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enWhy Is It Important to Study Math?
https://www.quickanddirtytips.com/education/math/why-is-it-important-to-study-math
<p><img alt="Playground" class="qdt-wrap-left" height="300" src="https://www.quickanddirtytips.com/sites/default/files/styles/insert_medium/public/images/9226/playground.jpg?itok=hxDSiIOL" width="448" />Today is a very special episode of the Math Dude. To begin with, it’s episode 300. And because we humans have 10 fingers, we love to give special meaning to multiples of 10. But while that’s fun, it’s not the big news of the day or what makes this episode special to me. The big news is that this 300th episode is my last. Between my day job as a physics and astronomy professor and my day-and-night job of being “Dad” to an awesome and bustling 3-year-old, my free time for Math Dude duties has dwindled. And although I will surely miss all of you math fans, after seven years on the job, it's time to say goodbye.</p>
<p>But before I go, I have one more thing to say—and I think it’s the most important thing I’ve ever said on the show. It’s not something that I would (or even could) have said when I wrote the first episode seven years ago, because I wasn’t yet a father and so I wasn’t yet watching somebody discover the world for the first time. So please take a few minutes and listen, because I think this is something that everybody who has kids or might have kids or works with kids or might work with kids should know.</p>
<p>Here it is: <em>Math is a playground … so play!</em> Allow me to explain.</p>
<h2>Math Is a Playground</h2>
<p>A few days ago, I was at the park with my daughter watching her play. She’s at a very adventurous age and is constantly testing out every possible pathway to the top of what she has dubbed the “mermaid castle.” As she stretched her relatively tiny legs from rung-to-rung over what comparatively looked like a gaping chasm, I squiggled and squirmed as I struggled to keep myself from jumping up and lifting her over what I perceived to be a great danger. But she was careful, she didn’t fall, and she learned a bit about the world.</p>
<p>To be sure, playgrounds can be dangerous. So why do we let our kids play on them? Because playgrounds exercise their bodies. And not just in the sense of improving cardiovascular health or building strong bones and muscles. Those are all lovely side-effects, but what playgrounds do is provide kids with a relatively safe way to learn about using their bodies to navigate the world—how to balance, how to get from here-to-there, what to do when you get stuck. In other words, how to solve problems in the physical world.</p>
<p>As I was watching my daughter, I realized that math too is a playground. But it’s not a playground for our bodies, it’s a playground for our minds. In a way I’ve always known this to be true, but I’d never thought about it quite like this. And the thing is that this is pretty much the opposite of the way kids are commonly talked to and taught about math (and many of the sciences,...</p> <a href="https://www.quickanddirtytips.com/education/math/why-is-it-important-to-study-math " class="views-more-link">Keep reading on Quick and Dirty Tips</a>Fri, 24 Feb 2017 23:20:46 -0500Fri, 24 Feb 2017 23:20:46 -0500https://www.quickanddirtytips.com/education/math/why-is-it-important-to-study-mathHow Are Distances and Absolute Values Related?
