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Math Teachers' Circle at CSUDH Meetings
The CSUDH Math Teacher Circle will meet the first Tuesday of each month during the 2023-2024 academic year.
All meetings are from 5:30 - 8:00 pm. Please check back for the format of meetings. We are excited to offer in-person meetings this academic year!
2024-2025 Meetings
9/3/24 "Making the Most of Things"
If you studied mathematics in college and you hear the word “optimization,” you probably immediately think about calculus and taking derivatives. But optimization questions — making quantities as big as possible or as small as possible — don’t always require such heavy machinery. And asking about the biggest, smallest, best, or worst case can turn an everyday problem into a more open-ended exploration. We’ll tackle lots of optimization problems, none of which require any calculus to solve.
10/1/24 "Is Fair Voting Possible?"
In the U.S., many elections use a system called plurality voting, where the candidate with the most votes wins. While this might sound simple, it can lead to situations where the winner doesn't actually have the support of the majority of voters. It also tends to make it harder for candidates outside the two major parties to have a real shot. But are there better ways to vote? In this session, we'll take a look at some alternatives to plurality voting and use mathematics to explore whether any of these voting methods offer a fairer way to run elections.
11/12/24 "Spot It!"
The rules of Spot it! are simple: match a symbol on your card to a symbol on a card drawn from the top of the deck. Could this simple children’s game give rise to interesting mathematics? Is there a deeper structure to this game? In this session, we will discover how the Spot it! game is constructed and explore some of the mathematics involved.
Click here for the flyer. Click here to register.
12/3/24 "Duck Duck Deduce!"
In this session we’ll explore SMP 3: Constructing viable arguments and critiquing the reasoning of others by playing two games. First, we’ll see if we can determine where to sit to be the last one remaining in a version of Duck Duck Goose. Then we’ll play the Eleusis card game, where we’ll deduce hidden rules through logical reasoning. Both games offer rich opportunities to foster logical thinking and collaborative reasoning, skills crucial in the math classroom. Come ready to think, strategize, and share insights on how to inspire mathematical curiosity and critical reasoning among students!
Click here for the flyer. Click here to register.
2/4/25 "TBD"
3/4/25 "TBD"
5/6/25 "TBD"
Archive of 2023-2024 Meetings
9/5/23 "What is Random?"
What is random? How do graphs help us answer questions about probability? In this session, we explore a variety of probability questions. We will see how graphs can be used to answer questions of probability, and how probability can arise. We will also see that our interpretation of what it means to be random can lead to surprising contradictions!
10/3/23 "Mathematical Magic for Muggles"
Learn how the simplest of mathematical ideas, like "an odd plus an odd is even" and "x + -x = 0" can help us to craft magic tricks that seemingly bestow superhuman powers on us. No skill required!
11/7/23 "Pancake Sorting and Recursion"
Have you ever wondered how and where mathematics and computer programming overlap? In this session, we will see that one example of the overlap comes in a very surprising place: pancakes. We will be exploring ideas related to sorting and recursion, and use them to flip our flapjacks into a nicely ordered stack.
12/5/23 "The Mathematics of Secret Santa"
Have you ever been part of a Secret Santa gift exchange? Did anyone ever draw their own name and have to re-draw? How often does that happen? What happens as the size of the group of participants grows? In this Math Teacher Circle, we look at the mathematics of these exchanges, called derangements. A derangement is a one-way assignment of each person in a group to another person. As the group grows bigger, what happens may surprise you.
2/6/24 "Four Game Night"
Come and play not just 1 but 4 games/activities:
- The Child and the Witch
- The Game of Nim
- The Fox and the Rabbit
- The Rook Game
As you experience the games, we will explore questions such as: Is there more than one productive perspective or approach to solve the game? What are some possible variations or generalizations of the game? See problem-solving strategies and make new mathematical connections!
3/5/24 "Rational Tangle Dance"
What is the "Rational Tangle Dance"? It's a blend of physical fun and intellectual group challenge. Devised by the renowned mathematician John H. Conway in 1967, it's a delightful way to explore the fascinating world of knot theory!
Here's the gist: You'll be part of a team of five. Four team members each hold one end of a rope, resulting in two lengths of rope between them. Your task? Create and then solve a "tangle" - a series of twists and turns that form intricate patterns. The fifth member plays a crucial role as the observer, guiding and strategizing the untangling process.
The Rational Tangle Dance is a fantastic way to engage with mathematical concepts in a fun, interactive setting. Come ready to think, collaborate, and maybe get a little twisted up in the process!
5/7/24 "Trust"
Let’s play a cooperative game and use math to learn about how trust works. What happens when little things about cooperating games change? Join us to play a couple of games and reflect about ways that math can help us to model and reason about fairness and trust.
Archive of 2022-2023 Meetings
9/7/22 "Tricolor Triangle Puzzles"
In this session we will explore tricolor triangle puzzles. In a tricolor triangle puzzle, a triangular shaped hexagonal grid is to be colored using three colors so that each group of three hexagons meeting at a point all have a different color or all three are the same color. How many such puzzles can we create? How many hexagons would need to be filled in so that there is a unique solution? Are there other versions of this puzzle we could explore? What other puzzling questions can we ask and answer? Come have fun with some colorful puzzles and learn how they connect to ideas from geometry, algebra, and combinatorics!
10/4/22 "Apples, Cups and JRMF"
Daniel Klein, Executive Director of the Julia Robinson Mathematics Festival (JRMF) will lead us in exploring some fun mathematics that is suitable for students in grades 4-12, and will explain what the JRMF is and how you can get involved! In this session, we will be exploring the following two activities:
Apple picking is a two-player game similar to Nim. Can you find a winning strategy? Can you extend your ideas to tackle new and progressively more challenging games?
Cup stacking is a puzzle where you stack cups using specific rules. You will practice creating procedures from experimentation, using mathematical structure like symmetries to create arguments, and generalizing your ideas to puzzles involving more cups.
11/1/22 "More Sprinkles"
How many ways are there to order an ice cream sundae if you can choose up to two toppings? How does this number change if there are more toppings to choose from? What if you want more toppings? In this session, we will explore these problems and find some surprising connections to a variety of other contexts.
2/7/23 "A Perfect Ruler"
What is a “perfect” ruler? Is it possible to measure all possible integer lengths on a ruler without marking every integer on that ruler? Come see if you measure up to what it takes to make a “perfect” ruler.
3/7/23 "Skyscrapers, Flowers & JRMF"
Daniel Klein, Executive Director of the Julia Robinson Mathematics Festival (JRMF) will lead us in exploring some fun mathematics that is suitable for students in grades 4-12. In this session, we will be exploring the following two activities:
Skyscrapers is a game where you place skyscraper towers on a grid where the heights of the skyscrapers matter for each row and column of the grid. Can you find a strategy that works for the different puzzles?
Magic Flowers is a puzzle where you arrange numbers on five flower petals in a way that the numbers in a line share a special relationship. Can you rearrange your numbers and find other solutions? You will use patterns and make generalizations to construct other magic flowers with more petals or that use different sets of numbers.
4/4/23 "Taxicab Geometry"
What is the distance between two points? How do different methods of measuring this distance affect geometric shapes? Usually, we measure distance as the length of the line segement drawn between two points. If you are in a city, this metric is more helpful if you are a pigeon! As a human, in order to determine the distance between two points, it makes more sense to consider the walking or driving distance along existing streets. In this session we will explore this new definition of distance by examining objects such as bisectors and circles to see how they function in Taxicab Geometry.
5/2/23 "Number Bracelets"
Choose any two numbers and apply a simple rule to get the next number, then repeat. What patterns can we find in the numbers generated by this rule? Will this sequence go on forever? How do different starting numbers change the sequence? What other rules can you come up with? Come explore these questions with us in our last Math Teachers’ Circle of the academic year.
Archive of 2021-2022 Meetings
9/7/21 Virtual "Number Puzzles"
Have you ever played Sudoku? What about other number games? Did you wish there was more math involved? In this session, you will learn about Hidato, Kakuro, and Minesweeper, three other number puzzles. See what strategies you can learn! Learn fun new ways to practice your logic and arithmetic skills! Find out which one of these has a connection to one of the million-dollar Clay Mathematics Institute prizes in mathematics!
10/5/21 "What Color Is My Hat?"
Imagine that you are being held captive in a dungeon by an evil mathematician with a number of other prisoners, and suppose that every prisoner is given a red or green hat (chosen at random). Your captor will allow you and all the other prisoners to go free if every prisoner successfully guesses his or her own hat color, but if even one person guesses incorrectly then the lot of you will be fed to a hungry dragon*. Are there strategies that will increase your chances of success? If we find a strategy, how can we be sure it is a good one? How does the number of prisoners affect our chances? In this session, we will explore variations on this problem and see what we can learn about probability along the way.
2/1/22 Virtual "I Walk the Line(s)"
Imagine that you live in the city of Cartesia whose streets lie on the lines of a square grid. How can you move around in such a city? How many ways are there for you to move from one point to another? How can you account for obstacles you might encounter as you are moving around the city? In this session, we will explore this situation, uncover what deeper mathematics lies behind it, and discover connections to other seemingly unrelated problems.
3/1/22 Bubbling Cauldrons
It’s the end of your first year at Pigwarts and you are stuck in Professor Snipe’s Potions exam. He has given you multiple cauldrons and you are tasked to see how many ingredients you can place in them before they bubble over. If they bubble over, you have start again. Just when you think you’ve passed the exam, he adds more cauldrons. What now? Can you still pass the exam?
Archive of 2020-2021 Meetings
9/1/20 "Examining Stop and Frisk"
What is stop and frisk? How was it applied differently to different communities? In this session, we continue our series on using mathematics to understand issues of social justice by examining data to understand the impact of stop and frisk as it was (and to some extent, still is) used in New York City. We will also discuss the role of mathematics in understanding social issues, and ways that we can take actions that will have a positive impact.
10/6/20 "Tools for Promoting Racial and Gender Equity in Mathematics Classrooms"
This session focuses on our work as mathematics teachers and how we can promote racial and gender justice in our classrooms. We will begin with a discussion of systemic oppression and biases, and how they can negatively impact our classrooms unless we explicitly address them. As an antidote, we will consider what it means for us as educators to show up authentically as our whole selves in a way that engages and empowers our students. Finally, we will focus on specific instructional moves that can be used to promote greater equity in our classroom activities.
11/3/20 "Cryptography: Secure Data Transmission"
How can you have a code that is almost unbreakable, even though the method of coding is public? Welcome to the world of public key cryptography and the RSA algorithm, a method that uses some number theory to encode data. This is the method used for secure data transmission, for such things as making purchases via credit card over the internet.
Have your students ever complained about how hard it is to factor? Find out why they were right! Learn how the system works, but don't expect it to help you steal any credit card information!
12/1/20 "Prejudiced Polygons"
In 2016, we looked at a game to consider the dynamics of a Polygon neighborhood (based on Hart and Case, 2014). In the neighborhood, Polygons preferred having neighbors who were like them. Triangles enjoyed having other Triangles as neighbors, and Squares enjoyed having other Squares as neighbors. At the time, we used the activity as an exploration in fractions and an opportunity to start talking about social issues. Now in 2020, we consider version 2.0. We will examine a different perspective with a newly-zoned Polygon neighborhood, and we will discuss real-world implications including how seemingly unbiased behaviors can lead to biased outcomes that reproduce social inequalities, and some actions we can take to address these issues in our own lives and communities. Experience with version 1.0 is not necessary for participation. All are welcome!
2/2/21 "Slaying the Mathematical Hydra"
You may be familiar with the Greek mythical animal they hydra. According to this legend, whenever you cut off one head, two more grow back! How is it possible to defeat such a monster? In this session, we will explore a mathematical version of this myth, where heads will grow back in a very specific way. Is it possible to kill these hydra? Are there some hydra that can’t be killed? Is there an optimum strategy for killing the hydra? You might have something to teach Heracles after this session.
