Tags

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. 

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...

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...

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...

15-75-90: Attack of the Dodecagon

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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)]

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.

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…

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...

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...

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 ...

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...

Pentagon + Quadrature of the Parabola

Last week, I saw this really fun parabola problem from @diegorattaggi and  I became interested for two reasons:

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...

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...

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...

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 ...

5/9 Dating for Elementary Students

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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...

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...

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.

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...

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...

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...

4/26 Pythagorean Theorem Day

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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.

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...

Cool Geometry Problem

I ran into another problem that I think demonstrates an unexpected and interesting fact

3/10 Pi Day (approximately)

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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:

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...

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 ...

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

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...

Cardano’s Method

This all starts with a fantastic new video from Mathologer: 500 years of NOT teaching the cubic formula.

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...

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...

Factorization Redux

Factoring must be in the air …

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.

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...

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...

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...

Polynomial Differences

Find the polynomial $ Ax^5 + Bx^4 + Cx^3 + Dx^2 + Ex +F$ given:

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...

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 @...

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...

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…

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...

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. 

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...

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...

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 ...

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...

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...

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...

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...

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...

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...

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.

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.

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.

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…

New Beginnings

I’m back

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…

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 ...

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.  ...

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

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...

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...

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

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...

Heron’s Formula

The MathCounts guide for the year arrived today and I was looking over the problems. The following one caught my eye.

Differentiation Part II

Continuing on my thinking from last time:  open-ended-problems I saw notes on an interesting recent talk from @cheesemonkeysf

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…

MathCounts Final

Since it was fun Last Year to think about the Math Counts final question, here is the 2017 version:

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...

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...

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.

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...

A quick note on the MathCounts final question

http://q13fox.com/2016/05/09/seattle-13-year-old-wins-national-math-bee/

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.

Squaring the Rectangle

This  Tiling Problem published in wordplay by Matt Enlow looks like a great first day activity.

Voronoi Diagrams

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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...

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...

Cool Geometry Problem

I ran into another problem that I think demonstrates an unexpected and interesting fact

Interesting Tool

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Simplifying a Proof

I found this problem online yesterday (briefly) via a post on the google+ k-12 education.  In the figure below

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...

Approaching the Tangent

Preamble

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...

Cardano’s Method

This all starts with a fantastic new video from Mathologer: 500 years of NOT teaching the cubic formula.

Carnival of Mathematics 203

Graphic scores by John De Cesare (1890–1972).

Carnival of Mathematics 193

Welcome

Carnival of Math 181

Welcome

Carnival of Mathematics 168

Turtles - Martin Holtham 

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...

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 ...

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...

Two Boxes in a Circle

The March MathsJam had an interesting geometry puzzle.

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...

Two Hinged Triangle Geometry Walk Through

Setup

Justifying complex number exponential notation i.e. Euler’s Formula without Calculus

Background

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…

Tilted Ellipse Problem Walkthrough

This problem from Matt Enlow is quite fun and as a bonus a chance to show off some geogebra formatting:

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

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...

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 ...

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...

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 ...

Continued Fractions Planning

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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...

Cardano’s Method

This all starts with a fantastic new video from Mathologer: 500 years of NOT teaching the cubic formula.

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...

Fantasy High School Part 2

[See: fantasy-high-school for part 1]

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...

Two Boxes in a Circle

The March MathsJam had an interesting geometry puzzle.

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...

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…

Virtual Math Club for Winter

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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...

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...

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...

Dot in a Box: Addendum

This is a continuation to my last post: dot-in-a-box

Dot in a Box

[@fleonsotelo]

Triangle trisection Proof 3 ways

Part I 

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 ...

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...

Cool walk through for geometric transforms

[Since its AMC 8 today - here’s a geometry walkthrough instead for the week]

More Piled Squares

–>

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 ...

Fantasy High School Part 3 (Statways)

I’m returning here to a perennial topic of mine: High School Curriculum Reform.