https://www.quickanddirtytips.com/education/math/how-are-distances-and-absolute-values-related
<p> </p>
<p>In the <a href="https://www.quickanddirtytips.com/education/math/what-are-absolute-values" target="_blank">last article</a>, we learned exactly what <a href="https://www.quickanddirtytips.com/education/math/what-are-absolute-values" target="_blank">absolute values</a> are and how you can find the absolute value of a number. In today’s article, we’re going to put this knowledge to work and learn about the very practical skill of using absolute values to find distances between numbers and places.</p>
<h2>Review: What are Absolute Values?</h2>
<p>As we talked about last time, the quick and dirty way to think about absolute values is that the absolute value of a number simply tells you how far away it is from zero on the number line. For example, since the numbers 5 and –5 are both 5 steps away from zero on the number line, they both have the same absolute value of 5.</p>
<h2>What is Distance?</h2>
<p>Does this idea that the absolute value of a number tells you how many steps away it is from zero on the number line remind you of anything in the real world…perhaps the idea of distance? The connection here is actually pretty straightforward, but let’s take a minute to look at an example that will drive home the relationship between absolute values in math and distances between objects in the real world.</p>
<p>As you know, the distance between two trees in your backyard is just a number that tells you how far apart the trees are. If you draw a <a href="https://www.quickanddirtytips.com/education/math/what-are-1d-2d-and-3d-coordinates" target="_blank">coordinate system</a> in your backyard (which is really just a number line) and set one of the trees at the origin of your coordinate system (the location marked zero), then the distance to the other tree is the absolute value of its location in your coordinate system. For example, if one tree is at the location marked 0 and the other tree is 7 steps away in whatever direction you choose to be the positive direction, then the distance to the tree is |7| = 7. If the second tree is instead at –7 in in your coordinate system (in the opposite direction), its distance to the first tree is |–7| = 7. In other words, independent of direction, the second tree is always 7 steps away.</p>
<h2>How to Find the Distance Between Positive and Negative Numbers</h2>
<p>So we know that the absolute value of a point on the number line (or the absolute value of the coordinate of a tree in your backyard) tells you the distance between that point (or tree) and the number zero at origin of your coordinate system. But how do we find the distance between any two numbers? In other words, what if the first tree in our example wasn’t located at the origin of the coordinate system? What if one tree is at 2 and the other is at –5? How do you find the distance between them in that case?</p>
<p>Let’s start by realizing that this problem with trees is the same...</p> <a href="https://www.quickanddirtytips.com/education/math/how-are-distances-and-absolute-values-related " class="views-more-link">Keep reading on Quick and Dirty Tips</a>Sat, 18 Feb 2017 02:34:38 -0500Sat, 18 Feb 2017 02:34:38 -0500https://www.quickanddirtytips.com/education/math/how-are-distances-and-absolute-values-relatedHow to Use Math to Fly Rockets to Space
https://www.quickanddirtytips.com/education/math/how-to-use-math-to-fly-rockets-to-space
<p><img alt="Space Shuttle" class="qdt-wrap-left" height="224" src="https://www.quickanddirtytips.com/sites/default/files/styles/insert_small/public/images/9055/edu_shuttle_launch_sts-43.jpg?itok=JRotYeJa" width="169" />… 5 … 4 … 3 … 2 … 1 … and liftoff!</p>
<p>Ever since I was a kid, I’ve loved rockets and everything about flying to space. So the sound of the countdown leading up to a rocket launch is music to my ears. Of course, the sound that follows the countdown is anything but musical because rockets are really loud … but they’re also beautiful. And they’re marvelous machines that will soon be playing an increasingly crucial role in our day-to-day lives as we begin the journey towards becoming a truly space-faring species. And to top it all of, they’re machines powered by math (and, of course, a bunch of physics and fuel).</p>
<p>What's the math that powers rockets? How does it help us get them to space? And how do we use that math to put a satellite or person in orbit around the Earth? Let's find out.</p>
