Solving Problems

I had an amazing lesson with my year 9 class today!
They’re such a beautiful bunch of kids – we get along well and they’re all so keen.

We’ve been working on solving linear and quadratic equations and we’re about to move onto simultaneous equations. I decided to introduce them to the concept and the mathematical ideas that they’re going to need, without actually telling them that they were doing these scary things called simultaneous equations.
I also wanted to force them to practice communicating mathematically, because they can always do with some practice.

I split the class into 5 groups and gave each group a problem that they needed to solve and would explain to the class later in the lesson. Some problems were harder than others so I strategically gave those to my stronger students.

The decorations on this mobile weigh 480g.  Find the weight of each diamond, star and circle.

The decorations on this mobile weigh 480g.
Find the weight of each diamond, star and circle.

How tall are the adults? How tall are the children?

How tall are the adults?
How tall are the children?

How much would one doughnut cost? How much would one muffin cost?

How much would one doughnut cost?
How much would one muffin cost?

What do each of the animals weigh?

What do each of the animals weigh?

What is the value of each of the coins?

What is the value of each of the coins?

Within a few minutes every group knew what the answers had to be, but they’d figured it out by trial and error. Now the fun part – forcing them to find another way to figure out the answers, and be able to explain their method to the class.

I gave a few hints but largely they worked really well together and had some really great discussions. Then each group got up in front of the class and explained how to solve their problem and answered questions from the rest of the class.

We had about 20 minutes left so I handed each student one of these game cards:

I asked them to choose values for x and y, substitute them in and then write their answers. Then they switched with someone else in their groups and had to try and guess their numbers. They started with “nice” numbers (small and positive) and then started challenging each other by choosing negative numbers and decimals.

Most students were just using trial and error, but a few were starting to experiment with substituting. Before we left I asked students to raise their hand if they liked trial and error as a way to answer a question. More than half the students raised their hands. Then I asked if anyone had been frustrated with using trial and error once the numbers got “trickier”. Almost everyone put their hand up. I told them that next week we’ll start looking at more formal ways to solve simultaneous equations.

As if to prove my point, one of my boys then called out “Miss! Miss! I’ve got one for you to try and solve!”. He handed me the card and it only took me a few seconds to use the elimination method in my head and come up with x=-0.5 and y=0.2.

They were amazed: “wow!” “what? No way!” “miss you’re a magician!”

It was brilliant! I ended the lesson with “that’s what I’m teaching you guys to do next week!”

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Communication

Each week we run a maths homework centre for any student in the school who wants help with homework or study. Two students from my strongest year 9 class come each week to help year 8 students as part of a program that requires them to complete a certain number of hours volunteering.

Today I overheard a conversation between one of these year 9 students and a girl from my year 8 class who was attempting an algebra question:

S1: Is it 10x?

S2: Why do you think it might be 10x?

S1: Because there’s an invisible 1 in front of the x that’s on its own

S2: How does that help us?

They figured out the answer was 9x, not 10x, but it was so nice to hear my students parroting both my questioning techniques and my explanations. I always try to encourage them to communicate effectively using mathematical terms but to hear it from them when they don’t know I’m listening makes my day.

Maths Trivia

A while back I had one of those days where there were a whole heap of things happening in the school that my students were involved in, so my 45 minute class with 34 students was reduced to 30 minutes with 10 kids. Rather than teach new content that I would have to re-teach I decided to give my students (and myself) the afternoon off and play a maths trivia quiz!

I made up some maths trivia questions, grabbed some lollies for prizes, and we had a tonne of fun getting really competitive.

 

They did make me feel incredibly old when not one student could answer the question “The quote “the limit does not exist” is from which movie?” – and even when I told them only 2 had seen the movie!

Why Algebra?

It’s the start of the new year, and I’m getting to meet all of my new classes. I’m really excited to be teaching a year 11 General Maths class for the first time, and even more excited to find out that I only have 14 students!

Our first topic is Algebraic Manipulation. Sounds like a whole bundle of fun to a group of kids who just told me that more than half of them don’t like maths, and at least 2/3rds of them think they’re really bad at it. Since I knew that at some point most students in the class would probably groan “wwhyyyy do we even have to learn this?” I decided to pre-empt this and have the discussion before we even started.

I started by asking them “So what is algebra?” expecting to get responses about using the alphabet in maths (there were a few along these lines), but I was surprised when students started to tell me that algebra was all about patterns. A good start!

I told them that algebra is a tool (and I think a few agreed with that statement on its own) – a mathematical tool that’s used for two things: describing patterns and relationships, and proving ideas. We had a look at a few formulas that they know already and talked about the relationship that each one was representing. Then I showed then a magic trick.

Pick a number between 1 and 10
Double it
Multiply it by 5
Divide by your original number
Subtract 7
The number you’re thinking of is 3!

