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)...

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...

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....

Designing your own planner? Pay attention to the end for some files that may save you a lot of work. Both Sarah and I have been working on our planners for the next school year. We're both using the Staples Arc system to completely customize them. Sarah's already blogged about starting to design hers. Here's what I've been working on. At my last school, all teachers were provided with a planner. While we were given the choice from a catalogue of the exact planner we wanted, I could never make it work in a way that suited me. Most planners have spaces for each class in a single day on the same page, but I don't like having all my subjects mixed up together. I want to have a separate section for each subject, with all my notes, lessons, grades and everything else for each subject self contained away from...

Following on from planning units for Geometry, I've created SGB score sheets for students that also act as dividers between units for their notebooks. If this idea seems familiar, that's because I've totally stolen it from my wife. I feel like that's justified, though, because she's already asked me to send her the template so she can use it herself this year. I've seen some of Sarah's students' notebooks that use these, and can attest that they work really well. That's Euclid, in case you were wondering. They work by folding the sheet of paper along the middle of the narrow rectangle, then gluing the sheet around one page of a notebook so that the unit name sticks out the side of the book. You can find my files here, including a blank template: dividers.pub dividers.pdf dividers template.pub You'll need Microsoft Publisher to edit the original files....

First, the good news. I have a teaching job lined up for this August! While I can't go into details about it quite yet (partly because I'm not sure of some of the details myself), I'm pretty certain I'll be teaching Geometry some of the time. Having to start planning everything from scratch is a little daunting, though with new standards being introduced in Oklahoma this year, I'm pretty much in the same boat as everyone else here. I've started planning what my units will look like. I've never taught Geometry as a single year long subject like this before. In Australia, all students take "maths" through Year 10, with the three content strands (Number and Algebra, Measurement and Geometry, and Probability and Statistics) taught each year. Even in Year 11 and 12, the subjects available are more split by difficulty rather than by mathematical area. This means I've taught...

In this period where I'm not in the classroom, I'm trying to keep myself busy with a few little projects. One of those things is working on updating my coding skills by creating interactive activities using Javascript. The first of these is a simple puzzle where the aim is to switch the positions of the two sets of counters by jumping them over each other. If it seems familiar, that may be because I posted about using this puzzle in class in 2014. (Or it may just be that this is a fairly well known puzzle). That post has more information about how I related the puzzle to a nice quadratic relationship, and used it to explore distributing and factoring*. The puzzle is embedded below, but the full version of the puzzle will be more useful for using in class. It explains the rules of the puzzle more clearly, and...

Four. Months. That's how long it's been since my last blog post here. Although, I think I've had a bit of an excuse. Things have been rather crazy for me lately. I'm as guilty as anyone of saying "things have been crazy" when I really mean "things have been the normal amount of excessively busy which comes with being a teacher". But these are pretty exceptional circumstances I've been in lately. So ever since Sarah and I announced our engagement, there's been a little of this going around: Well, the answer is... pause for effect I am moving to the US (Drumright, OK specifically) in a few short weeks. Sarah and I are getting married shortly after that. Moving to the other side of the world was never on the list of things I planned to do with my life, but it's funny how quickly plans can change when you...

Problem I gave to Year 9 a few weeks back: Imagine taking an A4 sheet of paper, and cutting the corners out so it folds into a box. What is the maximum volume possible? Or how I actually presented the problem: I'm sure that any non-metric types could easily adapt this to letter size paper. ;) This is the type of question I'd typically use with my Year 12 class, and expect them to use calculus to solve. But Year 9 had to use other strategies. (One student did manage to find a website that told him he would have to use differentiation, and wanted me to teach him what it is, there on the spot...) So, trial-and-error was the game instead. Some students realised this immediately, while others needed a little bit more of a push. I remember being a student and hating trial-and-error as a strategy, because it always...

I've been left in an interesting situation with my Year 10 class. This is their last semester before moving into VCE or VCAL, where they get to choose their own subjects. This means that they'll be studying a variety of maths subjects, at different levels of difficulty. Not to mention that under the Australian Curriculum, maths already has an extra level of content beyond Year 10 ("10A"). Further complicating things is the fact that I only took over this class halfway through the year. I want each student to have the best preparation possible for their plans for Year 11. How a student is planning to continue with their study has a lot of bearing on the content they need to be working on now. For instance, the students who want to study Mathematical Methods (the second hardest maths in VCE behind Specialist Maths), or are considering it, would be...

Continuing on from my last post, here is the feedback I got from Year 7. Like last time, I used Start, Stop, Keep and Change, and I'll go through responses for each question, adding my own reflections as I go. I'll be honest, a lot of this feedback wasn't particularly helpful, such as asking me to change things that are school rules or I otherwise have no control over. Or asking whether we can do no quizzes or no written work at all. It reminds me that Year 7 students still have a lot of maturing to do, and that I need to take a lot of the things they say to me with a pinch of salt. Start Teaching us maths that we use in our every day lives. I want to rant about this one, but I'm trying to resist. I don't blame the student for repeating the...

