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Patrick Honner
Works at NYC DOE
Attended University of Wisconsin-Madison
Lived in Brooklyn, NY
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Patrick Honner

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I challenged my students to construct the trisection points of a segment today.  One of them did it by constructing a triangle such that the given segment was a median, and then finding the triangle's centroid!  Brilliant!
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Excellent! A natural question what other fractions is it possible to obtain this way plus something more, say, classic
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Why is the sum of a rational number and an irrational number irrational?  Because the sum of a rational number and an irrational number is always irrational.

Brought to you by the New York State Algebra exam.
http://mrhonner.com/archives/14706
Here is another installment in my series reviewing the NY State Regents exams in mathematics. This is question 25 from the Common Core Algebra exam. I've already complained about the contrived, art...
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+Graeme McRae​ You implicitly used the rule that a rational minus a rational is rational. I'm not sure if you'd get full credit, which reminds me why I prefer interactive proofs -- it helps to have another human there to say what level of detail they require.

But of course this is impractical, both for tests and for much of real world mathematics. 
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Patrick Honner

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“Four students are playing a math game at home.  One of the math game questions asked them to write an algebraic equation.“

Why invent such a ridiculous context for a math question?

Another installment in my review of New York State mathematics exams.
Here is another installment in my series reviewing the NY State Regents exams in mathematics. This is question 8 from the Integrated Algebra exam. "Four students are playing a math game at home.  O...
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+Matt McIrvin and the question that follows:

What is the answer to this question?
A.) All of the above
B.) None of the above
C.) All of the above
D.) None of the above
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Patrick Honner

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Interesting summer opportunity for college students in NYC:  8-week intensive Data Science program from Microsoft Research.  Includes $5,000 stipend!
https://ds3.research.microsoft.com/
The Data Science Summer School (DS3) is an intensive, eight-week hands-on introduction to data science for college students in the New York City area. As we are committed to increasing diversity in computer science, we strongly encourage women, minorities, and individuals with disabilities to ...
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In addition to everything else, Leonard Nimoy will always be the voice of "If I Had a Hammer" to me.
https://www.youtube.com/watch?v=TAPoNXrWNMc
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Discussion -- General  - 
 
Cavalieri's Principle came up in Workshop 2, and I wanted to share a some related resources.

Here are two posts of mine about Cavalieri's Principle:
http://mrhonner.com/archives/4000
http://mrhonner.com/archives/3665

And the Wikipedia entry contains the classic application of the principle:  deriving the formula for the volume of a sphere.
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Homework -- Geometric Dissections  - 
 
Workshop 2 -- Problem 5

Prove the angle sum formula for sine.  
Extension  Do so using Euler's formula!
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There are nice diagrams of both angle sum formulas at Cut the Knot.
http://www.cut-the-knot.org/triangle/SinCosFormula.shtml
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Patrick Honner

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The inaugural winner of the million dollar Global Teacher Prize says she wouldn't encourage young people to go into teaching.  This says a lot about what it's like to be a teacher right now.
Nancie Atwell, winner of the Varkey Foundation's first Global Teacher Prize, speaks to CNN's New Day about the award.
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Ouch.
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Patrick Honner

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Could you eat on $2.50 a day?

Tons to learn about food, cooking, and shopping from Alan Eliasen as he blogs about his 45-day challenge.

https://futureboy.us/blog/twofifty.html
Engineer Eats Efficiently (for $2.50 a Day). For 45 days, I'm trying to spend less than $2.50 a day on food. This is an account of the food, the costs, the science, and the fun of that experiment. Table of Contents. Why? Why $2.50 a day? Rules and Guidelines; Day 1 - Tomato Soup and Toasted ...
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I think it's great. This level of detail provides insight on a number of levels and crosses that divide that can show all sorts of people how relevant mathematical thinking is to their lives. It can branch out, too. Like, I usually pick my own berries to freeze for the winter, which saves us a lot money, but those are hours I'm not working and therefore not earning money. But then there are social and ecological benefits hard (yet somewhat possible) to quantify.
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Patrick Honner

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Today I visited my son's fifth grade class to celebrate "pi day." (They won't be in school for the actual pi day, which is Saturday.) The math community is abuzz about this year's pi day because we will have 3/14/15 9:26:53—the first 10 digits of pi.

