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

]]>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.

]]>We have one week to go, which means one thing. Okay, it really means a lot of things, but I'm thinking of one thing in particular. Certain students are just realizing what I've been trying to tell them all year. Their grade is not high enough and they're going to have to retake a whole bunch of quizzes before the end of the year if they want to pass.

Let's try and make this a bit more positive. There's also a large contingent of students trying to turn Cs into Bs, Bs into As, and even some trying to turn 99% into 100%.

Whichever way you look at it, one result is that I have to spend a lot of time with my gradebook, entering quiz scores from random times throughout semester 2, and fielding requests from students to know their grade. The software my district uses doesn't make this the easiest thing to do. It separates each "Nine Weeks" and makes switching between them annoying, taking a few seconds of loading time and completely resetting the view I had open just before. Throw in that the same thing happens if I want to enter attendance, and that adds up to a lot of wasted time. My solution to date has been to open multiple web browser tabs with a different view in each. But that makes my browser cluttered and remembering which tab is which among all my other tabs becomes difficult. Not to mention, the address bar and tabs take up valuable space for seeing students and their grades.

I've come up with a solution. Google Chrome has a feature that can turn any webpage into a standalone web application, which is displayed as a separate window with a title bar and nothing else. It appears as a separate app on the taskbar (in Windows at least), which means it doesn't get mixed up with the rest of my random web browsing. The software my district uses is Wengage, but this applies equally to any gradebook you can access through Chrome (I haven't tried this with other browsers, but they might do something similar.)

To do this, navigate to the page you want to make an app in Chrome. Click the "three dots" button (I'm sure Google give that a proper name) and select **More tools**, then **Add to desktop...**

This will put an icon for your new app on your desktop (unsurprisingly).

Double click that icon to open the app! If you want, you can find the option to "pin" the taskbar icon (keep it there even when the app is closed) by right clicking it.

To be honest, it really is just a chrome tab that looks a bit different, but that's exactly what I wanted. By appearing as a separate window, it's out of the way but easily accessible. If you want multiple windows (say, one for grades and one for attendance) hold the shift key while you click the taskbar icon. (Useful tip: this works for almost all Windows programs.)

Is this going to revolutionize the way I manage grading? No, not even slightly. But it has made something I find annoying into something slightly less annoying. Which, to be honest, is exactly what I need as a teacher sometimes.

]]>Two weeks to go.

Do you remember what it was like to be a first year teacher? I do. I remember it really well, because I feel like I've lived through it again. It turns out that starting a teaching career again in a new country is really hard. But just like my actual first year, I know that pushing through it has taught me so much about education and will make me a much better teacher as a result.

I could make this a "these are the differences between Australian and American schools" type post, but I'm trying to avoid that. Suffice it to say, there are some very big differences, which have meant I've had to make so very big changes.

My math classes this year have been Algebra 2 and Geometry. All math teachers in Oklahoma have had to learn new standards this year, but I've had to learn new *subjects*. I mean, it's still math, but it's not arranged in a way I've ever seen before. My year 7 maths and VCE maths methods plans are not going to do me much good anymore. Even when teaching the same content I've taught in other classes before, I can no longer make the same assumptions about what students have been exposed to in previous years.

So I've basically had to start from scratch. I mean, I *could* just follow the textbook each lesson. That would certainly make my life a lot easier. But that would go against everything I've come to believe about math teaching since beginning my career. I've got no problem using a textbook from time to time, and some books come with very interesting questions or investigation ideas, but the textbooks I have available are *terrible*. They're old and falling apart, they're much more focused on procedure than understanding, and they don't even align to our standards now.

That means that on top of teaching subjects for the first time, I'm also doing interactive notebooks for the first time. That means creating a whole heap of resources throughout the year. I know there are many others who have shared their foldables online, but when it's the night before I have to teach a lesson, I usually end up making something myself. So many times I've found stuff this year and thought, "This is great... but it doesn't really fit with what I've done already."

You may have noticed my lack of blogging this year. I've found it really hard to find the time when I need that time for lesson preparation, and when I've had the time I've felt I need to stop thinking about school for a bit. I really wish I could've had more time for reflection during the year, rather than having to deal with the constant onslaught of "what am I doing tomorrow?"