<h2>The Mathematics of Getting to Space</h2>
<p>When people think about going to space, they usually think about going up. And that’s certainly true, but it’s only part of the story. It’s sort of hard to define exactly where the atmosphere ends and outer space begins (since the atmosphere gradually falls off as you go up in altitude), but one popular choice is the so-called “Karman line” at a height of 100 km (or around 62 miles) above sea level. A lot of people are surprised to find that space begins only 100 km up … since that’s really not that far. But the problem with getting there is that it’s “uphill” the whole way, which means you have to fight gravity the whole way.</p>
<p class="qdt-pull-quote-right">A rocket traveling at 8 km/s completes one orbit every 90 minutes.</p>
<p>But getting up that high is only half the battle of getting into orbit around the Earth. Because if you fly a spacecraft 100 km straight up and then turn off the engines, it will simply come right back down to the ground (this is called a sub-orbital flight). If your goal is to get a satellite into orbit around the Earth or to deliver a person to the International Space Station, the rocket doesn’t just need to get into space, it needs to stay there. And that means it needs to end up flying sideways really, <em>really</em> fast—around 8 km/s or almost 18,000 miles per hour!</p>
<p>How fast is that? Well, a rocket or satellite traveling at 8 km/s completes one orbit every 90 minutes. Which is amazingly fast considering it takes 5 hours to fly across the United States in an airplane. For comparison, a rocket in orbit crosses the US in about 10 minutes.</p>
<h2>The Mathematics of Orbiting the Earth</h2>
<p>But why does a rocket or satellite or space station need to be moving sideways so fast to stay in orbit? The answer is mainly geometry (...</p> <a href="https://www.quickanddirtytips.com/education/math/how-to-use-math-to-fly-rockets-to-space " class="views-more-link">Keep reading on Quick and Dirty Tips</a>Sat, 11 Feb 2017 00:27:15 -0500Sat, 11 Feb 2017 00:27:15 -0500https://www.quickanddirtytips.com/education/math/how-to-use-math-to-fly-rockets-to-spacePolygon Puzzle: How Many Degrees Are in a Polygon?
https://www.quickanddirtytips.com/education/math/polygon-puzzle-how-many-degrees-are-in-a-polygon
<p><img alt="Soccer Ball" class="qdt-wrap-left" height="224" src="https://www.quickanddirtytips.com/sites/default/files/styles/insert_small/public/images/6745/hexagons-and-pentagons-in-a-soccer-ball.jpg?itok=bDrgi8ue" width="224" />We recently talked about <a href="/node/6442">why the three interior angles of a triangle must always add up to 180º</a>. And at various points in the past, we've noted that the quartet of 90º “right" angles in a square must mean that the interior angles of a square add up to 360º. But we've never talked about what happens when we toss more sides into the mix.</p>
<p>In other words, we've never talked about how to figure out the total number of degrees in a pentagon. Or a hexagon...or an octagon. Or any other polygon, for that matter! And just as importantly, we’ve never dealt with whether or not there’s some clever way to figure all of this out without resorting to making <a href="/node/6269">measurements </a>with a protractor.</p>
<p>Until now, that is - because these are exactly the questions we’ll be talking about today as we dive into a delectably delicious polygon puzzler.</p>
<p class="qdt-adv-rte">Sponsor: Visit <a href="http://x.co/4trSA" target="_blank">GoDaddy.com</a> to get your $2.95 .COM domain. Some limitations apply, see website for details.</p>
<h2>Review: Interior Angles of Polygons</h2>
<p>Our big goal for today is to figure out exactly how the interior angles of polygons change as the number of sides in the shape increases.</p>
<p>As a super quick review, a polygon is any shape made up of three or more connecting sides that you can draw on a flat sheet of paper. For a more thorough look at the definition of a polygon, check out <a href="/node/6621">the episode on that topic</a>.</p>
<p>The angles formed in the interior of a polygon where pairs of sides intersect are called "interior angles." As noted earlier, we've talked about using a clever trick to prove that a <a href="/node/6442">triangle's interior angles</a> always add up to 180º. And we’ve seen that the four right interior angles of a square (or any rectangle) must add up to 360º.</p>
<p>Which might lead you to wonder...</p>
