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Mathematics

Within Mathematics

Star Maths cartoon. Side view of a boy and girl sitting at a dining table eating. Caption. Do you want all of them?

Star Maths cartoon. Large robot hovers next to an industrial floor scale in a warehouse. Text on the scale face reads, "100."

Star Maths cartoon. Person sits at a worktable in a manufacturing plant filled with equipment. 3 robots are to his side. Caption. But I'm making music, man!

Star Maths cartoon. Closeup of a digital number board with 3 rows ending in numbers of tens. The end of row 1 displays the numbers 8, 9, 10. The end of row 2 displays 18, 19, 20, and the end of row 3 displays 28, 29, and 30. Caption. 18, 19, 20.

Star Maths cartoon. A girl and boy use binocular-like devices as they scan the horizon off to the side of camera. Behind them, a vehicle sits on a dirt plain surrounded by brown hills. Caption. Go on, Ten! Go on!

Star Maths cartoon. A boy and girl are seated and turned towards each other in conversation. The girl points her index finger at the boy. Caption. You were channel-hopping.

Star Maths cartoon. Boy looks at a handheld device in 1 hand while his other hand is palm up. He stands outdoors with hills and mountains in the background. Text on the screen reads, "Meters." Caption. We need to measure out 1,000 meters.

Star Maths cartoon. A small and taller robot stand next to each other, conversing. Caption. Eleven, clear up the picnic.

Star Maths cartoon. Man walks through an archway as he speaks on a telephone. A boy and girl sit in the background in a living room and watch T, V. Caption. Do you want me to come meet you?

Star Maths cartoon. Girl sits on a couch in a manufacturing plant. Caption. Hi, I'm Lisa. You must be Amber!

Star Maths cartoon. 1 large robot and 1 small robot are standing and facing each other in a futuristic living room. Caption. No names, just numbers, Miss Amber.

Star Maths cartoon. Red, all terrain vehicle drives through a hilly dirt area with 2 trees that have sparse foliage. Caption. Amber as narrator. Well, there's not much junk this morning.

Star Maths cartoon. Girl holding a pen sits while a boy stands at the head of a table. A notebook rests on the table top which has a digital map display showing planets and stars. Caption. She was probably quite far away.

Star Maths cartoon. An empty all terrain vehicle with 3 wheels on each side is parked outdoors on a dirt surface in a desert-like area. Caption. Ha! Let's see where it landed.

Star Maths cartoon. A boy, girl and 3 robots stand on a smooth floor in a room with decorative, pipe-like structures and lighting. The boy points up towards a robot standing on a balcony above him. Caption. Botler, number 364, please.

Star Maths cartoon. Girl raises her hand with 3 fingers up and thumb folded in while using a beverage-making machine in a futuristic kitchen. She speaks and looks at a boy near her. Caption. 4 tablespoons of sugar.

Star Maths cartoon. Boy and girl face each other as they sit and talk over a dinner table. Caption. Probably typed the wrong numbers, again.

Star Maths cartoon. Girl stands in a spacecraft and holds 1 hand with thumb up in front of her face as she talks and looks to the side. Caption. Are you sure? 6 goes into 12 twice.

Star Maths cartoon. Hand extends over a paper with a painting of a butterfly's body and 1 set of wings. 6 pots of paint in different colors, brushes, and colored pencils sit on the table top. Caption. I'm making her a card.

Star Maths cartoon. A boy and girl approach a convertible-like car that is parked outdoors. Caption. Relax, Uncle Zak's miles away.

Star Maths cartoon. Boy looks upwards and stands with his arms outstretched on a blue floor outlined with green and black hazard tape. Caption. Help! Sam, get me out of here!

Star Maths cartoon. A boy and girl walk through a storage room with shelving. Flying robots are nearby and are restocking inventory on warehouse shelves. Caption. Boy as narrator. What was that? Caption. Girl as narrator. What?

Star Maths cartoon. Back view of a boy and girl outdoors and looking at a futuristic truck with a glass enclosed cabin and an open cargo bed. A green robot stands in the cargo bed. Caption. Where are you off to, Botler?

Star Maths cartoon. Girl in a spacecraft sits at a table with a microphone and monitor. She looks up at a person to her side. A spotted, cat-like creature sits on the table. A robot stands in the background. Caption. Will Lisa be able to get here?

Man looks slightly off camera with an impassioned look. Behind him, the Qualcomm Thinkabit Lab with a collection of colorful toys. Caption. But this is a way to give back in a personal way.

