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Mathematics

Within Mathematics

Cartoon of Robo, J, 5, a pink robot hovering next to Robo, O, 5, a short, squat blue robot. They are next to a fountain surrounded by a colorful flower border. Caption. Sound of Robots beeping.

Cartoon landscape of a rainbow-colored hot air balloon surrounded by dark gray clouds and rain. A helicopter hovers nearby with 2 balloon parachutes next to the basket. Caption. Allie as narrator. Both teams are now flying through the rainy clouds.

Cartoon of a kitchen with an angled wood plank leading down from the second shelf of the refrigerator to the kitchen sink. A few potatoes and tomatoes roll down the plank. Caption. 5 tomatoes.

Magnifying glasses over a book, letters enlarged. Caption. They wanted a new yard based on the laws of science.

An image of a girl outdoors below a yellow, sloping line going from the street level up to the sky. Caption. First, I'm going to work up the equation.

Title card in blue box on white background reads, "Brain and same both have long 'A'!"

Title card in blue box on white background reads, "Can you find the apostrophe in 'let's'?"

Title card in blue box on white background reads, "Can you find the long 'A' in taste?"

Blue box on a white background. Text reads, “Can you hear the ‘er’ in Water?”

Title card in blue box on white background reads, "Can you hear the long 'A' in rainbow?"

Title card in blue box on white background reads, "Can you hear the long 'A' in way?"

Title card in blue box on white background reads, "Can you hear the long 'E' in cheer?"

Title card in blue box on white background reads, "Can you hear the long 'O' in hole?"

Title card in blue box on white background reads, "Can you hear the long 'U' in unique?"

Still image from: Let's Learn: Do You Hear the "all" in Ball?

Still image from: Let's Learn: Do You Hear the "ck" in Luck?

Still image from: Let's Learn: Do You Hear the "ed" in Melted?

Still image from: Let's Learn: Do You Hear the "ind" in Kind?

Still image from: Let's Learn: Do You Hear the "ink" in Pink?

Still image from: Let's Learn: Do You Hear the "ong" in Song?

Still image from: Let's Learn: Do You Hear the "ou" in Sound?

Still image from: Let's Learn: Do You Hear the "oy" in Toy?

Still image from: Let's Learn: Do You Hear the “ch” in Choo Choo?

Still image from: Let's Learn: Do You Hear the Long 'U" in Unicorn?

Still image from: Let's Learn: Do You Hear the Short “i” in Pick?

Title card in blue box on white background reads, "How many syllables are in invent?"

Title card in blue box on white background reads, "How many syllables are in thinker?"

Title card in blue box on white background reads, "Super and power both end in 'E, R'!"

Light waves emitting from a lightbulb. Spanish captions.

Digital illustration of a cat on the roof of a blue house. A tall flower stands to the left and an apple tree to the right. Caption. The cat is made from circles for the head and body.

Illustrated cartoon. Back of a young girl's head. She has short, shaggy hair and wears a black and white checkered shirt.

Dry brushed animation of a smiling man in a chef's uniform with a red neckerchief and mustache. Caption. Narrator. Tito, you charge that.

Dry brushed animation of a girl turning around in her seat and gesturing to the side in a theater filled with people. Legs of a person and a stool appear on the stage in the background. Caption. Is this almost over? This guy is terrible.

Dry brushed animation of a man in a black beanie and bandit mask. Stacks of money fill background. Caption. I'll just fill the briefcase with these stacks of fifties.

Dry brushed animation of a woman wearing cat eye glasses and carrying a purse as she gestures toward a storefront with a sign that reads, "40 percent off everything!" Caption. Why do they make this so confusing?

Dry brushed animation of a smiling woman wearing cat eye glasses in a shoe store. Caption. This pair is free!

Dry brushed animation of a smiling boy with 1 hand held up to the side. Carnival rides and carnival goers fill the background. Caption. But it's too tall.

Cartoon sports scoreboard with a red team that has two hundred thirty points and a yellow whale team that has two hundred thirty-one points. A dodgeball is thrown in front of the board as a crowd of people behind the board cheer.

Cartoon scoreboard labeled, “Jugadores Restantes,” with a red E.M. team that has scored two hundred thirty points versus a Yellow Beluga whale team that has scored two hundred thirty-one points. Red dodgeballs fly through the air as a crowd of people cheer behind the board.

Photos of a smiling woman and a serious looking man are cut out and placed on cartoon bodies. They sit at a table with a vase of flowers in between them. Behind them is a chart with a graph showing that the woman spoke thirty-five words while the man only spoke six words.

Photo of a woman’s head cut out and placed on top of a cartoon body. She holds a phone up to her ear and has her mouth open like she’s talking. Over her head is the number thirty six.

Large square leans forward in front of a fence next to an oval that's next to a pole and flowers. There’s a ruler measurement under the image that’s labeled, “four, fifteen over three, six.”

Curved cartoon house with a fence around it. A person in front of the house stands next to two large eggs and a mailbox. Below the image is a ruler measurement labeled, “four, fifteen over three, and six.”

Cartoon characters that look like queens on playing cards are dressed in red and blue gowns. They look at each other with confusion and question marks over their heads.

Cartoon person that looks like the king on playing cards has an angry expression on their face. They point in front of them and say, “Pie de la Reina.”

Cartoon girl dressed in all black with a skull hair clip sits in a pink room as she holds a video game controller in her hands. An orange cat hangs from the ceiling and points at her. The girl looks angry and annoyed.

Cartoon girl dressed in all black with a skull hair clip sits in a pink room as she holds a video game controller in her hands. An orange cat hangs from the ceiling and points at her. The girl looks angry and annoyed.

Cartoon woman dressed in a black jumpsuit stands in a power stance and holds her arm out. Out of her hand is a green ray of powers. Text reads, “Outta Sight.”

Cartoon green tire labeled “Tamaño Normal" with lines that create a box around it labeled twenty-one inches tall and twenty-one inches at the base. There’s a question mark for the width measurement. Over the tire is a smaller version of the tire labeled “Tamaño reducido en escala" that only has the width labeled one inch. Text, “twenty one times que numero equals question mark.”

Closeup on a sheet of paper in a typewriter with the word, "Week," typed out in all caps. Caption. The Egyptian week was ten days long.

Person in a science lab working with complex machinery. Caption: There is almost no limit to the ways we transmute matter.

Cartoon of Max the Train, Jake the Fire Engine, and Blazin' Bill the Monster Truck floating down a river surrounded by dense trees on a log raft. Caption. Look! I see 1 of Bubble's wooden shapes.

Open wooden box with metal instruments to measure length. Caption. But how did we come up with rulers.

Empty aquarium with the formulas V equals open parenthesis 20 times 10 close parenthesis times 12 and one eighth. V equals 2,425 cubic inches. Caption. Like cubic inches or cubic feet.

Man leans against a wall and types on a keyboard inside the International Space Station. Caption. The metric system is also preferred in certain fields.

Boy wearing goggles floats underwater and holds his breath with his mouth closed. Caption. All of these forms of measurement are known as.

Green liquid pouring into a measuring glass. Spanish captions.

Periwinkle background with white title text across the top that reads, "Missing addends. Finding a missing part." Below is a clip art drawing of a black-haired woman thinking about a math problem with a missing part.

Spheres in a cube, lined up in an alternating positive and negative pattern. Caption: by mutual Columbic attraction in a regular pattern.

Pile of coins sits on a carpeted floor in front of a pair of crossed legs. Caption. To understand how this works.

Split screen of 2 fish tanks. 1 is labeled, "More," with an arrow pointing down and the number 15 below. The other is labeled, "Less," with an arrow pointing down and the number 13 below. Caption. So this tank has more fish and this tank has less fish.

Person on skis in a crouched position. Motion: change in position. Caption: This skier was in motion.

Still image from: Museum Access: National Museum of Mathematics

2 parallel lines outline grooves between wood planks and are intersected by a diagonal line. The 2 angles formed are labeled, "130 degrees" and "50 degrees." Title card reads, "Summary. Angle relationships." Caption. But they add to 180 degrees.

