Two Boxes in a Circle
The March MathsJam had an interesting geometry puzzle.
Archives
2026
New Beginnings
I’m back
2023
Trig identity Three Ways (at least)
This post starts with reading elsewhere about someone struggling with the following trig identity given a triangle with three angles x, y, z show: $$ \tan{x}...
2022
Mastodon: The Wild Wild Neolithic West
Its been a long while since my last social media post: how-i-use-twitter and everything is all of a sudden in huge flux. With all the turmoil on Twitter I’...
Unexpected Binomial Theorem Connection
Source: @ElyemGercek
Properly fitting Problems
What motivated this essay was two posts I recently saw. The first started with the idea that no student should take more than five minutes on a problem. If…
Carnival of Mathematics 203
Graphic scores by John De Cesare (1890–1972).
15-75-90 on the quarter circle
I just saw a nice visual proof of the ratios for the 15-75-90 on the internet via @ilarrosac. This one works via symmetry and the Pythagorean theorem.
Two Circumcircles Walkthrough
I really enjoyed working through this problem from Stanley Rabinowitz I saw recently on Twitter. This was one of those problems where I circled around it a...
Ptolemy’s Theorem via a bit of Trig and similar triangles
Here’s a straightforward trigonometric proof of Ptolemy’s Theorem using scale factors and the Law of Cosines. First we start with a cyclic quadrilateral and…
Cyclic Quad Area Problem
What follows is a walkthrough of the problem above which I had a lot of fun playing around with. Most of the solutions I saw online used trigonometry and so…
2021
Linear Algebra Retrospective
Everything I discovered after doing the linear algebra section of PreCalc last year
AP PreCalculus?
I read a really interesting post by David Bressound on joining the advisory board for AP PreCalculus: link. The gist of which was despite misgivings he tho...
Sine Hunt
Sine HuntThis is a working post to collect problems themed around sine. It all started during the last MathJam when a few came up: Criteria: only sine and ...
Trig Cheat Sheet Project
A few months ago, I saw a thread about writing a trigonometry cheat sheet for someone studying Pre-Calculus. I decided that I wanted to do a visual version ...
Facilitating a Virtual Math Circle
This year I haven’t written much about how my Math Circle is doing. That doesn’t mean it hasn’t been running the whole time. My routines were shaken by ...
Carnival of Mathematics 193
Welcome
Pascal’s Determinant
Tamas Gorbe posted the preceding tweet a few days ago and it caught my attention for two reasons. First, I’ve been doing a lot of linear algebra recently…
3x3 Determinant
There are definitely more general and less messy ways to derive the 3x3 matrix determinant (breaking it apart using the linearity property and finding the ...
Roots of Unity Application
Show that $ \sin\left(\dfrac{\pi}{n}\right) \cdot \sin\left(\dfrac{2\pi}{n}\right) … \sin\left(\dfrac{(n-1)\pi}{n}\right) = \dfrac{n}{2^{n-1}} $...
2020
Pushing the limits
I’m still playing around with the ideas from going-one-step-beyond-herons-formula And this time I looked at a more complex problem. Overall the approach l...
More Heron’s Formula Extensions
Continuing on the theme from the last post: going-one-step-beyond-herons-formula here’s another problem showing the power of the full conceptual framework...
Going one step beyond Heron’s Formula
Above I’ve found the incenter of the triangle at the intersection of the angle bisectors and rewritten all segments lengths in terms of the semi-perimeter a...
11/3 Math in the time of Covid
It took nearly a month longer than normal but I finally have the virtual math club setup for the year and we met for the first time on Tuesday. Given the w...
Fantasy High School Part 4 PreCalc
I’ve been looking around at sample curriculum sequences due to odd seeming topics I’ve seen at home via the Pre-Calculus class my older son is taking, In t...
Arctan Addition Formulas are really Sin/Cos angle addition Formulas in Disguise
An observation from this weekend
Tilted Ellipse Problem Walkthrough
This problem from Matt Enlow is quite fun and as a bonus a chance to show off some geogebra formatting:
Trigonometric Pythagorean Relationships
Very short post today to illustrate something I’ve never considered before. Everyone usually has a diagram to illustrate the Pythagorean relationship on the...
Cool Geometry Problem Redux
Find the area of the big triangle. [Matt Enlow]
Ratios vs determinants
Today’s post regards a small conceptual improvement. It all started with the following problem which caused some trouble for the kids:
What I like about Algebra 2
I worry about Algebra 2 from time to time. Its the class that is mostly likely to be target for reform, usually complete replacement. But my older son is cu...
Pershan Geometry Walkthrough #2
This is the continuation of a series from First Post I’m following Michael along and capturing my problem solving process for comparison. To capture the pro...
Everything is Connected (yet again)
The other week I was checking out the geometric puzzles at https://sciencevsmagic.net/geo/ as part of a MathsJam evening. A small part of the process requir...
Walkthrough of Geometry Problem from Michael Pershan
This post is motivated by a conversation I had with Michael where I asked if he would be willing to document his problem solving process and if so I would d...
Approaching the Tangent
Preamble
15-75-90 Some interesting relations fall out
I’m going to do a small dive here on another 15-70-90 problem from @_eylem_99. Unlike normal I’m going to skip most of the problem solving process and inste...
Carnival of Math 181
Welcome
15-75-90 problem meets an old friend or two
The theme of this post is connections. We’re going to start with a problem that suggests another few I’ve talked about before and I promise a 15-75-90 connec...
Dot in a Box: Addendum
This is a continuation to my last post: dot-in-a-box
Dot in a Box
[@fleonsotelo]
3/9 Napier’s Bone (or the calm before the storm)
I’ve delayed writing about last week’s Math Club session up as life in the form of the covid19 pandemic has disruptingly intruded. By the end of last week w...
Combinatorics from a (social) distance
I just found yet another combinatoric link with Pascal’s Triangle that I never knew before and its both fairly intuitive and a source for something to do lat...
2/24 Moems #3
We spent another week catching up on MOEMS tests. This unfortunately doesn’t make for exciting write ups because I’m not supposed to directly discuss the que...
2/11 Quick Catchup
I’m a bit behind on my session logging so what follows is an abbreviated account.
Deep Dive on a Problem
Once again the Math Circle didn’t meet this time due to MLK Day rather than snow. In fact, next week, I have an offsite at work which is going to interfere ...