<h2>How Many Degrees Are In a Pentagon?</h2>
<p>What happens when the number of sides increases beyond four? In other words, <a href="/node/6678">what’s the sum</a> of the interior angles of a pentagon, a hexagon, an octagon, or any other polygon?</p>
<p class="qdt-pull-quote-right">Interior angles get larger as the number of sides increases.</p>
<p>Let’s start by taking a look at the 5-sided regular polygon (meaning, its sides and angles are all equally sized), better known as a pentagon. If you sketch a pentagon, you’ll immediately see that its interior angles are all greater than 90º. So the first thing we can conclude is that the interior angles of a polygon get larger as the number of sides increases. But by how much?</p>
<p>At this...</p> <a href="https://www.quickanddirtytips.com/education/math/polygon-puzzle-how-many-degrees-are-in-a-polygon " class="views-more-link">Keep reading on Quick and Dirty Tips</a>Fri, 03 Feb 2017 23:52:46 -0500Fri, 03 Feb 2017 23:52:46 -0500https://www.quickanddirtytips.com/education/math/polygon-puzzle-how-many-degrees-are-in-a-polygonThe Simple Math Behind Crunching the Sizes of Crowds
https://www.quickanddirtytips.com/education/math/the-simple-math-behind-crunching-the-sizes-of-crowds
<p><img alt="Inauguration Crowd" class="qdt-wrap-left" height="149" src="https://www.quickanddirtytips.com/sites/default/files/styles/insert_small/public/images/9004/crowd-at-presidential-inauguration.jpg?itok=ml9bdFI3" width="224" />There are over 7 billion people on Earth today, and occasionally a bunch of them decide to converge for one reason or another. We’re talking thousands, tens of thousands, hundreds of thousands, or even millions of people in the same place at the same time. As those of us in the United States (and no doubt around the world) have recently witnessed, such events include things like U.S. presidential inaugurations and political marches.</p>
<p>In case you haven’t heard, there’s been a bit of a fracas brewing over the exact sizes of crowds at certain events held in the U.S. this past week. While I don’t want to get into the political aspects of these issues (nor the very reasonable questions about why we’re having these sideshow conversations at all), I feel that it’s important to note that estimating crowd sizes is a solved problem that’s actually pretty straightforward. And it’s relevant to us math fans because it’s really nothing more than a simple exercise in basic math.</p>
<p>So, how do crowd estimate experts estimate crowds? Let’s find out.</p>
<h2>Counting Crowds</h2>
<p>The most reliable method for estimating the size of a crowd is to actually count the size of the crowd. In truth, I’d say this method provides a <em>measurement</em> of the crowd size rather than an <em>estimate</em> since it’s just a matter of counting up people—there’s no other math involved. The beauty of this method is that the uncertainty in your measurement should be extremely low, which means you can be confident about the count’s reliability. Such a direct count is easy to do when crowd sizes are relatively small or when people have to pass through doors or turnstiles, but it’s hard (or even impossible) to do when crowds are large and spread out.</p>
<p class="qdt-pull-quote-right">The most reliable method for estimating the size of a crowd is to actually count the size of the crowd.</p>
<p>In such cases, we have to rely upon our math and reasoning skills. In particular, we have to change tactics from performing a count to performing an estimation. As with any estimate, there will be uncertainty in the final tally since the whole process relies upon a set of assumptions which each are accompanied by some uncertainty. But the beauty of math and statistics is that it provides us with a framework within which we can not only estimate the size of a crowd, but also estimate the quality of our estimate. Which means we can accurately calculate the range of the crowd size which, with very high probability, contains the actual number of people.</p>
<h2>Low-Tech Crowd Size Estimates</h2>
<p>For medium to large crowds spread out over medium to large areas, your best-bet low-tech solution...</p> <a href="https://www.quickanddirtytips.com/education/math/the-simple-math-behind-crunching-the-sizes-of-crowds " class="views-more-link">Keep reading on Quick and Dirty Tips</a>Fri, 27 Jan 2017 23:18:15 -0500Fri, 27 Jan 2017 23:18:15 -0500https://www.quickanddirtytips.com/education/math/the-simple-math-behind-crunching-the-sizes-of-crowdsMath Tips for Smart Shopping
