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This last week saw my Geometry classes finish off our introductory Reasoning and Logic unit, which means we’re ready to go with setting up the basic building blocks of geometry: the Undefined Terms.

I took similar notes last year, but they were constrained to a table on half a letter sheet. This year, I redesigned it to give us a bit more space.

My students questioned why we have terms that are undefined, especially after we went over the importance of good definitions in our last unit. I reminded them that definitions use existing terms to define new terms, but that can’t happen unless we have these few terms to build everything else on top of. (Is this a good explanation? Let me know if you know of a better reason to justify the undefined terms.)

Next was our first set of postulates and definitions for the year.

A change from last year is that these postulates are glued directly onto a notebook page, rather than folded inside a foldable. This is due to a decision I’ve made this year: all postulates, theorems and definitions will be visible immediately on the page they’re on. Examples, proofs and other content can be hidden in foldables. But if I’m going to expect students to look up certain parts of their notebooks frequently, I should make those parts easy to find.

Before we wrote these down, I did a little activity to get my students thinking about why these are true. I drew two points on the dry-erase board.

I didn’t get any photos of this, so I’m re-enacting these on my computer.

Then I asked if any volunteers could draw a line through them. That went well enough:

I asked if they could do this wherever I put the points. The consensus was that they could. So far, so good.

Then I asked if anyone could draw a different line that also went through the two points. Some kids started saying yes, but then took that back once they realized they didn’t know how to do it. One even got as far as standing at the board with a marker, before handing it back to me and saying it couldn’t be done. My plan had worked as I’d hoped. The class had figured out Postulate 1 without me having to tell them what it was.

After we had written Postulate 1 down, I set my next challenge. Draw two lines that intersect at one point. No-one wanted to stand up to do this, because they thought it might be another trick question. But eventually, I coaxed one student to the board, who drew something like this:

Then I asked for two lines that didn’t intersect at all. I heard a student say the word “parallel”, so I handed her the marker:

Then I asked if anyone could draw two lines that intersected twice. But they knew my game by this point, and let me know it couldn’t be done. So it was time to write Postulate 2.

We didn’t get through the rest of the notes in this lesson, but I’ve written them up in my notebook anyway.

If you want to download these, you can do so here:

• Undefined Terms
  .pub
  .pdf
• Points Lines and Planes: Postulates and Definitions
  .pub
  .pdf

Let’s cut to the chase. Here are my units with SBG skills (and alignment to the Oklahoma Academic Standards) for both Geometry and Algebra 2:

• geometry units.pdf
• algebra 2 units.pdf

Last year was my first year teaching under the American system, with brand new standards as well. There were some parts of my courses I was happy with, but a lot of things I’m changing this year.

I’m pretty happy with how Geometry went last year. I knew pretty much from the moment I was hired that I was going to be teaching it, so I had a lot of time to think about how I was going to arrange things.

The biggest change this year is moving Trigonometry from the end of the year. I realized as I went through other units that it would have been useful to have kids knowing how to use right-triangle trig to solve problems, especially ones involving area. I’ve also scrapped the introductory unit, which was mostly some Algebra 1 review and the Pythagorean Theorem. Pythagoras is joining the trig unit now, and I’ll review things like solving linear equations as the need arises.

Algebra 2 is changing a lot. Last year, my first non-introductory unit was Quadratics. I found the classes getting bogged down, not making a huge amount of progress. Having to cover both graphing as well as factoring and all the algebraic manipulation that goes along with it got to be a bit too much for my kids. I never really felt like we’d built a solid foundational context for the rest of the course to rest on.

This year, the start of the course is going to focus on functions, transformations and inverses. For quadratics that means only dealing with vertex form, as well as showing the relationship to square roots. We’ll cover all the functions that way, before coming back to all the other algebra we missed along the way. So we’ll cover quadratics again, including all the factoring and solving stuff.

While it’s not proper spiraling, I guess it’s sort of a slow spiral.

