“Math Explorations” Bonus Section.

The school where I taught the last nine years before retirement was Eleanor Roosevelt Community Learning Center, a charter school working with homeschool families. The most popular course I taught there I called “Math Explorations” (for younger students) and explained it as “Stuff that doesn’t look like math.” More recently I spent a few months as a volunteer in the Schoolhouse Teacher program, doing an online column that looked somewhat like Math Explorations, except it was for high school students. A part of each of my “lessons” was a series of videos on some topic, going beyond what is taught in regular school classes. Hopefully the videos and other material collected here will inspire you to think mathematically about the world we live in.

Learning the Multiplication and Division Combinations Once and for All

The Grandpa Project

This is a collection of tutorial videos reviewing basic arithmetic skills literally produced for my grandchildren.  They are targeted for upper elementary and middle school students not yet ready for Algebra 1.  I am releasing these as public domain.  Use them to learn or review basic arithmetic skills, with a little extra.

Schoolhouse Teacher Videos

The videos I developed in connection with the Schoolhouse Teacher project can be found in a playlist on the YouTube Math Without Borders channel called “Lessons of Interest on Assorted Topics”. There are quite a few videos, so rather than embedding them all here, see them on YouTube.

Solving a Maze

The Pi Series

A playlist of three videos introducing Pi and taking it to different levels

Introduction to the Pythagorean Theorem

Simplified Simulation of the Phases of the Moon

Simulation of the Motions of the Sun and the Moon in the sky

The Gravitational Slingshot Effect

Constructing a Regular Pentagon with Origami

The Joys of RPN

(Make Your Calculator an Extension of your Brain)

Using Free42

I used Calc98 as the onscreen calculator for my math courses, but since then I have since discovered another (better) option for obtaining an RPN calculator.  Free42 is an open source project emulating an HP 42s calculator, even better than an HP 35s mentioned in the previous video!  You can download it as an “app” for your iPhone or Android, as well as your computer, whether Windows, Mac, or Linux. A manual for it is available here.

Multiplying Positive and Negative Numbers

How to Subtract Without Ever Having to Borrow

Adding Fractions

Tying Your Shoes: Square Knot Bow

Yes, tying your shoes is mathematics too!

Tying Your Shoes: Surgeon’s Knot Bow

Yes, even you can learn something new!

Mathematics of the Rainbow

This is a bonus section from the Calculus course. It involves a little physics, a tiny bit of calculus, and a lot of algebra and geometry. It is a
great example of how mathematics can help us understand the natural world.

About The Math Without Borders, Inc., “Golden Logo”

Disney’s Donald in Mathmagic Land

A classic of educational video from 1959 that ties mathematics to music, art, nature, and games. IMHO, the best educational feature Disney ever made! It is frequently available on YouTube for a short time before being removed. Rather than this cat and mouse approach, I recommend the DVD, which is typically available very inexpensively.

The Ultimate Area Formula

Have you ever wondered how surveyors measure the “acreage” of parcels of land? Some years ago I found a method in a surveyor’s handbook for finding the area of any polygon that I had not seen in math textbooks. It is very simple and it is completely rigorous (i.e. it is not an approximation). I included this method in the supplementary materials for my HSC Geometry program. (I also did a series of videos for the Schoolhouse Teacher site on area, culminating in the Surveyor’s Formula.)