Desmos Activity: Sieve of Eratosthenes

Here’s a digital activity I made for exploring integers and discovering prime numbers.

One of my favorite ideas to use in class is the Sieve of Eratosthenes. Even if you’re not familiar with the name, there’s a chance you’ve come across it before. It’s the algorithm to find the prime numbers which are left after the multiples of earlier prime numbers have been eliminated. (Given the name of this blog, there’s not much surprise I like this topic.)

Prime numbers are not required in the Oklahoma standards for the classes I’m teaching, but I thought the Sieve would make a good start of the year activity. I’ve shared an activity and worksheet based on this, but that was from a more na├»ve time, when sharing papers and colored highlighters seemed like a good idea.

So I went looking for a digital alternative, and after trying a few different approaches… well, you’ve seen the title of this post. The solution, as it so often is, was Desmos.

This is what I came up with:

https://teacher.desmos.com/activitybuilder/custom/5f3eb1f440d78831973bcd4e

Weirdly enough, this is the first activity I’ve created using the Activity Builder and the Computation Layer in Desmos. But over the last few years, I’ve either been in grad school, or teaching where I didn’t have one-to-one devices.

The activity is very similar to the worksheet I shared above. It steps students through identifying prime numbers, crossing out the composite numbers as they go. But instead of literally crossing out the numbers, students type the list of numbers and Desmos takes care of the crossing. Here’s a partially complete step:

There are some limitations here. I’ve only gone to 100, rather than 150 as I did in the original worksheet, because it’s a lot easier to use a square grid in this case. I preferred 150 originally, because it means crossing out the multiples of 11 makes a difference. (I did consider using something other than 10 by 10, but the grid is already getting a little cramped at this point.) Also, typing in the lists of the multiples gets tedious. Though, I guess that’s no more so than crossing the numbers out by hand. If anyone from Desmos is reading this: would it be possible to allow tables in the Activity Builder to automatically follow a pattern, as they do in the calculator?

This is the final result:

(Note that this image is taken from this graph rather than the activity itself, but I did use the graph to make the activity.)

If you’re looking for a way to discover prime numbers in class which doesn’t involve a paper grid, hopefully you’ll consider giving this a look.

 

Algebra 2 Class Notes v 0.3

Here’s the next version of my notes. If you’ve missed this so far, I’m writing a complete set of fill-in-the-blank notes for Algebra 2, specifically with the Oklahoma Academic Standards in mind. See my post sharing the first draft of the notes for my reasons for doing this.

There’s a lot of small fixes here, with things that could be written clearer, some additional examples, and, sadly, a lot of typos and other mistakes. The most substantial edits were to section 8.4, on natural exponents and logarithms. I’ve always been dissatisfied with the way the value of the constant e is justified in classes which precede calculus. I’m hoping that this explanation will satisfy students by alluding to the calculus, without teaching it explicitly.

Downloads are available here:

 

Algebra 2 Class Notes v 0.2

UPDATE: version 0.3 of these notes are out now.

In my last post, I made available notes for the entire year of Algebra 2, following the Oklahoma standards. I mentioned that the notes are a work in progress. Hopefully in time for the new school year for most, here is an updated version.

Changes focus on the first six chapters, which should get anyone following the notes in order through the fall semester. I aim to have version 0.3, which will focus on fixes to the remaining chapters, done by Christmas.

Changes include:

  • Fixes to lots of errors and typos, both in the text and in the worked examples.
  • A number of paragraphs rewritten to be clearer.
  • A handful of additional examples.
  • Additional space for select examples.
  • Additional diagrams to explain concepts, including the picture below.

As before, there is a set of blank notes for students, and a set of the notes with all the blanks and examples completed. These notes remain free to use for teachers to distribute to their students in their own classes.

Download here:

 

Algebra 2 Class Notes v. 0.1

UPDATE: version 0.3 of these notes are out now.

I’ve been working on a big project over summer: a set of student notes with fully worked examples for an entire year of Algebra 2.

You might be wondering why I did this. I’m not even teaching High School currently, as I’m taking a couple of years to attend grad school. While I’m doing some teaching, it’s been as a TA for Calculus 1, certainly not for Algebra 2. Even so, I’ve still spent a lot of time thinking about Algebra 2 curriculum over the past year, and had a lot of conversations about it with Sarah, as she is has been teaching Algebra 2 since last August. It turns out, even after taking some time away, my passion is still for high school math.

These are the ideas I’ve had for the function of these notes:

  • They’re aiming to meet the Oklahoma Academic Standards, though in places they step back to strengthen the conceptual foundation, and in others they go beyond the standards. Eventually I’ll produce an alignment document to explain all the links.
  • This is not a complete curriculum, but I see it functioning as a “skeleton” on which a complete curriculum could be built.
  • The notes focus almost purely on the mathematics, not on “real world” applications (with a few exceptions in statistics topics). This is not because these are unimportant; on the contrary, they are vital. But I believe these are better addressed using methods other that pre-prepared notes.
  • The intent is that the notes would be hole-punched and kept in a binder. This means if a teacher doesn’t like how I’ve done something, they can change it. Remove the parts you don’t like. If you don’t think there are enough examples, add more.
  • Teachers can incorporate the notes and examples as they wish into their lessons. While textbooks give they answers to examples away from the start, with fill-in-the-blanks, the teacher can choose at what point in the class discussion they make the correct answers known.

You might remember that I was working on a book of Algebra 2 practice questions. That’s still ongoing, but it’s been overtaken somewhat by these notes. But that’s okay, because I see these as two aspects of the same long-term project. Having the notes planned out should make planning questions a lot easier.

If all of this sounds good, here’s the great news: I’m going release the notes as I work on them. And while they’re still just a first draft at this point, that first draft is entirely done, and hopefully in a usable form for the upcoming school year.

Download them here:

 

Quadratic Vertex Form Card Sort

Over the weekend, I needed a break from working on grad school assignments. At the same time, Sarah needed a card sort on the vertex form of quadratic functions. Being the nice husband I am, I thought I’d help. Being the nerd that I am, I did it in LaTeX.

This took a bit longer that I’d expected to create. I’ve a little experience creating graphs, so they weren’t too bad, but tables in LaTeX can be a little fiddly to get right. I also wouldn’t claim that took much thought went into choosing which functions to use. But, I’m pretty happy with the result.

You can download the files here. Included is the shuffled set of cards (pictured above), the cards sorted into the correct order, and a zip file of the original .tex files in case you want to modify them at all.

Edit (Oct 23): There were a couple of mistakes in the original version, it has been fixed now.