Former MEGL Director of Outreach Speaking about Outreach at a Recent Activity

What are some different ways to sort shapes? How can we fit shapes together to cover an entire area? And how should we color that area of shapes? In this activity, students will investigate Polygons, Tilings and Coloring Theorems in a very hands-on way.

Prerequisites:

- Knowledge of what shapes are
- Knowledge of Straight vs. Curvy
- (optional) experience with shape classification

Topics covered:

- Shape classification
- Polygons vs. non-polygons
- Types of polygons
- Regularity of a polygon

- Tilings
- Which regular polygons tile
- Mention of angles being important

- Colorings
- The 4 Color Theorem

Main takeaway: **Serious mathematicians play with shapes.**

Created by Martha Hartt

The students learn about prime numbers, the “atoms” of the counting numbers. They arrange glass beads into rectangular arrays and then decompose them, while drawing a “number tree” to keep track of their work. When they’re finished they create paper plate Monsters that represent the prime number decomposition of their original number. Then they try to decode each others’ Monsters to figure out what numbers they represent. This activity is inspired by a book (with the same title) by Richard Schwartz.

Prerequisites:

- Familiarity with whole numbers
- Familiarity with Rectangles
- (Optional) Some exposure to Prime Numbers
- Ability to multiply single digit numbers
- (Recommended) Previous experience with number classification of some sort
- Familiarity with basic patterns (odd and even numbers)

Topics covered:

- Prime vs. Composite (Rectangle) Number classification
- Pattern recognition
- Factor trees
- Multiplication of prime factors to get original numbers

Main takeaway: **Prime numbers are the building blocks of all whole numbers**.

Created by Sean Lawton

A 1×1 square has area 1. A 2×2 square has area 4. Can we make a square with area 2? Students begin to make sense of irrational numbers by engaging in a variety of activities that showcase all the places they pop up in our lives. After drawing the elusive square of area 2, students discover the role that pi has while throwing straws at a felt wall in a live simulation of Buffon’s Needle. They then learn about nature’s affinity for a particular irrational ratio and create their own Fibonacci spiral.

Prerequisites

- Very familiar with fractions, capable of adding/multiplying them
- Very familiar with decimals, capable of adding/multiplying them
- Exposure to fraction/decimal conversion
- Have good number sense
- (Optional) Have heard of pi and perimeter of a circle
- (Optional) Knowledge of square roots
- Familiarity with basic shapes: Square and its area, drawing circles.

Topics covered:

- Representing numbers as fractions
- Whole numbers
- Terminating decimals
- Non-terminating decimals

- How to represent numbers that cannot be represented as fractions:
- Square root of 2 (using squares)
- Pi (using circles)
- The golden ratio (using spirals)

Main takeaway: **Not all numbers can be neatly represented using symbols we’re familiar with.**

Created by Aidan Donahue, Susan Tarabulsi, Martha Hartt, Harry Bray, and Lujain Nsair

How big is REALLY big? How can we imagine numbers like a Googol, which has 100 zeros? What about numbers that make a Googol seem tiny? How far up do numbers go? This activity is designed for elementary school students. By stepping through different orders of magnitude, using hands-on activities along the way, students gain an intuition for the sheer magnitude of the real numbers. This activity is inspired by a book (with the same title) by Richard Schwartz.

Prerequisite:

- Familiarity with whole numbers
- Familiarity with addition and multiplications
- (optional) Familiarity with growth
- (optional) Familiarity with functions

Topics covered:

- Growth rates:
- Linear
- Polynomial
- Exponential

Main takeaway: **Numbers can be really big.**

Created by Sean Lawton and Jack Love

It stands on its own but also is a great sequel to Really Big Numbers. Students use a variety of interactive puzzles and games, and activities to explore the strange world of the infinite. What is infinity plus one? Are there different sizes of infinity? Join us to find out! This activity is inspired by a book by Richard Schwartz (titled Gallery of the Infinite).

Prerequisites:

- Decent number sense
- (Optional) Experience with input/output machines

Topics covered:

- Definition of finite and countably infinite
- Input/output machines
- Arithmetic involving infinity
- Different types of infinity

Main takeaway: **Infinity works differently from regular numbers**

Created by Sean Lawton, Jack Love, and Anton Lukyanenko

Students will gain a firmer understanding of how computers work by investigating search algorithms. They will then learn about the difference between classical algorithms and quantum algorithms and get to explore the idea of superposition by playing a familiar game.

Prerequisites:

- Basic Knowledge of Computers
- Knowledge of “Input/Output” Machine
- Basic Knowledge of Probabilities
- Basic knowledge of Measurement

Topics covered:

- Black boxes
- Algorithms
- Searching Algorithms
- Quantum Physics

Main takeaway: **Quantum Computing takes advantage of tiny particles to do things quicker than regular computers.**

Created by Martha Hartt

Is there more to math than numbers? Can we “multiply” things that aren’t numbers? How about the motions (or, symmetries) of a snowflake? What does a symmetry multiplication table look like, and what can it tell us about the motions a snowflake makes as it falls? How are snowflake symmetries the same as numbers? How are they different? In this activity students create their own paper snowflakes and experiment with them to explore these questions. Along the way we discover beauty hiding just beneath the surface, and find there is more to math than we thought!

Created by Sean Lawton

The students learn what they’ve been taught in school isn’t necessarily the truth! They experience simple mathematical “facts” being turned on their heads by changing the context in which they appear. Through kinesthetic activities and manipulatives including balloons and special clocks, they see that 2+2 isn’t always 4, that triangles aren’t what they thought they were, that some squares have negative area, and that it is possible to divide by 0.

Prerequisites:

- Activity 1:
- Basic Number Sense
- Familiarity with whole numbers and simple addition
- Familiarity with time

- Activity 2:
- Familiarity with squares and area formula
- (Optional) familiarity with complex numbers
- Familiarity with basic arithmetic

- Activity 3:
- Knowledge that there are 180 degrees in a triangle

- Knowledge of right angles

Topics covered:

- Activity 1:
- Regular arithmetic
- Modular arithmetic

- Activity 2:
- Imaginary numbers, defined directly as sqare root of -1
- How to visualize multiplication by i

- Activity 3:
- Non-Euclidean geometries (spherical)

- Activity 4:
- Mobius strips have only 1 side

Main takeaway: **All mathematical statements depend heavily on context.**

Created by Sean Lawton

We first teach participants about the “Cinderella” of geometry–the least appreciated and most beautiful. We then teach participants how to crochet so they can make their own exotic shapes in yarn. This activity is inspired by a book by Daina Taimina .

Created by Sean Lawton

**Ask Us About:**

- Follow-up lesson plans for all activities for interested teachers/students.

- Training for Geometry Labs and other interested mathematicians to reproduce MEGL outreach in your location.