La Fête des Maths, Beaumont de Lomagne

We were invited to have a stall at the wonderful Fête des Maths at Beaumont de Lomagne this year.

As well as having some excellent help from some of our students, it was brilliant to see so many families from school coming to enjoy the day at the birthplace and home of Pierre de Fermat.

There were lots of fine stalls there, with all sorts of things to play with: puzzles, games, cooking-related activities, origami; We seven different activities on our stall, and they attracted quite a crowd!

Here's a slideshow of the event:

ISMTF Middle School Competition

Information for ISToulouse families

Some time ago, the International School of Toulouse volunteered to host the ISMTF middle school Mathematics competition in 2015. The International Schools Mathematics Teachers Foundation (ISMTF) has been running competitions for many years and students from the International School of Toulouse have taken part in many of them

They run three competitions every year,

1. The middle school competition for 14 year old
2. The junior competition for 16 year olds
3. the senior competition for 18 year olds

Their continued success depends on schools volunteering to host the events. In recent years, students from the IST have taken part in competitions in Paris, Basel, Vienna, Milan, Luxembourg and Geneva all of which have been fabulous experiences. We hope to have many more and, as such, we are only too glad to take our turn of hosting. The competition takes place between the 27th and 29th of March 2015.

This year the competition will involve 11 students from IST in years 8 and 9 as part of a total of 117 students and 29 visiting teachers from schools from Europe and beyond. We are delighted to welcome all of the schools some of who are coming from as far a field as India, Dubai, Cairo and Tunisia.

Huge Organisiation

Obviously the event has taken a huge amount of preparation lead by the Mathematics department at the school with terrific support from the whole school community. We are so very grateful for all of the support we have from our colleagues, students and parent and governing body. It has been a wonderful coming together of the whole school to work towards a truly international and hopefully very successful event that shows the value of goodwill within the school community. I expect to spend a good deal of time saying thank you after the event and paying back a considerable debt of support that I will owe.

What does it involve?

• This competition will involve 117 students between the ages of 11 and 14 in two competitions.
• The International School of Toulouse has also entered teams and will provide substitutes for any absentees from other schools.
• Students come from International schools in Europe and beyond.
• Students will stay with host families from the International School of Toulouse and Coaches will stay in a hotel in Toulouse.
• The first competition on Saturday takes place in teams of three where students will represent the school they come from.
• The second competition on Sunday involves students competing in teams of 6 where students will be mixed in teams with students from different schools.
• On the Saturday afternoon, there will be an excursion to the Airbus A380 final assembly line and the Aeroscopia aviation museum.
• We are delighted to welcome author Simon Singh as a guest speaker on Saturday where he will talk about his book, Fermat's last Theorem, which is a story of great local significance.

Host Families

A significant part of the experience is that the visiting students are hosted by families rom our school community. This was always a tall order given how small a school we are, but with the very able Friends of IST and the very obliging parent community we are delighted to be able to offer this experience to students. This also allows the school community to be more involved with the event. Thank you to all of the families who are able to help us with this. We are very grateful.

Simon Singh

We are particularly pleased to welcome author Simon Singh to the school for that weekend. He is best know to mathematicians as the author of 'Fermat's last Theorem' which tells the wonderful story of this enigmatic mathematical problem that local mathematician Pierre de Fermat brought to the world's attention and was finally proven by mathematician Andrew Wiles nearly 400 years later. Some students at the IST will have the opportunity to listen to Simon Singh Speak about his latest book 'The Simpsons and their mathematical secrets', while he is here.

Information for participating schools is hosted here. 

