Making a box

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...

Managing different student learning

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...

Student Feedback - The Less Serious Ones

I've been doing student feedback reflections recently. As much as I stressed to students to take this seriously, I was always going to get a bunch of silly suggestions. So, without comment, here are some of them. Give us stuff. Mostly food. Mr carter should start bringing us food so we are more motivated. Give rewards to people who finish all of there work. Give us prizes. Give us pizza. Give us all the answers. More food involved lessons. Change your style. Start growing a beard. Stop shaving. Change the lack of beard. Change your serious lack of facial hair! Grow a moustache. Start wearing better clothes. Stop wearing bad clothes. Change your hair style. You should strut into the classroom with your shades on with The real slim shady playing from your massive speaker as you get to the front of the class you whip your shades off and...

Student Feedback (Year 7)

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...

Student feedback (Year 9)

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...

3D Perspective Drawing

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...

Rotations around a point

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...

"Why didn't you show us that first?"

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...

Graphing using intercepts (including worksheet)

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....

Football scores problem solution

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...

Football scores problem

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....

Un-building equations

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...

Exciting news!

To be clear, this is the strangest post I'm ever going to write. Completely unlike any other you'll see on this blog. This is about what's been happening in my life personally. But also totally about teaching math. And blogging. And the MTBoS. And the fact that I dropped the 's' off the word maths just now. This kangaroo is also related to the story. Sort of. I'm not exactly sure how to explain what I'm about to share. I've been thinking about this for a while, but haven't really gotten anywhere. But I promise what I'm about to share is totally worth hanging around to read. Last year I started dating this really amazing girl. Someone who really inspires me. She is so wonderfully talented and passionate about what she does. She is so incredibly cute. A couple of months ago, I got down on one knee and asked...

Building equations

Year 7 are currently working on solving equations with pronumerals for the first time. Specifically, we're using backtracking to solve multi-step linear equations. This year, I realised there's a problem with getting students to understand backtracking. Before I can expect students to work backwards through steps to solve an equation, I need to make sure they understand how the equation goes forwards. I think that in the past I've been too quick in jumping into backtracking, without spending time on fortracking (I know that's not a word, but I'm running with it). I'm at an advantage over my students when they see an equation I've written. I've seen the entire process. I started with a variable and its value, then I applied a number of steps to build it into an equation. Then I know that the solution can be found by working backwards through those steps. But students only...

Solving Linear Inequalities

Semester 2 has started, which means the Computer Science elective I was teaching has ended. The good news is, I've taken over Year 10 Maths, which means my teaching load is more maths than it's ever been before. I haven't taught Year 10 for a couple of years now, and I've changed the way I teach a lot even in the last 12 months. Luckily, I had this same class last year so they're pretty used to how I do things. The first unit I'm teaching is Linear Relationships: Most recently we've been working on LR2, linear inequalities. If these are taught as a totally procedural matter, it's a fairly easy topic: solve them the same way as equations, just being careful with the direction of <, >, ≤ or ≥ if dealing with negatives. But as I always tell my students, I believe our aim is not to 'get...

Petals Around the Rose

Firstly, credit where it is due: I was given this idea by Sarah Hagan, who found it on Annie Forest's blog. So, thanks! So, Petals Around the Rose (the name is really important!) is a game/puzzle which, if you followed that link just now, is likely making you really frustrated (sorry about that). Five dice are rolled, and you have to predict what score those dice make (and I promise that there is logic to how the computer decides the scores). If you use the site I linked to, you enter your prediction before seeing what the actual score was. For the last couple of days, I've been using the puzzle in the last 5 minutes of my lessons with Year 7. One student has already seen the puzzle before (and is taking great pleasure in keeping the solution a secret), but as of yet, none of the others...

Unit Circle Poster (plus bonus poster!)

Not much to say here. I made a poster featuring the unit circle. Here's a picture: Here's some download links: PDF: circular functions.pdf Publisher: circular functions.pub Come to think of it, I made a poster about Exponents and Logarithms a while back which I never shared. So, here's that: PDF: exp log graph.pdf Publisher: exp log graph.pub 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. :)...

Pythagoras Problem Solving Redux

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...

The Square Root Game

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...

Classroom rules 2015

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...

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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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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