3/2/21 "Operating on Numbers"
In school, we may first learn multiplication as a new operation built from addition, and exponents are built from multiplication. What if we wanted to make new operations by combining standard operations? What properties might these new operations have? Do these properties lead us to similar formulas to those for addition or multiplication? We will investigate these ideas and along the way learn about symmetry and functions of more than one variable!
5/4/21 "Square Wars"
A long time ago (1795) in a galaxy (okay, island) far, far away (England), someone patented the first graph paper. In this session, we will investigate the infinite space created by graph (or grid) paper. How many squares are on a given grid? What are interesting sets of points that can be found on a grid? A simple sheet of graph paper is fertile ground for generating questions that lead to the combinatorial reasoning, finite arithmetic series, algebraic identities, and the Pythagorean Theorem.
Archive of 2019-2020 Meetings
9/3/19 "Bulgarian Solitaire"
Come learn to play Bulgarian Solitaire, a fun example of a dynamical system. Given a fixed number of beads arranged into piles, and some rules for rearranging them, will there eventually be a stable configuration of the beads, or will it cycle through different arrangements? How many arrangements are there, and how do we sort them? Made famous by Martin Gardner in the 1980’s, mathematicians have come up with numerous conjectures and proofs related to this system. Come see what has fascinated others for more than 30 years!
10/1/19 "Risk in the Stock Market"
Are there good reasons to buy stocks or other assets with negative returns? Why is diversification in the stock market important? In this session, we will use probability, statistics, and some simulation to explore these questions and see why blindly buying high-return stocks (and associated high volatility) can be catastrophic for a portfolio. We might also just learn something about the dot-com bust and the financial crisis!
11/5/19 "Multiplication Madness"
Does 3 x 4 have to be 12? Are there other ways we can multiply numbers? Do the resulting multiplication tables have any interesting properties? In this session, we find out that the answer to the first question is no! We will explore multiplications defined by looking at the intersections of lines, counting rectangles, and hosting dinner parties, and learn what these three constructions have in common.
12/3/19 "Harmonic Numbers"
Harmonic numbers get their name because they arise as ratios of musical tones. What numbers can you make as differences of harmonic numbers? How do you know when a difference cannot be made? How can we use harmonic numbers to understand the long-standing, as-yet unsolved, abc conjecture? In this session, we will learn about harmonic numbers, use them to understand the abc conjecture, and perhaps even meet up with Euler's largest lucky number!
2/4/20 "Euler and Hamilton: Two Travelers"
What do Mathematicians Euler and Hamilton have in common? It turns out more than you might realize, as they both considered questions about travelers: Can a traveler travel every road? How can a traveler visit every destination efficiently? In this session we will investigate several real world problems and the graph theory spawned by these problems.
3/3/20 "Nearest Neighbor: Voronoi Diagrams"
Have you ever wondered how Netflix is able to suggest shows or movies that you actually like? What about selecting the best location for your next business? Are you interested in creating wonderful patterns for your next DIY project? Come and learn about Voronoi Diagrams and see how this beautiful geometry can resolve these questions.
4/7/20 "Cryptography: Secure Data Transmission" ***POSTPONED***
5/5/20 "Partition Like Piet (Virtual Session)"
Piet Mondrian (1872-1944) was an artist whose work involved rectangles of different colors. Inspired by this work, mathematicians have created a set of puzzles in which the objective is to cut a square into a set of rectangles, and you earn a score based on the difference in area between the largest and smallest rectangles. What is the best score you can get? Is there a pattern or an algorithm for creating a best score? Do these puzzles have any practical implications? We will try to answer help you answer all of these questions from the comfort (or craziness) of home in our session.
Archive of 2018-2019 Meetings
9/4/18 "What I Learned About Sharing Long After Kindergarten"
Have you ever tried sharing a dessert, like a birthday cake, with someone, and wondered how to share it fairly? What happens when you have a batch of cookies to share, some with nuts and some without--how can you share them fairly? What if you are dividing up a number of items between two people, say a jewelry collection, where the items cannot be broken apart? What does it mean to share fairly?