Still image from: Number 1 Newton Avenue: Bullseye

Still image from: Number 1 Newton Avenue: Buried Treasure

Still image from: Number 1 Newton Avenue: Cupboard Chaos

Still image from: Number 1 Newton Avenue: Dominoes

Still image from: Number 1 Newton Avenue: Goal

Still image from: Number 1 Newton Avenue: Hide-and-Seek

Still image from: Number 1 Newton Avenue: Jigsaw Puzzle

Still image from: Number 1 Newton Avenue: Mom's Moves

Still image from: Number 1 Newton Avenue: Pack, Pack, Pack

Still image from: Number 1 Newton Avenue: Plant Sale

Still image from: Number 1 Newton Avenue: Postie Puzzle

Still image from: Number 1 Newton Avenue: Prickly Problem

Still image from: Number 1 Newton Avenue: Racing Cars

Still image from: Number 1 Newton Avenue: Shops

Still image from: Number 1 Newton Avenue: Snug as a Bug

Still image from: Number 1 Newton Avenue: Star Jumps

Still image from: Number 1 Newton Avenue: Stay Up

Still image from: Number 1 Newton Avenue: The Puppet Show

Still image from: Number 1 Newton Avenue: Toy Champion

Still image from: Number 1 Newton Avenue: Troublesome Trifle

Cartoon. Centipede in a graduation cap and bow tie gestures to pencils on a table. Caption. Can you count how many pencils I have here?

Girl stands at carnival booth facing a small basketball hoop that hangs from a wall covered with stuffed animals. A young woman wearing an apron stands to the side. Caption. Numbers allow us to count and keep track of information.

Still image from: One Big Pair of Underwear!

The periodic table of elements. A color-coded grid with letters representing each element. Caption: Each row of the table represents a pattern of chemical properties

Closeup of a black and red chess board with white pieces in the foreground and black pieces in the background. Caption. As we investigate perimeter and area.

White ball with craft eyes sits on top of a red, plastic pedestal. 1 side of the ball has its outer layer torn away and exposing the ball's inner core. It appears to have been damaged by some type of impact.

Dianna wears a navy shirt with red, yellow, and pink stripes on the wrists and shoulders. She sits behind a large piece of paper and holds a black marker. A colorful background with science items on a shelf is behind her, and equations appear on screen.

Overhead view of a person's hands demonstrating how to solve a physics problem related to rotation on a large blue sheet of paper.

A C, G, I graphic of a spaceship made in the shape of a planetary ring rotates around a brown planet. The side closest to the planet looks like oceans with clouds and green continents, and the other side looks like a spaceship with glowing lights.

Aerial closeup of 2 arms. The left has a pink sleeve, the right has a red sleeve and uses a black marker to write on a large sheet of paper. The paper shows an X, Y axis with Y axis labeled Force in Newtons and X axis labeled X in meters. Next to this, a drawing that looks like a spring coil.

Host Dianna Cowern, a blonde woman in a red sweater and black scarf, smiles as she holds an old, large book up. Text on screen reads, "Newton's Principia, Original Manuscript," and an arrow points at the book.

In front of a blurred-out shot of this video's set, text reads, "Very Useful Trick. When any two objects collide elastically and energy is conserved, then the difference in their two velocities before the collision equals the negative of the difference between the two velocities after the collision."

Video host looks at us while sitting at a table with physics equations written on a large sheet of paper. Behind her, the set is decorated with a modular shelf holding scientific models, floating equations, and hanging gears.

Aerial closeup of 2 arms wearing denim sleeves with white stars. The right hand uses a large black marker to write on a large sheet of paper. The paper reads, "Energy and work" and has various physics equations.

Man is suspended in the air by a clump of large balloons over a crowd of people. There are multiple desert towers and rock features in the distance behind them. Text on screen reads, "David Blaine," with an arrow pointing to the man.

Aerial closeup of 2 arms in light blue sleeves over a paper. The right hand writes on a large sheet of paper with a thick black marker. The paper reads, "Equation of motion. Y equals Y sub 0 plus V sub 0, T plus 1/2, A, T sup to the power of 2."

Man wearing a gray winter hat, a dark gray hoodie, black snow pants, and red gloves snowboards down a snowy ski slope on a foggy day. A yellow snow making machine and a little building with a red roof are nearby.

Physics equation related to orbital motion is written on a large blue sheet of paper. The host's hand points at a line that represents the Earth's radius.

Aerial closeup of 2 arms. The right hand uses a thick black marker to write various physics equations on a large sheet of paper.

Video host speaks to us with her hands clasped together while sitting at a table with physics equations written on paper. Behind her, the set is decorated with a modular shelf holding scientific models, floating equations, and hanging gears.