Near the start of Term 3, I gathered feedback from some of my classes about what they think of the job I do as a teacher. My plan was to write reflections about it shortly afterwards, but this got pushed back as other things got busy. With a week to go in the term, it's about time that I do this. This is the feedback I got from Year 9. Hopefully I'll get to Year 7 soon. I never took feedback from Year 10, because I had only just taken over the class in the middle of the year, but I plan to to this with them early next term. Just like other times I've gathered feedback, I used the Start, Stop, Keep, Change format, and since our students have one-to-one laptops, it was easy to create a simple Google form. I'll go through each section one at time, and...

Today's lesson with Year 7 looked at front, side and top perspective drawings of 3D shapes. The moment of inspiration hit me when I woke up this morning (which is an improvement over the more common 10 minutes before the lesson starts), but I decided I wanted students to create their own perspective drawings using their imaginations, then turn them into 3D themselves. This is a lesson in three parts: Task 1: Warm-up practice I expected that my students had seen drawings like this before, but I was unsure how confident they would be. So, I gave each pair of students an arrangement of blocks to draw from the three perspectives. Block shapes for practicing 3D perspective drawing with year 7. #teach180 pic.twitter.com/akH7dDy5bA— Shaun Carter (@theshauncarter) September 7, 2015 I had one colleague comment in the morning that it was nice to see me playing with...

In introducing rotations to my Year 7 class, I had them create a... thing. "Foldable" isn't really the word I'm looking for here. I think it's better described as a "spinable". Anyway, it looks like this... ...and this. The main idea is that students aren't just told what a rotation is, and they aren't just shown, but they actually create the rotation themselves. To do this, each student will need: An A5-ish sheet of paper (or half a US letter sheet will do). An piece of tracing paper half the size. One of these pin things. I always called them "split pins" growing up, but I think they're actually called paper fasteners. Get students to fold their paper in half, and draw any picture they like (school appropriate, of course) in one half. I only gave them 30 seconds to draw a picture, because I didn't want them spending the...

The gradient of ax + by = c is -a/b. This is what Year 10 wish I had told them lessons ago. They've been looking at parallel and perpendicular lines lately, which involves finding lots and lots of gradients. They like it when the equation of a line is in gradient-intercept form. The gradient is m from y = mx + b, and everyone is happy. As an aside, why is m used for gradient/slope? Does anyone know? I've had kids ask me that so many times, and my honest answer has been "I haven't got a clue." I was annoyed at the lack of images in this post. So here's some parallel and perpendicular lines, just because. Anyway, they aren't so happy with standard form. They know how to rearrange between the forms, so they've been changing them into gradient-intercept form to find...

There was sport on today, so a large portion of my Year 7s were away. As a result, I had an exchange with some of the remaining students at lunch time that went a little like this: Student 1: We've only got 6 students in our class today! [Stretching the truth a fair bit, it was more like 15.] Me: Okay. Student 1: So we don't have to do maths, right? Student 2: Or if we have to, you can only make us do easy maths. Unfortunately for them, I had a different idea. Sometimes when a lot of kids are away, it's necessary to not continue with normal plans so those kids don't get left behind. However, I still think that having the students that are left with me for 50 minutes is still an opportunity for them to learn. So today, we looked at intercepts of linear graphs....

The other day I posted this problem that one of my students discovered. We played around with it for a while and came up with this solution. I don't know if this is the easiest or most elegant solution, but it's what I have. Quick recap, we're trying to solve the equation 6a + b = ab, where a and b are non-negative integers. In Australian rules football, if a is the number of goals (worth 6 points each) and b is the number of behinds (worth 1 point each), the solutions to this equation are the scores where the total score is equal to the product of the goals and behinds. Solutions can be found by trial and error, but how can we be sure we've found all of them? How do we know the solutions don't just continue on forever? Well, it turns out that a...

As a maths teacher, one of my aims is to get students to think about the world mathematically. So there aren't many things more exciting than having a student come to me with a problem they noticed and are trying to solve themselves. Just for the fun of it. This is the story of one of those moments. The other day I had a student stay back after school and told me of a problem he was going to figure out. He had noticed a pattern in the football scores he'd seen over the weekend, and wanted to know how many different ways that pattern was possible. Now, unless you are from Australia, this going to take some explaining. In this part of the world, "football" refers to Australian rules football (which is not rugby, despite the fact that I've blogged about that before). Credit: Tom Reynolds. Sourced from Wikipedia....

The other day I wrote a post about having students build their own equations. I decided to use this idea as a starting point for solving equations by backtracking. The class has already solved equations in a number of ways, and even used flow charts to solve them with backtracking. But now I'm trying to introduce them to more formal algebraic notation to show their backtracking. As it turns out, they've already written their working out like this before, last lesson. Now they need to learn to write each step working backwards. I wrote the following on the interactive whiteboard: I made it clear that I was making this equation up as I went, and that I was following the exact same process as they did when they constructed their own equations. The only difference being that I haven't written down all the steps for them to see. Their job...

### author

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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### my website

The place where I put other stuff, usually math related coding:

primefactorisation.com

### my other blog

My journey from Australia to the United States:

Dropping the S

### my wife's blog

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

Math Equals Love