Scholars, I wonder if you know: Will it sink or will it float? Just sing this song and don't forget That water really is wet So when you engineer a boat, Will it sink or will it float? It's all about the density D = M over V The mass is the amount of stuff And volume, space that it takes up So when you engineer a boat, Will it sink or will it float? Will it sink or will it float now? Will it sink or will it float now? You need to maximize displacement Or else you'll sink down to the basement So I wonder if you know... And Archimedes said, "Of course! The water has a buoyant force!" A quick experiment will prove: One gram per centimeter cubed. So when you engineer a boat, Will it sink or will it float? So let's be sure to get it straight: Floatation ain't about the weight A heavy ship can float on top A penny sinks just like a rock So when you engineer a boat, Will it sink or will it float? Will it sink or will it float now? Will it sink or will it float now? You need to maximize displacement Or else you'll sink down to the basement So I wonder if you know: Will it sink or will it float?

Climate change, climate change It's more than global warming Scientists are warning What could be to blame? Climate change, climate change Hurricanes and fires Water's getting higher Weather's getting strange Climate change, climate change So much carbon dioxide Melting glaciers worldwide Isn't it a shame? Climate change, climate change But we can save the planet If we understand it What is climate change? Do you ever think that the Earth is just right? In summer, lots of sun; in winter, lots of ice It's true that every day the weather can change Seasons come and go, but the climate stays the same Our planet's atmosphere has a mixture of gas To trap that solar warmth, like a greenhouse made of glass Without it, we would freeze. All the heat would escape But too much greenhouse gas can make our climate change I know you love those fossil fuels Like coal and natural gas and oil We use them every single day To make heat and electricity But the carbon dioxide they release Is trapping too much solar heat We're doomed if we don't stop the burn When will all these people learn? Climate change, climate change It's more than global warming Scientists are warning What could be to blame? Climate change, climate change Hurricanes and fires Water's getting higher Weather's getting strange Climate change, climate change So much carbon dioxide Melting glaciers worldwide Isn't it a shame? Climate change, climate change But we can save the planet If we understand it What is climate change? The climate of the earth wasn't always this way In fossils from the past, we can see how it changed Three hundred million years was a long time ago The carbon in the air made it hotter, don't you know With warm and humid air, there was no type of snow The dinosaurs evolved, and enormous plants did grow And when these giants died, they decayed underground Their fossils turned to fuel that the humans later found I know you love those fossil fuels Like coal and natural gas and oil We use them every single day To make heat and electricity But the carbon dioxide they release Is trapping too much solar heat We're doomed if we don't stop the burn When will all these people learn? Climate change, climate change It's more than global warming Scientists are warning What could be to blame? Climate change, climate change Hurricanes and fires Water's getting higher Weather's getting strange Climate change, climate change So much carbon dioxide Melting glaciers worldwide Isn't it a shame? Climate change, climate change But we can save the planet If we understand it What is climate change?

Constant of proportionality We're multiplying constantly In tables, in equations, and in graphs Look for proportionality To comprehend reality To understand proportions, you need math! Let's start with a table: we'll have to divide Make certain the numbers are on the right side It could be dollars earned per hour Or touchdowns scored per game In proportional relationships, the constant is always the same! Constant of proportionality We're multiplying constantly In tables, in equations, and in graphs Look for proportionality To comprehend reality To understand proportions, you need math! Now how 'bout a line graph? That's easy as pie! It starts at the origin, then climbs to the sky Find x = 1. That's your unit rate. y there is the constant, no need for debate. Another method you can use: Find an ordered pair to choose. Divide the second by the first -- Be careful, don't get it reversed! Constant of proportionality We're multiplying constantly In tables, in equations, and in graphs Look for proportionality To comprehend reality To understand proportions, you need math!

Climbing up a mountainside Hanging on by a rope Two steps up and one step right I won't fall down, I hope When I saw a warning side That said "Increasing Slope" I calculate the unit rate. Math can help me cope! Oh, let me show you how to find the slope: Plot two points, then count rise and run (Rise over run) Oh baby, slope is just a ratio Rise and run and you're almost done Rise over run) Zooming down a waterslide, Picking up that speed It started very gradually, But now it's getting steep Every yard I zoom along, I drop a yard in height The slope it gives is negative, Falling left to right Oh, let me show you how to find the slope: Plot two points, then count rise and run (Rise over run) Oh baby, slope is just a ratio Rise and run and you're almost done Rise over run)

Let's talk about slope, baby y = mx + b Begin at the intercept, then rise and run It's so easy! Let's talk about slope Let's talk about slope Let's talk about slope for now To the scholars at home or in the crowd It keeps going up or down Don't confuse, abuse, or refuse the topic 'Cause that ain't gonna stop it Now, we talk about slope on the slides and amusement park rides Many will know: it's how a line goes Let's tell how it rises and how it runs Where it starts -- it's so much fun! Those who think it's boring have no choice: Pick up the pencil, press play, and turn your thinking cap on Nothing can stop a scholar All right then, come on, kids Let's talk about slope, baby y = mx + b Begin at the intercept, then rise and run It's so easy! Let's talk about slope Let's talk about slope Fifty dollars in my savings account And every Saturday, I deposit the same amount Ten bucks a week, now that's a constant rate This line's increasing steadily, so go on, let the haters hate Per, each, every, daily, or yearly These are the key-words to help you severely They mean slope or speed, rate of change Rise over run, or m -- you know they're all the same But what about b? That's where it begins, it's true The starting point, fixed cost, or initial value The line intercepts the y-axis And if you're confused, that's why we're gonna practice You know lines that are parallel Never intersect. They've got the same slope, very well Then on the other hand you have the perpendicular 90 degrees, slopes are opposite reciprocals Straight lines, constant rate of change And you'll always recall, I hope, That slope is dope Let's talk about slope, baby y = mx + b Begin at the intercept, then rise and run It's so easy! Let's talk about slope Let's talk about slope