Fairground Games

Year 9 have completed their annual probability project where they design, test and run a ‘fairground’ for visiting year 6 students. It is always great fun and this year was no exception. The exercise is all about experimental probabilities. By designing games carefully, you should be able to predict that more people will lose a game than win it. With theoretical games, you can calculate it. The challenge is to make a game that people want to play, that is possible to win, but that people are mostly likely to lose so the stall holder wins in the end. So it is great to put these games to real test. Year 6 obliged and were very discerning with their money. Some of them went home with more than they came with, but on balance the fairground won - just. This years winners were Nicholas and Kieran whose brave ‘wet sponge throw’ (it was cold outside) won the most money. A direct hit in the face was required to win, but apparently the punters felt a body hit was worth the cost! Great design and aesthetics from the ‘Jungle challenge’ and ‘jungle hoops’ and lots of terrific ideas involving everything from Nerf guns and roulette wheels! A terrific event - well done to all who took part! 

Mirror Dancing

For a number of years we have run this annual mirror dance activity at the International School of Toulouse, but this year we decided to make a bit more of an event of it! I first got the idea from a Workshop run by Anne Watson at the UK based ATM conference a few years ago!

The idea is simple! In groups of two or more, students must make a dance routine lasting between 60 and 90 seconds. The routine must be based on symmetry. in the first instance, reflective symmetry where students are each others reflection either side of an imaginary mirror line. Afterwards, students can consider using two (or more) mirror lines, before going on to consider translation, rotation and enlargement! Students were judged and given a score out of 10 in three different categories!

1. Aesthetic appeal
2. Technical difficulty
3. Symmetrical accuracy

The total scores were then divided by the year group the team came from as a bit of a leveller!

More important than that was amazing creativity shown by all of the students involved. It is wonderful to see how students will play with these mathematical ideas when the right circumstances are created and we are really impressed with and proud of the work our students did on this. We are also particularly pleased with the willingness they have shown to both take part and then perform in front of each other! Well done to all students who took part!

Students have chosen their own prize and that is that they are able to throw wet sponges at the maths teachers!

See also 'Maths and Feet' from Simon Gregg based activities from http://www.mathinyourfeet.com/ from Malke Rosenfeld 

Here are some photos for now and there will be some videos to follow......

And now following the comment below, evidence of the prize giving!!!

Modelling World Population Growth

So you will have seen Simon Gregg's post about our joint project (Secondary, primary, maths and Geography) 'If the World was a village' The great thing about this exercise was the way that so many students of different subjects and different ages could be involved! This blog post is about how year 12 IB Maths Studies students had a go a modelling population growth. (A good summary of the whole project with lots of photos and videos can be found here.)

To stat with - watch this video and see if you can describe how you think the population growth is growing. Each person represents 93 Million and the worlds population has been organised in to 4 geographical regions - Asia, Europe, The Americas and Africa...

What do you think? We asked students to fill in the blanks on this table....

 This exercise prompted lots of fabulous reasoning about how the population was growing in different regions. For example what do you put in between 0.10 and 0.21? Should it go half way? What kind of growth would that be? We had a lot of discussion around this exercise and concluded that we wanted to try and fit an exponential model to the data! Here are some of the results....

Here we discovered that we could use an exponential model up until the present day for world population growth, but that predictions for there after suggested that that our model would give an inaccurate prediction.

For Africa on the other hand..... it looks like population will continue to grow exponentially!

The Americas seem to follow the pattern of the whole world....

As does Asia...

We tried hard but could not really fit an exponential model to population growth in Europe.

This is where it becomes really interesting to look at what happens when we look at how the population of the world is changing by proportion. The next video shows the world as a village of 100 people, changing from 1810 onwards. This is a tricky idea, because there are always 100 people in the picture even thought the number of people they represent changes. Look what happens to the number of Europeans!

The whole activity prompted lots of discussion and reasoning and was a fine demonstration of exactly why mathematics is such an important tool for understanding our world.

Mathematics is Everywhere

Douglas Butler

On Monday 10 June 2013, Douglas Butler paid a visit to The International School of Toulouse. He joined the mathematics department for the day visiting lessons and delivering a session to our Year 9 students. Douglas, a world renowned mathematics educator and great advocator of the use of technology in the mathematics classroom, was impressed by the students, the quality of teaching and learning and the facilities at the school.  The Year 9 students, the school principal and myself enjoyed his whizz-bang lesson that I’m calling “Mathematics is everywhere!” The students used Google Earth to skip around the world and visit some places of mathematical interest. Here’s a summary of some of the fascinating discoveries we made.