I really do feel like this has been a year of learning everything over again. I've been bringing a lot more work home with me than I have in a long time. I've taught a lot more lessons that I would describe as awful than I have in a long time. I've been challenged with a group of students that are not very willing to give my lessons a chance. I've questioned my ability as a teacher a lot this year.

But I don't want you to think I'm in a negative mindset about teaching here. Because all of this also describes 2010, my first year teaching in Australia. And I know that year was the necessary challenge to get through to be the teacher I am now. And I'll look back at this year too, and see how much I developed through it.

I'm already excited about what I'm doing next year. I've already completely revamped my list of skills for Algebra 2, and have even begun writing problem sets for topics I think I can teach much better the second time through. I've slowly been evolving my classroom structures over this year, after seeing which things work for me and which things work, and I'm keen to implement more cohesive routines from day one next year. I know I'll get to reuse a lot of the stuff I've spent all that time on this year. And having a foundation to build on top of will give me the chance to craft much more engaging lessons with more student creativity and problem solving.

Just like my first-second year, my second-second year will start with me as a much stronger educator.

]]>As I was planning, I was thinking about how to motivate teaching factoring. In

]]>I invented a new game for factoring quadratic trinomials over the summer break. After waiting to get to quadratics, I'm excited that this week I was finally able to play it with my Algebra 2 classes.

As I was planning, I was thinking about how to motivate teaching factoring. In particular, I was inspired by Dan Meyer's thoughts, where he mentioned that locating zeroes is the key problem that factoring helps solve. I decided to find a way to make finding those zeroes the focus of how I introduced this topic.

This game, which I'm calling "ZERO!" is about evaluating expressions and finding zeroes. Students are in groups of four, and each group receives a set of 36 cards with a range of expressions on them. Most are quadratic trinomials, but there are some linear expressions, quadratic binomials and a handful of factored quadratics.

As a warm-up, I had students each choose a card, which I required to be a quadratic trinomial. I gave them a value for x, and they evaluated their expression with that value on dry erase boards. They then checked their answers with a calculator. My students are only just getting to grips with the TI-84, so I showed them how to store the value in x to evaluate the expression. Then I gave them a couple more values for x, which they also evaluated with the same card and checked with their calculator.

I asked if anyone got zero for any of the values of x, and a few students put their hands up. I revealed that this is the aim of the game - to get a card that evaluates to zero. The game works like this:

- Each group turns all of their cards face up so everyone can see all the expressions.
- Everyone chooses a card to place in front of themselves.
- The teacher chooses a number randomly between -5 and 6 (inclusive).
- Each student evaluates their expression with that number. I let them use their calculators so the game would go as quickly as possible, but I can see the benefits of having them do it by hand.
- If a student gets zero, they shout "ZERO!"* and turn their card face down, scoring one point in the process. If multiple students in a team get zero, they still only get one point.
- If a student scored, they replace their card for the next round. Other students can swap their card too, if they wish.
- Most points win. I went with first to ten points, before revising it to six, but a time limit isn't a bad idea either.

As we worked through the game, I started prompting students with questions about which cards are the best ones to choose, and which cards are easiest to evaluate. I was also asking kids which numbers they needed to come up for them to get zero.

Students started realizing that the quadratics were better than linears, because they have two different zeroes - mostly. There are a few quadratic cards with only one zero. I decided against choosing any expressions that couldn't be factored, because I didn't want a student to be stuck with a card they couldn't get zero from.

They also slowly realized that it was best to have different zeroes for their cards than the rest of their team (which is why I only allow one point per team each round). Four cards means eight possible zeroes, which is a better than even chance when there are twelve possible values for x. Of course, knowing what those zeroes are is easier said than done.

Well, until they know how to factor, that is. ;)

To play this game, you'll need the following:

A set of cards for every four students. I printed each set on different colored paper so they wouldn't get mixed up, and laminated them. I printed the word "ZERO!" on the back, but that's not really necessary. Download here:

You'll also need a way to choose the values of x. The easiest way would be to just own a 12 sided die numbered -5 to +6. Which I don't. So instead, the next most sensible thing to do is write your own web app to generate the numbers. Wait, that's not sensible at all. Oh, well. The good news, I already did that, so you can just use mine.