To the left, to the left Negative exponent, move to the left Scientific notation More than zero, less than one From the width of a human hair To the mass of a molecule of air Protons, neutrons, and electrons One PPM, that's one part per million Circling the decimal because I'm not a fool Every time I see the sign, I know the rule: I'm gonna say Just move that decimal, just move that decimal! It could be a tenth, a hundredth, a thousandth It could be a millionth, billionth; counting places Just move that decimal, just move that decimal It could be a trillionth or a quadrillionth When you're working with scientific notation, Just move the decimal To the right, to the right Positive exponent, move to the right Scientific notation To infinity and beyond From the length of the Milky Way To a galaxy far, far, away Population of our nation Everybody loves scientific notation Circling the decimal because I'm not a fool Every time I see the sign, I know the rule: I'm gonna say Just move that decimal, just move that decimal! It could be a ten, a hundred, a thousand It could be a million, billion; counting places Just move that decimal, just move that decimal It could be a trillion or a quadrillion When you're working with scientific notation, Just move the decimal

All right now, everyone listen: I got a song with precision We got some rules for these exponents I'm a mathematician We've got square roots and cubes And orders of magnitude I'm an exponent proponent Let me sing it to you Exponents are your friend When you need to comprehend Multiplication and division Again and again and again It all starts with the base Gonna raise it to a power Before you know it, you're in space At half a billion miles an hour So watch me simplify Watch me evaluate I am an expert, it's true With all these exponent rules Yeah, I know just what to do All right now, everyone listen: I got a song with precision We got some rules for these exponents I'm a mathematician We've got square roots and cubes And orders of magnitude I'm an exponent proponent Let me sing it to you Now when you have to exponentials You know they have some potential When the bases are the same Come on and sharpen your pencil With a product of powers, here's the rule of thumb: Just take your exponents and find the sum Example: 10 to the sixth times 10 to the fourth Equals 10 to the tenth. Need I say more? A quotient of powers is a simple action Remember division can look like a fraction You already know that the base doesn't change And for the exponents we can use subtraction So watch me simplify Watch me evaluate I am an expert, it's true With all these exponent rules Yeah, I know just what to do All right now, everyone listen: I got a song with precision We got some rules for these exponents I'm a mathematician We've got square roots and cubes And orders of magnitude I'm an exponent proponent Let me sing it to you A zero exponent will be one-of-a-kind Except for zero to the zero, which is undefined And a negative power means we're dividing by the base It's the reciprocal, with the base in the denominator place For a power of powers, here's the explanation: Combine the exponents using multiplication There's only one base, so it stays by itself Remember this song if you need exponent help! So watch me simplify Watch me evaluate I am an expert, it's true With all these exponent rules Yeah, I know just what to do All right now, everyone listen: I got a song with precision We got some rules for these exponents I'm a mathematician We've got square roots and cubes And orders of magnitude I'm an exponent proponent Let me sing it to you

It's metric! A folded umbrella - it's metric! (Meter, liter, gram) A Pepsi vanilla - it's metric! (Meter, liter, gram) A Lego Godzilla - it's metric! (Meter, liter, gram) exa- peta- tera- giga- mega- kilo- hecto- deka- deci- centi- milli- micro- nano- pico- femto- A big anaconda - it's metric! (That's a deka-meter) A bucket of water - it's metric! (That's a deka-liter) And you know it's there Here, there, and everywhere I've got to move I'm gonna move the decimal I'm gonna times ten, times ten, times ten, Or, if I'm going left, divide Are you comin' with me? We're gonna move it left and right And I will teach you, teach you, teach you I'll teach you the metric slide The real Godzilla - it's metric! (That's a hecto-meter) And too much Nutella - it's metric! (That's a hecto-liter) This fresh mozzarella - it's metric! (That's a hecto-gram) exa- peta- tera- giga- mega- kilo- hecto- deka- deci- centi- milli- micro- nano- pico- femto- The length of a pencil - it's metric! (That's a deci-meter) A shot of espresso - it's metric! (That's a deci-liter) But you know it's there Here, there, and everywhere I've got to move My decimal from side to side And I'll teach you, teach you, teach you I'll teach you the metric slide The hole in a bagel - it's metric! (That's a centimeter) A shot can be painful - it's metric! (That's a centi-liter) The mass of a staple - it's metric! (That's a centi-gram) exa- peta- tera- giga- mega- kilo- hecto- deka- deci- centi- milli- micro- nano- pico- femto- A crystal of sugar - it's metric! (That's a millimeter) A big drop of water - it's metric! (That's a milli-liter) But you know it's there Here, there, and everywhere.