Another example of a problem that’s much harder one way
We had a snow day this Monday and so there was no Math Club. Instead, I’ve written a continuation in my series of posts on the curious way geometry problems ...
1/9 New Year Math
Another new year, another chance to do some math around it! I saved a group of posts off of twitter but ended up leaning the most on a post on Math Misery by...
2019
12/9 Closing out 2019 with a bang
I knew after last week I wanted to do a game this time around to balance things out but I wasn’t quite sure which one to pick. So I looked around a few sites…
Trig Angle Addition Two Ways
I’m really enjoying contrasting these two approach right now to deriving the since and cosine angle addition formulas. Just like in the normal pedagogy for t...
12/3 Geometry while Randomized
This week I had a bit of a change of heart while in the middle of my planning process. Originally I was attracted to a triangle inequality problem and start...
Tilted Parabolas (Or all the stuff they didn’t tell you in school about them)
“A rose by any other name would smell as sweet” W. Shakespeare
11/25 First MOEMS
(Half of the room that fit in my camera focus hard at work) Randomization (VRG) I once again moved the kids around into semi-random seating. Partly…
11/18 Connecting all the dots
Interestingly the teacher I share the room with mentioned that it was a hard day for her and I also had more trouble than I like getting everyone to listen t...
Cool walk through for geometric transforms
[Since its AMC 8 today - here’s a geometry walkthrough instead for the week]
11/4 YAPSMAD (Yet Another Platonic Solid Math Art Day)
Continuing the focus from last week, I decided to concentrate on getting everyone to ask more questions today in the Math Club. To that end, I started with ...
10/28 Halloween
Planning-wise my weekend was busier than expected so I decided to go with an easier to setup problem carnival structure for this week: roughly themed around ...
10/21 Sharing is Caring
The overarching personal theme for this week is I’m starting to feel more comfortable with the large size of the group. So far I’m able to keep things flow...
10/14 Radicals and other scallywags
There’s a lot to reflect upon after today. Going into the session I had 2 main goals:
Fooling Around
I came across the following interesting piece of Algebra in my son’s textbook. Solve for a and b $ \in \mathbb{R}$:
NWMC ‘19 Post Conference Thoughts
Once again, I went and spoke at the NWMC conference. This year it was conveniently located down in Tacoma. That meant, no hotel or extended travel. Instead ...
10/7 Once more into the breach
Math Club for this year is finally up and running. As I’ve alluded to before, there are 28 kids which is by far the largest group I’ve ever led. So I’ve be...
Heron’s Formula vs Trigonometry
This random pedagogical thought occurred to me today: Both Heron’s Formula and the Law of Cosines provide ways to find the area of a triangle with just its ...
Variance Formulas
I’ve been dabbling in Statistics to help my older son out who has encountered them for the first time in a Biology Class. As a result, an interesting observa...
Fantasy High School Part 3 (Statways)
I’m returning here to a perennial topic of mine: High School Curriculum Reform.
An Update on Setting Things Up
An Update on Setting Things Up I’ve stayed fairly on top of things this year. School started on Wed. The first PTSA newsletter went out with the Math…
Taking my shiny hammer and looking for nails
I was thinking some more about the Casus Irreducibilis and other weird forms of solutions derived from Cardano’s Method for cubics last night. (See: Last Pos...
Book Review: Some Applications of Geometric Thinking
This summer, I’ve been doing a fair amount of Mathematics reading from Strogatz’s “Infinite Powers” to the Intermediate Algebra textbook from AoPS. I also…
15-75-90 Alternate Forms
Its been a while since I’ve talked about one of my favorite triangles the 15-75-90. So here’s a short post on a new detail that I realized about them the oth...
Cardano’s Method
This all starts with a fantastic new video from Mathologer: 500 years of NOT teaching the cubic formula.
Seattle MathJam: Paper Folding in a Pub
Its been about a year since I last wrote about MathsJam: [seattle-mathjam-or-pints-and-polynomials]({% post_url 2018-08-29-seattle-mathjam-or-pints-and-polyn...
Summer ‘19: What did I do last summer?
Six years ago I really viewed many Mathematical topics as cut and dry. How hard can it be to learn everything there is to know about say Algebra I? Is the...
Only a Guest
Only a Guest
Angle Pairs
Visual proof that $ \angle{BCA} + \angle{DCE} = \pi / 4 $ or alternatively $ \arctan \left( \dfrac{u-v}{u+v} \right) + \arctan \left(\dfrac{v}{u}\right) = \p...
Regular Heptagon puzzle walk through
There are too many wildly different an interesting ways to attack this problem to not document.
2018-2019 Year In Review
This is a bit delayed but better late than never. My overall experience this year was definitely a continuation of last year: (See: 2018-year-in-review)
Sometimes one way is trickier than the other: angle bisectors
Here’s another example of one the most interesting parts of geometry for me. (courtesy of a mathjam participant last month) See: earlier post Given an isosc...
Pentagon + Quadrature of the Parabola
Last week, I saw this really fun parabola problem from @diegorattaggi and I became interested for two reasons:
6/21 Last Day
This post was a bit delayed by my chaotic schedule right. I’ve decided to dash it out now before the details fade too much more. As is traditional I brought…
6/10 Penultimate Session
The year is winding down and the weather is ramping up. We’re having a mini heat wave in Seattle and the room today was stuffy and warm today. My plan for ne...
Quadrature of the Parabola Proposition 2
I’ve been reading Steven Strogatz’s “Infinite Powers” recently and that briefly mentioned Archimedes’s use of limits and infinitesimals while calculating the...
6/3 Tesselations
I skipped blogging last week given a hectic schedule and the fact I had outlined my plan already here: 513-checkers-redux but I’m still thinking over one pa...
Langley’s Adventitious Angles
I’ve been working through “Geometry Revisited” and have come to a section of old chestnuts one of which was Langley’s Adventitous Angles.
Noticing and Wondering is for Everyone
One very common prompt seen online is “What do you notice and wonder?” I like the frame of mind it suggests and often use it or variants with the kids in Ma...
5/13 Checkers Redux
I have a lot of chess players in Math Club this year and partly based on that interest and partly because I happened on a James Grimes video I decided I want...
