World-renowned math educator Dr. James Tanton shows you how to think visually in mathematics, solving problems in arithmetic, algebra, geometry, probability, and other fields with the help of imaginative graphics that he designed. Also featured are his fun do-it-yourself projects using poker chips, marbles, paper, and other props, designed to give you many eureka moments of mathematical insight.

Running Time

747 mins

Nb videos

24 videos included

Kanopy ID

2681777

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The Power of a Mathematical Picture

Professor Tanton reminisces about his childhood home, where the pattern on the ceiling tiles inspired his career in mathematics. He unlocks the mystery of those tiles, demonstrating the power of…

Visualizing Negative Numbers

Negative numbers are often confusing, especially negative parenthetical expressions in algebra problems. Discover a simple visual model that makes it easy to keep track of what's negative and what's not,…

Visualizing Ratio Word Problems

Word problems. Does that phrase strike fear into your heart? Relax with Professor Tanton's tips on cutting through the confusing details about groups and objects, particularly when ratios and proportions…

Visualizing Extraordinary Ways to Multiply

Consider the oddity of the long-multiplication algorithm most of us learned in school. Discover a completely new way to multiply that is graphical--and just as strange! Then analyze how these…

Visualizing Area Formulas

Never memorize an area formula again after you see these simple visual proofs for computing areas of rectangles, parallelograms, triangles, polygons in general, and circles. Then prove that for two…

The Power of Place Value

Probe the computational miracle of place value--where a digit's position in a number determines its value. Use this powerful idea to create a dots-and-boxes machine capable of performing any arithmetical…

Pushing Long Division to New Heights

Put your dots-and-boxes machine to work solving long-division problems, making them easy while shedding light on the rationale behind the confusing long-division algorithm taught in school. Then watch how the…

Pushing Long Division to Infinity

"If there is something in life you want, then just make it happen!" Following this advice, learn to solve polynomial division problems that have negative terms. Use your new strategy…

Visualizing Decimals

Expand into the realm of decimals by probing the connection between decimals and fractions, focusing on decimals that repeat. Can they all be expressed as fractions? If so, is there…

Pushing the Picture of Fractions

Delve into irrational numbers--those that can't be expressed as the ratio of two whole numbers (i.e., as fractions) and therefore don't repeat. But how can we be sure they don't…

Visualizing Mathematical Infinities

Ponder a question posed by mathematician Georg Cantor: what makes two sets the same size? Start by matching the infinite counting numbers with other infinite sets, proving they're the same…

Surprise! The Fractions Take Up No Space

Drawing on the bizarre conclusions from the previous lecture, reach even more peculiar results by mapping all of the fractions (i.e., rational numbers) onto the number line, discovering that they…

Visualizing Probability

Probability problems can be confusing as you try to decide what to multiply and what to divide. But visual models come to the rescue, letting you solve a series of…

Visualizing Combinatorics: Art of Counting

Combinatorics deals with counting combinations of things. Discover that many such problems are really one problem: how many ways are there to arrange the letters in a word? Use this…

Visualizing Pascal's Triangle

Keep playing with the approach from the previous lecture, applying it to algebra problems, counting paths in a grid, and Pascal's triangle. Then explore some of the beautiful patterns in…

Visualizing Random Movement, Orderly Effect

Discover that Pascal's triangle encodes the behavior of random walks, which are randomly taken steps characteristic of the particles in diffusing gases and other random phenomena. Focus on the inevitability…

Visualizing Orderly Movement, Random Effect

Start with a simulation called Langton's ant, which follows simple rules that produce seemingly chaotic results. Then watch how repeated folds in a strip of paper lead to the famous…

Visualizing the Fibonacci Numbers

Learn how a rabbit-breeding question in the 13th century led to the celebrated Fibonacci numbers. Investigate the properties of this sequence by focusing on the single picture that explains it…

The Visuals of Graphs

Inspired by a question about the Fibonacci numbers, probe the power of graphs. First, experiment with scatter plots. Then see how plotting data is like graphing functions in algebra. Use…