Woman stands next to an overhead projector. Caption. Yeah, okay, let's do that. Let's make these a zero.

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Aerial view of a building surrounded by a body of water in the middle of a large city. Caption: (Scott) Here at the National Aquarium in Baltimore,

Medium view of a man speaking while sitting before a backdrop of the U, S flag and an overlay of the Georgia state flag. Title card below the man reads, "Randy Howe. Author. Flags of the 50 States."

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Tessellation pattern of equilateral triangles with 3 circles, each placed at different intersections of 6 triangles. Caption. Each vertex must be the same.

A cartoon says, by nature, I am naturally natural. Caption: Nature of science.

Person in a lab setting filling a container from a faucet. Caption: A calorimeter is simply anything used to measure heat.

Person with a lit candle melting the wax into a dish. Spanish captions.

Color illustration of a child working on a math problem using a table with columns for Hundreds, Tens, and Ones held up by a green dinosaur.

Diagram of a circuit showing a battery with leads on the positive and negative side and a lightbulb in the middle. Reduction. Caption: During this process, one substance must gain electrons,

Closeup of a T, V screen with black and white still of Fred Flintstone sitting in a stone chair and turning toward viewer with cigarette in his hand.

Man stands outside in a park setting and appears to be teaching geometry. Next to him, an overlay of a square has the number 4 labeled on each side. Caption. Perimeter of this square.

Man sits on a colorful geometric form on a stage set as he faces and speaks to camera. Text box appears next to him and reads, "If you roll a die 6 things can happen." Caption. "1 meets requirements of our question."

Logarithmic scale shows a horizontal line with equal-sized notched increments labeled 1, 10, 100, and 1,000. Notches between each point are spaced out differently to represent the scale difference. Between 100 and 1,000, the notches representing smaller numbers are labeled "far," while the notches representing the larger numbers are labeled "close."

Digital art. Zoomed-in superscript number 2, representing a number squared, to the left of the quotation-mark notation for "inches."

Geometric illustration of atoms. Caption: So here we've drawn in all the atoms.

Cartoon of Diego and Mica standing outside next to a large colorful box. They are looking up at Alterio who appears to be speaking into a megaphone. Spanish caption. No, no lo suelten todavía.

Cartoon of a ferris wheel with Diego, Mica, and Alterio riding in one of the baskets. Spanish caption. Ah, me encanta la vuelta al mundo.

Cartoon of Alterio the hamster standing on a patchwork quilt in a home setting. A thought bubble leads to an image of a bicycle. Caption. Una bici no vendría nada mal.

Cartoon of Diego, Mica, and Alterio standing outside on a grassy hill next to a white banner stretched across posts that reads, in Spanish, "Entrenamiento para exploradores principiantes."

Cartoon of Alterio the hamster standing on a wood surface with an interested expression on his face. He's holding up a finger and looking up like he's talking to someone. Spanish caption. Cada 15 minutos, es un cuarto de hora.

Cartoon of an outdoor basketball hoop in front of a garden wall with hills and cacti in the distance. A basketball flies in towards the hoop from offscreen. Spanish caption. Oh, ahora es más difícil porque estoy más lejos.

Cartoon aerial view of a hand pointing down at a game board with a colorful patchwork of various geometric shapes. The hand is pointing to the orange triangle. Spanish caption. Se pueden hacer un montón de figuras.

Cartoon of Diego and Mica standing in front of a red trash container looking up and away in the same direction. Spanish caption. Traemos tapitas para reciclar.

Cartoon illustration of a green ring with show lights surrounded by a seated audience. Diego stands on a calculator that shows 83. Alterio stands on a blue box with the thought bubble, 37 plus 46. Mica stands behind a pink podium looking out.

Cartoon of Diego and Mica standing next to a chalkboard and looking at a list with a number tally. The list is labeled Camiones on the left and Ruedas on the right. Spanish caption. ¡Perfecto!

Cartoon of Alterio the hamster jumping in the air above colorful cards with number sequences. Spanish caption. Traidora, jamás lo hubiese esperado de una amiga del alma.

Cartoon of Alterio the hamster holding a purple $100 bill with eyes closed and hand pressed to his cheek like he is upset. Spanish caption. Mi último billete.

Cartoon of a hand holding a measuring tape across what appears to be blue shelves in partial view. Spanish caption. Mide en total 110 centímeters.

Cartoon of Diego, Mica, and Alterio walking across a calendar. The date reads 21 and is decorated with flowers, grass, and the label ¡Día de la primavera! Spanish caption. 21 de septiembre, el día de la primavera.