Euler Line Walkthrough
http://www.gogeometry.com/problem/p742-circumradius-orthocenter-centroid-midpoint-distance-square.htm
5/6 Purple Comet Day - VRG
Where we last left off: The Purple Comet math contest wasn’t well aligned this year with our schedule. It ran from Tue - Fri over a period of time that onl...
Roots of Unity: Pursuing Extra Roots
Background: This piece all started with my last post thinking about equalities of the form $ \cos (nx) = \cos(mx) $
Trigonometry Walk Through Three Ways
I saw the following trigonometry problem the other day and decided it would make another good walk through since it hits several themes I’ve been exploring.
4/29 Prepping for STEAM Night
Its crunch time this week getting ready for STEAM night, basically the Science Fair, on Wednesday. The kids had voted last week to ambitiously attempt three...
4/22 Some Experimenting with Math History
About 5 months ago we were asked to participate ion STEAM night (basically the Science Fair) and enough kids were interested that I agreed. We’re now about ...
4/15 We’ve found a correlation
This session was inspired by a twitter conversation I saw a few weeks back over a problem set @bowenkerins presented at a conference from PCMI.
Good Problem but Guessable
Last week as usual I scanned through the Purple Comet problems looking for interesting one this year. I’m usually drawn to geometry problems but this Algebr...
Spring Break - Geometry Walk Through
Note: with Spring I really have no kids. Even my own are with my parents so here’s an old walk through I had laying around. On reread after a significant ga...
4/1 I put a Hex on You
In the lead up to this week I had been debating whether to participate in the https://purplecomet.org/ contest. The start was a little too close to when we h...
Carnival of Mathematics 168
Turtles - Martin Holtham
3/25 Guest Lecture on Apportionment
As is now a 3 year running tradition today we had a guest lecturer from the WXML group at UW. This time Jonah Ostroff was kind enough to come a talk with the...
The curious case of the equilateral triangle and 3 concentric rings or the hidden angle bisector
Each of the vertices of an equilateral triangle lie on one of the three concentric circles with radii 1, 2 and 3. Find the length of the side of the equilat...
3/11 Parker Pi Day
I’ve been using Matt Parker’s videos on Pi day for several years now:
3/4 A series of interludes
As I previously mentioned I’ve been collecting a group of mathematical issues I want to discuss with the kids. So today rather than a large overarching them...
Let’s use the Angle Bisector Theorem extensions!
What is the ratio of the ellipse’s width to its height?#math #maths #mathchat #mathschat #nerdsniping #MTBoS #iteachmath pic.twitter.com/CGntV3U1f3 — Matt En...
Julia Robinson Festival
The Julia Robinson Festival is my favorite volunteer activity of the year. Here we’re setting up all the tables and just getting ready for ~500 kids from…
2/25 So Little Time
The theme for this week was definitely time pressure. After losing 2 weeks to snow days and another one to the mid-winter break I’m feeling behind. The most…
Triangle in a Square: Areas
So this happened today:
There’s more to the Angle Bisector Theorem
I just ran into a few very simple extensions of the angle bisector theorem which I’ve never noticed before. Since I couldn’t easily find this anywhere online...
1/28 MOEMS #3 and Posters
Scheduling has been tight very tight this winter. Because last Monday was off for MLK day, this is only our third session so far. The last two weeks were bo...
Trig Walk Throughs
I’m in the process of writing a bigger piece on the role of trig formulas but I was looking for an example of their use during a geometry proof and came to t...
1/14 Randomness
Going into today I wanted to do something interesting and non-competitive especially for the new kids who just joined. I have MOEMS test I need to do in the...
Reexamining the Law of Sines
I’ve been working my way through Geometry Revisited over the last few days and so far I’m really happy with the purchase.
1/8 Semi Prime kind of Life
Everyone’s finally back from Winter Break and as you can see from the out take above in good spirits. If you’ve been following along you might also notice t...
2018
Countdown to 2019
This is a collated version of the series of tweets I put out over the last week or so. I had a fun time reminiscing about all the mathematics I liked over ...
Factorization Redux
Factoring must be in the air …
Proof of Pentagon Construction
I was walking through the following construction of a regular pentagon from the AoPS Geometry textbook recently.
12/17 Game Day
I decided to do a photo diary for Game Day today which was a mixture of my familiar old favorites and a special packet of coloring pages from Edmund Harriss
12/10 MOEMS Olympiad #2
I always enjoy Olympiad days even if I’m not allowed to explicitly discuss the problems because of the white boarding opportunities they afford. There are…
12/3 Origami Puzzles
This week started with a unexpectedly interesting discussion about the problem of the week.
Some notes on this year ‘s AMC 8
Now that the AMC problems have been publicly released: Link to 2018 set I thought it would be fun to discuss a few from the last five. Before starting I al...
11/19 Phi Day (or winging it when disaster strikes)
This day was a bit humbling for me. After 2 weeks of competitive activities I really wanted to do something fun and low stress. I had just seen some cool L...
Dot Product Discovery
I was reading twitter yesterday and saw this tweet:
Revisiting the 15-75-90
[This is an old post I kept around which seems appropriate to publish today before AMC 8 (which unfortunately makes for poor blogging fodder)]
11/5 First MOEMS Day
I went back and forth on what to do today. Initially I had been thinking about exploring truchet tiles. I’ve found some starter points on chalkdust but the q...
Followup: And Substitution is Awesome(ly powerful)
To continue why I think emphasizing substitution early is a good idea see: Previous Post
Everything old is new again
This will be a short post but I’m excited enough to write this all down. Yesterday I had one of those moments where you go through a range of feelings. It al...
10/29 Stick Figure Circle of Death
Thinking about this week, I’m strongly reminded of a year ago: 1031-put-a-bird-on-it Like then, it was near…
10/22 Recursive Art
Since I’m behind blogging: this is a bit of an abbreviated summary of the last session. I decided I wanted to do some of the art projects from Clarissa Grand...
NWMath Reflections
This weekend I returned from the Northwest Math Conference in Whistler. Overall I had a blast. If one were to sum it up, the whole event was an exercise in…
Math Circle Talk Slide Deck
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10/8 Euclid’s Algorithm
Today the four kids who were not present the first time all came so I decided to start with everyone reintroducing themselves to the group. I had a few kids...
10/1 Year 5!
This is my fifth year doing a math club and its still just as thrilling to start again as it was the first time. (Although a lot less nerve wracking now that...