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...

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.

Pentagon + Quadrature of the Parabola

Last week, I saw this really fun parabola problem from @diegorattaggi and  I became interested for two reasons:

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...

Euler Line Walkthrough

http://www.gogeometry.com/problem/p742-circumradius-orthocenter-centroid-midpoint-distance-square.htm

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.

15-75-90: Attack of the Dodecagon

!

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...

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...

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...

Triangle in a Square: Areas

So this happened today:

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...

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.

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.

Interesting Geometry Walkthrough: Inscribed trapezoids/hexagons

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Dot Product Discovery

I was reading twitter yesterday and saw this tweet:

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...

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.

Fantasy High School Part 2

[See: fantasy-high-school for part 1]

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...

Sometimes representation does matter

This is a small observation based on a post from @samjshah on the topic of the trig double angle formulas:

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...

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...

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...

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.

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...

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. 

Elegant Solutions vs. Hacking

This is a study in contrasts around a fun problem by @eylem:

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...

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.

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…

Not so Innocuous Quartic

$x^2 - 16\sqrt{x}  = 12$

Mid-Winter break Geometry

By tradition, I’m going off on some problem solving walk-throughs:

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...

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 ...

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...

More Geometry in a Box (Trisection)

Continuing an occasional topic, I saw another great simple box construction.

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...

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...

Memorial Day Miscellania

Pedagogy Riff

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...

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.

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…

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...

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...

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. ...

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...

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...

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 ...

On Hints

I’ve been reading the following thought provoking post by Michael Pershan @

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...

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...

10/20 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

10/11 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:

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...

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

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...

11/28 Egyptian Fractions

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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...

3/29 Euler Characteristic

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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...

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...

Euler Line Walkthrough

http://www.gogeometry.com/problem/p742-circumradius-orthocenter-centroid-midpoint-distance-square.htm

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...

Justifying complex number exponential notation i.e. Euler’s Formula without Calculus

Background

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...

Factorization Redux

Factoring must be in the air …

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...

Not so Innocuous Quartic

$x^2 - 16\sqrt{x}  = 12$

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.

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...

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 ...

5/15 Chaos + Mod Arithmetic

We started the day looking at the problem of the week (from @mpershan):

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

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 ...

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...

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...

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...

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...

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...

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...

Fantasy High School Part 3 (Statways)

I’m returning here to a perennial topic of mine: High School Curriculum Reform.

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...

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…

3/28 #VNPS

Today was a fascinating learning experiment for me. I recently watched the following lecture:

Memorial Day Miscellania

Pedagogy Riff

Winding Down, Filling Away?

Next Quarter

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...

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...

On Hints

I’ve been reading the following thought provoking post by Michael Pershan @

Two Boxes in a Circle

The March MathsJam had an interesting geometry puzzle.

Two Hinged Triangle Geometry Walk Through

Setup

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...

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…

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...

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...

Dot in a Box: Addendum

This is a continuation to my last post: dot-in-a-box

Dot in a Box

[@fleonsotelo]

Triangle trisection Proof 3 ways

Part I 

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 ...

Cool walk through for geometric transforms

[Since its AMC 8 today - here’s a geometry walkthrough instead for the week]

More Piled Squares

–>

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...

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.

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:

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...

Euler Line Walkthrough

http://www.gogeometry.com/problem/p742-circumradius-orthocenter-centroid-midpoint-distance-square.htm

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.

15-75-90: Attack of the Dodecagon

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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...

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...

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...

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...

Proof of Pentagon Construction

I was walking through the following construction of a regular pentagon from the AoPS Geometry textbook recently.

Interesting Geometry Walkthrough: Inscribed trapezoids/hexagons

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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)]

Golden Ratios in Regular Polygons

Here’s the first 3: for the triangle, square and pentagon.

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

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...

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.

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...

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. 

Heron’s Formula

The MathCounts guide for the year arrived today and I was looking over the problems. The following one caught my eye.

