Functions INB Page

I've decided to make functions the key focus of the first few units of Algebra 2 this year. I mentioned this in my post about my SBG skill lists: This year, the start of the [Algebra 2] 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. With that in mind, I thought I'd better make sure my students understand what a function is. This is the front, basically just explaining what a function is. The examples on the bottom section were actually done after the notes inside. You could really use any examples you wanted. I chose these ones...

Solving Linear and Absolute Value Equations INB Pages

This is the second skill for Algebra 2, which is pretty much what it says in the title. At this point, we're almost ready to start talking about functions, but I wanted to "review" a few things about solving equations first. Which brings us to these pages. Except, lets just pause for a moment, and examine those quotation marks around "review". The linear equation stuff is straight-up review, but solving absolute value equations is one of those used-to-be-in-2-but-now-in-1 topics I wrote about last time. Which means it's new to my students this year, but should be something my future Algebra 2 students have already seen. With that out of the way... Nothing terribly complicated here. These should be equations my students know how to solve, but as I suspected would be the case, they needed some help shaking some of the cobwebs loose first. I find students get a lot...

Simplifying Radicals INB Pages (with adding and subtracting)

Our very first skill in Algebra 2 this year was this: IN1: I can simplify radical expressions. Even though it isn't particularly related to the rest of the first unit (it's called "Introductory Algebra Skills", but it's really functions and transformations, focusing on linear and absolute value functions), there are a number of reasons I wanted to start with this skill: In the change over to the new (now one year old) Oklahoma Academic Standards, this content migrated from Algebra 2 to Algebra 1. Meaning my students (who mostly took Algebra 1 two years ago) missed out. So, starting with this is one way of bridging the gaps between the two subjects and the two sets of standards. To a certain extent, this topic stands on its own, so I saw it as a way to get into our course quickly and let my kids start to get the feel...

Undefined Terms INB Pages

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...

SBG Skill Lists 2017-18

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...

Planner Calendar 2017-18

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...

Algebra Graph Sketcher (aka Parabolator 2)

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...

Parabolator: A quadratic sketching tool

There's a new version now, with more functions! https://blog.primefactorisation.com/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,...

Making my Gradebook more managable

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...

My first year. Again.

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...

ZERO!

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...

Building Equations... Again

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...

Order of Operations Posters

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: GEMDAS.pdf GEMDAS.pub...

Inequality Symbols Posters

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...

Converting Units Posters

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: converting units.pdf converting units.pub 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....

Classroom Rules Posters

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: classroom rules.pdf classroom rules.pub The fonts are Archistico and Coming Soon....

Parent Functions 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: parent functions.pdf parent functions.pub Font is Wellfleet, which is quickly becoming one of my favorites....

Algebra 2 Units and Skills

New standards means new plans. Except I've only just moved to Oklahoma, so I'm teaching Algebra 2 for the first time anyway. Good timing, I guess? 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: alg2units.pdf alg2units.docx Your browser does not support iframes. I've already shared my Geometry units and SBG skills list for this year....

Planning Geometry Notes

I'll be teaching Geometry for the first time this year. Actually, everything is for the first time this year, as I've never taught discrete high school math subjects before*. It feels like I'm starting from scratch with my planning. 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: geomnotesv1.docx geomnotesv1.pdf To be clear, this is not a document I'm giving to my students. This is for me, to make sure...

Perfect Cubes Images

You may have seen Sarah's recent post about making posters of perfect square and cube numbers. She was talking to me about how she would go making the cubes. I thought about it for a bit, and thought there must be some way to do it in Geogebra. Turns out, there is! 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: cubes.ggb cubes.zip (Contains PNG image files for 1³ to 10³)...

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Shaun used to be maths, IT and ocassional physics teacher at a small P-12 school (primary and secondary) in rural Victoria, Australia. He is currently in the process of starting his career again in the United States.

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Dropping the S

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Sarah is also a math teacher, and she's much better at this blogging thing than I am:

Math Equals Love

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Shaun Carter
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