Where is the middle?

Finding an easy Geogebra challenge for Year 5s that's just right is itself a challenge, but this one went well.

Where is the centre of a regular pentagon?

We know how to make these, because we've had a go at making stars (another interesting and more open-ended challenge).

Some of the children remembered how to find the mid-point between two points (we'd done this finding the parallelograms inside any quadrilateral).

So they found the mid-point between A and B. Here it is, F. Then they found the midpoint between F and D and "I've found it!"

There it is - G.

Except that it isn't.

We checked and, doing the same thing on the four other sides, we got four other "centres":

So, it's got us close, but not close enough. After a bit more experimenting, some of the class did it with lines: We were now pretty confident that we'd found the centre! To finish off, I asked the children to play a little, and see what they could create from that. Later on, some of them had a bit of spare time to colour in their creations on Paint.

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!

Exploring HIV Stats

Students in years 10 and 11 have marked World Aids day (Dec 1st) by learning about some of the stories that are told through statistics on HIV and AIDS. The idea was to give students a sense of what the numbers mean and the impact that HIV has had on different parts of the world. The idea is a cross curricular project between PSCHE/homeroom and Mathematics and some resources are available here - HIV - AIDS Statistics.

In an assembly, students were asked to put them selves in to different groups that eventually represented the ratio of those with and those without HIV in different countries. They were watching themselves do this live as a camera image was projected so that they could decide how they looked before photos were taken. The idea was to work on visual representations of some of these statistics. They were eventually asked to think about their own visual representations of these numbers and to be inspired by other infographics about HIV like these examples. Hopefully we will soon be able to post some of the examples students came up with here.

After that students were asked to solve a puzzle involving bits of information and some graphs about 8 different countries. the aim is to put the right piece of information with the right country.

The puzzle is here and involves looking at graphs like the one below where you can see what has happened to life expectancy in this particular country over the last 60 years. Which country do you think it is?

Here are some photos from the activity in action! This is the students moving themselves in to different groups to represent the proportion of people with HIV in different countries. As you can see, some of the groups have as many as 1 in 4 people standing up.

Data Week

Well this quickly turned in to data month! We started the year by collecting data from all of the students in the secondary school and some from the primary school. As mentioned ina previous post, we collected information on physical measurements, computer use, daily habits, homework, reading, religion and much much more.  The idea was that we would work towards a display of 'Who we are' in September 2012 which is now currently up in the schools reception. A gallery of photos is included below! When I say we, I mean the different subject areas in the school. We really wanted a cross curricular project that showed the relevance of data collection and analysis across the curriculum!

Who, what and why?

So the English department were keen to find out about students reading habits as students got older and the things that eventually stop people from reading. There were some interesting results that did show how reading time decreased as homework demands increased.

The French department were keen to find out about languages spoken at home and the influence this has on students. They have processed and displayed the data too!

Mr Podbury in Geography collects information every year on summer holiday travel and it is remarkable to see how far we spread out during these holidays and our collective distances travelled.

For History, we included a spot test on the student body's knowledge of world leaders with the intention to look for patterns. Actually, whilst in general students got a little better at this as they got older, we found know patterns between people from different nationalities. We also did some PSCHE/History work on discovering our political persuasion which included a lovely exercise in weighting our different views according to how strongly we felt. This is shown in a display of diamond 9 diagrams.

Students in ICT lessons collected data on there typing speeds and there were various exercises in the Primary school too. Students in maths lessons processed lots of the other data to make a variety of different 'infographic style' displays about who we are in September 2012.

Building Charts

Just recently, and as part of our whole school data project' year 7 stuendts have been exploring both bar an pie charts trying to get them to show information as clearly and as interestingly as they can! We docided that this year we were going to build these charts out of things before we drew them. We started with multilink cubes but went on to make a series of bar charts out of piles of books! See below for some pictures.

With pie charts in particular, there is something much more intuitive about actually building them and this can lead nicely in to the discussion about how we define parts of circles. Even if circles are not specified from the beginning, students often find a circle the best way to show the information which is terrific!

Building Bar charts

Building Pie charts and Bar charts out of books

Some particular examples and their observations!

This bar chart shows the number of books read in a year by different year groups going from year 7 to 13 from left to right! Whilst year 8 stand out as being in to their books it it the last two bars that really stand out with years 12 and 13 arguing that they have so little time left for reading!

That theory is backed up by this graph that shows minutes spent doing homework on a particular Thursday evening. This on goes from year 13 to 7 from left to right!

4D Scattergraphs

The current media machine is full of beautiful infographics - variations on classic graphs and clever combinations of graphs and images. The great skill as the consumer is to look beyond how attractive these graphics can be and towards what they might actually tell you! There are some super examples and one of our favourites is 'Information is beautiful!' Anyway, as part of our whole school data project, some year 11 students set about creating some of their own! The challenge they faced was to create something that was good to look at and contained as much information as possible! So here we have, the 4D Scattergraphs. They are scattergraphs of height against armspan for students in our school. One graph for girls and one for boys. The points (butterflies in the case of the girls!) get larger to denote students in different year groups and the points are coloured according to the nationality of the students.

