Mr Honner

What Hot Dogs Can Teach Us About Number Theory — Quanta Magazine

My latest column for Quanta Magazine was inspired by the true story of me being frustrated by a six-pack of hot dogs.

If you’ve ever had to buy hot dogs for a cookout, you might have found yourself solving a math problem involving least common multiples. Setting aside the age-old question of why hot dogs usually come in packs of 10 while buns come in packs of eight (you can read what the National Hot Dog and Sausage Council has to say about it here), let’s stick to the math that gets our hot dogs to match our buns. A simple solution is to buy eight packs of hot dogs and 10 packs of buns, but who needs 80 hot dogs? Can you buy fewer packs and still make the numbers match?

Trying to get hot dogs and buns to match up is a simple exercise in least common multiples, but it also opens to the door to more complicated math using the Chinese Remainder Theorem, a 2,000 year old algorithm for solving systems of congruences. Learn more by reading the article, which is freely available here.

By MrHonner, 4 yearsNovember 30, 2021 ago

Resources Teaching

Workshop — It’s All Linear Algebra

Tonight I’ll be running my workshop “It’s All Linear Algebra” for teachers at Math for America.

This workshop is designed to show teachers how the big ideas of linear algebra — linear combinations, vectors, systems, dependence — are present in all the courses in the middle school and high school curriculum. Making these connections can help enrich the teaching of these topics in earlier courses, create threads that connect ideas throughout the sequence, and preview what lies ahead in more advanced courses.

This workshop is based on my experience teaching linear algebra in high schools for the past 10 years. After a short break I’m teaching it again this year, and I’m having a blast revisiting the ideas with a fresh perspective.

Today in Linear Algebra two students were trying to show a pair of vectors were linearly dependent. One said “Maybe we can twist them and do the Gaussian thing”, which made me think I might have actually properly taught and contextualized row reduction for the first time ever.
— Patrick Honner (@MrHonner) October 5, 2021

I’ve been learning a lot this year and I’m excited to share my experiences, and some great math, with teachers in this workshop.

Teaching

Back in the Classroom — Week 3

Being back in person has reminded me of the power of names.

I’ve always made it a priority to immediately learn all my students’ names. At the beginning of my career I’d do it on the first day. Twenty years later it takes a little bit longer, but it still gets done quickly.

Much of teaching comes down to relationships, and the first step in building a relationship with a student is knowing their name. Not just reading it off a participant list, but really knowing it. Saying it sharply to get their attention, saying it solemnly to make a point, saying it proudly when attaching their name to a conjecture, saying it in the hall when you recognize them outside their usual corner of the room.

I was able to accomplish some of this last year during remote learning, but not with all of my students. And it took tremendous time and effort. After only a few weeks back in the classroom I’ve already built relationships that would not have been possible last year, because I’m able to look all my students in the eye every day and really learn their names.

Geometry Teaching Technology

Teaching Triangle Angle Sum

The Triangle Angle Sum Theorem is one of my favorite topics in Geometry class. It’s a foundational fact about triangles, and in geometry, every problem is a problem about triangles.

I love the standard proof of the theorem, where a line is constructed through a vertex that is parallel to the opposing side. It highlights the crucial role that parallel lines play in our conception of geometry, and it points to the assumptions we make about them as well. With a little nudge, this standard proof is eminently discoverable, and makes for a great classroom activity.

But I also love showing students some non-standard proofs of the theorem. Here’s a demonstration I built in Geogebra meant to mimic a paper folding activity that shows how the angles of a triangle form a straight line.

You should do it with actual paper, too! Here’s a short video. Stick around for the bonus tearing at the end!

Apart from being fun and surprising, what I like about these demonstrations is how they illuminate something important and essential about result: It’s the straight line, not the number 180, that’s important. Plus, the tearing activity works with more than just triangles! Unfortunately it’s not so adaptable to spherical geometry, but that’s another lesson.

Appreciation Numbers

10/22/2021 — Happy Permutation Day!

Today we celebrate a Permutation Day! I call days like today permutation days because the digits of the day and the month can be rearranged to form the year, as seen in the above animation.

What Hot Dogs Can Teach Us About Number Theory — Quanta Magazine

Workshop — It’s All Linear Algebra

Back in the Classroom — Week 3

Teaching Triangle Angle Sum

10/22/2021 — Happy Permutation Day!

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