After studying James Tanton’s MTC session about bicycle tracks, avid bicyclist Michael Nakamaye started questioning the mathematics behind how a bike works.
How do gears work? How many teeth are there usually on the different gears? Why? How is a bike like a ratio machine?
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.
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?
A Mad Veterinarian has created three animal transmogrifying machines…
While grappling with the posed questions, players will explore a set of problems, figuring out how and if the machines can complete a given transformation. Connections can be made to invariants, abstract algebra, graph theory, and Leavitt path algebra.
Cryptography is the study and practice of secure communication, making it an interesting and relevant application. In addition to number theory concepts like modular arithmetic, this session uses locks, codes, and ciphers to explore functions (definition, inverse functions, linear functions).
Using the standard arithmetic operations (addition, subtraction, multiplication, division and exponentiation), what is the largest number you can make using three copies of the digit “9”? While this would be a pretty large number, with a little cleverness you can do far better. This session explores VERY large numbers!
“Using just that 5 pint jug and that there 12 pint jug, measure me 1 pint of water!” Is this possible with just the two jugs? What about a 7 pint jug and 17 pint jug? Or p pint and q pint jugs?
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?
What shapes can result from the following fold-and-cut process?
Take a piece of paper.
Fold it flat.
Make one complete straight cut.
Unfold the pieces.
Are all shapes possible?
Students will explore existing equity themed murals to identify themes, and the mathematics necessary to plan/create a city mural. Students will utilize Google maps tools to begin connecting Mathematical representations to precisely interpret circle properties and apply them to the mural design.
What if we graphed with parallel axes instead of perpendicular ones? This intriguing transformation exchanges points and lines; replacing points being on the same line, with lines passing through the same point. By changing the way we usually graph functions, new patterns and deeper understandings can emerge.
There are many card tricks based on simple mathematics as opposed to sleight of hand. In this session, participants will play with a number of such tricks, test them out and work on discovering the math underneath, with a goal to formalize the mathematics that makes the trick work.
Are there more fractions than counting numbers? Surprisingly, an investigation into binary notation can help us answer this question! This session explores the binary number system. Participants will investigate Hyperbinary numbers, create a Fraction Tree, and discover connections between them.
How can mathematics help us understand the phenomenon of a pandemic? What factors impact the spread of a disease like Covid-19? Which of these factors can we influence? (society, in schools) How can mathematics help us act during a pandemic toward better outcomes?
What is the three-dimensional shape inside the classic Mattel Magic 8-Ball toy? This hands-on activity explores the intriguing fact that there are only five different types of Platonic solids, whereas there are infinitely many regular polygons.
This session is also suitable for student math circles or the classroom.
Mathematicians have long been fascinated by prime numbers and a great deal of number theory revolves around the study of primes. Develop a deeper understanding of these intriguing numbers by exploring the questions presented in this session.
Kenken is a puzzle whose solution requires a combination of logic and simple arithmetic skills. The puzzles range in difficulty from very simple to incredibly difficult. Students who get hooked on the puzzle will be forced to drill their simple addition, subtraction, multiplication and division facts.
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.
Counting problems can involve the counting of combinations, permutations, factorials, pathways using Pascal’s Triangle, partitions and complements, and many more. In this lesson many different types of counting problems (some easy and some harder) were given to groups of teachers to solve in whatever way they preferred.
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.
A simplex lock is a type of combination door lock that involves pushing-in buttons. Given the set of rules for using a 5-button simplex lock, how many different combinations are there?
Dutch artist M. C. Escher is well known for his amazing prints of interlocking lizards, fish transforming into birds, and angels and devils intertwined, just to name a few. His intricate tilings offer a beautiful and engaging way to explore ideas related to geometric transformations and symmetries.