10/2/18 "Winning the Lottery"
The lottery: many will play, few will win. Have you ever played? Did you ever think about looking for a winning strategy? Would you expect to win the same amount every time you win? Is there a way to use geometry to understand the lottery? In this session, we consider all of these questions and will come up with a winning strategy!
11/6/18 "Blokus and Polyominoes"
Have you ever played Tetris and wondered if there could be other shapes? Or have you thought of Dominoes as geometric tiles? These are both games involving polyominoes. In this session we will investigate a different polyomino game - Blokus. Blokus is a 2 - 4 player game involving polyominoes, geometry, and tiling. Come and play and see what math we can discover in this game!
12/4/18 "Factoring in Time for Numeracy"
Have you been looking for a fresh math game you can use in class? Have you ever wondered how you can build numeracy (or number fluency) in a fun, interesting, and exciting way? Come see how playing Prime Climb can help! Prime Climb is a game of luck and strategy that can help build strong number fluency.
2/5/19 "Match or No Match"
In this session, we will explore the Match-No Match game: two players each draw one chip out of a bag – if the color of the chips match Player 1 wins, if not Player 2 wins. Is this a fair game? How do we know? How can we construct a fair game? What variations of this game are possible? How does this connect to other mathematics? Come and see how much mathematics can arise from a bag of chips!
3/5/19 "Symmetry and Algebra"
How can we relate ideas from geometry to those from algebra? There are many ways! If we look at a regular polygon, we can see various symmetries. How do these symmetries connect to algebra? In this session, we will explore the symmetries of a variety of shapes and ways to "operate" on the shapes to create “multiplication tables” that demonstrate an interesting underlying structure with properties from algebra.
5/7/19 "Getting Nim-ble with Binary"
Nim is a game played with counters arranged in piles. Each player takes turns removing counters according to certain rules, and the last player to take a counter wins. Is there a guaranteed winning strategy? Are some starting positions better or worse than others? What happens if we vary the game rules a bit? Come and see the surprising depth and connections between this game and the larger world of mathematics.
Archive of 2017-2018 Meetings
9/5/17 "Simon Says, Four Gallons"
Given a 5 gallon jug and a 3 gallon jug, is it possible to measure out exactly 4 gallons? That's the problem faced by John McClane and Zeus Carver in Die Hard 3. In this session, we'll not only solve this problem, but we will also look at questions such as: Is there a shorter way to do this other than trial and error? How can we use geometry to solve this problem? How is this kind of problem connected to number theory?
10/3/17 "Estimathon"
How many airline passengers are there in a year? How many miles long is the Mississippi River? In this session, we will play a game called Estimathon, where the questions involve giving a range in which you think the correct answer lies. You and your team will have to select your ranges carefully to maximize your score in the game. We will also look at how to use what we learn from one estimate to make estimates of related values and explore estimation tasks you can use with your students. Come and hone your skills at estimation!
11/7/2017 "Candy Sharing"
In this session we will play a game called Candy Sharing. Can you create a game that results in an infinite loop? Can you predict how long the game will last? When is the game over before it begins? In this session, we will investigate these and other questions and see the mathematics of dynamical systems in action. Come get a taste of candy sharing--the sweetest math!
12/5/2017 "Is Santa Secretly Deranged?"
Have you ever been part of a Secret Santa gift exchange? Did anyone ever draw their own name and have to re-draw? How often does that happen? What happens as the size of the group of participants grows? In this Math Teacher Circle, we look at the mathematics of these exchanges, called derangements. A derangement is a one-way assignment of each person in a group to another person. As the group grows bigger, what happens may surprise you.
2/6/2018 "Pick Connects the Dots"
When it comes to measuring the area of a simple polygon all you have to do is take out a measuring tape and your area formula, right? But what do you do if your simple polygon is not so simple? Is there some way to find the area without measuring all the edges? In this Math Teacher Circle, we take a look at how the connect the dots grid game helps us calculate the area of any simple polygon. Pick’s Theorem will help us do the rest.
3/6/2018 "The Game of Hex"
In this session, we will investigate the game of Hex - a two player “grid” game that seems to always have a winner. Does Hex really always have a winner? Can you discover a winning strategy? Or can your opponent always keep you from winning, as in Tic-Tac-Toe? Come and see what you can find out.
