Topic B: Problem solving with measurement
Let's talk a little bit about the US customary units for distance. If we go to a human scale, the most typical used unit in the US customary system would be the foot. And as you could imagine, the term foot, and if you have many of them, you are now talking about feet, comes from the same word on the human body. We have a foot or we have two feet. Now, not everyone's feet are the same length. But the length of a foot is roughly a little bit larger than most people's feet. And there are definitely people whose feet are the size of a foot. And if you're in the US, you've probably heard of people measuring their height in terms of feet. So for example, a slightly above average man of slightly above average height would have a height of 6 feet. So for example, right over here, this gentleman right over here was slightly above average height. His height might be 6 feet. And that might also be his wing-span. So it would be a distance something like that. If you wanted to measure things that are a little bit smaller, say smaller than a foot, or if we wanted to measure parts of a foot, then you would go to the inch. And the relationship between the foot and the inch is that 12 inches are equal to one foot. So for example, this little mouse right over here, it might be reasonable to measure it in inches. On this scale, an inch might be, depending on the size of the mouse, an inch might be something like that. And it's also useful for measuring things like human height, because very few people are a whole number of feet. They're usually some fraction of feet. So for example, I am 5 feet and 9 inches. And sometimes this is denoted as 5, and you have this apostrophe here, one apostrophe, and then 5 foot 9 inches, and this is two apostrophes, kind of saying hey, you're going to the next unit down. These are the inches right over here. Now if you want to go to things that are larger than maybe human scale, we have units for that as well, including the yard. The yard is equal to 3 feet. And 3 feet, well, each foot is 12 inches, so this is the same thing as 36 inches. And this is most typically used for measuring distances of a lot of some kind. And in the United States, most famously for in football. So your regulation-size football field, the playing field, the distance between the end zones, is exactly 100-- I know you can't see my writing there-- is exactly 100 yards. This distance right over here. Right between the end zone. Now, if you want to measure even longer distances, that's where we go to the mile. And all of these units are ancient units, going back, actually, thousands of years. And the mile, based on the reading I've found, was even used in Roman times. And actually, that's some of the first examples of this term being used. And it really comes from the same root word as 1,000, of mil, of 1,000 footsteps of a Roman soldier. And now, a standard mile is exactly 5,280 feet. And if you wanted to figure out this in inches, you could just multiply by 12. But just to get a sense of a mile, here is a mile on this map of New York. So if you wanted to put it right on Manhattan, this distance right over here is about a mile. So you want to measure really far distances, either from one point in a city to another, or maybe even the distance between cities, or maybe even the size of the planet, or even the distance from the Earth to the moon, or something like that, you will hear that referenced in miles, even the distance between the Earth and the sun. People say it's 93 million miles. If you're talking about maybe, a plot of land, you want to measure its dimensions, or you're talking about a football field, then yards feel appropriate. If you're kind of getting to human scale, well, human scale on one level, but you could get a little bit larger if you're maybe talking about the height of a building or something like that, or you're still talking about measurement of say, a plot of land, you will still hear people talk in terms of feet. And if you're measuring either parts of a foot, or things that are smaller than a foot, that's when inches come into play.