Author: Shaun Carter

In my Year 9 textbook, the start of the chapter on area and volume starts with a “review” of areas from past years. And by that, I mean it says something along the line of “you should remember these formulas from Year 8,” then proceeds to list the formulas for the areas of various shapes.

Uhhh, no. Wasn’t going to cut it. I’m not doubting the importance of remembering the formulas, but the book makes a huge assumption that all students understood the formulas completely last year, and just needed a quick reminder before they jumped back into, I don’t know, completing boring lists of questions from the book I guess.

Instead, I didn’t just want my class to remember the formulas, I wanted them to explain how they work, where they come from. I broke the class into groups and assigned them different shapes. They had to produce a poster demonstrating how we can discover the areas of their shape using other shapes – ideally this would be something of an informal proof. Here’s some of the results:

This group didn’t end up showing the formula, but they did show the general idea behind the proof. With a bit more prompting, I’m sure they would have gotten to the formula.

This group showed two different methods for proving the area of a parallelogram, which is awesome. I especially like that the one using the rectangle didn’t involve any words. I think my students are slowly getting around the idea of using mathematics instead of English to communicate.

I made this one. I thought the circle was a bit beyond my class, but I still wanted a poster for it.

Rather than trying to explain my poster myself, I showed the class this video from Minute Physics:

Happy National Science Week everyone!

While maths and IT are my main teaching areas, I do dabble in science from time to time. This is the first year I haven’t taught VCE Physics, and I do science pracs once a week with my Year Nines and another teacher.

And anyway, science is mostly just maths anyway 😛 (though I will admit, there’s a lot more setting things on fire in science, which is fairly cool).

So my link to the science department was enough to get me recruited for an excursion last week, which we did for National Science Week (which is actually this week). The theme this year is “Food for our future: Science feeding the world”, so we visited the Grains Innovation Park in Horsham. The GIP is a world class research facility in our region that I was barely even aware of until this excursion was being organised.

Broadacre cropping is the major driver of the economy around our school, and many of our students live on farms (also, I’m from a farming family myself). So being able to relate science to what many of our students see every day is pretty awesome. Because our school’s so small, we were able to take all of our Year 9-12 kids along.

I took my camera along, and made it my person mission to find any references to maths that I could. The biology teacher who organised the trip teased me about this. I probably deserved it.

Foil packets storing seeds in the multi-million dollar Australian Grains Genebank.

Freezer used for storing seeds in the Genebank. These are kept at -20°C. We actually got to go in here briefly. It was a little worrying when we were warned not to touch any surfaces, “or you’ll be frozen stuck to it.”

A few small examples of seeds kept in the Genebank.

Lentils growing in an “igloo”, or greenhouse.

MULTIPLICATION! Oh, not that type…

This lab is basically a fancy bakery. They produce bread from various varieties of wheat and test it to give information back to grain breeders and growers.

They also test how quickly various legumes can be cooked. Australia exports a lot of legumes to Asia, so they are trying to reduce the cooking time and therefore the amount of fuel required by poor peoples. A great example of using science (and maths, by extension) to make the world a better place!

This machine stretches dough, basically. It’s really expensive. Okay, that’s not fair – testing how far the dough stretches indicates … something I can’t remember.

The Australian Grains Free Air Carbon Enrichment Project has the greatest acronym ever: AgFACE! Here a ring of tubes pumps out carbon dioxide around growing crops, to see what affect future atmospheric carbon levels will have on our ability to produce grains.

My search for maths wasn’t fruitless. (Fruitless! Because it’s about grain? Oh, forget it.) I found some research posters with some really cool scatter plots and all sorts of interesting data that I got pictures of, but I think I’ll get in trouble with the copyright police if I post them here.

If you read different teaching blogs, you will find thousands of brilliant ideas that have taken a lot of creativity, effort and planning to create.

This is not one of those. This was an idea I had during lunch, literally less than half an hour before the lesson started. And really, I should have done it earlier given how obvious it seems now.

So my Year 12 Maths Methods class has just begun Probability – so hooray, we’ve reached the home stretch! While combinatorics is a Year 11 topic, my students often forget how they work – indeed, most of the class had even forgotten what factorials are. In the past, I’ve demonstrated combinations by choosing from whatever set of objects I had close to hand – often my coloured whiteboard markers.