Overhead view of the host's hands as she demonstrates how to work out an equation dealing with the relationships among centrifugal and centripetal force and the Earth's rotation.

Overhead view of the host demonstrating how to work out equations of motion involving acceleration, derivatives, sines, and cosines.

Aerial closeup of 2 arms in black sleeves. The right hand writes on a large sheet of paper with a thick black marker. The paper reads, "tangent equals opposite over adjacent (tan). S, O, H, C, A, H, T, O, A. 1." There's a diagram of a 37.5 degree angle and an directional axis labeled N and E.

Video host speaks to us, holding a marker while sitting at a table with physics equations written on paper. Behind, the set is decorated with a modular shelf holding scientific models, floating equations, and hanging gears.

Video host speaks to us, glances to the side and gestures with her hands while sitting at a table with physics equations written on paper. Behind, the set is decorated with a modular shelf holding scientific models, floating equations, and hanging gears.

A screenshot of 2008 physics exam problem 4, labeled sticky disks.

Cartoon train engine chugs down the tracks, blowing steam out its chimney. The front of the train resembles a camera lens. Caption reads: "Counting 1 to 10."

On the side of a red cartoon train car, a drawing of blue dots inside boxes in two rows and five columns. Caption spells out the number ten.

Cartoon train engine chugs down the tracks, blowing steam out its chimney. The front of the train resembles a camera lens. Caption reads: "Counting 11 to 20."

Cartoon train engine chugs down the tracks, blowing steam out its chimney. The front of the train resembles a camera lens. Caption reads: "Counting 21 to 30."

Cartoon train engine chugs down the tracks, blowing steam out its chimney. The front of the train resembles a camera lens. Caption reads: "Counting 31 to 40."

Cartoon train engine chugs down the tracks, blowing steam out its chimney. The front of the train resembles a camera lens. Caption reads: "Counting 41 to 50."

Cartoon train engine chugs down the tracks, blowing steam out its chimney. The front of the train resembles a camera lens. Caption reads: "Counting 51 to 60."

Cartoon train engine chugs down the tracks, blowing steam out its chimney. The front of the train resembles a camera lens. Caption reads: "Counting 61 to 70."

Cartoon train engine chugs down the tracks, blowing steam out its chimney. The front of the train resembles a camera lens. Caption reads: "Counting 71 to 80."

Cartoon train engine chugs down the tracks, blowing steam out its chimney. The front of the train resembles a camera lens. Caption reads: "Counting 81 to 90."

Cartoon train engine chugs down the tracks, blowing steam out its chimney. The front of the train resembles a camera lens. Caption reads: "Counting 91 to 100."

On the side of a cartoon purple train car, a picture of two rows of green apples, with five on the top row and three on the bottom row. Caption spells out the number eight.

The numeral 1 appears in black on a white background, on the side of a cartoon red train car. Caption spells out one.

The number 100 appears in black on a white background, on the side of a red cartoon train car. Caption spells out one hundred.

The number 25 appears in black on a white background, on the side of a green cartoon train car. Caption spells out the number twenty-five.

On the side of a cartoon brown train car, a picture of one large blue dice with two white dots on diagonal corners. Caption spells out the number two.

On the side of a cartoon brown train car, one large blue dice with two white dots on diagonal corners. Caption spells out the number two.

Cartoon train with cars the color of a rainbow chugs down a long track, through a hilly desert, as steam puffs out of its chimney.

On the side of a cartoon yellow train car, a picture of three round oranges. Caption spells out the number three.

On the side of a cartoon turquoise train car, a picture shows six tally marks, where a group of four marks are crossed diagonally by a fifth mark, followed by the sixth mark.

On the side of a purple cartoon train car, a picture shows nine red tomatoes, with five on the top row and four on the bottom row

Cartoon train engine chugs down the tracks, blowing steam out its chimney. The front of the train resembles a camera lens. Caption reads: "Learning Shapes."

On the side of a brown cartoon train car, a picture of a large purple circle on a white background. Caption reads: "Circle."

Slide shows a white banner on a light blue background with faded numbers that reads, "Learn Bright. Place Value."

Book cover titled, "Pocket Piggies Colors!" Miniature pig with brown spots hangs over the side of a sky blue tea cup with white polka dots. Text reads, "Featuring the Teacup Pigs of Pennywell Farm. Photos by Richard Austin."