The Exmouth Hexagons

Zoom in to Exmouth Penisula in Western Australia and discover these strange hexagons in the ground. What transformations could you apply to one to get the other?Why are they there?

Washington Airport

At each end of every runway you may notice different numbers. At Washington Airport there are numerous different runways. Why is there a 4 at the end of one of the runways and the number 22 at the other? On a second runway you will find the numbers 15 and 33. What is the mathematical significance of these numbers and if the third runway has 19 at one end what number will you find at the other?

Melbourne Airport

Continuing on the theme of airports we used Google Earth to look at the elevation profile of the runway at Melbourne Airport. As mathematics teachers we are acutely aware how easy it is to misinterpret graphs – it is important to study them with a critical eye. Looking at the following graph what might you conclude about this runway?

Elevation of Melborne Runway

Unless we look carefully at the axes we might be misled into thinking that the runway is quite steep. Using graphing software carefully we can see that the gradient of the straight line is not at all steep and that planes can land quite safely at Melbourne Airport!

Denge Sound Mirrors

Denge Sound Mirror, Kent

Returning to Europe there exist some wonderful parabolic structures in Kent. Before the invention of radar, the Denge Sound Mirrors  were intended to provide early warning of enemy aeroplanes crossing the Channel towards Britain. This mirror is shaped like the graph of a parabola (y=x² is the simplest parabola) and this was critical  in their efficiency of amplifying the sound.  Where would you stand to best hear the sound? Just like flat mirrors, the angle of incidence equals the angle of reflection. The animated gif below might give you a clue as to why they were so efficient. 

You can find all the resources created by Douglas Butler for his visit here.

So you think you can count?

Students, parents and teachers all having fun in a night of maths!

To so many that would sound unlikely, but we now have evidence to the contrary!

***(just found this blog post in draft format never published so just decided to!)

At the International School of Toulouse this week, we had a really fantastic evening aimed at helping everyone understand the aims of maths education, to give students a chance to show off what they do and to have some fun. The focus of the evening was a competition where parents and teachers were in teams of 4 - 6 and they had to visit different stalls, which were run by students. Each stall involved students offering an short version of an activity that they had done in their classes to the teams of parents. There were 5 points available at each stall and parents had 1h15 minutes to visit as many of them as they could and collect as many points as they could.

Well, we had everything! Teams were really engaged in the task, some with serious determination to collect all the points on offer, some with real determination to solve problems, and some prepared to offer cash in exchange for points! (I should add we were collecting for the charity - Theatre against oppression - on the evening as well, so all bribes went to a good cause and there was a good bit of theatre involved!) A priceless faux pas from me at the end added some delicious irony - I tried too quickly to pick the top three scores from the list and got it wrong. This prompted much well deserved mickey taking and surely many of the audience to ask - So you think you can count?'

Above all else, the students were brilliant and the parents equally enthusiastic and so the aims of the evening were well and truly achieved. Having done it once I can really recommend the idea and wouldn't hesitate to do it again!

Here are some photos and video of the evening in action!

We also used this opportunity to fill our school's reception with inetractive displays about what goes on in our maths classrooms. This was a lot of effort but it was really terrific to see the front of the school as a shrine to mathematics! Below is a slideshow...

and video..

and I had forgotten that I had blogged about this already here! 

Dynamic Symmetry

Years 7, 8 and 9 have been working on some dynamic symmetry problems. These are exemplified by the videos below. The task is quite simply described but less simply achieved..... 'Can you make the following animations using dynamic geometry? ( See the following links for more details... Kaleidoscope, Animated Questions for a discussion on these ideas and 'One Question Lessons' for more thoughts on this type of lesson.)