This year, I made these instead:

Six laminated pieces of paper! Okay, I know I’m not really blowing any minds, but sometimes the really useful ideas are the simple ones. And I made four sets, so it’s twenty-four laminated cards, anyway 😉

Hopefully the paperclip gives some idea of how big they are – they’re actually a quarter of an A4 sheet each. There’s something about my class that I’ve never mentioned that makes the large size important. One of my students looks like this:

Okay, my student isn’t a TV and a camera, not really. One of the issues of being in a small rural school is the difficulty in offering VCE classes. Sometimes not enough students choose the subject to justify it, and sometimes it’s difficult to get teachers who can teach those subjects. We have a few options for dealing with this, one of which is receiving classes via video conferencing from other schools. We contribute by delivering some subjects ourselves, including Maths Methods 3 & 4 by me.

One of my students is in another school, but is taught by me. At the other end, the student uses two TVs – one shows the view of the camera, and and the other shows my laptop’s screen. Because I use an interactive whiteboard, he can see everything I write, as well as anything I else I choose to display.

I made the cards big so they would be easy to see over the camera. There’s many challenges to teaching this way, but that’s a post for another time.

By the way, if you didn’t work it out, that’s me in the TV taking the photo.

Because this lesson was about combinations, we also got to talk about the ten pin bowling thing I mentioned a while ago.

If anyone wants the file I used to make the cards, you can get it here: lettercards.docx. Though I only spent a couple of minutes making it, so I’m sure a little effort could make something much better looking.

As my students and I are starting to fall into the rhythm of SBG, I’m seeing benefits I didn’t predict. Though they found it a little uncomfortable at first, my students are getting their heads around the idea of seeing the quizzes as chances to show what they know, and aren’t afraid of questions they can’t do yet. Because they know there’ll be opportunities to demonstrate those skills in the furture.

Which has this side-effect: I can include questions for skills we haven’t actually covered yet. If students can’t do it, that’s fine – I explain it’s a skill we still need to learn, and they’re not bothered by it. But if it turns out they can figure it out, well, hooray!

I don’t think this is appropriate all the time – don’t worry, I’m not going to start putting calculus questions on my Year 9 quizzes. But in certain situations…

We’re still working through expanding and factorising, and I was hoping to have had covered Perfect Squares (and maybe even Differences of Squares) by the quiz we did last week. But alas, we hadn’t. I really wanted to include a Perfect Squares question on that quiz. Most of the class already had a really good understanding of using the Distributive Law, so I thought if I rewrote the question a bit to both teach and test Perfect Squares. This is what I ended up with:

I have to admit, I thought one or two students might get it if I was lucky.

But it turns out, 25% of the class had a go at it and they all pretty much got it.

I’ll repeat that in case it wasn’t clear: I set a question for a skill I hadn’t taught yet, and a quarter of my students were still able to do it. If you give students opportunities to surprise you, they’ll probably go ahead and do just that.

Now I realise that doesn’t mean I can skip Perfect Squares for these students. For starters, they haven’t shown they can recognise them apart from other quadratic expressions.

One other interesting point – all the students who got it were girls. I’m not sure what to make of that. I really think my female students are thriving under the learn-test-improve-repeat mindset that I’m trying to develop with the class. So, yay! But I’m wondering why some of my higher achieving boys didn’t even attempt the question. Maybe removing test scores has reduced the competitive motivation for some of them. As I said, I have no idea why, I’m just guessing. But it’s something I need to pay attention to.

If you get the chance, find a primary teacher and talk about maths.

A friend of mine, a primary teacher in another school, asked for some help around fractions and decimals. So one night last week we spent an evening doing just that. It’s been a couple of years since I taught fractions to Year 7s, so I didn’t have many resources close to hand, but with a stack of plain paper, a handful of markers, scissors and glue, we were able to do a lot. I wish I had a photo of all the notes we made.

So we did maths. And it was awesome. We covered a lot of different concepts in a short amount of time. But not only that, but every time I explained an idea, drew a picture or cut out strips of paper (there was a lot of that), I also explained why I would teach those concepts that way. Which meant I was going through the teaching-reflection cycle at an incredibly rapid rate. It’s not that I don’t reflect on my regular teaching (this blog is part of that), but the reflection is never as immediate as this.

Given that I teach in a P-12 school, it’s fairly ridiculous that it’s taken this long for me to realise this is a good idea. But I’m trying to rectify that. I spent some time in the Year 4 classroom the other day which I’m hoping to do more regularly.

One resource I think is essential to teaching fractions is “fraction strips” sheets. I used to have a better template which I can’t find, so here’s one I quickly threw together instead:

Download: fraction strips.docx