Golden Ratios in Regular Polygons
Here’s the first 3: for the triangle, square and pentagon.
Seattle MathJam or Pints and Polynomials
Last night I launched a small project I’ve been thinking about for a while. I’m now officially the host for the Seattle MathJam. [https://mathsjam.com/wh...
Parabola Equations and the related Coordinates
I put this together partly because I’ve been thinking about: Vieta Formula Brainstorming but mostly because I haven’t seen it elsewhere. The symmetry is mor...
Roots of Unity and Cyclotomic Polynomials
Most of the treatments of this topic are fairly grounded in Abstract Algebra and for this post I wanted to record my hopefully simpler conceptual framework.
Getting Back into Gear
Never put off till to-morrow what you can do day after to-morrow just as well.—B. F “Mark Twain falsely attributing a quote to Benjamin Franklin” Its that ...
Vieta Formula Brainstorming
I’ve on and off thought a bit about Vieta’s Formulas over the last few years. The AoPS Algebra textbook introduces them and has a few beginner problems. The...
Trig Problem Walk Through
John Rowe posted the fun puzzle pictured above on twitter. The goal is to find x.
Fantasy High School Part 2
[See: fantasy-high-school for part 1]
Visual Proof: The mediant is in the middle
Usually I’ve seen this done algebraically. See: 213-farey-sequences But from a vector addition standpoint (or
Forward to sender
This week I had been thinking of writing about the Big Internet Math Off but instead was invited to write about it on aperiodical.com itself. So go to https:...
Fantasy High School
@carloliwitter was tweeting recently about re-imagining High School mathematics and asking for ideas. The topic has caught my fancy even though its a bit off...
Book Review: Introduction to Number Theory and An Illustrated Theory of Numbers
Over the last 5 months, I worked through both Introduction To Number Theory and parts of An Illustrated Theory of Numbers with my son at home so I thought ...
Sometimes representation does matter
This is a small observation based on a post from @samjshah on the topic of the trig double angle formulas:
geom walk through 40-40-100
Thought process - subdivision creates more interesting angles 2 possibilities 3x/4x or 4x/3x
2018 Year in Review
Unlike the last three years (2017, 2016, [2015]({% post_url…
More connections
I’ve been thinking alot about polynomial deltas recently. See: polynomial-differences. It turns out, that there are a variety of problems where its fun to u...
6/5 Woven Math
I’ve been wanting to do this math/art project since I first saw Allison’s artwork on twitter. I finally had enough time to practice and find the supplies. O...
5/29 Phi Day
This week I wanted to extend some of our talk about the golden ratio. For the last reference see: 515-chaos-mod-arithmetic I’m also not quite done testing...
5/22 Cycles and Circles
[Memorial Day delayed me getting this one out. Hopefully it was worth the wait.]
Exponent Tower Redux
I saw a different version of the tower of 7’s problem in a book I’m reading on number theory. This is the mostly rambling thought process I’ve been going thr...
I’m going to a Conference!
Dear Benjamin Leis,
Tangles and Symmetry
This is a description of Dr. David Pengelley’s talk “All Tangled up and Searching for the Beauty of Symmetry” which I just attended. This makes an excellen...
5/15 Chaos + Mod Arithmetic
We started the day looking at the problem of the week (from @mpershan):
5/9 Square Roots
Today I returned to a topic, square roots, I’ve done before with younger kids : 53-square-roots. My thinking was that I had a cool video I wanted to show th...
5/2 Following my passion
This week I ended up switching my focus on the fly. I had been originally been planning on doing a graph theory math circle activity centered around chicken...
Polynomial Differences
Find the polynomial $ Ax^5 + Bx^4 + Cx^3 + Dx^2 + Ex +F$ given:
4/24 Tic Tac Toe (Naughts and Crosses)
Today started with some administrative tasks.
4/16 Purple Comet Online Contest
Three years ago I discovered the Purple Comet contest @ purplecomet.org. It has close links to the AwesomeMath and I really liked the problems in the old t...
Tricky Geometry Problem
In this walkthrough we start with one that didn’t look too hard at first:
4/3 Spring is Sprung
The last few weeks I’ve been concentrating on arranging the topics up to the last MOEMS Olympiad. This week I looked forward enough to realize that first Spr...
In praise of the Rational Roots Theorem
First some personal historical background. In my school district, you could do Algebra in middle school but unlike a standard class it only covered linear eq...
3/27 Olympiad #5
As is our routine, I started by going over the problem of the week:
3/20 Visible Math
This week started with a walk through of the MathCounts problem that I gave out last week to do at home.
3/13 Pi Day - 1
This is my fourth experience with Pi Day or “Pi Day - 1” as I called it since we meet on Tuesdays.
CoCa Photo Diary - Art Math Intersection
I had a chance during lunch to look at Dan Finkel’s brainchild at the Center on Contemporary Art.
3/6 Infinite Countable Sets or more fractions
It was a big weekend for the Math Club or should I say team. We finally participated in the rescheduled MathCounts chapter contest. I was very lucky the new ...
Carnival of Mathematics 155
Welcome to the 155th Carnival of Mathematics which collects a sampling of interesting math(s) related posts from around the web. This is my first time hostin...
Aloha
I’m on mid winter break with the kids for the week in Oahu. In the meantime check out my collected problems which are almost at 30 in total: [http://mymathcl...
2/6 Olympiad #3 and AMC 10
I almost cancelled this week’s math club due to feeling ill the night before. But in the end I was well enough and the activities were straightforward so I w...
1/30 Math Counts Prep Day
We’re only two weeks out from MathCounts and I’ve been so busy with various topics and activities that I haven’t really specifically focused on it. For the ...
1/20 Fold and Cut II
Today started with an interesting whiteboard demo for the Problem of the Week. This is a fairly straight forward combinatorics problem on a small 2^9 total ...
1/17 Graphs and Paths
This week I saw a numberphile video with a fairly charming problem that inspired me:
Fun with Pentagons
I’m in the mood for a geometry walk-through. I’ll start out by saying this one has tons of solutions. I’ve thought of 3 or 4 and seen several additional ones...
1/9 Olympiad #2
Recruitment
1/2 Math for a New Year (2018)
It was a good winter break. I took off some time from work to spend with my family, my parents flew in, we hosted a New Year’s Party for a large group of fri...