Screenshot of a colorful math equation that reads 7 times 5 equals 35. Spanish caption. Hizo cinco por siete, que es igual a siete por cinco.

Diego and Mica stand in a kitchen decorated with birthday balloons and banners. A woman and girl stand and watch them from across a party table. Spanish caption. ¡Ah, una fiesta sorpresa!

Cartoon of Diego using a long colorful pointer to point at a dartboard with red darts at 150 and 500, blue darts at 100 and 250, and green darts at 150 and 400. Spanish caption. Con este, hiciste 500 puntos.

Diego stands behind a store counter looking at a man who is also behind the counter and holding up a notepad for Diego to see. Behind them, there are sundry items stacked on shelves. Spanish caption. Tienen que sumar todos los números de esta hoja.

Cartoon of Mica holding a tray of food and holding up the number 4 on 1 hand. She looks down at a table in front of her that has 5 plates filled with the food on her tray. Spanish caption. Y ahora sobran 4.

Timed video game showing Diego holding a fork and Mica standing by. Next to them, a column of vegetables with number points in the hundreds. Spanish caption. Computerized voice as narrator. Puntos sumados, 1,700.

Cartoon of Diego, Mica, and Alterio standing next to a structure made of rods and circular joints. Mica plays the flute which appears to make a few rods and joints float in the air above the structure. Spanish caption. Se llaman caras laterales.

Cartoon of Alterio the hamster standing on grass with a smug expression on his face. He's holding up a finger and aiming a blue pen with the word Narcado on the side. Spanish caption. Seguro como que me llamó Alterio.

Cartoon of a woman holding a cardboard box reacting with surprise to something out of view. Behind her, there are orange lockers with numbers on them. Spanish caption. Bueno, les voy a mostrar.

Cartoon first person aerial view of Alterio the hamster holding a package of mints. He has turned the package and is looking down at the ingredients section. Spanish caption. Um, no puedo leer esta letra.

Cartoon of Mica standing outside next to a homemade cardboard castle. She's wearing a crown decorated with buttons and hugging Alterio the hamster to her chest. Spanish caption. Ay, gracias, mi príncipe.

Cartoon of Diego driving a truck along the border of a field of planted young sprouts. Spanish. Y lo resolvemos dividiendo.

Geometric design of a large cat. Caption: (narrator) First, define the surface of the shape geometrically.

Digital map of the United States divided into six vertical blocks of color with clocks above each section. Text reads, "Time Zones."

Cartoon of Robo, J, 5, a pink robot hovering above a paved outdoor surface looking off at something out of view. Caption. Watch out for the rolling circles.

Cartoon of a yellow toy construction truck parked at an outdoor construction site with various materials scattered about, such as red pillars, gray bricks, and wood pallets. Nearby, a smaller green forklift lifts a blue and green panel in the air. Caption. Forklift as narrator. Okay, lower the rectangle.

Cartoon of a bright purple convertible raised up on monster truck tires driving across a paved outdoor area surrounded by trees. Nearby, a blue raised truck is partially visible.

Trigonometry diagram overlayed on a real photo of a bridge with a labeled triangle. Labels include an 85-degree angle and opposite side of 120 feet, with adjacent side and hypotenuse not defined. A written equation reads sine theta equals opposite over hypotenuse. Below that, sine 85 degrees equals 120 feet over hypotenuse. Caption. Is the ratio of the opposite side to the hypotenuse.

Man crouches down to hold up a yellow rod in vertical position as a girl crouches a few feet across from him. A triangle overlay is drawn to show the angle of elevation. Next to this, an identical triangle is drawn, this time with a tall metal sculpture in a plaza. Caption. The angle of elevation is the same.

Person holding a twisted strip of material. Caption: This shape is called a Möbius strip.

Trace wears scarfs around his shoulders and talks. Caption: We are here, today, to lay to rest the kilogram.

Children sit next to each other in rows of desks in a classroom. Below them is a headline on a blue banner that reads, “Comparing and Ordering Fractions Meaningfully.”

Child sits at a desk in front of a teacher, answering a question. Below him is a headline on a blue banner that reads, “Letting Algorithms Emerge Naturally.”

Four students sit at a table holding small dry-erase boards. A girl points to an equation on her board that reads, “½ = 1 half.” Below them is a headline on a blue banner that reads, “Teaching the Concept of Equivalence, Not Just the Rule.”