https://www.quickanddirtytips.com/education/math/math-tips-for-smart-shopping
<p><img alt="Calculator in a Shopping Cart" class="qdt-wrap-left" height="224" src="https://www.quickanddirtytips.com/sites/default/files/styles/insert_small/public/images/6711/calculator-in-a-shopping-cart.jpg?itok=Q_YbNM18" width="189" />I recently ran across a 2012 article from <em>The Atlantic</em> called <a href="http://www.theatlantic.com/business/archive/2012/07/the-11-ways-that-consumers-are-hopeless-at-math/259479/" target="_blank">The 11 Ways That Consumers Are Hopeless at Math</a>. The title of this article hooked me, and as I began reading I found that there are indeed a few ways in which consumers misunderstand math - and pay the price as a result.</p>
<p>But I also found that most of the so-called “math tricks" that people get caught up in are really better described as number-based psychological hacks, which marketers use to extract every last penny from us that they can.</p>
<p>So it's not so much that consumers are <a href="/node/6036">hopeless at math</a> as they are susceptible to being tricked. Which is precisely what a <a href="/node/6625">savvy shopper</a> knows how to avoid.</p>
<p>What are some of these mathematical misunderstandings that you should be aware of? And what are some of the most common number-based psychological hacks? Those are exactly the questions we’ll be looking at today, as we finish up the year with <a href="/node/1397">a resolution</a> to become even smarter shoppers in the new year.</p>
<p class="qdt-adv-rte">Sponsor: This episode is brought to you by NatureBox. Discover smarter snacking with a new NatureBox each month. Get your first box FREE when you go to <a href="http://naturebox.com/qdt" target="_blank">naturebox.com/qdt</a>.</p>
<h2>How Much Bang For Your Buck?</h2>
<p>The article I mentioned from <a href="http://www.theatlantic.com/business/archive/2012/07/the-11-ways-that-consumers-are-hopeless-at-math/259479/" target="_blank"><em>The Atlantic</em></a> begins with an anecdote that nicely points out one of the biggest flaws in the way the average consumer shops. Namely, that when it comes to <a href="/node/1521">pricing and deals</a>, most people go with their gut instead of taking a few seconds to <a href="/node/6412">think things through</a>.</p>
<p>Here's the story: Imagine you walk into a <a href="/node/3153">coffee shop</a>, take a look at the day’s specials, and see a sign that says, “Today only, your choice—get 33% more coffee for the regular price, or pay 33% less for the regular amount of coffee!” If you were presented with these two options, which would you choose?</p>
<p>In truth, choosing the best deal isn't always just a question of numbers. For example, if you really wanted more than your regular amount of coffee that day, then the extra coffee option would be a fine choice. But that’s not really what I’m talking about here, so let’s rephrase the question a bit to <a href="/node/3175">focus on the math</a>.</p>
<p>The real question is...</p> <a href="https://www.quickanddirtytips.com/education/math/math-tips-for-smart-shopping " class="views-more-link">Keep reading on Quick and Dirty Tips</a>Fri, 20 Jan 2017 23:53:50 -0500Fri, 20 Jan 2017 23:53:50 -0500https://www.quickanddirtytips.com/education/math/math-tips-for-smart-shoppingHow to Measure Time Without a Stopwatch
https://www.quickanddirtytips.com/education/math/how-to-measure-time-without-a-stopwatch
<p><img alt="Burning Fuse" class="qdt-wrap-left" height="149" src="https://www.quickanddirtytips.com/sites/default/files/styles/insert_small/public/images/7372/burning-fuse.jpg?itok=cLmrdBdN" width="224" />A math puzzle a day keeps your brain saying "Yay!"</p>
<p>I know that’s not the most memorable saying in the world, but it’s definitely true—puzzles are a fantastic workout for your brain. As such, you’d be wise to try your hand at tackling at least a few different kinds of puzzles every week. And the best part of this is that mental exercise like this is fun!</p>
<p>To help you in your endeavor to start puzzling more, today we’re going to take a look at a great brain teaser that I recently ran across. This puzzle is all about time and how you can measure intervals of time in a rather unusual way: by burning bits of specially crafted string. How does it work? And what’s the big brain teaser?</p>
<p>That’s exactly what we’ll be talking about today.</p>