4/3/2018 "Length Spectrum of Numbers"
This session begins with the question, ‘Which natural numbers can be written as sums of (more than one) consecutive natural number’?
Note that a number may be written as such a sum in more than one way, e.g. 9 = 4+5 = 2+3+4. We call the collection of the lengths of these sums the length spectrum of the number, so the lspec(9) = {1,2,3}. In this session we will explore some natural questions that one may ask about these spectra. Along the way, we will have some fun in playing a guessing game. Be prepared for some surprises!
5/1/2018 "Knot Mosaics"
Knot theory is an area of mathematics concerned with, well, knots, loops of string crossed over and around each other in different ways. How can you tell two knots apart, or if two knots are really the same? This is the core of knot theory. In 2008, a new perspective on this theory, knot mosaics, took hold. These mosaics enable a knot to be represented using tiles. In this session, we explore basics of knots and questions such as, What tiles are required to make knot mosaics? How can knots created using mosaics be classified? Come and get tangled up in learning some new mathematics!
Archive of 2016-2017 Meetings
See the links below for more information about each session.
9/6/16 “Pancake Sorting and Recursion”
Have you ever wondered how and where mathematics and computer programming overlap? In this session, we will see that one example of the overlap comes in a very surprising place: pancakes. We will be exploring ideas related to sorting and recursion, and use them to flip our flapjacks into a nicely ordered stack.
10/4/16 "Rational Tangle Dance"
In 1967, mathematician John H. Conway presented seminal results on the classification of knots through a study of “rational tangles.” In order to explain some of the key ideas behind the theory, he developed an activity, the “rational tangle dance,” that four people holding the ends of two lengths of rope, and a fifth person looking on, can perform. The magic of this activity has captivated many over the decades, and the rational tangle dance is now considered a favorite in many math circle groups.
Description by James Tanton
11/1/16 "The Mad Veterinarian: The Mathematics of Mad Science”
In this session, we will explore a situation from science fiction, in which a scientist can transform one animal into others. What mad configurations are possible with an initial set of animals? When can we undo the transformations and get the original animals back? More importantly, what kind of mathematical structures are involved? We will examine these questions and the underlying mathematics involved. White lab coat not required!
12/6/16 "Pirates, Prisoners and Chicken: An Introduction to Game Theory"
How should a pirate share the loot with fellow cutthroats? Should two captured prisoners each confess to a lesser crime? Did President Kennedy play Chicken with Russia? In this session, we will explore answers to these questions. We will see how these three life-or-death situations are part of a larger mathematical landscape known as game theory, and discuss how game theory can be used in an array of situations to decide on a course of action.
2/7/17 "SET: The Mathematics Behind the Game"
Set is a fascinating card game developed by Marsha Falco in 1974. The rules specify how certain groups of three cards can be formed to make a "SET". While the rules are fairly straightforward, beneath the surface lurks some deep mathematics. The game leads to questions such as: "How many cards do you need to guarantee a SET?", "How many SETs are possible?", "How is this game like doing geometry?" In this session, we will learn and play SET, and explore some answers to these questions.
3/7/17 "KenKen"
Invented by Japanese math teacher Tetsuya Miyamoto, KenKen is a popular puzzle that enables the player to exercise arithmetic skills as well as logical thinking. In this session, we will learn about KenKen and solve some KenKen puzzles, from beginner level on up, and then look at the math behind the math. You will even get to create your own KenKen puzzle!4/4/17 "Liar's Bingo"
Do Bingo cards have patterns? Can you lie about what’s on your card and get away with it? Do mathematicians know something special about how to find the truth? In this session, you get to put your tall-tale skills to the test. In the process, we will learn some of the mathematics of information transmission, and how to use mathematics to find the truth.
5/2/17 "Spot-It!"
The rules of Spot it are simple: match a symbol on your card to a symbol on a card drawn from the top of the deck. Could this simple children’s game give rise to interesting mathematics? Is there a deeper structure to this game? In this session, we will discover how the Spot it! game is constructed and explore some of the mathematics involved.
