Author: Shaun Carter

I’m currently working through our “Primes and Indices” unit with Year 7. We’ve already looked at square roots of perfect square numbers, and did a quiz on them today. But we also wanted to look at find the square root of other numbers. For this we played The Square Root Game:

Basically, teams of four students try to find the closest estimate they can for the square root I give them. I find students really struggle with answering questions on estimating. They often seem to have the idea that ‘estimating’ is the same as ‘guessing’, and don’t realise the importance of trying to be as accurate as possible.

With competition, being as accurate as possible became paramount to the students. Also, being in teams, students had to be able to be able to communicate with each other and justify the answers they chose. After giving them a little time to discuss, I asked each group to hold up their whiteboard with their answer. Then I calculated it using the IWB and calculator in Google, as this was the quickest and easiest way to display the result.

The students were a little blown away that you can do this in Google. 😉

I found this game worked well. Students quickly figured out how to use the perfect square numbers to find which integers their answer needed be between. But shortly after, this itself wasn’t good enough, as every team knew how to do this. So as the game went on, they became more and more precise with their estimates, trying to outdo the other teams.

I started the game with the square root of 4, just as a warm up, and to give everyone an easy point at the start. Unfortunately, one team wasn’t paying attention and missed out on that point. But I think this made an important point for the class: some square roots give us exact answers, but some do not.

A nice side effect that I hadn’t planned for were the discussions around how close decimal values are to each other. One of the square roots was √30 (approx. 5.4772), and there were estimates of 5.45 and 5.49. At first the students weren’t sure which one was closest, so we were able to discuss around that.

So the title of this post suggests that I’ve updated my classroom rules for this year. The truth is, though, this is the first time I’ve really set out my rules clearly. I know, that sounds terrible. In the past just told students to defer to the school rules. They have a list of behaviours mapped with consequences in their student diaries. That should be enough, right?

Well, that’s what I’ve thought previously. But I want to take a more proactive approach to behaviour this year. I want to set very clear expectations for my classroom. But at the same time, I want to be directing students towards the positive class habits I want, instead of just steering them away from the habits I don’t want.

So, my rules are very simple: Be organised. Be attentive. Be respectful. Be persistent. Be awesome.

This is printed on a bright pink slip of paper glued into the front cover of each student’s workbooks. Don’t worry, I did get these out at the start of the year, even if I’m only getting around to blogging now. 🙂

I feel like the first three rules cover the “PLEASE, PLEASE JUST SIT DOWN AND BEHAVE YOURSELVES SO I CAN ACTUALLY GET AROUND TO TEACHING, FOR GOODNESS’ SAKE!!!” type rules. But I don’t want just that to be good enough. Because I want to see positive attitudes applied to work. I don’t students to give up the first time they have to think for themselves. And I don’t want to settle for a mediocre effort.

I also feel like I should be applying these rules to myself. These should be the attitudes I model as a teacher. I definitely need to be more organised. And I should always be striving to “be awesome”. 🙂

Warning for maths people, you may want to ignore this post. 😉

While maths will always be my first teaching love, I do teach a few ICT classes, including VCE Information Technology. A requirement of the subject is that all our work is based around a process called the ‘Problem Solving Methodology’. This consists of four stages: Analysis, Design, Development and Evaluation.

I recently made some posters explaining the four stages of the VCE IT Problem Solving Methodology. These probably aren’t very useful to many people (you’d have to be a teacher or student of IT in Victoria), but I thought I’d post them anyway. There’s nothing new here, this is all from the VCE IT Study Design, though I have reworded a lot of it so it makes more sense to students.

Note that with the new Study Design coming in next year, these are really only good for 2015. But I’m pretty sure the only thing that needs to change is the renaming of the subject to ‘VCE Computing’.

Downloads are below.

Downloads:

• Microsoft Publisher: Problem solving methodology.pub
• PDF: Problem solving methodology posters.pdf

To start by stating the obvious: I have not blogged enough this year. As in, my last post was before the school year had even started. I could make excuses (which would basically consist of ‘way too busy’, ‘not enough time’, ‘seriously, I’m crazy busy’), but I know I’m a better teacher when I blog. I know the constant process of self reflection is good for my ability to be self-critical.

Now that I’m starting my favourite topic of all time with Year 7, Primes and Indices, I thought this was a good chance to get back into this blogging thing. As my girlfriend reminded me the other day, I’ve been known to write ‘#primenumbersaremyjam’ in messages before. Number Theory was my favourite uni subject by far. And, I guess you noticed the title of this blog. I also may have gone through the proof that there are an infinite number of primes with my Year 12s today (which has very little to do with the differentiation we were supposed to be doing).

