math and stuff
Not much to say here. I made a poster featuring the unit circle.
Here’s a picture:
Here’s some download links:
Come to think of it, I made a poster about Exponents and Logarithms a while back which I never shared. So, here’s that:
The font on both of these is “ChunkFive Roman”. I tend to go through phases with fonts I love. This seems to be my current obsession.
🙂
Year 9 and I are working through Pythagoras’ Theorem at the moment. After a little shuffling of units around, this is a little earlier than last year. An interesting consequence of this is that this is the first unit I’ve taught that I’ve blogged about previously.
Getting to go back and see what I did last year has made planning this year’s unit so much easier (which is why I really need to make more of an effort to blog this year). Today I took one of my previous lessons and improved it in the best way possible: by adding Desmos!
(One of my students stated that I’m a little too obsessed with Desmos. I can’t really deny that.)
The task was Problem Solving using Pythagoras. Students were given triangle problems for which they weren’t given all the information to answer the question. I had them go through a process of drawing a diagram, defining variables, choosing values for those variables as an example, and finally defining a general solution using a formula.
My students struggled with the last part a little last year. They seemed to be able to go through the mechanical steps of rearranging formulas, but couldn’t necessarily understand the connection between the formula and the problem, or the reason for finding the formula.
This year, we used Desmos to support finding the formula. For all of Desmos’s graphing awesomeness, it’s easy to forget it works really well as a calculator too. After students solved the problem using their own chosen values, I had them use Desmos to verify their formula agreed produced the same answer:
Firstly, this let students check their working. But also, it let students see the value of defining the formula: by changing the values of the independent variables, they could find their new solution, without going through the process of solving the entire problem all over again.
That image also shows the way I often use Desmos and the IWB together. If the graphing area is not being used, it can serve as empty space for me to draw all over.
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: