Pythagoras – “a model MYP student”

ythagoras would have been a model MYP student, as there are so many Learner Profiles and Approaches to Learning that you can link him to.

Math-ilde 8BD, UNIS, Ha Noi


What a great success that project was. The kids enjoyed finding out about the man himself, that he wasn’t just a guy into something called the hypotenuse. There was so much more to Pythagoras and our Grade 8 kids know it.

If you teach MYP, then it’s a really great way to discuss the IB Learner Profile. I grabbed a quote from one of my students for the yearbook, alongside the likes of Pythagoras, Andrew Wiles and other notables.

This particular student has improved greatly this year in her reasoning and investigating, but most importantly in her enjoyment of mathematics. Her name was Mathilde, but her father has decided she is Math-ilde. This is, of course, mortifying when he uses it in notes and comments on assessments. It tickles me, so I tried to sneak it in to her report. We shall see.

It’s also a project where I don’t like to tell them what the AoI is. One of the things they discuss is which AoI(s) they think are relevant.

If you aren’t an MYPer, then basically we are asking what characteristics did Pythagoras embody and how does all of this relate to today’s world as a student and just to the way things are. How did he push the development of mathematics and world around us. How do we still do that? TEDtalks are another great way to open kids’ eyes to cool mathematics and pushing the envelope.

A few weeks on and kids still refer to him, Pythagoras, and mathematical challenges with prizes attached.  They used their knowledge of Pythagoras and his theorem for our poetry in mathematics lesson.

Cool Maths – Deadly Maths

Before I start to go on about what my kids are doing in my grade 8 class, a link…

Professor Marcus du Sautoy is behind this:

It ticks so many boxes of what I am trying to get my kids to see.  Maths is everywhere, and in a pleasing way. My hope is that some of my kids run with this and even enter. I haven’t read the fine print, but maybe I can meet Marcus if I enter and get a symmetrical object named after me.  Maths in Hanoi, chaos theory, surely!

Hanoi Traffic
Hanoi Traffic by mr clearview licensed under CC by A NC SA

Marcus du Sautoy is someone you should follow, @marcusdusautoy, if you teach or even like mathematics. Google him and you’ll find amazing things you can use from television to websites and he’s involved in Manga High.

My grade 8s are almost ready to submit their latest assessment task. I rejigged the old Pythagoras investigation as I do each year. This time, however, it was more of an overhaul. The biggest change was to drop the very popular approach of getting students to ‘find’ the relationship all by themselves (with some guidance *ahem*).

Instead they were shown the theorem and how it worked. Part of their job, this time, was to prove it geometrically and with data. Some students also looked into algebraic proofs. Still, that isn’t anything new. What was truly cool about Pythagoras and his precious right angled triangles were the blasphemous irrational numbers he found in his calculations. Rumours surround how he died, how he was murdered. These numbers upset all of the Greek Gods and that’s a lot of anger.

Day 85/365: We Love Diversity

Day 85/365: We Love Diversity by Kugel licensed under CC by A NC SA

Pythagoras and his apostles were burnt inside their school is one legend. There are so many more too. Students were fond of the one where he was chased to a field of beans and couldn’t go any further, so they cornered him and the rest is history. Pythagoras and his followers did not eat beans, they represented testicles. Student: “I don’t think I would have run into the field of beans either.”

Students enjoyed looking up the stories of his death and about Pythagorean beliefs. They were told very little and I learnt some new things too.

To introduce this part of the task I asked students to name some mathematicians. As ever lots of dead ones were mentioned. Then I asked for some that were still alive and expected silence…

Silence was not what I got. I was so impressed with my class of budding mathematicians. You may not agree with all of these, but I don’t want to edit out what the kids contibuted.

Ngo Bao Chau

Bill Gates and Steve Jobs

TED Talk peopleRobert Lang and Kashima and Margaret Wertheim

Professor Rose – teacher of Stephen Hawking

Stephen Hawking

Mr. Khan

Professor Du Sautoy (“Manga Maths guy”)

Dr. Dan (he visited us not so long ago and led some cool probability activities)

8BD and Ms. Griffin (I supplied 8BD, they threw me back to me)

Grigori Perelman 

Andrew Wiles

The last two were mine because they proved theorems too, just like Pythagoras did so many years ago.  When they succeeded in their task they were offered a reward of $1,000,000. Perelman said no thank you. He was in it for the mathematics. Not that Wiles wasn’t. He loves mathematics, really loves it. Pythagoras wasn’t offered any riches, they killed him. There are of course some million dollar prizes still for grabs

We very briefly discussed Fermat’s Last Theorem. They understood the concept, particularly as we have just been immersed in the Pythagorean Theorem. Andrew Wiles was a similar age when he read about in a library and was inspired to prove it, because he understood it.

So my students set out to show that perhaps a death sentence for being right was a little harsh. Poor clever Pythagoras, a band of barefooted dedicated apostles and a whole new number system to explore, but it only led to his death.

Athenian Temple by Jonathan Burr licensed under CC by A SA NC

Interested in why irrational numbers angered Zeus and all of his buddies? You are already online. Telling you everything ruins the thrill of deadly mathematics.  

And on a final note for this incredibly enjoyable task (there will be a little MYP speak at the end) at parent-teacher-student conferences tonight I had a parent say that they were enjoying the mathematics and learning something new too. They even had a question. Excellent, they are discussing maths at home.

For the MYPers out there: This is assessed using criteria C Communication and D Reflection.

The famous mathematicians lead in was from Charles Lovitt, a great sharer of resources, lessons and ideas from a workshop last week.

Don’t Eat the Beans!

Rearrangement proof for Pythagoras' theorem. P...
Image via Wikipedia

If you read this blog from time to time and don’t like too much maths in your eyes, read on, it will be okay. I won’t go into proofs, this is more about how the kids would be introduced to the revolutionary blasphemous mathematics that got Pythagoras in all sorts of bother. For the record there are many stories about how he may have died. For the class I have ignored the less interesting ones.  But was it his theorem?

One of the things that didn’t work so well in #AoD, mostly with pacing, was letting kids do a summative MYP assessment task when they were ready. They were all working on different things, so were ready at different times. Not that I’m saying they should when they aren’t ready, but it would have been better to get my classes to do the Gradient Task at the same time, perhaps even take them to the water park to photograph more interesting surrounds.

They still got some enjoyable and valid mathematical experiences out of it, but as with all new things tried it won’t necessarily be right first off. I am already looking forward to fine tuning the program next year. Three weeks after the winter break we had a week off for Tet (Vietnamese New Year – chuc mung nam moi!). We also churned out set two of the four sets of reports for the year, so my tippy tapping blogging fingers were a bit distracted. It didn’t mean I wasn’t thinking about mathematics and blogging. I found time to read some blogs and comment on blogs. Must try harder. I’ve also been very distracted by Africa.

Puzzling over the not so perfect fit

Our latest adventure is all about Pythagoras and his famous theorem. I looked at what worked and what didn’t last year. This included how much and what students had learnt, but also what was ineffective or dull or both. Pythagoras’ Theorem features in mathematics curriculum all over the world, but I never did anything interesting with it when I was kid and I never take the time to apply it to see just how much distance or time I could save by cutting through rather than follow a path. Amazingly I can see it is shorter and that is enough. What I think is so cool about the theorem are the stories around it, the history and the impact it had on mathematics and the beliefs of the people at the time. And the murders. 

It was time to throw out the construction of squares on the sides of right angle triangles to help kids ‘discover’ the relationship all by themselves, using calculations and analysing data. We, maths type folk, are very into nutting out patterns, it’s in our nature, but that has been done to death with Pythagoras. It’s rumoured that he was killed, along with his apostles, for unearthing irrational numbers. Why beat him to death again?

The angle taken (you see what I did there?) is with Criterion D: Reflection and C: Communication and getting the students to show that his theorem does work, rather than find it. Not all students are ready for algebraic proofs so we are using geometry and data. If a student feels the urge to present an algebraic proof, they will be most welcome to do so.

Today, The Geometric Proof It was so much fun.

Kids like “make and do” (so do I) and even though I LOVE teaching with 1:1 tablets, it’s nice to touch things again – blocks, scissors, tape measures, paper. Finding the right balance is so important.

Each pair had some coloured paper and some white paper. They had to make squares. Two coloured with sides of 15cm and 20cm and the white one with sides of 25cm. Fluoro paper everywhere, short stubby ruler owners were challenged  moreso than those who had remembered their 30cm rulers. I gave them 5 minutes to get their squares ready, then asked them to clear their tables of everything except for their beautiful squares, and to sit back and just admire them.

Then I asked them to imagine they represented something wonderful, like gold or chocolate or…

My favourite commodity were the “squares of love”. That student had been one the singing telegrams for Valentine’s Day not so long before.

Once chosen I then said they had to choose between them. One member got the two coloured squares and the other member of the group got the white square. It was important not to use any adjectives meaning big or small. There was some friendly banter and in under a minute happy and resigned faces placed their squares in front of them.

“Who got the white square?” lots of whooping and shouting of victory about scoring the big square.

I praised those who decided to forego the big white square for the smaller colourful ones, then told them they were equal. The confusion about the lack of victory was amusing.

The task of showing me they were equal was then assigned. Confused faces. “Show me, any way you’d like to, that the area of the white square is the same as the coloured squares”. One voice pipes up: “Can we use scissors?”. And they were off. No mention of the right angle triangle at this point, though, some students were talking about it.

The girls prove it. Step one in getting closer to the deadly numbers

 One pair found it didn’t work, but their 25cm sides were actually 30cm. Problem fixed, mostly.

Time to reveal the right angled triangle and where the squares fit. Story telling time begins too.

We then discussed the famous rule, which many had seen before. We looked at the diagram of the squares  sitting on their right triangle and then in their pairs they discussed the accuracy of their geometric proofs

It was a fun hands on, no tablet lesson. My next post will show the groovy technology we use to show this theorem at work.

Here is a preview

Mathsnet has a great section on Pythagoras and his theorem. Proofs 2 and 11 are accessible to any student, and proof 11 is pretty groovy in its simplicity. One of my kids then found this online version of number 11..

Braining Camp is new to me, so it has been added to this task too, for practice.

I haven’t told the kids why Pythagoras and his followers did not eat beans and I won’t tell you yet. We have one lesson for the history and the numbers that led to his death. Would you die for mathematics?