The Astounding Power of Area

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 Geri Lorway (specifically, Geri Lorway’s PDF ), and we’ll have the whole adult and student experiences covered. WHOA again!

A1

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Lessons

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

Resources

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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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