Resources

To Win This Numbers Game, Learn to Avoid Making Math Patterns — Quanta Magazine

My latest column for Quanta Magazine starts with a simple game of numbers and ends with some unsolved problems in mathematics.

For example, let’s change the rules to make the loser the first person to complete three in a row of any step size. This means you lose if you make 2-3-4, as in the original game, but also if you make 1-3-5 (three in a row of step size 2) or 1-4-7 (step size 3). These patterns are “arithmetic progressions”: sequences of numbers with a common step size, called the common difference.
Let’s return to our first game board and use the new rules. It’s still your turn. And you’ve lost.

This simple game, where each player tries to avoid completing an arithmetic progression, leads to some complicated math, involving open questions about Salem-Spencer sets and a new result about polynomial sequences.

The full article is available here and includes several exercises to test your game play!

By MrHonner, 5 years5 years ago

Resources Testing

2020 AP Calculus BC Practice Exams

The 2020 AP Calculus BC exam will be very different in scope and structure than previous years, as a consequence of logistical issues brought on by the COVID-19 pandemic. The College Board has indicated the test items will be similar to those on past exams, but there aren’t many existing practice materials designed with the 2020 format in mind.

I’ve created two sample practice exams for my BC Calculus students and will share them here for teachers and students looking for additional resources. All are welcome to use them, but keep in mind that these are merely guesses about what the exam might be like in terms of scope and difficulty. I will say that I intentionally tried to make these more challenging than the College Board’s sample exam, which is just a re-combination of existing 2019 items. (I referred to this as Practice Exam #1, which is why you see #2 and #3 below.)

Please use as you see fit. And let me know if they are helpful!

2020 BC Practice Exam #2 Download

2020 BC Practice Exam #3 Download

By MrHonner, 5 years5 years ago

Resources

STEM for All Video Showcase

Next week I’ll be a facilitator and judge for the 2020 STEM for All Video Showcase. This event highlights hundreds of innovative projects designed to improve Science, Mathematics, Engineering, and Computer Science education in both formal and informal settings.

Thousands of educators, researchers, policy makers, parents, and students actively participate in the event, and the videos are watched by hundreds of thousands of people worldwide. The showcase runs from May 5th to May 12th, and everyone is invited to watch the videos, participate in the conversations, and vote for their favorites!

Find out more at the STEM for All Video Showcase website.

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By MrHonner, 5 years5 years ago

Data NYT Resources Teaching

7 Ways to Explore the Math of the Coronavirus Using the New York Times

My latest piece for the New York Times Learning Network is “7 Ways to Explore the Math of the Coronavirus Using the New York Times”, a collection of ideas for using NYT articles, infographics, and interactives to explore the mathematics underlying the current coronavirus epidemic.

The opportunities range from statistical literacy to network theory. Here’s an example of some data analysis you can engage in using a wonderful NYT interactive:

By using sliders to change, for example, the level of intervention (e.g., moderate or aggressive) or the length of intervention (e.g., 14 days or 60 days), students can see how outcomes change. And, by playing with the model, they will be able to answer questions like: “What is the impact of shortening our social distancing period?” or “What happens when we delay the start of our interventions?”

The full article is freely available on the New York Times Learning Network.

By MrHonner, 5 years5 years ago

Numbers Resources Teaching

How Rational Math Catches Slippery Irrational Numbers — Quanta Magazine

My latest column for Quanta Magazine is about a clever technique for finding rational approximations to irrational numbers. The technique, developed by the German mathematician Gustav Dirichlet, works by covering the number line with tiny intervals centered at certain rational numbers.

But Dirichlet did better. He improved this method by figuring out how to shrink the intervals around their centers while still keeping the entire number line covered. As the intervals shrink, so does the distance to any irrational number we are trying to approximate. This means we’ll get better and better rational approximations, even using relatively small denominators. But we can’t shrink the intervals too quickly: Even though there are infinitely many of them, if the intervals get too small too fast they won’t cover the entire number line. In the battle between the infinitely large and the infinitely small, Dirichlet had to find the right balance to prevent some irrationals from slipping through the cracks.

Dirichlet’s technique explains why we can always find good rational approximations to irrational numbers using small denominators, like $\pi \approx \frac{22}{7}$ . Developed nearly 200 years ago, this technique ultimately led to the proposal of the Duffin-Schaeffer conjecture which was finally proved this past year.

You can read the full article here.

By MrHonner, 5 years5 years ago

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