Man and woman in white lab coats look at a computer while pressing buttons on a controller. Caption. They also rely on ballistics to match bullets and guns.

Weather illustration panels for a Monday to Wednesday forecast, with Monday as "Sunny", Tuesday as "Chance of Rain," and Wednesday as "Rain". An arrow labeled Unlikely points to Sunny. Caption. From unlikely on Monday to very likely on Wednesday.

10 seashells lined up in the sand by color next to a yellow bucket. 4 of the shells are black, and 6 of the shells are white. Caption. If 4 out of the 10 shells are dark.

Probability tree with 3 generations on a green background. There's 1 boy and 1 girl child in the first generation, 2 boys and 2 girls in the second, and 4 boys and 4 girls in the third. Caption. Each branch represents a different 3-child outcome.

Closeup of a hand using a black marker to write on a white paper on a clipboard on the grass. The paper reads, "Read and Reread." Caption. Step 1, read and reread the problem.

Woman in a white coat sitting and looking into a microscope in a lab. A graphic of 6 human cells appears at the bottom of the screen. Caption. Doubling the total number of cells each time.

Gloved hand holding an electronic chip with a pair of tweezers. Caption: they call it an artificial leaf.

Woman stands with fingertips touching and lips parted in mid-speech. Bar graph superimposed on left side of screen. Caption. If we were to run the experiment over again many times.

City map with a text overlay that reads, "Map, 1 inch. Actual distance, 25,000 inches". Caption. Represents an actual distance which is 25,000 times longer.

Closeup of a forearm with palm up and 2 fingers pressing on the wrist. Caption. The concept of ratios as well as the use of rates.

Still image from: Read Along With Me Picture Books: Christmas Train

Still image from: Read Along With Me Picture Books: Count on Me 123

Person holds up a book called "Peg and Cat, the Pizza Problem," by Jennifer Oxley and Billy Aronson. The cover illustration shows Peg and Cat in a restaurant, where Peg holds up four stacked pizzas and Cat, standing on a checkered tabletop, holds up three pizzas.

Hand picks up a pair of scissors from a tabletop covered with construction paper, a paper plate, a glue stick, crayon, pencil, and several small triangles, circles, squares, and rectangles cut out of orange, red, green, and yellow paper.

Closeup of an open green eye with a purple colored contact lens, black mascara on the eyelashes, and black eyeliner on the top lid. Caption. With several special properties.

White background with faint gray gridlines and math equation that reads, "23 and seven eighths equals 23.875." A big red arrow points at and labels the decimal point. Caption. Fractional quantities, such as 23 or seven eighths.

Closeup of a person holding a segment of orange with an arrow pointing to a halved orange. Segments on the halved orange are labeled 1 to 10. Caption. Each segment is a tenth of the whole orange.

Several ocean going sailboats docked with sails down is in front of a street lined with multi-story buildings with many windows and pitched roofs. Caption. The city of Copenhagen in Denmark is at sea level.

Top side view of a pizza with cheese, red sauce, and Canadian bacon on a large stainless steel pizza spatula over a gray background.

Centered, front view of the Taj Mahal. A dashed white line is overlaid down the center, with an arrow and the word "Axis" overlaid and pointing to it. A white rectangle overlay is around one of the pillars on the left. Caption. 1 side is a reflection of the other side.

Top side view of a pizza with cheese, red sauce, and Canadian bacon on a large stainless steel pizza spatula over a gray background. Caption. Most likely, family or friends ate the rest of the pizza.

Cartoon of an ancient Roman woman and man wear togas and stand on either side of the Roman numerals one through ten. Text reads, "Roman Numerals."

Middle-aged man with mustache wears sunglasses and holds onto railing of a boat as he leans forward. Caption. That's too fast in there.

Person looking at a computer screen with a complex image. Spanish captions.

Crowd of mostly young people. Spanish captions.

Person at a computer looking at a projection of a wire frame human face on a screen. Caption: how robots interact with humans,

Small airplane midflight. Caption: Momentum is the same direction as velocity.

A sliding scale weighing something. Caption: Weight is a scalar.

Math equations written on a chalk board. Spanish captions.

Two people looking at yellow fluid in a bottle. Caption: in a universal scientific language.

Speedometer. Caption: Velocity is a vector quantity.