2017
2017 AMC 8 Questions
We finally received our scores. Overall I always have to remind myself that “comparison is the death of joy”. But really I think the kids did very well and ...
12/12 End of Quarter
The end of this quarter really snuck up on me. In my planning process I decided to finally use the video below on Schumann’s enumerative Geometry. What I p...
Motivating Kids
I recently saw this tweet
12/5 Olympiad #1
Today was the very delayed first MOEMS middle school contest day. As I mentioned before this contest was supposed to be on the same day as AMC 8 so we had t...
11/21 The intersection of History and Mathematics
My goal for this week in Math Club was to do something low key after AMC 8. Originally, I had been thinking about some tangram or panda block puzzles. I also...
11/14 2017 AMC 8 and a digression
Math Club was super easy for me today. I paced outside the classroom while everyone took AMC8.
11/7 Decoding
I decided to do a second smaller sampler of AMC 8 problems for Math Club this week. Unlike last week (see: 1031-put-a-bird-on-it) this time I wanted to app...
10/31 Put a bird on it.
Its the math worksheet version of “Just put a bird on it.” https://t.co/lNP3fs0wA2 — Benjamin Leis (@benjamin_leis) October 31, 2017
10/25 Strange Bases
This was a funny week. All the eighth graders were out on the class trip so Math Club skewed younger. That played a part in my planning. I aimed a bit less c...
This year’s Math Count Poster
The poster arrived in the mail with the rest of the contest materials. I think its charming and hopefully I can get permission to post somewhere in the school.
Heron’s Formula
The MathCounts guide for the year arrived today and I was looking over the problems. The following one caught my eye.
10/17 Pythagorean Triples
12-triangles-and-their-link-to-pythagorean-triples The inspiration for this week was a puzzle from the recent Pythagorize Seattle event thrown by MoMath that...
10/10 Middle School
In a careless move I deleted my original post on this one. Here’s a skeleton version until I have time to rewrite it.
Teasers for this year
Things are moving along. I have a provisional process to get going in 3 weeks and I’ve sent out the initial signup forms.
Status Updates
Logistics
Elegant Solutions vs. Hacking
This is a study in contrasts around a fun problem by @eylem:
How I use Twitter
This post started with some musing about the meta conversations occurring online right now in twitter over hashtags. There was enough activity that I was di...
Angle bisector
I’ve officially reached the point of the Summer where I’m missing interacting with kids besides my own. In the meantime, this is another geometry walk-throu...
Differentiation Part II
Continuing on my thinking from last time: open-ended-problems I saw notes on an interesting recent talk from @cheesemonkeysf
Open Ended Problems
I’ve been thinking more about open ended problems after reading a couple of different posts recently. Full disclosure: I actually engage in problem solving e...
Double angles
I’ve been thinking about a generalization of the 15-75-90 construction over the last few days and have realized there are a lot more interesting consequences...
And yet more 15-75-90 fun
Continuing on the theme of 15-75-90 triangles (See: Last time and First Time) several interesting riffs on 15-75-90’s in a box have come up recently.
First Impressions: A Decade of the Berkeley Math Circle
After seeing a recommendation online, this book arrived at the house in the mail yesterday. I started reading it after dinner and was immediately inspired. ...
Factoring Proof
One of the fun possibilities next year is that we can do problems with polynomials and factoring (at least by the end of the year.) I was reading a post by @...
Ideas for Next Year
It was a good week for finding inspiration on the internet (and in some books from the library). This is a grab bag of ideas for next year based on what I ha...
2017 Year in Review
One of the big questions I had going into this year was “Will the Math Club be very different this year? Am I going to continue…
6/13 And its a wrap
I was really heartened after sending an email out last week that all of the kids made it to Math Club today despite the…
6/6 Rational Tangles
This Math Club was a growth exercise for me. I had decided a few week’s ago that I wanted to do John Conway’s rational tangle game: http://www.geometer.org/...
15 - 75 Triangle Redux
I came up with this problem after looking at the original one from @five_triangles (Find the area of the trapezoid ABCD) That’s a lot of fun but along the way…
5/29 Combinations and Pascal’s Triangle
This week I decided to hit a bit of combinatorics before the year ends. I know most of the kids understand permutations fairly well but not combinations and ...
5/23 Triangle Conundrum
In the middle of last week, the MOEMS awards for the year arrived. So I started handing out patches and medals. I’m fairly happy with our overall performance...
5/16 Expected Values
My planning process this week went something like this: after last week’s talk I either wanted to do some group white-boarding or find a new game to explore....
MathCounts Final
Since it was fun Last Year to think about the Math Counts final question, here is the 2017 version:
5/9 Dating for Elementary Students
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Questions for Mathematicians
I’ve been prepping for our guest talk from the UW Math Dept. One of the tasks I’ve done is survey the kids to generate questions for the talk. Jayadev Athrey...
5/2 Assessment
This is a short placeholder entry. I decided to administer the AoPS algebra assessment last week since the 5th graders are currently choosing next year’s ma...
4/25 Platonic Solids
This week’s inspiration started with a very late school bus. My son’s bus driver has been on vacation and the substitute drivers have been really, really tar...
4/18 the series “Infinite Series”
Spring break really flew by and yesterday to my surprise Math Club was already resuming. Things started with small snafu, the door to our room was locked. Wh...
Spring Break Geometry
[In exciting real news, I almost have a guest speaker from the UW Math department lined up for May. My hope is that this will be helpful in showing the kids ...
4/4 Spring Quarter Begins
This quarter began with a seamless transition the week after the old one ended However, I had a little bit of turnover with 2 kids leaving and 2 new boys an...
Not so Innocuous Quartic
$x^2 - 16\sqrt{x} = 12$
3/28 #VNPS
Today was a fascinating learning experiment for me. I recently watched the following lecture:
3/21 Graph Pebbling
This week I went back to a pure math circle format with my favorite activity from the recent Julia Robinson Festival: Graph Pebbling. Based on my experiences...
3/14 Pi Day
Every 7 years or so accounting for leap years, Pi day actually occurs on a Tuesday. Yesterday was the first time that occurred…
3/7 Olympiad #5
Today started with a small mix-up. A boy I recruited at the Julia Robinson Festival to join Math Club showed up. But the next quarter doesn’t start for 3 wee...
