SET is a card game that inspires many mathematical questions from players of all levels—from primary students to research mathematicians. Mathematical ideas in SET include counting and combinatorics, probability, geometry, modular arithmetic, vectors, and linear algebra. The book 'The Joy of SET' is a very accessible deep dive into many of these topics. I've outlined … Continue reading Connecting SET with geometry
Category: puzzles
Skyscrapers
This is a quick post mainly for the benefit of my 'Developing Mathematical Thinking' (#math1070) students. Introducing the puzzle Skyscrapers are one of my favourite logic puzzles. They are a Japanese creation, introduced at the first World Puzzle Championship1 in 1992. Skyscrapers are a type of Latin Square puzzle. A Latin Square in an n × n … Continue reading Skyscrapers
#NoticeWonder and Rational Tangles
Yesterday we held the first of this year's Maths Experience days. We invite students in Years 10 and 11 from different schools onto campus for an intensive one-day program. Students find out about mathematical research, talk to professionals who use mathematics in their careers in some way, and participate in hands-on mathematics workshops. Importantly, they also meet and connect with other students … Continue reading #NoticeWonder and Rational Tangles
Tangling and untangling
This is the seventh in a series of posts about my course ‘Developing Mathematical Thinking’, a maths content elective for pre-service teachers training in primary and middle maths. All posts in the series are here. WARNING: It's a long post. Edited to fix the confusion between × (multiply) and x (the letter). I have been itching to try Conway's Rational Tangles … Continue reading Tangling and untangling
How many triangles?
It's been quiet on the blog, but a lot has been happening. University classes in Adelaide have just resumed after a two week mid-semester break. To warm up, I gave my MATH 1070 students the following problem. I found it via Tanya Khovanova who states that it was an entrance problem for the 2016 MIT PRIMES STEP Program. (Read more on Tanya's … Continue reading How many triangles?
Counting in unexpected ways
It was a delight to recently spend five days working with students and teachers in Alice Springs at the invitation of MTANT, the Mathematics Teachers Association of the Northern Territory. I then spent a week in bed with the flu, which is one reason I've recently lost my voice (both physically and online). The main purpose of the visit was to join … Continue reading Counting in unexpected ways
Another party puzzle
More party puzzles! This one is from a thoroughly-recommended book, Puzzle Based Learning1. Mr and Mrs Smith invited four other couples for a party. When everyone arrived, some of the people in the room shook hands with some of the others. Of course, nobody shook hands with their spouse or themselves, and nobody shook hands with … Continue reading Another party puzzle
Ramsey’s party problem
I love games that require no special equipment because they can be played at a moment's notice. This is one of my favourite pen-and-paper games. It is played on the complete graph K6. In other words, a board with six dots where each dot is connected to every other dot by a line. Although the game-board can … Continue reading Ramsey’s party problem
Fold-and-cut
Whenever I say this, the unfinished sentence in my head is 'Fold-and-cut, baby! Fold-and-cut.' I am totally weird. The fold-and-cut theorem states states that any shape with straight sides can be cut from a single sheet of paper by folding it flat, possibly with many folds, and making a single straight complete cut. I have been impatiently waiting to try this … Continue reading Fold-and-cut
K to 2, to infinity
Okay, so 'infinity' might be a bit of a stretch but I'm talking about the latest low-threshold, high-ceiling task to become my favourite puzzle1. Louise Hodgson shared this activity at the Mathematics Association of Tasmania conference at the weekend. The learning intention, as might be voiced to students, was: "There are patterns in the hundreds chart and the patterns can help us answer questions … Continue reading K to 2, to infinity
