Math Circle Activity Database
In teams, participants will create body movements related to geometry facts and will use their body to create a convincing argument as to why the statement is true. Please bring your fun-meter, your creativity, your body, and open physical space (for moving) to this session.
Place our numbers into the cauldrons in ascending order – you can choose which cauldron each one goes in. However, if two numbers in one cauldron add up to a third number in that same cauldron, they bubble up and cause an explosion! This means that all the numbers, leave the cauldrons, and you must start all over again.
Our goal is to find the largest number we can place in our cauldrons without them exploding… do you think you’re up for this daunting task?
What do adding positive and negative fractions have to do with tying knots? In this entertaining lesson, students will use ropes to explore and identify mathematical operations that untangle knots and lead to new thinking. Simple operations of twists and rotations circle back to practicing the addition of positive and negative fractions.
A teacher challenges students to a game. The rules are explained as the game progresses. The player with the highest total wins! Students then play against each other. Afterwards, while analyzing the game, prime, composite, perfect, deficient, and abundant numbers are discovered and defined. Students again play the game using the strategies they determined.
In a professional development video, teachers focus on the topic of number systems and number theory using a game setting to investigate the properties of prime, composite, abundant, deficient, and perfect numbers. This video can be used in conjunction with The Factor Game lesson plan.
The Pancake Problem, first posed in 1975, is a sorting problem with connections to computer science and DNA rearrangements, which leads to discussions of algorithms, sequences, and the usefulness of approximations and bounds.
The original problem was first posed by mathematician Jacob Goodman under the pen name “Harry Dweighter” (read it quickly) in 1975, and it has delighted math enthusiasts (including undergraduate Bill Gates) ever since!
Imagine you’re packing for a trip, and you’re planning on bringing your favorite tie. It’s too long to fit in your suitcase, even after folding it in half. You would fold it into fourths, but you don’t want all of those creases ruining your tie. You’ve decided folding it into thirds will be the perfect length to fit in your suitcase without noticeable creases on your tie. However, you don’t have a ruler or any means of making sure your tie is folded into perfect thirds. Is there anything you can do about this?
Merriam Webster defines gerrymandering as “the practice of dividing or arranging a territorial unit into election districts in a way that gives one political party an unfair advantage in elections.” This activity tries to make sense of that definition using a few examples.
“When I grew up in the Soviet Union, all we used for math was grid paper. Grid paper leads to discovery.” This is how Tatiana Shubin, San Jose State University, begins her lesson demonstrating the myriad of wonderful math questions arising from a simple sheet of grid paper. Attempting to count all squares of any size on a limited grid will require participants to persevere, organize their thinking and construct viable arguments.
A town faces an epidemic of zombies! Luckily, the virus has just started to spread and the infected are able to stave off their hunger for human brains… for now. In fact, they’re willing to work alongside the remaining humans to help them get across a river to safety. Can you get all the humans and zombies across safely?
Your regular commute begins at your house and ends at your office at the corner of 5th street and 6th avenue. You have been making this trip for years, but you are the restless (or adventurous) type, and you try to take a different route each day. At some point, you start to wonder how long it will take you to try all of the routes.
Oh, did I mention that you have to avoid the zombies?
Is it possible to measure all possible integer lengths on a ruler without marking every integer on that ruler? This is an engaging and challenging problem for all. Beautiful mathematics can be revealed while delving deeper into this seemingly easy question.
For the Math Mind Reading Trick, you’ll need a volunteer who’s willing to have their mind read. The person performing the trick holds out the four cards and askes their volunteer to pick a number (whole numbers only, no fractions allowed!) between 1 and 15 and keep it a secret. Next, the mind-reader asks the volunteer if their number is on the cards one-by-one. The volunteer answers the questions with yes or no answers, and with some magic and a little math, the mind-reader figures out their number!
You’re Mondrian’s mathematical boss. Instead of allowing Mondrian to randomly draw rectangles and colors -you lay out requirements: 1) Mondrian must cover an N by N canvas entirely with rectangles. 2) Every rectangle in the painting must have different dimensions. 3) Mondrian must use as few colors as possible, and rectangles with the same color cannot touch one another.
Under these rules, Mondrian must try to minimize his score. A painting’s score is the area of its largest rectangle minus the area of its smallest rectangle.
Gambling casinos are there to make money, so in almost every instance, the games you can bet on will, in the long run, make money for the casino. However, to make people gamble, it is to the casino’s advantage to make the bets appear to be “fair bets,” or even advantageous to the gambler. Similarly, “sucker bets” are propositions that look advantageous to one person but are really biased in favor of the other. We’ll examine what is meant by a fair or biased bet and look in detail at some casino games and sucker bets. Various problems can be...
Triangles and Squares live together in neighborhoods. However, the Polygons all believe two things: “I am unhappy if fewer than 1/3 of my immediate neighbors are like me.” and “I am unhappy if I have no immediate neighbors.”
Students will explore a game between two players moving a chess Queen from place to place on a square grid. The Queen may move any number of spaces to the left, any number of spaces downward, and any number of spaces on the downward-left pointing diagonal. Each player takes turns using these moves. Whoever gets the Queen to the bottom-left square first wins!
Skyscrapers come in so many different sizes! Sometimes you can’t see small skyscrapers if tall ones are in front of them. Using clues about how many skyscrapers you can see from each side you look at them, can you figure out the layout of the entire city?
Each puzzle is a rectangle made up completely of smaller squares. These squares have numbers inside that represents the length of their sides. Just knowing a few of the squares side lengths, can you figure out all the size of all the squares in the puzzle?
Developed as part of the Math Circles of Inquiry project, this session is a good introduction to the 8th grade or Algebra Math curriculum using inquiry based instruction. Students are asked to use their problem solving skills in order to determine the relationship between the number of Supreme Court justices and handshakes that occur when each pair shakes hands exactly once. Students will begin exploring with simpler numbers and work up to creating an algebraic expression to represent the function. This lesson allows for multiple representations by using a table, list, circle diagram, matrix and manipulatives.
SET is a fun game that can be enjoyed by kids as young as 6 and is challenging even for adults. It is rich in counting problems and is great for getting people to pose problems. It is also an example of a finite geometry and interesting to explore how well one’s geometric intuition works.
The game of Tic-Tac-Toe has roots going back centuries. Grid-style game boards have been found in Ancient Egypt, during the Roman Empire, and in our current age on restaurant placemats. Multiple avenues of exploration are possible with this simple children’s game. A related game called “Gobblet Gobblers” takes Tic-Tac-Toe to a whole new level!
In 2005, while researching the expected value for lottery tickets in various states, a group of MIT students won millions of dollars in the Massachusetts $2 Cash Winfall drawing. Do you want to know how they did it? This teacher led activity starts with a lottery, explores expected value, and finally ties into finite projective geometries.
The rules are simple: you want to place the sheep on the board so that the wolves can’t eat them. A wolf can eat a sheep if it has a direct path to it – or is in same row, column, or diagonal as that sheep. Can you place all your wolves and sheep on an nxn grid so all the sheep are safe?