2/28 Infinite Series
For this session of Math Club I wanted to revisit one of the ideas from the “free the clones” games: (See: 131-chessboard-problems-or-manipulatives-on-the-ch...
Julia Robinson Festival
(The flatland talk at the end of the afternoon.) For the second year in a row, I volunteered at the Julia Robinson Math Festival over the weekend. This is…
My own Geometry Puzzle
(This is based on my previous explorations of the @solvemymaths problems. As far as I know its a new so I’m very happy with it. Usually I just collate probl...
Mid-Winter break Geometry
By tradition, I’m going off on some problem solving walk-throughs:
2/14 Valentine’s Day Math Olympiad #4
By the luck of the draw (well really modular arithmetic), this year Valentine’s day fell on a Math Club Tuesday. I don’t really go in for holiday themed acti...
Making Explorations Successful
In a fit of perhaps excessive caution, the district cancelled all after school activities today despite the snow being almost completely melted. So I’m tabl...
1/31 Chessboard Problems or manipulatives on the cheap
This week’s planning revolved around my desire to pivot away from the more conventional topics of last week. I needed to give the kids more exposure to expo...
1/24 Curve Ball
Sometimes random events complicate the best of planning. I was on my way to work when I received an email from my co-coach Kristie that her plane was delaye...
1/17 3rd Olympiad
We started this week with the pdf from further maths that I gave out as a problem of the week: http://furthermaths.org.uk/docs/FMSP%20Problem%20Poster%201.pd...
1/10 New Year’s Celebration
Its gratifying when you plan a Math Club session where your time estimates work out and you achieve really good engagement. I had a few goals for this time ...
Knight’s of Pi 2017
High School full of mathy kids assembling for a Math competition. This weekend was my third time back at the Knight’s of Pi math competition and I brought 2…
2016
Technology
I saw a funny ignite talk “Algebra Inferno” the other day comparing disliked teaching practices to the various circles of hell a la Dante.
Winter break cyclic 3-4-5
This is another exercise in documenting geometry problem solving. I chose this problem because again it has a 3-4-5 triangle within it and the overall setup ...
2016 AMC 8 Results
The wait is finally over. We received the results for the 2016 AMC 8. Now comes my least favorite part sending them out to the parents. This is the message...
12/13 End of the Quarter
And just like that, another quarter has wound down. I’m always amazed how fast time flies. Its a lot of work planning and running the sessions of Math Club ...
12/6 Catching Up
As I alluded to in my last post I had to miss last week’s Math club meeting. This was one of those times when expanding to two instructors really paid off. T...
Grab bag of problems
Sadly, I have to miss Math club on Tue. given a family emergency. In the meantime, these are some of the problems I’ve enjoyed looking at recently that I mi...
Photo Diary of my visit to MoMath (Natl. Museum of Math)
The highlight of my recent trip to New York for Thanksgiving was a chance to get into Manhattan and finally checkout MoMath with my sons. I really wish we ha...
11/15 AMC8 and some Topology
What a difference a week makes. I left yesterday feeling very upbeat. To start off, I drove to the school early to help escort nine of the kids over to our s...
11/8 Election
This was a pretty raucous session. I didn’t really anticipate how much the kids in the Math club would be invested in the election. I was peppered with reque...
11/1 Grid Puzzles Again
This is a short placeholder for my records. The synopsis for this week is I did the following logic grid puzzle:
1:2 triangles and their link to Pythagorean triples
I’ve mentioned before how instinctively it feels like the 1:2 triangle ought to have a more natural angle measure. In fact its in a 90 - 26.57 - 63.43 degree...
10/25 Gozen
It was an interesting week from a planning perspective. I’m almost finished emphasizing divisibility and trying to decide what area I’d like to turn to nex...
10/18 More divisibility
After a slow start last week, this time almost all of the kids in the Math Club finished the problem of the week. (See the end of this post) I had one of t...
More Geometry in a Box (Trisection)
Continuing an occasional topic, I saw another great simple box construction.
10/11 Don’t Fence Me In
My initial thinking for how to structure the start of Math Club was influenced by last week’s problem of the week:
10/3: Year 3 (Bigger and Better)
I always get an odd mixture of impatience and trepidation right before after school activities start up. This time most of my concern is around getting two r...
Another Fundamental Square Construction
Its amazing how much for want of a better word beauty is lurking in very simple constructions. I’ve talked about some square variants before: sometimes-one-d...
Book Review: The math book : from Pythagoras to the 57th dimension, 250 milestones in the history
Last weekend I finally had enough down time to read through [The
Continued Fractions Planning
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Summer Odds and Ends
This is mostly a process update during the quiet days of summer.
Prime Number Planning
I’ve been thinking about what a prime-number themed day would look like based on some questions on Facebook. I’ve done prime related topics here and there bu...
2016 Year in Review
With another year under my belt, its time to look back and think about what I’ve learned over the process. (Here’s my review from last year: the-year-in-rev...
Two problems I’m looking at
I was reading a fun post over @ http://eatplaymath.blogspot.com/2016/06/my-first-problem-set-for-my-problem.html where Lisa is brainstorming problem sets. Sh...
6/14 End of the Year
And so we reached the end of another year. I wanted to celebrate a bit for the last day so I ordered a supermarket cake and we had a small party in the…
6/7 Hinged Polygons
I was pleased that this week ran much more smoothly than last time.
6/1 Art Math Intersection
I farmed out picking candy for math club to my wife this week and she was very generous in her purchases. So I started the day handing out skittles and gumm...
Memorial Day Miscellania
Pedagogy Riff
5/26 Magic Squares
My new numberphile t-shirt from the latest video arrived in the mail last week.
5/17 Battleship
The kids surprised me twice today during Math Club. We started by going over the Math Counts problem of the week I tried out: https://www.mathcounts.org/site...
A quick note on the MathCounts final question
http://q13fox.com/2016/05/09/seattle-13-year-old-wins-national-math-bee/
2 Fun 3-4-5 Pythagorean Triples
I’m going to warehouse these problems from @five_triangles here. I really like how they both show constructions for a 3-4-5 Pythagorean Triple. My plan is t...
5/10 Connect the Dots
Around the middle of last week I received a surprise phone call from the school office: “Your package arrived and we’re holding it for you.” As expected, it...
WSMC Math Olympiad
I brought a small team over the weekend to the WSMC Math Olympiad down in Maple Valley.