The activity ticks a lot of boxes, 

1. The task is easily understood, 
2. Students really want to have a go because they want to make these really cool animations,
3. As they work and try things out, they can see straight away if they have achieved what they set out to do. As such, they are getting instant regular feedback on what they have done. they then refine each time trying to get closer to the stated aim. 
4. In doing the above, students have to reason with each other and articulate mathematical definitions of what they think is going on, of what properties give rise to what behaviours. these are the sort of conversations that make me as a maths teacher delighted and they are very productive for students!

The end results are very pleasing indeed, both in terms of what students produce, but perhaps more importantly in terms of what exploration and discovery they have done together.

For the ambitious, we can then move on to this combination of rotation and reflection!

Older pupils, perhaps in year 9 or above might get interested in this great problem!! Watch carefully to see if you can figure out how this was made! there are lots of surprises in this one. See Dr Who for more details!

Students might go on to making some of the fabulous designs on show with this task - Olympic Logos

Our provision for technology opens lots of doors for us here in Toulouse! Firstly the ease with which we can have a go at these types of tasks and secondly, our choice of media for students to work in. Below are some of the videos that students created whilst doing this task!....

Minecraft Plans and Elevations!

This year we have had our first go at using minecraft in teaching maths! Love it or hate it people, are playing minecraft and whilst the addictive nature of the game is a genuine cause for concern, there seems to be a wonderful element of creativity involved along with some real potential for learning! With some yr 7 and 8 mths classes, we thought we would have a little go at seeing how we could use it. We went for something quite simple and used it as a context for exploring the drawing of 3D shapes, plans and elevations! Students made the shapes on my iPad whilst it was being projected and then we had a go at drawing their plans and elevations. With another class, we took screenshots of the shapes from different angles and used them to try and make isometric drawings of them. It is lovely that minecraft allows you to ‘orbit’ what you have built and look at it from different angles. Students then went on to make their own shapes in mincraft for homework and draw the corresponding plans and elevations. Some even did this in minecraft too! This is a real help with what we were trying to do. There is little doubt that, for now at least, the context was deeply engaging! Thats good enough for now, but we will keep thinking about ways to try and benefit from the minecraft craze! Below are some pictures of what we did. 

Trig Function Families

This is just a quick post about some fun year 11 had with this 'Trig function families' activity. Fun is in somewhat shorter supply as exams approach and so it was great to do something that can really help to understand ideas. The aim of the exercise is to help students understand how the shape of a trigonometric function and its equation are linked. Working with the general form of ....

f(x) = asinbx + c

Students were asked to try and make some of the different images that had been made by varying the values of a, b and c. This is quite different from simply seeing what happens when you vary the values, because you have a particular shape and image to work towards! The results can be very satisfying on the eye! See the slideshow below for some examples.

A slightly different take on the same idea is to try and make the following animations! They are quite are challenge! Are you up for it?

We did find that this was an excellent use for the brilliant online graphing calculator at Desmos. All in all this is an engaging and effective exercise!

The Art of Fractions

Year 8 students have been making some fabulous ‘mondrianesque’ pictures all based on the idea of different fractions. here is the 'Art of Fractions' activity. All pictures are based on a particular fraction. Starting with any rectangle students mark off the chosen fraction of that rectangle so that it is split into two new rectangles. Each of the new rectangles can be split in the same way, but they don’t have to be. Rectangles can be split horizontally or vertically by the given fraction or left alone. The artists then add their chosen colour scheme and ‘hey presto’ we have ‘The Art of Fractions’. It is good to do creative things and have students thinking about the fraction as they make their decisions. The whole process is great practice of calculating fractions of amounts in an engaging context! Looking forward to this year’s productions! Here are some examples!

Venn that tune!

A new twist on an old game! Can you figure out what the song title is by the area that is shaded on the Venn diagram?

This is all inspired by this lovely book ‘Venn that tune’. Maths Studies spend a lot of time with Venn diagrams and link them thoroughly logic, sets and probability moving to understand about dependent events and conditional probability. With this in mind, we enjoy playing with them at the start to make sure we understand the implications of intersection etc. We have started a shared presentation to share some of these and are hoping to get others to contribute their examples and get quite a collection. Maybe you can add one!