Overview

Here is a flowchart showing the story of area-thinking throughout the upper curriculum. Combine this with the story of Exploding Dots and WHOA, what a profound student experience of mathematics (especially with the spectacular collision of the two stories in high school polynomial work)!

These notes are written for educators wanting to look back over the 6-12 curriculum. Actual classroom materials for students based on these notes will be developed by an eager community folk and will soon populate the site too.

For superb guidance on the supporting K-5 piece, see the work of  (specifically, Geri Lorway’s PDF ), and we’ll have the whole adult and student experiences covered. WHOA again!

Lessons

 1.0 The AREA MODEL in Arithmetic and Algebra 1.1 Let’s be clear: What do we mean by AREA? 1.2 The Long Multiplication Algorithm: Its woes and new ease. 1.3 Expanding Brackets with Ease 1.4 An Aside on Negative Numbers: PILES AND HOLES 1.5 Why is NEGATIVE TIMES NEGATIVE POSITIVE? 1.6 An aside on Finger Multiplication 1.7 A Brief Discussion on FRACTIONS 1.8 Multiplying Mixed Numbers; Multiplying Decimals 1.9 An Aside on TAPE DIAGRAMS
 2.0 The AREA MODEL and Polynomials 2.1 Have you Noticed their Names? 2.2 Multiplying Polynomials 2.3 Doing it Backwards: Dividing Polynomials 2.4 Don’t Forget: $$x$$ can actually be a number! 2.5 (OPTIONAL) Dealing with Remainders 2.6 The Remainder Theorem/Factor Theorem 2.7 A Comment on Synthetic Division: AVOID IT! 2.8 EXTRA: The Binomial Theorem
 3.0 The AREA MODEL and Quadratics 3.1 Why the name “Quadratic”? 3.2 Level 0 and Level 1 Quadratics (and a taste of Level 2) 3.3 Level 2, Level 3, and Level 4 Quadratics 3.4 Level 5 Quadratics = All of Them! 3.5 (OPTIONAL) The Quadratic Formula 3.6 A Comment on Factoring Quadratics
 4.0 The AREA MODEL and Probability 4.1 What we Like to Believe about Probability 4.2 Garden Paths 4.3 Does “and” mean multiply? 4.4 The Geometric Series Formula 4.5 A Historic Problem 4.6 The Infamous Boy-Boy Paradox 4.7 EXTRA: Pushing Infinite Examples Further – Part 1 4.8 EXTRA: Pushing Infinite Examples Further – Part 2
 5.0 LIBRARY of Classroom Resources developed by Teachers 5.1 Classroom Resources

Books

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

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Guides & Solutions

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

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