And from that ‘trick’ one of the best classroom discussions I’ve ever seen ensued:

Student 1: Why did it have to be a number between 1 and 10? Would it work with other numbers?
Me: Give it a go with other numbers and see if it works!
Everyone picked a new number – bigger than 10 – and were amazed when the magic still worked
Student 2: What if you pick a negative number?
Me: Try it out, see what happens!
There was even more excitement when these numbers worked too
Student 3: What about if it’s not a whole number? What if I pick, like, a half?
Me: What do you think? Will it work or not?
A few nods and shakes of the head. When these worked as well I posed the question:

Will this always work? How do you know?

After a short silence a student tentatively offered the answer “algebra?”
Me: Yes! So we want to pick a number, but we don’t know the value of that number yet. How do we represent it?
Ss: x!
Me: Do we have to use x?
Ss: Nope, you can use any letter
Me: Good. But it doesn’t have to be a letter – it can be any symbol – I could draw a picture of a fish if I really wanted to

Then we went through the process using x (and fish) and showed that our original number divides out, so it’s completely irrelevant.

One student picked up on the fact that we didn’t need to subtract 7 – we could have finished the trick with one less step, but we decided that it makes the trick look more impressive it there’s an extra step in there.

If this lesson is any indication of the year to come, it’s going to be awesome!

Silver Lining

About a month ago, inspired by the wonderful folks from the MTBoS and an amazing teacher that I get to work with every day, I decided to make a few phone calls to parents. I’d collected and checked my students books, and as well as talking to those students who had quite a bit to catch up on, I called the parents of the 5 students who were completely, 100%, absolutely up to date.

The conversation went a little like this:

“I just wanted to have a quick chat about how _____ has been going in Maths recently” At this point I could almost feel the parents tense at the other end of the line.

“It’s been a while since I’ve checked students books, and as a top class I’ve discussed the importance of making sure that they keep up to date, even without me constantly on their backs.” Overall, we are lucky to have very supportive parents at our school, so now I could feel them preparing to lecture their kid on my behalf…

“I wanted to call just to let you know how impressed I am with ______’s work ethic and motivation in my class. He is entirely up to date with all the work, including the optional extension exercises, and generally has a great attitude towards his learning.”

*Cue the sigh of relief at the other end of the line*

One parent wholeheartedly thanked me for calling… the rest seemed incredibly awkward. There was a pause once I stopped talking as if they were trying to comprehend the idea of a nice phone call from a teacher. When I walked away from the phone, I couldn’t decide if it had been worth the awkwardness of the whole situation.

Two weeks later, I’d had a horrible week at work – tears and all. Afterwards, I’d been sitting outside in the sun at lunch talking things through with my mentor, when a few of her seniors walked past. In her class that afternoon they’d commented on how cute we were having our lunch together, and one of them told her all about how I’d phoned her dad just to say how well her little brother was going in my class. She said that he was incredibly impressed that I’d gone to the trouble, and he was so proud of his son.

That had been one of the most awkward phone calls I’d made, and with no mention of any of the calls from any of my students, I hadn’t been sure it was worth it. But a passing comment to another teacher was the silver lining to my awful week, and reminded me that people will make much more of an effort to give negative feedback than positive, but that doesn’t mean that the positive isn’t out there.

Maybe the happy phone calls home will help to change that culture.

One Good Thing

“Every day may not be good, but there is one good thing in every day”.

A few days before I started teaching in my very first teaching job ever, I found this site. I loved it so much I went out and bought a really fancy little notebook to record one good thing from every day.

I love teaching – love love love – but the first 6 months were tough. I’m at an amazing school, and I have so many supportive people around me, but I’ve only recently (3/4 of the way through my first year) felt like I have things under control. This little notebook helped keep me sane. 

Every day, no matter how tired I was, or how grumpy I was at students, I sat myself down and thought of one good thing. Some days I could have written pages – lessons went amazingly, students were excellent – other days I struggled to find something.

Gradually I stopped writing, and I’m disappointed that I didn’t keep it up. I still keep it in my top desk draw, and when I’ve had a bad day i’ll pull it out and remember that while playing softball I told students to spread out, and one girl replied with “like jam Miss?”. Or how a student came running over to me in the playground to tell me about getting 100% in his commerce assignment. I suppose now the book is helping me get through hard days in a different way.

One Good Thing helped me to shed a positive light on days that seemed terrible. The tagline of this website is right up there with Bowman Dickson‘s comment in a letter to first-year teachers that “very few things in a room full of teenagers go according to plan” – both are things that I find myself repeating on a regular basis.

Travel Graphs

We were looking at travel graphs in class today and I gave students the task of coming up with a reasonable story to describe a few graphs. The first one stumped a some students, because they couldn’t think of a story where something would move so slowly – hooray for imagination!

Some students spent a lot of time on their answers, making me laugh so much I got weird looks from the teacher next door.

These are three of my favourite answers:

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