### Some of the topics covered in the Math Explorations class

at Eleanor roosevelt Community Learning Center

Choosing the Class’s Favorite Dessert (i.e. voting systems)

How do you decide what a *group* wants?

Finding the Sum of the Angles of Polygons

What is the sum of the angles of a 33-sided polygon?

Equilateral triangles, Regular Hexagons, Dodecagons, and Flowers

Use a compass to lay out geometric figures and artistic patterns.

Learning to use a Chinese Abacus for Adding and Subtracting

(See abacus tutorial and online virtual abacus)

Knots / Shoe Tying

Have you ever looked at the knot that results if you pull out the bows?

(Learn to tie a square knot bow and a surgeon’s knot bow.)

Treasure Hunt

Hunt for treasure with a map and compass.

So You Want to Be a Billionaire?

Visualizing big numbers.

On Beyond Billions

Writing and computing with numbers of *any* size.

Solar System Walk

Getting the sizes and distances right.

Construct Squares, Parallelograms, Rhombuses, and Parallel and Perpendicular Lines

Find more than one way to construct a square

Cut out Paper Dolls

How about alternating skirts and pants? How about a ring of paper dolls?

Perspective Drawing: I

1-Point Perspective

Perspective Drawing: II

2-Point Perspective

Real-world Perspective

Finding vanishing points in photographs

Isometric Drawing

Do quick sketches of 3-dimensional objects.

3-D Photography

Have fun using twice as much film on your vacations (or break down and get a digital camera)!

3-D Drawing

You can draw stereo pairs in 3-D if you know the principle.

3-D Videos

Regular camera + neutral density filter = 3-D video

Permutations

How many ways can you ABCDEFG?

20 Guesses

Think of any word in the dictionary. Learn to guess it in under 20 guesses.

Binomial Distribution

If you toss five coins together, what is the probability of getting 1 tail and 4 heads?

Dice Probabilities

Why do 7’s come up more often than 12’s when rolling a pair of dice?

Population Growth Simulation

Why does population growth keep getting faster and faster?

Radioactive Half-lives

Why not just talk about whole lives?

Real Lives Simulation

The *Real Lives* simulation game is driven by real-life statistics and has spinoffs for students in understanding data, graph reading, and probabilities.

Adding Up

What is the sum of all the numbers from 1 to 1000?

Film Break

*Donald in Mathmagic Land*

Fibonacci Numbers

How many spirals are there in sunflowers and pine cones?

Fibonacci Rectangles & The Golden Rectangle

Perfection and approximate perfection.

Model Polyhedra

Fold Models of the Platonic Solids

Constructing Pentagrams

Golden Rectangles and 5-Pointed Stars with Compass and Straightedge

Cat’s Cradle

String figures and How to Make Them

Mathematical Origami

Fold Equilateral Triangles, Hexagons, and Pentagons

Ellipse with String and Pins

Really cool curves!

Ellipse, Parabola, and Hyperbola by Paper Folding

Cooler still.

Phases of the Moon

What causes the phases of the moon?

Constructing the Phases of the Moon

What will the moon look like 3 days after first quarter?

Twisted Geometry

One-sided surfaces and their children

Making Small Jobs out of Big Ones

How to draw complex pictures easily and lay out murals.

Photomosaics

Create your portrait using your vacation pictures

Funhouse Mirrors

Distorted picture + distorted mirror = undistorted image!

Deriving the Distortion

How to lay out the grid for the funhouse mirror activity.

Through the Looking Glass

Why mirror images aren’t “on” the mirror.

Raise Your Right Hand

Are images in mirrors always mirror images? Why left-right reversed? Why not up-down reversed?

Right-Right vs. Left-Left

What two people inhabit your body?

How Tall Does a Full-Length Mirror Need To Be?

Less than you think!

Where Do They All Come From?

How many images will you see in mirrors forming a 45° or 60° wedge?

Amazing Mazes

Working out maze strategies

Maze Creation

Weave your own mazes

Sudoku

It’s not the numbers–it’s the logic

Rectified Globe

Model the earth under your feet

Sun Dials

Sun dials can be simple (and approximate) or complex (and accurate)

Times and Seasons

You can better understand the motions of the earth, moon, and sun, by acting them out