Part of the Series: The Power of Mathematical Visualization

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 a straightforward way to convert repeating decimals to fractions using the dots-and-boxes method? Of course there is!

Running Time

32 mins

Year

2016

Kanopy ID

2681795

Features

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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 operation in any base system--including decimal, binary, ternary, and even fractional bases.

Arithmetic

The 8 videos in this collection focus on all aspects of Arithmetic, from fractions to percentages and ratios.

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 repeat? Prove that a famous irrational number, the square root of two, can't possibly be a fraction.

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.

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 take up no space at all! And this is just the start of the weirdness.

Algebra

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

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.

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 polygons of the same area, you can dissect one into pieces that can be rearranged to form the other.

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 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 strategy and the factorial operation to make combinatorics questions a piece of cake.

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 to find the line of best fit on a graph.

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.

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