So I get just a little bit excited when I get to teach this. 😉

So, the Sieve of Eratosthenes, aka ‘that thing where you cross off a bunch of numbers to find the prime numbers’. If you’re not familiar with it, the process is this:

• Ignore 1, because it is neither prime or composite. 🙂
• Select the first number, which is of course 2. We’ve found our first prime!
• Eliminate all the multiples of 2 (except 2 itself), as these are not prime.
• Select the next number that is left, which should be 3. This is also prime.
• Eliminate all the multiples of 3.
• Select the next prime number, which is 5. (4 was eliminated by 2). Eliminate its multiples.
• Continue this process to find the rest of the prime numbers.

I googled for a worksheet for this (or really any number grid would’ve done), but I wasn’t really happy with what I found. Most number grids seem to go up to 100 or 120, but I wanted to go to 150. Mostly so I could include 121, and make it necessary to cross off the multiples of 11 (there are smaller multiples of 11, of course, but they’re all eliminated by the smaller primes). The next step, then, was to throw together my own worksheet, which looks a little (or exactly) like this:

Some people may have decided that ‘Finding Prime Numbers’ would make a better, less confusing title for students, but I disagree. I think we need to expose our kids to the accepted terminology, so they can communicate in correct mathematical language. We just need to teach them what the terms mean, which is our job, by the way. I get rather annoyed when I see students being told they’re studying ‘chance’, say. Call it ‘probability’. Because that’s what it’s called. #pettyrantover

I decided that this time I would be really precise with how I wanted students to mark off their sheet:

• Colour in each prime completely using a different colour. (After 11, I let them start using a single colour, because they would have run out.)
• When eliminating composites, draw a single line through each multiple in the same colour as the prime number. If a number has multiple prime factors, it gets multiple lines through it.

My partially completed sheet. Unfortunately the rest of my awesome highlighters are at school, and I am at home. But it should give you the idea.

This, for one thing, made the sheets a lot neater. But it also made it easier for kids to notice patterns. Patterns which they kept showing me completely un-prompted. I had students not only tell me that the multiples of 11 make a diagonal line, but they explained why that happens. #mathsteacherjoy

Another moment of joy came when I saw students write down their reasons that 2 is prime, using the definition of prime numbers. 🙂

Downloads for this worksheet are here:

• PDF: The Sieve of Eratosthenes.pdf
• Editable Word document: The Sieve of Eratosthenes.docx
  (You’ll need the font ‘Josefin Sans’ if you don’t want it to look weird.)

Hi there! Despite possible reports to the contrary, I am still alive. Yeah, I know it’s been a very long time since my last post. It’s not that I haven’t had anything to write about. Things have been very busy for me. But that’s really just making excuses.

So new year means new school year (which always seems to surprise northern hemisphere readers), which means a whole heap of changes. Here are some of the things I have to look forward to this year:

New classes

My maths class this year are

• Year 7 Maths
• Year 9 “Exploration”
• Year 10 Maths (in Semester 2)
• VCE Maths Methods Unit 3 & 4

as well as IT classes

• Year 9 & 10 Software
• VCE Information Technology Unit 1 & 2

(I’m probably just a little bit too excited about not having to teach physics this year!)

These are mostly subjects that I’ve taught before (if a few years ago), but I’m excited to see how I’ll be able to refresh the way I teach each of these. The exception is…

New subject

… Year 9 & 10 Software. This isn’t just a new subject for me. This is a new subject for the school which I basically invented, am currently developing and will teach for the first time this year. Okay, claiming I “invented” the teaching of programming is going way too far, but it was my idea to make it an elective at our school. This is part of an ongoing effort to refresh our ICT offerings, which also involved me teaching “Web Development” last year.

There will be a lot of experimentation as I figure out the best way to deliver this. We will be using Python as our language, but there are many different things we could actually end up doing with it.

The nice thing is that I’ll be able to teach whatever I want (within reason), which means sneaking a lot of maths into the course. 😉

New classroom stuff

I’m tweaking the way I do a lot of things in the classroom, including my marking, quizzing, classroom rules, notetaking, and more. It’ll be interesting to see how these go. Hopefully I’ll elaborate more in the future.

New Old responsibilities

My non-teaching responsibilities are mostly the same as I had last year, but I’m hoping that the year of experience will allow me to consolidate and build on those roles this year. In particular, I’m hoping we make significant progress on examining and improving our sequence of maths pedagogy throughout the entire school.

New blog posts!

Yay! Hopefully a bit more regularly! (I can dream, can’t I?)

New, um, personal stuff

The last part of 2014 and my summer holidays were, for lack of a better word, amazing. I’m not going to go into any of that now, but hopefully (if you care) I’ll get around to sharing more information eventually. Let’s just say that I while I hoped that getting involved in the MTBoS would affect my professional life, I never knew it would change the rest of my life quite this much. If you really have no idea what I’m talking about, there are clues on twitter and in other blogs. 😉

*EDIT (2015-08-12): So, that got a bit cryptic at the end. 😉 If you really want to know what I was talking about, you might want to read this.