One bonus of having these cards is that I have practice questions ready to go. After going through factoring, I had students choose three cards each, which they factored and wrote as examples in their notebooks.

** I guess this part is optional.*

In Geometry we're going through our introductory review unit. I wanted to see what my students' algebraic

]]>I'm teaching again! There's so much that I can share about the start of my new job, but for now I just really want to blog about lesson ideas. So let's do that.

In Geometry we're going through our introductory review unit. I wanted to see what my students' algebraic skills are, especially with solving equations. I decided to expand on an idea I used last year.

The original idea was that students could get a better understanding of the way equations work by constructing equations themselves. If students are going to be expected to "backtrack", it makes sense that they should see how the equations go forwards in the first place.

So students choose a value to assign to a variable, then perform operations on that variable and value, step by step. They then exchange equations with each other, which they solve by finding the steps that created the equation in the first place.

My latest version has two main aspects. Firstly, it's now an INB foldable.

And secondly, there's a second part for creating problems with variables on both sides of the equation. This is a little more involved. I had students create two equations, starting with the same value and ending at the same result on the right-hand side of the equation. Then, they equated the left-hand sides of the equations to create the complete equation.

A big difference with these equations, however, is that solving the equation doesn't take the student through the same steps as the person who created it. But I think that's a good thing, as it highlights that equations like these require a different approach to solve. I hoping my students will recognize that having variables on both sides means that just backtracking won't get to the solution.

I realizing that one of my go-to ways to structure a lesson is having students construct their own problems for other students so solve. It really helps to "pull back the curtain" and show students what's really going on with different problems. Math seems completely opaque to so many students, particularly when they're only taught procedural methods. Instead, let's work on making math transparent.

Downloads:

]]>I've heard different people have different opinions between GEMA and GEMDAS. I like the idea of arranging the letters like this as a compromise between the two. It emphasizes that multiplication/division and addition/subtraction occur in pairs, at

]]>Next up in the back-to-school posterpalooza, it's the order of operations.

I've heard different people have different opinions between GEMA and GEMDAS. I like the idea of arranging the letters like this as a compromise between the two. It emphasizes that multiplication/division and addition/subtraction occur in pairs, at the same time, but students will hopefully not forget about the division and subtraction.

Sarah designed the Grouping Symbols poster. I thought it'd be nice to have my order of operations posters match her style.

Downloads:

]]>Okay, before I go any further, I feel I should clarify: I have not just been working on posters for the last week, despite them completely taking over my blog. I have been working on lesson ideas, too. I just want actually try them out in class, so I can reflect on how they went, before they make it to the blog.

Anyway, for today, another poster set: Inequality Symbols!

I guess equals is there too. But I thought "Inequality Symbols (and equals is there too)" wasn't a very succinct title, so there you go.

I was very tempted to redo these bigger, with a single symbol to a page. If you think that would look better, you have my blessing to change it. :)

The prime numbers next to it are courtesy of my wife. In this case, I didn't even need to print and laminate them myself. Sarah came into my room with an extra set she made for a reason she can't remember. They're designed to be one long column, but I thought I'd better at least contribute a little creativity to them in my room.

As always, downloads are PDF and the original editable format. Font is Marvel.

]]>Okay, I can measure stuff. But, like most of the world *except* the nation I now live in, I learned* to measure everything in metric. Mostly. I grew up on a farm, so I'm very used to measuring area

I'm a Geometry teacher who doesn't know how to measure anything.

Okay, I can measure stuff. But, like most of the world *except* the nation I now live in, I learned* to measure everything in metric. Mostly. I grew up on a farm, so I'm very used to measuring area in acres and rainfall in points and inches. But aside from that, I just know metric.

So this poster set is for me, more than the kids, if I'm perfectly honest. Or it is for them, when Mr. Carter is silly enough to give them all their measurements in millimeters.

Downloads:

Fonts are ChunkFive and Patrick Hand.

* *I also had to fix this word after typing "learnt" just now. It's going to take a while to break some of these habits.*

This tweet basically summarizes what the last week has been like in our house:

Rest assured, all. Laminating continues because we found an unopened box of 100 pouches. @reilly1041 @theshauncarter @druinok @misscalcul8

— Sarah Carter (@mathequalslove) July 31, 2016

The latest contribution for my walls are my classroom rules:

These basically are a slightly revised version of my rules from last year. You can download the posters here:

The fonts are Archistico and Coming Soon.

