Resources

Math Haiku: Geometry Class

I personally enjoy writing, and as a math teacher I love getting my students writing about math.

One of my favorite writing assignments for students is math-themed haiku. The rigid constraints of haiku make it an easy exercise, it allows students to access and interact with mathematical ideas in a different and creative way, and the elegance and efficiency of the for evoke the character of mathematics itself.

Here are some selections from this year’s Geometry class. Enjoy!

We are both equal

We look exactly the same

We are congruent

Postulates assumed

Leading to certain theorems

Web of proof and math

Three lines have converged

Meeting at a single point

They are concurrent

Scalene triangles

Angles are dissimilar

Sides are unalike

CPCTC

A simple explanation

For congruent things

Math is easy now

Calculators do all the work

Sit back and relax

Geometry Resources Technology

Circumcircles in Desmos

I’m presenting on Desmos at today’s AMAPS meeting in New York City, and preparing my talk was an object lesson in how wonderful this technology is.

Part of my presentation demonstrates simple ways that Desmos can be a part of every high school math class: Algebra, Geometry, Trigonometry, Pre-Calculus, and Calculus. While Geogebra is generally more suitable for demonstrating and exploring geometry, Desmos certainly can be useful in that course, so I wanted to show something relevant and interesting as part of my talk. I thought, “Why not compute the circumcircle for an arbitrary triangle?”

While all the pieces of the mathematical puzzle were there for me, figuring out how to put them together in Desmos was a fun, frustrating, and worthwhile challenge. I had to play around with the basic concepts associated with perpendicular bisectors and think creatively about some mathematical problems and equations. I even ended up using the new regression feature in Desmos in a clever way!

I often get caught up in little challenges like this, and this is why Desmos is so wonderful: it provides us a mathematical makerspace. It invites us to play around, to create, to engineer, to build. And all of this happens through using the language and concepts of mathematics.

You can see my circumcircle demonstration here, and you can find more of my work in Desmos here.

By MrHonner, 12 yearsDecember 10, 2014 ago

Resources Teaching Technology

Derivatives of Vector Functions

One way to think of a curve in the plane (or in space) is as a collection of terminal points of vectors whose initial points are all at the origin. The vectors are given by a vector-valued function.

For example, the parabola shown at right can be thought of as the graph of the vector-valued function

$r(t) = < t , (t-1)^{2}+1>$

I’ve created a Desmos demonstration that shows how graphs of vector-valued functions are related to their vectors (shown in blue), and how the derivative of a vector-valued function is related to both difference vectors and tangent vectors. You can access the demonstration here.

You can find more of my Desmos demonstrations here.

By MrHonner, 12 yearsNovember 22, 2014 ago

NYT Resources Teaching

Exponentials and Ebola

My latest piece for the New York Times Learning Network is a lesson on the underlying mathematics of the spread of contagious diseases, like Ebola.

In this lesson, students use a basic exponential model to explore the fundamental mathematical ideas of transmission and replication.

Mathematically, the spread of disease can be modeled in a manner similar to the spread of a rumor. Although a number of simplifying assumptions must be made, the simple exponential model captures the basic impact of transmission rates on the dispersion of a disease among a population. Students can explore the consequences of transmission rate using multiplication, algebra, graphing utilities and elementary statistics.

After exploring the essential behavior of various simple exponential models, students then compare real-world data to their theoretical models. Those that are capable can perform regressions on the data to approximate actual transmission rates. The students’ work and the real-world data establish a context for discussing the strengths and weaknesses of this simple model of disease transmission.

This lesson is part of a series of Ebloa lessons at the NYT Learning Network and is freely available here.

By MrHonner, 12 yearsNovember 6, 2014 ago

Geometry Resources Teaching

MfA Workshop — Surfaces in Space

I’m looking forward to a a workshop I’ll be running tonight at the Math for America offices on three-dimensional coordinate geometry.

This workshop will cover the basic algebraic and geometric techniques for analyzing functions and relations in x, y, and z, as well as some simple methods for building interesting surfaces in space.

Sketching in space is a favorite topic of mine, and I’m really excited to share it with a group of MfA teachers. Three-dimensional coordinate geometry is an accessible, fun, and rich area that few math teachers have experience with. But given the advances in graphing technology and the applications to 3D printing, it’s something that more people can, and should, learn about!

By MrHonner, 12 yearsOctober 27, 2014 ago

Math Haiku: Geometry Class

Circumcircles in Desmos

Derivatives of Vector Functions

Exponentials and Ebola

MfA Workshop — Surfaces in Space

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