Two children sit at a table in a classroom. Below them is a blue banner that reads, “The Importance of the Unit.”

Student sits at a table in a classroom. Below her is a blue banner that reads, “The Meanings and Representations of Fractions.”

Blackboard background with a clip art graphic of a brown-haired woman next to a big pencil. Above that is text that reads, "Using a ruler to measure inches. Can you help me learn how to measure?"

Blackboard background with a clip art graphic of a brown-haired woman next to a big pencil. Above that is text that reads, "Using paper clips to measure. Can you help me measure my pencil?"

Woman with glasses in a blue shirt demonstrates sign language in front of a black curtain. White text in a red box at the bottom of the screen reads, "Exponent slash power."

Closeup of 3 boulders in a row with grass and trees in the background. Caption. During the next few minutes.

Gray background with a clip art graphic of a smiling brown-haired woman on the left, and a yellow hand sketching 2 suns and 3 clouds on the right. Text in the middle of the screen reads, "Ways to make 5 using drawings. Teaching without frills."

Gray background with a clip art graphic of a smiling brown-haired woman on the left, and 4 math equations that add up to 5 on the right. Text in the middle of the screen reads, "Ways to make 5 using equations. Teaching without frills."

Gray background with a clip art graphic of a smiling brown-haired woman on the left, and 2 red and 3 green apples on the right. Text in the middle of the screen reads, "Ways to make 5 using objects. Teaching without frills."

Gray background with a clip art graphic of a brown-haired woman holding her arm up and smiling on the left, and a yellow waving hand on the right. Text in the middle of the screen reads, "Ways to make 5 using your fingers. Teaching without frills."

Large envelope being weighed on a scale. Spanish captions.

Top view of scale with objects on weighing plate. Caption. It's important to know how light or heavy things are.

Split screen. The left is a white background with a polynomial math equation written and simplified in blue. To the right, a woman works through the problem using a screen in front of her. Caption. Now I need to distribute that negative 1 to that negative 6.

Aerial side view of a computer screen displaying a white screen with a math word problem written and worked out in long form in blue. The text at the top reads, "Example 3. What is the slope of the line that contains the given points?" Caption. The slope of the line that contains these two points.

Split screen. The left is a white background with a math word problem written in blue. Text at the top reads, "Example 3. Determine if the situation presents a direct variation. Below this, the problem is in typed text and the answer is in handwritten text. To the right, a woman works through the problem using a screen in front of her.

Split screen. The left is a white background with a math word problem written in blue. The prompt reads, "Determine if the situation represents an inverse variation." To the right, a woman works through the problem using a screen in front of her. Caption. We want to determine if this is an inverse variation situation.

Aerial side view of a left hand touching a computer screen displaying a partially visible math problem written in blue. Caption. After you've factored your numerator, it's smooth sailing.

Split screen. The left is a white background with blue text that reads, "Example 2. Evaluate 3 minus 10, X, when X equals 2 over 5." Handwriting below reads, 3 minus 10 times 2 over 5. To the right, a woman works through the problem using a screen in front of her.

Aerial side view of a hand touching a computer screen displaying a math problem written and worked out in long form in blue. The problem at the top reads, "How did I get that?" Caption. And I know there's going to be a plus sign in between."

Split screen. The left is a white background with blue text that reads, "Example 4, factor completely. 4x squared minus X minus 3." To the right, a woman works through the problem using a screen in front of her.

Split screen. The left is a white background with blue text that reads, "Example 5, factor completely," above a handwritten polynomial equation in the midst being solved. a woman works through the problem using a screen in front of her.

Split screen. The left is a white background with an algebra equation being worked out in long form in blue. Given F, X equals 6, X minus 4, Find F, 1. To the right, a woman works through the problem using a screen in front of her.

Aerial side view of a computer screen displaying a math problem written and worked out in long form in blue. The problem at the top reads, "How did I get that?" Caption. When negative 2 is my input, 12 is my output.

Split screen. The left is a white background with an algebra equation is being worked out in long form in blue. To the right, a woman works through the problem using a screen in front of her.

Aerial side view of a computer screen displaying a math problem written and worked out in long form in blue. The problem at the top reads, "Example 1. Find the zeros of the quadratic function." Caption. I'll set both parts equal to 0, individually.

Split screen. The left is a white background with blue text that reads, "How did I get that?" followed by the algebra equation, 9, X, sup 5, Y minus 4, X sup 3, plus X squared. To the right, a woman works through the problem using a screen in front of her.