To be honest, I don't love pi day. I think a lot of the activities are kind of goofy and non-mathematical. However, I honestly love the number pi—its mathematical connections and its history. So my presentation was a mathematician's take on pi. I'm very happy with how it went.

I talked about the history of pi (and I stated my belief that we should call pi "Archimedes's number"). We talked about how to calculate digits of pi. I had them compute some approximations from polygonal approximations to circles. I told them about Archimedes's 96-gon and Van Ceulen's 2^(62)-gon approximations.

Rather than calling pi "an infinite number" (which it isn't) we talked about rational and irrational numbers and what their decimal representations look like.

We had a few pi-related activities (like: if one string is wrapped around the equator and a second string is around the equator but one foot off the ground, how much longer is the second string?)

I talked about the importance of proof in mathematics, and I gave a sketch of the proof that if C=2πr, then A=πr^2. (I also tried to impress upon them how cool and surprising it is that this same number appears in both formulas.)

Finally, I told them that the book of mathematics is not yet finished. We are still making new discoveries and there are proofs still to be discovered. For example, we still don't know if pi is "normal"—roughly speaking, that there are the same fraction of 0's as 1's as 2's as 3's... in the decimal expansion.

We ate pie afterward. Some of the kids brought in pie—including this one that my wife and son made (please don't tell them that the last digit is wrong...).

As a side note: if you have the opportunity to go in and speak to your kids' class—do it! It is extremely fun and rewarding. They have so many great questions and comments. Their enthusiasm is unbelievable. I do it every year, and I love it—and I think the kids do too.
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Homework -- Geometric Dissections  - 
 
Here's an image showing some of the important dihedral angles.  [All edges have length 1].

Notice the amazing relationship between dihedral angles in the tetrahedron and square-based pyramid:  glue them together and they become coplanar!
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Homework -- Geometric Dissections  - 
 
Workshop 2 -- Problem 6  
Find all the dihedral angles in the following solids.
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Have him in circles
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Math Teacher in Brooklyn, NY
Introduction
I write about Mathematics and Teaching at www.MrHonner.com.
I am a two-time recipient of Math for America's Master Teacher Fellowship, a Sloan award winner, and the runner-up for the Inaugural Rosenthal Prize for Innovation in Math Teaching, presented by the Museum of Mathematics.
Education
  • University of Wisconsin-Madison
    Mathematics
  • Wayne State University
    Mathematics, Philosophy
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Patrick Honner's +1's are the things they like, agree with, or want to recommend.
Tell Me Why You Blog
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So, as much to my surprise as anyone's, I'm not only talking at NCTM in April but they made me a featured speaker? Only freaking out a littl

What do we learn from our students?
anglesofreflection.blogspot.com

It's been a while--partly because of work, and partly because I just found out about the death two summers ago of one of my former students,

Mathematical Association of America
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The largest professional society that focuses on mathematics accessible at the undergraduate level.

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FEATURES:- New Feature: Google+ Communities - Enjoy magazine style layout in the new tablet version - Automatically share photos to an Event

Sage Mathematical Software System
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open-source mathematics software system

Math Photo: Sculpture of Spheres « Mr Honner
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Math Photo: Straw Cylinders « Mr Honner
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Math Art: Kolam Spirals « Mr Honner
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Math Art: Starburst, by Tim Locke « Mr Honner
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White Group A level JC H2 Maths tuition: 92nd Carnival of Mathematics
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Ninety-two isn't any ordinary number; it is associated with "royalty". How does that work out? It represents the number of solutions to whic

Math Art: Student Sliceforms « Mr Honner
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Math Photo: Sharp Tangency « Mr Honner
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9/15/12 — Happy Right Triangle Day! « Mr Honner
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The Algebra of Coffee Consumption « Mr Honner
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