 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 are moving from a culture that is 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 per sense. Per cent 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 MasterCard, one, two, three rewards card. When I'm ready to cash in my bonus rewards, MasterCard will match my rewards with a 10% bonus in my savings account. Oh, I don't have to get out my formula. Some kind of contrived is over of, is per cent over 100 like in math class. That doesn't really make sense to me. But what makes sense is, if I had $97 in rewards points, I would get $9.70 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. Car dealer wants to put me in a brand new car today at the low, low price of $200 a month. Well, can I handle that? I have to think about what per cent of my monthly budget is that $200 going to be. Another way to think about per cent, and this is an important one, what per cent of my income will I be using to pay back student loans? And there are ways to figure that. But per cent is a proportional reasoning idea that just standardizes something to be out of $100.