 Have you ever been reading a news article or listening to the news on television or maybe googling something, scrolling through your Facebook news feed and some numbers, somebody gives you some statistics about something or numbers jump out at you, for which you have no real reference? It happens to me all the time. That's what this module is about, it's proportional reasoning. When you hear the word proportion you might think of some old formulas that say all you have to do is cross multiply and divide, well what are you doing when you do that? That's kind of an algebraic proportion formula, but what does it mean to reason proportionally? For instance, when you hear the national debt, it's a really, really big number which is unmanageable and hopeless, right? What does it really mean? What is a context for thinking about a number that's in the trillions? That's something we're going to look at in this unit. We're going to think about putting that very large number into a context for which we do have a reference. What does it have to do with me? How can I internalize this really big number? Other large numbers, things that have to do with maybe death rates or weather disaster or very large or very small salaries, how do we put those into proportions so that they mean something? How do I contextualize that for myself? That's one idea about proportional reasoning. Here's another idea. This did happen to me just yesterday at the grocery store. I was in the health food aisle, picked up some kind of new energy drink, and I picked it up to read the ingredients. It's in the health food aisle, right? It must be good for you. One of the ingredients listed was caffeine. It said 120 milligrams of caffeine. Well, I thought about that for a minute. I don't have any context for what 120 milligrams of caffeine is. I have a pretty good idea about what the number 120 is. I can get my head around that, but what does milligrams of caffeine mean to me? Here's an opportunity for proportional reasoning. I think about that in terms of coffee intake. I do have a reference for how much coffee I drink. I'm kind of middle age. I have some sensitivity to caffeine. I can drink some caffeine. I don't want to overdo it, so I want to know how many of these drinks can I take in in a day or an afternoon? I need a context for that. I went right to, I Googled a fairly reliable source I thought about, and I found out, or I actually looked at a few, researched a few sources. The average adult, healthy adult, can tolerate 200 to 300 milligrams of caffeine, which is about two to four cups of coffee. I needed to think about that in terms my pointer reference was coffee. So I determined, yes, I can substitute one cup of coffee for one of these energy drinks. But before that, I didn't have a reference for how many milligrams of caffeine I can intake. This brings us to another point about thinking about mathematics. Is precision and accuracy important? Are they the same thing? Precision and accuracy? Well, if I am thinking about maybe intakeing insulin, if an adult or a child were diabetic and needed a certain amount of insulin, precision would be very important. We couldn't say, oh, somewhere between 200 and 300 milligrams, somewhere around here, precision could mean the difference between life and death. But I just want to know how many drinks of this energy drink can I have? And so precision might not be so important, but accuracy is, I want to have a good source for what I'm reading. I want to have a good source to find out how much of this can I take in. So there's something else to consider as you think about mathematics. Another source that I heard recently was from NPR, also listening to the radio on my way to work, Dr. David Reynolds from the University of Pittsburgh was doing a study about dementia in older adults. Well, he determined in this study that something about treating depression for middle-age adults and dealing with mood disorders was very impactful on later-age dementia. And the conclusion was this, that having these particular treatments could reduce the number of dementia cases in older adults from one in four to eight or nine percent, which reduced it by two-thirds. What do all these numbers mean? This is a good example of proportional reasoning. How do we go from one in four, is that a very big number, to eight or nine percent? And that's the reduction of two-thirds. When you hear a report like that, do you stop and give yourself time to think about those numbers? You get a reduction of two-thirds from one in four to eight or nine percent. And how I take in this information might be different based on my experiences. So it's important to be able to back up and reason through the numerical data that report, reason through it, not just dismiss it or interpret it differently based on my experiences or my age. So it's always important when you hear numbers, put them in a context that you can understand. And that takes time and ability to think about that situation numerically. You're always allowed to ask, is this a very big number? Is this a lot? You're always allowed to ask, what does this mean to me? That's what proportional reasoning is about, so we're going to be studying in this module.