]]>I actually put these up a couple of weeks ago, but unfortunately didn't have any photos of them. Then the floors of the school hallways got waxed and we weren't allowed in. Until today!

Here's them next to my Geometry Symbols Posters

]]>New posters today for Algebra 2: Parent Functions!

I actually put these up a couple of weeks ago, but unfortunately didn't have any photos of them. Then the floors of the school hallways got waxed and we weren't allowed in. Until today!

Here's them next to my Geometry Symbols Posters.

Downloads:

Font is Wellfleet, which is quickly becoming one of my favorites.

]]>Anyway, I'll be using SBG this year. Here you'll find my complete list of units, containing the relevant OK math standards and 'Critical Gaps',

]]>Anyway, I'll be using SBG this year. Here you'll find my complete list of units, containing the relevant OK math standards and 'Critical Gaps', along with my SBG skills lists.

Downloads:

I've already shared my Geometry units and SBG skills list for this year.

]]>I've already posted my list of Geometry units and skills, mapped

]]>I've already posted my list of Geometry units and skills, mapped to the new math standards that Oklahoma is introducing. (I've done my Algebra 2 units too. I really need to get around to posting those.) Recently, I've been working on filling out a bit more of the details of what I'll be teaching. I don't plan on making too much use of the textbook, but I still want a list of the definitions, postulates and theorems written out. So, that meant making the list myself.

Downloads:

To be clear, this is not a document I'm giving to my students. This is for me, to make sure that my students are getting all the background knowledge they need as we progress through the course. There are still the day-to-day decisions about how I'm going to introduce these concepts in class, and how we will take INB notes each definition and theorem. I am very keen, though, to have students proven many, if not most, of these theorems themselves.

I'm considering this a first draft. I tried my hardest to make sure that everything that needs to be there is, but I'm not guaranteeing it. I would love feedback about anything, whether something could be worded a little more clearly, or there's a giant hole of content that I've missed completely. I know I'll be revising this document throughout the year.

* *You could read this post and change every 'UK' or 'Britain' to 'Australia' and get a pretty good idea of what I'm used to.*

Drag that slider, and you can change the number of cubes from 1³ to 20³.

This took a little bit of messing around to get right, mostly because I've never used the spreadsheet view in Geogebra before. Once I worked out that spreadsheet cells can contain graphical elements that get displayed, it was just a matter of plugging in the right formulas to generate all the lines.

Anyway, if you'd find this useful, you can download the file here:

]]>Firstly, my recent exciting news that I don't think I've blogged about yet:

- I have a job at the same school as my wife! :D
- I have my own classroom! This was in doubt for a while, as it seemed I might need to be a roaming teacher (which didn't bother me that much, because we all had to roam when I was in Australia.) But people got shifted around, and it turned out there was a room free.
- My teaching certification for Oklahoma finally came through last week!

The result of all that is that I'm teaching Geometry and Algebra 2 next year, and I have an empty classroom with no posters. Well, *had* an empty classroom. I'm working on that. :)

Here's my set of Geometry Symbols posters. Sorry about the glare. I've never taught "Geometry" as a single subject before. In Australia, maths is still integrated through high school, so there's just a little bit of geometry each year. So I found it very useful going through the units I have planned, figuring out what specialized symbols students will need to learn to take Geometry as a class. And putting them onto posters helps add a bit more color to my room.

Downloads are here:

Font is Arvo.

]]>Another coding project to share today: an online interactive for demonstrating the areas under a curve for a Riemann sum.

I started work on this a couple of months ago, then forgot about it. I'm probably not teaching Calculus in the near future, so I lost some of my enthusiasm for completing all the ideas for this project. But given the work I'd already put into it, I thought it would be worth sharing what I've got anyway.

You can find it here: http://www.primefactorisation.com/areaapprox/

I might come back to this at some point. Let me know if you've got any suggestions, or any functions you'd really like me to add to it.

I've also done this concept as an activity involving cutting and pasting.

]]>