I’m also teaching Statistics this year, but I won’t be using SBG for it. I feel like I need to learn a bit more about how a standalone stats class works before I attempt that.

Last year I created quite and elaborate set of calendar pages for my Arc planner. I was really pleased with how they turned out and thought they looked really nice.

And then I didn’t really use them. There was much more space than I ever really needed, and having multiple levels of pages (monthly and weekly views) meant I never really knew where to put anything. I really want to be the type of teacher to make constant use of my planner. I’m hoping that I’ve found a layout that actually suits the way I approach my planning.

I like having a broad view of a lot of days, but a monthly page doesn’t really help. Because the cycles of school don’t really occur in months, they occur in weeks. But one week to a page doesn’t show enough in my personal opinion. So I created a design that shows three weeks to a page.

I usually create this sort of thing in Publisher or Word, but this one is Excel, using formulas to set all the dates.

Download: calendar2017.xlsx

All the values reference the date in cell A2. If you want to change the starting point of the calendar, change that value (type the full date, not just the day). If you want, say, two weeks to a page, make the columns wider. The font is Wellfleet, but feel free to change that if you want.

A couple of months ago I shared a tool I created for sketching graph of parabolas. I called it the Parabolator. I don’t know why. It made sense at the time.

Anyway, I wasn’t satisfied with it. It has a lot of limitations – mainly, it can only sketch parabolas. Also, the code behind it is a mess. I thought I could do a better job, and thought it’d be much more useful if it could handle other types of functions.

I spent a few days working on a replacement. Then we went to Australia for two months, and I forgot about it. Then I remembered it today.

So, here it is! Introducing the Algebra Graph Sketcher. I know it’s a much more boring name than Parabolator, but I guess my desire to be accurate won out over my desire to be silly this time.

For anyone who’s interested, I’m using Vue.js for the control interface, D3.js for the actual graph, and Lodash for… something? I guess this is why you should post about something while you still remember how you made it in the first place.

There’s a new version now, with more functions! https://www.primefactorisation.com/blog/2017/08/06/algebra-graph-sketcher/

Yesterday was the last day of our school year, so it’s finally time to relax! And by relax, I mean write code.

I was thinking about the tasks I want to set for next year, and wanted to find a tool to help create sketches of graphs. Not plots of graphs: there’s already an obvious solution for that. No, I mean a bare sketch that shows only the most important points. It doesn’t need to precise, but it does need to be clear, and easy to copy.

I searched for a while, but couldn’t find anything that was really what I wanted. There are plenty of tools that can do the job, but not without a bunch of messing around first. So I decided to write my own.

Introducing: the Parabolator.

To be honest, the code behind it is kind of a mess, and it’s extremely limited, but it works. Mess around with it yourself to see what it does. Basically, it draws a parabola based on the location of the vertex and one other point. The vertex and the “second point” can be dragged wherever to set the parabola’s position, while the “third point” will position itself on the existing parabola when dragged. The axes can be moved by dragging the whole sketch. Each of the points can be toggled invisible, have labels added, and can be “locked” to the axes. When you’re done, click the download button to save your graph as a SVG file.

To be clear, this is not intended to be a learning tool, and the target audience is not students. I made this purely to help myself create graphs for assignments, and I’m sticking it online because I figure other teachers might find a use for it as well.

The use case I see for this is the rapid creation of a graph that can put into an assignment or quiz paper. It saves as a vector image, so it won’t create big ugly pixels when printed as can happen when a graph is created from a screenshot. One thing I happily discovered today is that SVG files can be directly inserted into a Word document.

I’m not going to promise it works perfectly. I’ve really only tested it with Chrome, so use that if you want the best chance of it working properly. I did also have success in Firefox, but Microsoft Edge has problems with the download feature. The most obvious drawback to the whole thing is that it only does quadratics. I do want to modify it to support other types of functions, but I’ll leave that for another day.

This is just a hobby project, so I’m not sure if I’ll spend much more time on it. That said, I do have some ideas about what I want to do (especially with adding other functions.) If you’ve got any suggestions, I’d love to hear them.