5/3 Square Roots
This week’s theme was inspired by some of questions the kids had while working on the Pythagorean Theorem about finding square roots. I have a small collect...
You don’t always win
“I want to thank everyone for coming out over spring break. I hope your kids had fun. I really enjoyed seeing everyone competing and talking with all the ot...
Geometry - Similar Triangles again
For spring break here’s a geometry walk through I wrote up a while back but never got around to publishing.
4/5 Snap Cube Hotel
Before this week’s Math Club meeting I had an extra math adventure. This weekend was the Julia Robinson Festival at the UW (http://jrmf.org/). I drove to the...
What’s the best way to talk about the Pythagorean Theorem?
I’ve been reading Martin Gardner’s “Gardener’s Workout” recently and came across the following section at the end.
Looking for a more elegant approach
This is a continuation of my geometry problem solving posts. I spent the last few days thinking about the above problem from @five_triangles. This ends up…
3/22 Winter Game Day
I had to hold back a laugh this week. While waiting for everyone to arrive in the cafeteria, one of the kids asked if we were going to have pie again. “If yo...
3/15 Pi Day 2016 (more or less)
One of these years Pi Day will actually occur on the day Math Club meets. Until that happens it also serves as a demonstration of approximation for the kids...
3/8 Olympiad #5
We finally reached the last Math Olympiad for the year. Earlier in the week I had received a mail from MOEMS giving some corrections for the third problem. S...
3/1 Fold and Cut
Even after two years, I’m still experimenting and searching for new material. Case in point, yesterday was notable for two changes. I had decided after last...
March Mathness Blog Hop
Welcome
2/23 Prepping for Pi Day
Riff on the what I want the group to focus on I was reading a post on the natural math site: http://naturalmath.com/math-circles-1001-leaders-course/ around...
President’s Day Break Geometry
There’s no school on Tuesday for President’s day and therefore no Math Club. If I had realized this more fully I would have perhaps picked an extra problem o...
2/9 Olympiad #4
This week started with the kids getting agonizingly close (19/20 problem of the week points) to a reward. I’m hoping this tension plus the fact I printed thi...
2/2 Space Math
This week started with lower problem of the week participation than in the past probably due to the fact I didn’t provide a handout and just orally gave the ...
Extra Reading
There’s been a spate of an interesting articles popping up on the web recently. The first one was from David Wees: http://davidwees.com/content/planning-less...
1/26 Recycler
It was another good week for participation. I had 8 responses to the problem of the week and almost everyone found the answer. Interestingly, this is officia...
1/19 Third Olympiad
There was lots of good stuff this week. First off, I had 9 kids work on the problem of the week including several of those who just joined. That meant I coul...
Sometimes its Harder the other way Part 2
I spent some time thinking about what initially looked like a very simple triangle congruence problem last night which I’ve outlined below. Given a perpendic...
1/12 Human Calculators
This week Math Club started up again although sadly without my son who had a fever and stayed home. There are seven new kids to get to know and I’m on a goo...
Preparing for the new Quarter
Next Tuesday will be the first session of Math club for this quarter. As a result, I’m in the last stages of planning this week. One monkey wrench for me is ...
An Update on DreamBox
I’ve now watched about a month more of my son’s play with DreamBox. So this constitutes an update to my prev. post: a-review-of-dreambox
2015
Geometry Diversion / corny geometry pun.
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12/15 Olympiad #2
Once they get started, the MOEMS Olympiads come quite frequently. This month’s version surprised me because in my first glance I had thought we had only had ...
Knights of Pi 2015
Last Saturday I once again found myself at Newport High School in Bellevue for the Knights of Pi Math Competition. This year I brought one team mostly of fou...
12.8 (Math) Game Day
This will be a shorter post than usual since I left my camera at home, I have a math contest to talk about after Saturday and today was all about play.
Blog Anniversary.
Why Blog? Its been about a year, 75 posts and 3900 hits since I first started blogging. So it seems appropriate to step back and ask some bigger questions. ...
12/1 The power of 37
This week I led math club by myself. I decided I would focus on a pair and share exercise where we’d work through 3 problems and spend time explaining answer...
Winding Down, Filling Away?
Next Quarter
A review of dreambox
This week is Thanksgiving break and there are no Math Club meetings. Instead I thought I’d write down my thoughts about dreambox.com, an online math app. I’v...
11/17 First Olympiad
Today was a really fun day in the math club. We started with me handing out whoppers to everyone as they arrived since the kids had reached our next goal for...
That article in Atlantic about explaining your work
The Atlantic recently published an interesting article about requiring students to explain their work http://www.theatlantic.com/education/archive/2015/11/ma...
11/10 Relay Madness!
After my bad activity complexity estimation last week it was a relief to properly size the planned exercises for math club this time around. We started by g...
11/3 Oops I did it again
This week I did a great job planning to ensure continuity, rolled with how things played out in the room and didn’t finish nearly as much as I wanted to. sig...
10/27 First Practice Olympiad
The most exciting part of this week was I think I’ve found another father who is willing to help assist me. Today was his first time coming and helping out. ...
10/20 Grids and Graphs
This week I planned a series of more playful activities. We started with a review of the take home problem of the week: (September from www.moems.org/zinger....
10/13 The Distributive Property: not just a good idea
After last week I knew that I needed to start with a review of the problem that I handed out to do at home. The great news was 8 of the kids worked on it ove...
Distributive Law Worksheet
The Distributive Law
10/6 And we’re off to the races
This afternoon was finally the first meeting of the math club for the year! Things started with a rude shock when I checked out my assigned room and found it...
Reversing digits
Moderator Note: What’s better than one semi math-crazy after school coach? How about two of them. My friend Dan has agreed to run our feeder Middle School’s...
Demographics
I just received the roster list. So some quick demographics for the beginning of the year.
Procedural Updates
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Arthur Benjamin’s talk: Exploring the Hidden Magic of Math
Last night I attended Arthur Benjamin’s lecture circuit promoting his new book: The Magic of Math: Solving for x and figuring out why.
Using Symmetry: More complex proof walk through
This is a continuation of the last 2 posts exploring using symmetry in proofs. This example is the most complicated yet. Symmetry via reflection produced the...
Using Symmetry: Geometry Walk Though #2
This is another in my series exploring geometric problem solving through rigid transformations (and creating diagrams with geogebra). See: using-symmetry-rat...