<h2>How Can You Measure 45 Minutes?</h2>
<p>Imagine you’ve been given several pieces of string with varying lengths and thicknesses. Not only do the lengths and widths of the pieces vary, each piece of string isn't even uniform in width along its own length. In other words, they get thicker and thinner (by different amounts and in different places) as you go from one end to the other. While all of the pieces are therefore different, they have one thing in common: if you light one end on fire, it will always take exactly 1 hour to burn through to the other side. But since each piece gets thicker and thinner as it goes, a given piece of string doesn’t necessarily burn at an even rate. By which I mean that a string doesn't necessarily burn half its length in 30 minutes—all we can say is that it burns its entire length in exactly 1 hour.</p>
<p class="qdt-pull-quote-right">Is it possible to use these pieces of string to measure a 45 minute time interval?</p>
<p>So that’s the setup. Here’s the question: Is it possible to use these pieces of string (as many as you want) to measure a 45 minute time interval? And, if it's possible, how would you do it? As with every puzzle, it’s a lot more fun if you give it a try before finding out the answer. So I encourage you to pause for a few minutes to give it a go. Then, when you’re ready, continue on for the answer.</p>
<h2>A Simpler Problem</h2>
<p>Before we solve today’s puzzle, let’s imagine a slightly simpler puzzle in which the pieces of string we’re given all burn at a uniform rate. In this case, you could solve the puzzle simply by folding a single piece of string in half, and then by folding this in half again to make creases in the string at 1/4, 1/2, and 3/4 its total length. Since this string burns at a uniform rate, all you have to do to measure 45 minutes of time is simply light one end of the string on fire and wait until it burns to the mark that's...</p> <a href="https://www.quickanddirtytips.com/education/math/how-to-measure-time-without-a-stopwatch " class="views-more-link">Keep reading on Quick and Dirty Tips</a>Sat, 14 Jan 2017 02:30:21 -0500Sat, 14 Jan 2017 02:30:21 -0500https://www.quickanddirtytips.com/education/math/how-to-measure-time-without-a-stopwatch4 More FAQs About Percentages
https://www.quickanddirtytips.com/education/math/4-more-faqs-about-percentages
<p><img alt="FAQ" class="qdt-wrap-left" height="224" src="https://www.quickanddirtytips.com/sites/default/files/styles/insert_small/public/images/8957/faq.jpg?itok=Yi5f4gPX" width="224" />We here at the Math Dude ranch get numerous questions every week from math fans around the world. By far the most common questions we receive have to do with calculating percentages. In particular, how to quickly calculate percentages in your head. You know, things like: What’s 25% of $14,000? Or what’s the final price after a 33% discount on a $25 item? Or what’s the percentage increase from 30 to 40?</p>
<p>It’s not hugely surprising that this is such a popular line of questions since people in lots of different industries love to express changes in terms of percentages. So today we’re going to take a look at four of the most frequently asked questions about percentages.</p>
<h2>Holiday Puzzle Solution</h2>
<p>But before we dive into percentages, I want to fill you in on the solution to the puzzle I posed last time. Actually, it’s the puzzle <a href="https://mobile.twitter.com/RichardWiseman/status/811172770138718208" target="_blank">tweeted</a> by psychologist, magician, and guest of the show <a href="https://www.quickanddirtytips.com/education/math/how-to-win-every-bet" target="_blank">Richard Wiseman</a>. In case you’ve forgotten, here’s how it works. First, grab a calculator. Then do the following:</p>
<ul><li>Type your house number (i.e., your address) into a calculator.</li>
<li>Now double it.</li>
<li>Next add 5 to the result.</li>
<li>Then multiply this answer by 50.</li>
<li>Now add your age.</li>
<li>And then add 365 to the result.</li>
<li>Finally, subtract 615 from the whole thing.</li>
</ul><p>What do you get? If you did it right, you should see your house number and age (so long as you’re under 100 years old). Why? It’s actually fairly simple to understand with a bit of algebraic thinking. To begin, let’s call your house number “A” and your age “B”. If you follow the steps in Richard's tweet, you’ll see that the whole sequence of actions is equivalent to the algebraic expression:</p>
