Overview

The world of science is about collecting data and understanding the patterns in the numbers we see. So let’s begin our course with this core practice of science: understanding patterns in sequences of numbers! Although not a part of the standard curriculum, this work motivates our work on quadratics (and beyond). It also motivated the great Galileo in his study of projectile motion, often considered the prime appearance of quadratics in nature. This part 1 of the course reveals and explains all.

Part 2 explores the symmetry of squares making the algebra of quadratics ridiculously natural and easy. And part 3 shows the extreme advantage of having symmetry at hand when graphing. All you need is common sense and all is obvious! (You’ll go whoa!)

We then finish all the standard content (and more) with continued absolute ease.

Lessons

 1.0 Getting Started – Playing With Numbers 1.1 Sequences… For When You Believe in Patterns 1.2 Sequences – Getting Formulas 1.3 Can We Trust Patterns? 1.4 Galileo’s Discovery 1.5 Galileo’s Mistake
 2.0 The Algebra of Quadratics 2.1 Why the name “Quadratic”? 2.2 Level Zero and Level One Quadratics 2.3 Level Two, Three and Four Quadratics 2.4 Level 5 Quadratics – and VICTORY!
 3.0 (OPTIONAL) The General Quadratic Formula; Imaginary Solutions; Cubics? 3.1 (OPTIONAL) The General Quadratic Formula 3.2 (OPTIONAL) An Aside on Imaginary Solutions 3.3 (OPTIONAL) The CUBIC formula, the QUARTIC formula, and BEYOND!
 4.0 Graphing Quadratics – The Natural Way 4.1 Messing with the Basic Graph 4.2 A Steepness Factor 4.3 A Necessary Piece of Theory 4.4 Common Sense Graphing – The Power of Symmetry 4.5 Some Traditional Textbook Questions 4.6 More Traditional Textbook Questions
 5.0 Fitting Quadratics to Data 5.1 Just do it! 5.2 Some Typical Textbook Questions 5.3 (OPTIONAL) Finding Quadratics with Specific Zeros
 6.0 Quadratics in Nature 6.1 Projectiles 6.2 Light Cones 6.3 Folding Paper, Equidistance, and Reflections
 7.0 Things Missing from the Course that might Surprise Educators 7.1 The Discriminant 7.2 Properties of the Quadratic Formula 7.3 Calculator Use 7.4 Factoring

Books

Take your understanding to the next level with easy to understand books by James Tanton.

BROWSE BOOKS

Guides & Solutions

Dive deeper into key topics through detailed, easy to follow guides and solution sets.

BROWSE GUIDES