more precise with our measurement. But this was just thinking about the proportions that made sense to me and extracting the mathematics out of it instead of some kind of contrived formula, finding a common denominator, something that would happen in math class. Another example for proportional reasoning is the idea of concentration. Here's something else you've done all your life depending on where you are, what stage you are in your life. You've used a concentration idea whether you're mixing Kool-Aid or mixing Margaritas or mixing Metamucil, you are still thinking about some kind of solute and mixing it with some parts to make a solution. That's what you're going to do in the lab. You're going to take the mathematics that you already do and bring it into the lab. A sister idea to proportional reasoning is percents. Percent is simply literally per hundred cent, right? There's a hundred cents and a dollar, so this is what per cent literally means, out of a hundred. It's simply standardizing what we're talking about, whatever the quantity is, so that we have a base of 100. And again you probably do it all the time. An example is my master card, one, two, three rewards card. When I'm ready to cash in my bonus rewards, master card will match my rewards with a 10 percent bonus in my savings account. Well I don't have to get out my formula, some kind of contrived is over of, is per cent over a hundred like in math class, that doesn't really make sense to me. But what makes sense is if I had 97 dollars in rewards points, I would get 9 dollars and 70 cents from them to go into my savings account. I think about that in ways that make sense to me. Another example, say I was buying a car. A car dealer wants to put me in a brand new car today at the low, low price of 200 dollars a month. Well, can I handle that? I have to think about what percent of my monthly budget is that 200 dollars going to be. Another way to think about percent, and this is an important one, what percent of my income will I be using to pay back student loans? And there are ways to figure that. But percent is a proportional reasoning idea that just standardizes something to be out of 100. Here's something you do every day. You use units of measure, very important in the lab to know what we're measuring. You use units of measure when you're measuring shoe size, temperature, speed, price per gallon of gasoline, cold medicine dosage, tire pressure. And related to that is unit conversion. I did it when I was using my grits, making my grits, pan of grits. Another kitchen example, I was making muffins. Okay, and I needed a quart of buttermilk for this massive muffin recipe, and I bought buttermilk in a half gallon. I didn't set up an equation, I just actually made sense that there are four quarts in a gallon, and I had a half gallon, which is two quarts. If I needed one quart, I just poured out one half of the amount of buttermilk that I have. Another example, unit conversion, I was traveling in Canada last year, last summer, and I had to convert my speed because they have their speed posted in kilometers per hour. So I had to convert back and forth between kilometers per hour and miles per hour, very important one, so I would not be going 100 miles an hour and be in danger and also getting a ticket. Metric units are very nice to work with because they're base 10. Base 10 makes operations very friendly, so embrace the metric system. It's your friend and it will be easy to make unit conversions. Here's another good one, descriptive statistics. This is simply thinking about on average what happens, what is the mean of something, what does the data look like, how is it spread out? Is most of the data like the average, or is there a lot of data that's not like the average? You are bombarded with data and statistics every day. If you read Facebook, if you read the newspaper or magazine or an advertisement, listen to the news, listen to NPR, you are bombarded with statistics, and so it's important to be able to think about that. What does this statistic mean when it's coming to me from some sort of media source? What does it mean to me or my family, my community, my state, my country, my world? And you're going to be using certainly averages, finding means when you are in the lab. Another one is solving equations. This might bring you memories of algebra class. For no particular reason we're going to set up an equation and name a variable and do something to both sides and find out what x is and then move on and it didn't really mean anything or matter. Well, you might use equations in everyday life but you don't really might think of it that way. It's simply thinking backwards to find out something I want to know. Maybe you are going to dinner with your significant other and you have $100 to spend because you've saved up and you know that a babysitter is going to cost $35 and then you have the rest to think about, well, will we be able to afford dessert or cocktails or a movie? How are we going to divide up what's left after we take away the babysitter money? You could set up a fancy equation and name a variable but it's something that you do anyway is thinking backwards to find out an unknown. These are things that you're going to bring into the lab. Notation. Notation is a man-made convention. Some things that you might see that might not be in your everyday encounters are using exponents, something written in scientific notation or using logarithms. Well, these are man-made conventions really to make dealing with numbers easier, more manageable for our finite minds when we're dealing with very large numbers or very small numbers. So, when you encounter some sort of mathematics in your program, confidently go forward into that mathematics into the lab and use the mathematics that you need to use knowing that you already do that somehow in your everyday life. Leave that old baggage, the anxiety of math class at the door and come in knowing that you are already a mathematics thinker and just revise the way that you think about number so that it suits your job and that you'll be productive in the lab.