<p>(((((2 x A) + 5) x 50) + B) + 365) - 615</p>
<p>Which is quite a mess! How does it help us make sense of the trick? Well, if we simplify the expression a bit, we see that we can combine and arrange the terms to turn it into the equivalent expression:</p>
<p>((2A + 5) x 50) + B - 250</p>
<p>Admittedly, this isn’t much better, but if we simplify this even more we find that we can multiply and then combine terms to arrive at a much simpler equivalent expression:</p>
<p>100A + B</p>
<p>And now we’re getting somewhere. Because this expression tells us that all you're really doing is multiplying your address by 100 (which has the effect of padding the end of it with a pair of zeros) and then adding your age (which has the effect of sticking it on the end). Once you know this,...</p> <a href="https://www.quickanddirtytips.com/education/math/4-more-faqs-about-percentages " class="views-more-link">Keep reading on Quick and Dirty Tips</a>Fri, 06 Jan 2017 23:10:35 -0500Fri, 06 Jan 2017 23:10:35 -0500https://www.quickanddirtytips.com/education/math/4-more-faqs-about-percentagesThe 5 Steps of Problem Solving
https://www.quickanddirtytips.com/education/math/the-5-steps-of-problem-solving
<p><img alt="Problem Solving" class="qdt-wrap-left" height="211" src="https://www.quickanddirtytips.com/sites/default/files/styles/insert_small/public/images/5817/problem_solving.jpg?itok=UFP6a3Hi" width="224" />If the phrase "word problem" sends a shiver down your spine, you're not alone. A lot of people have trouble with so-called word problems in math. But, believe it or not, these problems usually aren't any harder to solve than non-word problems—they just look very, very different. And they require a slightly different mindset to solve.</p>
<p>Today, I'm going to tell you about my simple 5-step method that will help you solve all your math problems—including those pesky word problems. In particular, we're going to talk about how to turn a word problem into an <a href="/node/4596">algebraic equation</a> and then solve it.</p>
<p class="qdt-adv-rte">Sponsor: Netflix Instant Streaming. Watch thousands of TV episodes and movies on your PC, Mac, iPad, iPhone or Touch. Or on your TV through your XBox, PS3 or Wii. All streamed instantly by Netflix, saving you time, money and hassle. For a free 30-day trial, including the new Netflix Original Series <em>House of Cards</em>, go to <a href="https://www.quickanddirtytips.com/offers" target="_blank">www.quickanddirtytips.com/offers</a>.</p>
<h2>A "Real World" Math Drama</h2>
<p>Today's word problem begins with a story about <a href="https://www.quickanddirtytips.com/pets/cats">cats</a> and <a href="https://www.quickanddirtytips.com/pets/dogs">dogs</a>. It goes something like this…</p>
<p><em>Like all dogs, your <a href="/node/4085">dog loves toys.</a> And you love giving them to him. Your cat, on the other hand, does not love your dog and therefore finds it amusing to hide his toys. Being quite clever, you suspect that the cat is the culprit, so you begin to monitor his favorite hiding spot: the pile of towels next to his bed. </em></p>
<p><em>But (perhaps being a little too clever for your own good) instead of constantly checking this spot, you decide that you'd like to rig up an ingenious system to automatically report to you exactly how many toys are missing.</em></p>
<p><em>The question is: How can you do this?</em></p>
<h2>Step #1: Stop and Think Before Doing Anything</h2>
<p class="qdt-pull-quote-right">The biggest mistake people make when solving problems is trying to solve them too soon.</p>
<p>The most important thing to do when faced with a problem like this is to stop working on it. Honestly, it sounds paradoxical, but the biggest mistake people make when solving problems is trying to solve them too soon. Instead, stop and think about what you need to do. Make sure you understand exactly what the question is asking and make sure you understand exactly what you are trying to solve for.</p>
<p>In our problem, we should ask ourselves: Can we actually build something that will discern the numer of hidden dog toys? Sure, all we need to do is...</p> <a href="https://www.quickanddirtytips.com/education/math/the-5-steps-of-problem-solving " class="views-more-link">Keep reading on Quick and Dirty Tips</a>Fri, 30 Dec 2016 22:53:25 -0500Fri, 30 Dec 2016 22:53:25 -0500https://www.quickanddirtytips.com/education/math/the-5-steps-of-problem-solvingHow Many Gifts Are in the 12 Days of Christmas?