Symmetry: Revitalizing Quadratics Graphing

Throw away the quadratic formula you learned in algebra class. Instead, use the power of symmetry to graph quadratic functions with surprising ease. Try a succession of increasingly scary-looking quadratic…

Symmetry: Revitalizing Quadratics Algebra

Learn why quadratic equations have "quad" in their name, even though they don't involve anything to the 4th power. Then try increasingly challenging examples, finding the solutions by sketching a…

Visualizing Balance Points in Statistics

Venture into statistics to see how Archimedes' law of the lever lets you calculate data averages on a scatter plot. Also discover how to use the method of least squares…

Visualizing Fixed Points

One sheet of paper lying directly atop another has all its points aligned with the bottom sheet. But what if the top sheet is crumpled? Do any of its points…

Bringing Visual Mathematics Together

By repeatedly folding a sheet of paper using a simple pattern, you bring together many of the ideas from previous lectures. Finish the course with a challenge question that reinterprets…

Visualizing Ratio Word Problems

Word problems. Does that phrase strike fear into your heart? Relax with Professor Tanton's tips on cutting through the confusing details about groups and objects, particularly when ratios and proportions are involved. Your handy visual devices include blocks, paper strips, and poker chips.

Symmetry: Revitalizing Quadratics Graphing

Throw away the quadratic formula you learned in algebra class. Instead, use the power of symmetry to graph quadratic functions with surprising ease. Try a succession of increasingly scary-looking quadratic problems. Then see something totally magical not to be found in textbooks.

Math Series 1

A math series designed for grades 7th to 9th to help students learn and understand math concepts.

Algebra

The 18 videos in this collection focus on all aspects of Algebra, from logarithms to quadratic equations and partial fractions.

The Power of a Mathematical Picture

Professor Tanton reminisces about his childhood home, where the pattern on the ceiling tiles inspired his career in mathematics. He unlocks the mystery of those tiles, demonstrating the power of visual thinking. Then he shows how similar patterns hold the key to astounding feats of mental calculation.

Visualizing Probability

Probability problems can be confusing as you try to decide what to multiply and what to divide. But visual models come to the rescue, letting you solve a series of riddles involving coins, dice, medical tests, and the granddaddy of probability problems that was posed to French mathematician Blaise Pascal…

Visualizing Pascal's Triangle

Keep playing with the approach from the previous lecture, applying it to algebra problems, counting paths in a grid, and Pascal's triangle. Then explore some of the beautiful patterns in Pascal's triangle, including its connection to the powers of eleven and the binomial theorem.

The Visuals of Graphs

Inspired by a question about the Fibonacci numbers, probe the power of graphs. First, experiment with scatter plots. Then see how plotting data is like graphing functions in algebra. Use graphs to prove the fixed-point theorem and answer the Fibonacci question that opened the lecture.

Visualizing Negative Numbers

Negative numbers are often confusing, especially negative parenthetical expressions in algebra problems. Discover a simple visual model that makes it easy to keep track of what's negative and what's not, allowing you to tackle long strings of negatives and positives--with parentheses galore.

Pushing Long Division to New Heights

Put your dots-and-boxes machine to work solving long-division problems, making them easy while shedding light on the rationale behind the confusing long-division algorithm taught in school. Then watch how the machine quickly handles scary-looking division problems in polynomial algebra.

Symmetry: Revitalizing Quadratics Algebra

Learn why quadratic equations have "quad" in their name, even though they don't involve anything to the 4th power. Then try increasingly challenging examples, finding the solutions by sketching a square. Finally, derive the quadratic formula, which you've been using all along without realizing it.

Health Science, for Middle School

Specifically designed for and correlated to the curriulum of a middle school science course, this collection contains a number of video series that explore Healthy Living and help instructors to teach challenging concepts. The films, and accompanying teacher materials, are a great asset for teachers and teachers in training to…

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