Split screen. The left is a white background with blue text that reads, "Example 3. The bill at the restaurant was split evenly 4 ways." Handwriting below reads, B is to Bill. To the right, a woman works through the problem using a screen in front of her.

Split screen. The left is a white background with a solved math equation with division and exponents. To the right, a woman works through the problem using a screen in front of her. Caption. I could represent this as X to the 3 minus 5.

White background with blue text that reads, "Example 1, simplify. 5 sup 3 to the power of 10. Multiply exponents." Caption. So 3 times 10, that's 30.

Blue handwriting working out a math problem in long form on a white background. The equation reads, open parentheses 5, B cubed times C closed parentheses, squared.

$White background with blue writing showing how to solve the math equation 7 over 2 to the power of 3 using fractions. Caption. That means that 7 halves to the third power.$

Split screen. The left is a white background with blue text that reads, "Simplify the following expressions," followed by 2 math equations. X sup 11 times X sup 5. And, 5 sup 8 times 5 sup 20. Answer buttons are next to each equation. To the right, a woman works through the problem using a screen in front of her. Caption. Work through these problems.

Aerial side view of 2 hands touching a computer screen displaying an algebra problem written in blue. Text above the equation reads, "Find the Product" and the letters, F, O, I, L. Caption. Then the last term came from distributing the 3 to the 7.

Split screen. The left is a white background with blue text that reads, "Properties of Real Numbers. Let R, S, and T be real numbers." Beneath is a table with title fields labeled Property and Explanation. To the right, a woman works through the problem using a screen in front of her. Caption. Still keeps the equation equal and balanced.

Closeup of a large screen on top of a podium with a hand holding a pen writing numbers. Title on the screen reads, "Multiplication Property of Inequality. A equals 1, B equals 2, C equals 3." An if and then table appears below and reads, "If A is less than B and C is positive, then A, C is less than B, C."

White background with blue text that reads, "Properties of Real Numbers. Let R, S, and T be real numbers." Beneath is a table with title fields labeled, "Property, Addition, Multiplication." Caption. Now for multiplication.

$White background with blue text that reads, "Example 4, Simplify," above a math division problem with fractions and exponents written and worked out in long form. Caption. Just subtract my exponents.$

Split screen. The left is a white background with a partially visible math word problem written and worked out in blue handwriting below. To the right, a woman works through the problem using a screen in front of her. Caption. You really just need to pick one, one ordered pair.

Woman with dark hair in a bun wearing a green shirt stands at a podium in front of an illuminated blue and purple background. She holds a pen in her right hand while looking down at a screen in front of her.

Aerial side view of a hand using a stylus to work out a math problem on a computer screen. Text on screen reads, "Example 2. Write the numeric expression in its simplest radical form."

Split screen. The left is a white background with blue text that reads, "Solve for x. 3 times 2 over 3, X equals 4." To the right, a woman works through the problem using a screen in front of her. Caption. Put my multiplication symbol and a 3.

Aerial side view of 2 hands touching a computer screen displaying a white screen with a long form algebra problem written in blue. Caption. That's how we represent that solution.

Woman with dark hair wearing a gray shirt stand at a podium in front of an illuminated blue and purple background. She holds a pen in her right hand while looking down at a screen in front of her.

Aerial side view of 2 hands touching a computer screen displaying a math word problem involving tickets sold for a high school sporting event. Some parts of the problem are highlighted yellow.

Split screen. The left is a white background with a solved polynomial math equation in blue. To the right, a woman works through the problem using a screen in front of her. Caption. Let's look at this last one.

Split screen. The left is a white background with a chart with 2 rows and 3 columns labeled, "Verbal, Explanation, Example." The boxes are filled in with a combination of typed and handwritten text. To the right, a woman works through the problem using a screen in front of her.

White background with an X,Y axis with gray grid lines and a blue line sloping downward from left to write. Blue text in the top right reads, "Write the equation of the line." Caption. The Y intercept and count off that slope.

Computer generated image of a sphere composed of twisted interlocking tubes of various colors. Caption: Fractal research is changing fields such as biology.

Chunk of rock sitting partially submerged in water. Caption: Matter is anything that takes up space.

Two glasses with colored liquid in them. One glass has a person holding a cylindrical electronic device in the liquid. Caption: and check the parts per million of solutes.

Closeup of computer screen with text that reads, Problem Solving Plan. 1. Identify important information, 2. Plan a Strategy. 3. Solve the problem. Caption. We'll follow this plan for word-problem mysteries.