Graph of North and East. Spanish captions.

Speedometer. Caption: Velocity is often confused with speed.

A speeding train. Spanish captions.

Still image from: SciShow: The Weird Truth About Arabic Numerals

Simple line drawing of a house on a hill with a roof and 2 windows.

Animation of a rover rolling across a red rocky surface against a red sky. In the center of the frame is a rainbow-colored circular shape. Caption. Here are some more facts about shapes.

Closeup of twisting yellow and red roller coaster tracks. Title card reads, "Shedding light on motion, Episode 2. Acceleration."

Plane with shining lights takes off from a runway and flies above a grassy field. Title card reads, "Shedding light on motion, Episode 1. Speed."

Person turning a spigot. Caption: it is multiplied at the axle, overcoming the resistance force.

School of fish swimming in a tank. Caption: Sometimes they sink like these rocks.

$Black and white closeup of a spiral notebook with equations. Caption. But that fraction doesn't look too good.$

Written equation, pi equals 3.14. Caption. So, pi turns out to be 3, 14 over 100 or 3.14.

Dense points of light on a black background. Caption: The oldest could be 11 to 13 billion years old,

Rotational motion theta equals s over r. Caption: We showed you that equation awhile ago.

An illustration depicts a blue down arrow and a red up arrow representing T A L and T H 2 O in contact with each other. The junction of the two arrows is labeled T e. On screen text, Physics, Part 5, Section A. Caption: is higher than the initial temperature of the water.

Animation of a circular wheel in motion. On screen Text, Projectile motion A. An arrow indicates same time. Caption: It takes the same time to rise as to fall.

A graphical representation of the x y coordinate plane. 2 units from the origin are marked on the positive and negative sides of the x and y axes. An upward arrow extends from the origin to (0, 2). On screen text, what are scalars and vectors. Caption; woman, this vector's direction is 90 degrees.

A woman is in ski outfits. An animation of a red sphere with on screen text, more inertia, greater mass. Caption: The red sphere has greater mass.

Multiplying vectors c. Vector A and Vector B roughly parallel in the same direction. Caption: in the direction of the first vector.

Inset of a young man gesturing with his hands and opening his mouth to speak. Text reads, "Part 1, section A. Integer." Caption. Then we'll get to exponents.

Digital illustration of a Christmas tree. Title bars read, "Part 2, section B. Tree diagrams and factorization." Caption. Except they have numbers on them.

Teenage boy and stuffed animal lie in bed and look up at the ceiling with their mouths gaping open. Caption. Hanging like a mobile from your ceiling.

Circular inset of a young man with pursed lips. Title bars read, "Part 5 and Section B, Putting Inequalities on the Number Line." Math equation on background reads 9 is greater than or equal to X. Caption. All right, with that beneath our belts.

Algebraic equation on maroon and green color block background. Title bars read, "Section B. Equations. Part 1." Math equation on background reads 3, X plus 5 equals 20. Caption. We've got to figure out the value for X.

Algebraic equation on green background. Title bars read, "Section B. Graphing linear equations. Part 2." Text at bottom reads, "In letter form first." Caption. We'll look at it in letter form first.

Man faces camera and speaks slightly off to 1 side like he is in an interview. Text on image reads, "Easy to remember, and a little bit enjoyable."

Rear view of teenage girl sits at ia control panel in a room filled with equipment monitoring panels with switches, lights and racks from the mid-1900s. A man wearing a hard hat stands between the control panel and equipment panels as he speaks to the girl.

Medium view of a man facing camera like he is giving a lesson as a subject expert. Caption. Either by the lengths of their sides or by their angles.

Man faces and speaks directly to camera like he's lecturing. An overlay formula reads, "Right triangle hypotenuse minus leg theorem over hypotenuse and leg of right triangle."

Man crouches on asphalt pavement. He rests his head on his hand which is propped on his knee. He gazes into the distance like he is thinking. An overlay measurement is labeled as 14 feet.

Seated man faces camera while holding a book in a living room setting. He speaks directly to camera as if he is being interviewed as a subject expert. Caption. As we continue our geometric portrait series.

Star Maths cartoon. Rear view of a girl and a boy standing. The boy holds a gun in his hand. Piles of metal and other debris lay before them in an outdoor salvage area. Caption. These label guns aren't very accurate.