Using Symmetry: Ratios in square problem
I’ve been trying to put together a tutorial for working on geometry problems over the summer based on the various problems I’ve tried out. The outline is onl...
Book Review: A beginner’s guide to constructing the universe + some updates
Events After returning from our last road trip of the summer I received news that the back to school night was cancelled due to a teacher contract vote. For...
8/17/15 Pythagorize Seattle Photos
Today MoMath celebrated the Pythagorean Triple comprised of the date: **8^2 + 15^2 = 17^2 **with a math happening at South Lake Union. In case its not obvio...
A quiet week
Updates
Squaring the Rectangle
This Tiling Problem published in wordplay by Matt Enlow looks like a great first day activity.
Sometimes one direction is a lot tricker than the other
I was looking at a twitter post yesterday:
The Geometric Mean
I’ve been thinking a bit about the geometric mean this week after it turned up in two separate
Summer Reading
This book just arrived in the mail yesterday. I tried the first few problems out last night to escape the heat and they were pretty fun. They also despite t...
How to make homework work
Just yesterday AoPS released a new online problem resource for Middle School level (MathCounts) material: http://artofproblemsolving.com/mathcounts_trainer. ...
Random Geometry Recursion
You can recursively keep halving the length of the diagonals in this fashion. Creating a series of smaller 30-60-90 triangles in the process. (I promise I ...
Geometric Translations
Recently inspired by some posts on problem solving over at problemproblems.wordpress.com I’ve been combing through the geometry problems at gogeometry.blogsp...
The Year In Review
Now that the last session of the math club is done for the year it seems appropriate to look back and reflect on my experiences. Going into the process, I th...
6/9 End of the Year
Today was the last meeting of the math club for the school year. I feel a bit elated to have made it through an entire year and sad at the same time to see…
On Hints
I’ve been reading the following thought provoking post by Michael Pershan @
6/2 Pentagrams and some inspirational math.
Just in the nick of time for the end of the year, I received the notice that Jo Boaler’s Week of Inspirational Math. https://www.youcubed.org/week-of-inspira...
The problem I’m thinking about right now.
I worked with my son on this problem last night from AMC8 and I think its really interesting and plays off the previous pentagon problem I had given to the k...
5/26 Gamification
Today I tried something completely different with the math club. We participated in the Washington State Algebra Story Problem Challenge. http://wa.algebrach...
Cool Geometry Problem
I ran into another problem that I think demonstrates an unexpected and interesting fact
Virtual Math Club
Tomorrow our district is shutting down while the teachers go on a one day walk out. As a result there will be no math club session. But that’s no problem - ...
5/12 Dog + God
I have a lot of interesting observations from math club today. First up, for the warm up I went with some decoding problems:
Triangle Number Worksheet
Triangle Numbers
4/21 Purple Comet Online Meet
This week of math club we tried out the online Purple Comet Math Contest. http://purplecomet.org. Running the contest required a few modifications to our nor...
Book Review: Love and Math -The Heart of Hidden Reality
Spring break brought a lot of time to catch up on my reading this year. Best of all, one my reserves
Simplifying a Proof
I found this problem online yesterday (briefly) via a post on the google+ k-12 education. In the figure below
4/7 Spring Quarter Starts
Today was the first day of our last quarter for the math club. I lost 2 kids from the winter session that were replaced with 3 new ones. (I’m embarrassed to ...
4/2 Math Night
Tonight was the annual school Math Night. Since we didn’
Math is Cool 5th Grade Contest
This was my second contest experience. I brought 2 teams of four this time and because of a late withdrawal ended up drafting my son to fill the last spot. S...
Digression: Is this problem broken?
Update: As Dan pointed out I made an incorrect assumption in my sequence generation. The better technique is to generate the 2 lowest integers find the third...
3/10 Pi Day (approximately)
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3/3 Olympiad #5
After many of the kids asking about them, I finally brought some Sudoku puzzles to warm up on this week. I learned my lesson from ken-ken and only printed an...
2/24 Combinatorics
This session I decided to try out some more of the fivetriangle problems. I gave out a double sided sheet with 2 problems on it and let the kids decided whet...
Triangle Number Exercise
Admin note: This is my first experiment getting latex formatting working for formulas so there’s going to be more sigma notation than I would use in class. W...
2/10 Olympiad #4
Olympiad days usually go well and this one was no different. (Perhaps this means I should introduce more competitive tasks on regular days despite my instinc...
Field Testing
Whiteboard in the hallway at My Office
2/3 Finish what we started
My main goal for this week was to get to all the problems we didn’t do last week after our KenKen digression. So I started reviewing the AMC8 6-10 problems....
1/27 KenKen Collaboration
As originally planned I wanted to work more on collaborating together today. So I had everyone give me their names on a slip of paper and I then paired ever...
Can we get from here to there?
I’ve been looking at the five triangles site recently: fivetriangles.blogspot.com and I like alot of the problems there. I’m now considering whether the most...
1/20 Math Olympiad #3
So this week was our third MOEMS Math Olympiad. I brought cupcakes again since they struck such a deep chord with the kids the first time. In the interest of...
1/6 Winter Session Starts. Pythagorean Theorem.
Today was the first session coming back from break. We first talked about our goals for the quarter:
Rescuing a poorly designed worksheet
So my son brought home a math worksheet/game to do over the winter break. It involved rolling four six-sided dice and adding them into 2 sums and then multip...
2014
Puzzle for the break
I love breaking substitution ciphers. I sent one out before the first meeting in the fall and I decided I would do another one before our second quarter.
Odds and Ends
So officially we’re on winter break and the club will not meet up again until January. It’s also reregistration time. This had led me to imagine a few scenar...
Knights of Pi Math Competition
Finally, our first off site competition! Nevermind that it was scheduled for the first Saturday of the winter break so most kids couldn’t come, I was really ...
12/17 Math Olympiad 2
So MOEMS released the January test last week and I realized that given our school schedule it would be best to run the contest this week rather than scrambl...
Classroom Management
Going into the process, I worried most about handling a large group of kids at once. I’ve never done anything exactly like this before and my closest experi...
12/9 Prime Climb
I’ve already tried a few different games out and they’ve always worked really well especially for drawing out kids who don’t raise their hands as often. Howe...
In the beginning ….
Background