Elegant Solutions vs. Hacking

This is a study in contrasts around a fun problem by @eylem:

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...

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.  ...

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…

5/23 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...

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...

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:

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 ...

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...

More Geometry in a Box (Trisection)

Continuing an occasional topic, I saw another great simple box construction.

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...

Summer Odds and Ends

This is mostly a process update during the quiet days of summer.

Memorial Day Miscellania

Pedagogy Riff

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...

4/26 Pythagorean Theorem Day

!

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.

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…

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...

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...

Geometry Diversion / corny geometry pun.

[](https://blogger.googleusercontent.com/img/proxy/AVvXsEgPgXksiZCbttG33WOzISgxJx-EnZrBWycp9kY3QFiu8xWoCwpBwCc91Mc6zew7HdE4WljtUQnA4FKdFzjRDgB6vk0EXc67Wi4dmy...

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...

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 

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...

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...

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 - ...

Interesting Tool

!

Simplifying a Proof

I found this problem online yesterday (briefly) via a post on the google+ k-12 education.  In the figure below

3/10 Pi Day (approximately)

(function(i,s,o,g,r,a,m){i[‘GoogleAnalyticsObject’]=r;i[r]=i[r]||function(){ (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),...

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...

Pentagon + Quadrature of the Parabola

Last week, I saw this really fun parabola problem from @diegorattaggi and  I became interested for two reasons:

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...

Golden Ratios in Regular Polygons

Here’s the first 3: for the triangle, square and pentagon.

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...

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...

5/22 Cycles and Circles

[Memorial Day delayed me getting this one out. Hopefully it was worth the wait.]

1/17 Graphs and Paths

This week I saw a numberphile video with a fairly charming problem that inspired me:

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...

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…

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...

Dot in a Box

[@fleonsotelo]

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 ...

Heron’s Formula

The MathCounts guide for the year arrived today and I was looking over the problems. The following one caught my eye.

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...

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...

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}...

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.  ...

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…

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…

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...

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...

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 ...

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…

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.

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 ...

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:

5/26 Magic Squares

My new numberphile t-shirt from the latest video arrived in the mail last week.

Motivating Kids

I recently saw this tweet

3/28 #VNPS

Today was a fascinating learning experiment for me. I recently watched the following lecture:

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...

Winding Down, Filling Away?

Next Quarter

Procedural Updates

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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...

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’...

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 ...

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.

Continued Fractions Planning

<iframe width=”560” height=”315” src=”https://www.youtube.com/embed/CaasbfdJdJg?si=1e3b9N7Qd4zP2bdp” title=”YouTube video player” frameborder=”0” allow=”a...

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...

Two Hinged Triangle Geometry Walk Through

Setup

Continued Fractions Planning

<iframe width=”560” height=”315” src=”https://www.youtube.com/embed/CaasbfdJdJg?si=1e3b9N7Qd4zP2bdp” title=”YouTube video player” frameborder=”0” allow=”a...

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...

Motivating Kids

I recently saw this tweet

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…

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.

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...

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...

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...

Memorial Day Miscellania

Pedagogy Riff

A quick note on the MathCounts final question

http://q13fox.com/2016/05/09/seattle-13-year-old-wins-national-math-bee/

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.

March Mathness Blog Hop

Welcome

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:

4/2 Math Night

Tonight was the annual school Math Night. Since we didn’

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...

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...

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…

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...

5/15 Chaos + Mod Arithmetic

We started the day looking at the problem of the week (from @mpershan):

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…

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...

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...

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 ...

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...

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...

Squaring the Rectangle

This  Tiling Problem published in wordplay by Matt Enlow looks like a great first day activity.

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...

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 ...

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...

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...

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...

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...

Squaring the Rectangle

This  Tiling Problem published in wordplay by Matt Enlow looks like a great first day activity.

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...

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 ...

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…

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...

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...

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...

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

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...

Parabola Equations and the related Coordinates