https://www.quickanddirtytips.com/education/math/how-many-gifts-are-in-the-12-days-of-christmas
<p><img alt="Partridge In a Pear Tree" class="qdt-wrap-left" height="224" src="https://www.quickanddirtytips.com/sites/default/files/styles/insert_small/public/images/8942/partridge-in-a-pear-tree.jpg?itok=lM23elh_" width="224" /><em>Once upon a time, in a far away land, a young girl and boy were playing in the dining room of their castle when they discovered a story scrawled on the back of a painting. As legend has it, the story read …</em></p>
<p>So Christmas was weird for me last year. It all started on December 25 when my true love gave me a potted pear tree upon whose branches sat a befuddled bird. Things got even weirder the following day when I received yet another pear tree (complete with yet another bird), as well as a pair of doves. The story on the third day was similar—another pear tree, two more doves, and this time a trio of chickens. As you might imagine, I was wondering: What’s up with all the birds?</p>
<p>This sort of thing continued for more than another week. With each new day came a new gift—actually a predictable number of that new gift: 3 on the 3rd day, 4 on the 4th, 5 on the 5th, and so on—as well as a repeat of <em>all</em> the gifts given on all of the previous days. By the time we got to the 12th day, we ran out of space in the castle living room and had to move our holiday celebration to the very dining room in which this painting is hanging.</p>
<p>That evening as we sat around the table, somebody asked me how many presents my true love had given on each day? With that question we began a quest to understand the mathematics of those epic twelve days of Christmas. To the best of my recollection, dear reader, the following contains an accurate recounting of that tale of discovery.</p>
<h2>The Wonderful (and Distracting) World of Puzzles</h2>
<p>As so often happens, our journey towards counting my true love’s gifts was quickly derailed by another math puzzle. Somebody at the table mentioned that someday far into the future (in the year 2016), psychologist and magician Richard Wiseman (who was once a<a href="https://www.quickanddirtytips.com/education/math/how-to-win-every-bet" target="_blank"> guest on the famous “Math Dude” show</a>) would <a href="https://mobile.twitter.com/RichardWiseman/status/811172770138718208" target="_blank">tweet</a> the following series of instructions (which you should feel free to follow along with … you might want to go grab a calculator):</p>
<ul><li>Type your house number (i.e., your address) into a calculator.</li>
<li>Now double it.</li>
<li>Next add 5 to the result.</li>
<li>Then multiply this answer by 50.</li>
<li>Now add your age.</li>
<li>And then add 365 to the result.</li>
<li>Finally, subtract 615 from the whole thing.</li>
</ul><p>What do you get? As Wiseman points out: “Voila—your house number and age!” Needless to say, all of us at the table gave it a go, and much to our amazement we found that it does indeed work (...</p> <a href="https://www.quickanddirtytips.com/education/math/how-many-gifts-are-in-the-12-days-of-christmas " class="views-more-link">Keep reading on Quick and Dirty Tips</a>Fri, 23 Dec 2016 23:10:18 -0500Fri, 23 Dec 2016 23:10:18 -0500https://www.quickanddirtytips.com/education/math/how-many-gifts-are-in-the-12-days-of-christmas