Infographics have been a bit of a theme in recent years. have a look at 'Olympic Circles' and 'The Rice show' to see some of the activities we have done before!

Visualising Indices

Year 8 had some fun trying to 'Visualise indices'. The activity is published here - Visualising Indices. The main aim of the task is to try and create images that help us understand what 4 to the power of 5, for example, actually means! Try yourselves, what number does the picture below represent?

Here is a gallery of the work that students produced! Some brilliant stuff!

In addition to this we had a whole new take on the task this year as well. One student decide to make a stop animation video to visualise the number the video is shown below,

Who are we? A data project!

Students have been embarking on a whole school data collection exercise this last week. We have asked the whole school community about their daily habits, physical measurements,  nationalities, backgrounds, languages, reading habits, homework habits, computer usage, summer holiday travel and religion! The result is a huge database of information about us as we are in September 2012 which we are in the process of turning in to a display for our school reception! Other departments are collaborating with us as well as we try to look at how data and statistics are relevant across the curriculum. Our other goal is to try and bridge the gap between standard graphs and meaningless infographics to try and present the data in an interesting style whilst still being accurate. I am most looking forward to how we all interpret the data about students favourite subjects. In maths we are determined to develop an algorithm that ensures we come out on top!

Projects on the go so far....

• Life size cut outs of the average students for each year group
• Gapminder style scattergraphs showing the relationship between height, armspan, age, nationality and gender all in two graphs!
• Barcharts made out of piles of books showing homework and reading habits !
• All the nationalities of the school represented by their flags where the size of the flag represents the proportion of students with that nationality!
• and more......

We'll try and post photos of our efforts here!

The real thing

You get a lot of those coloured-balls-in-a-bag questions in maths lessons. But you don't see it very often in real life. So I was pleased and surprised to see a real-life example in the boulangerie near school. I asked if I could take a couple of photos:

So you can win:

● An isothermal bag

● An inflatable cushion

● A set of beach rackets

● Nothing

There are a number of mathematical questions you could ask here...

Summer Challenges

Fantastic, summer holidays are upon us! Fun, relaxing, resting and more in store. It’s a really long time to go without doing any mathematics and so the following are some suggestions of puzzles, problems and activities you can have a go at to keep your mind active! This has been offered to students at the International School of Toulouse but we would love it if we thought other people were using it too! Even better if some discussion opened up about some of these problems on this blog! Good luck and have great summer!

Games from around the world http://nrich.maths.org/8261 Try playing some of these when you are on the go, in the car or wherever! Strategy games are great brain activity and most of us like a good game.

Challenge area 1 – Logic puzzles

Logic puzzles are a lovely model for mathematics, so much of what happens in this subject boils down to logical deduction. Below is a selection of some great logic problems to challenge you!

• Whose Fish http://coudal.com/thefish.php
• Logic problems from nrich http://nrich.maths.org/8073
• Puzzlers paradise http://www.puzzlersparadise.com/page1034.html
• Logic Games http://www.mathplayground.com/logicgames.html
• Sudoku - Dont forget this classic puzzle and all its variations. There are hundreds of sources for this one.

If you come across some really good logic puzzles then please share them with us via this blog!

Challenge area 2 – Problems with geometry

You might need a computer with dynamic geometry to have a go at these so maybe it is not so easy on the go but they are great problems!

• Dr Who http://www.teachmaths-inthinking.co.uk/activities/dr-who.htm
• Kaleidoscope http://www.teachmaths-inthinking.co.uk/activities/kaleidoscope.htm
• Olympic Logos http://www.teachmaths-inthinking.co.uk/activities/olympic-rings-logo.htm
• Kite in a square http://nrich.maths.org/8301

Please, if you get any good solutions or animations you can share then do so via this blog!

Challenge area 3 – Number problems

Here are some good number problems to work on!

• Divisibility http://www.teachmaths-inthinking.co.uk/activities/divisibility.htm
• Concentric Magic Squares http://www.teachmaths-inthinking.co.uk/activities/concentric-magic-squares.htm
• Visualising indices http://www.teachmaths-inthinking.co.uk/activities/visualising-indices.htm=cl Cut to the chase with this one and try producing a work of art based on tis idea.
• 2012 Game – if you didn’t try this one already, see how far you can get! http://www.teachmaths-inthinking.co.uk/activities/2012-puzzle.htm

Challenge area 4 – Algebraic Sequences

• OXO – be ambitious and go for the 3D case, any length of line in any cuboid – a real challenge! http://www.teachmaths-inthinking.co.uk/activities/oxo.htm
• Fibs http://nrich.maths.org/537Loopy http://nrich.maths.org/475

Which Team is the Fastest?

A QUESTION OF TIME..?

As part of our IPC topic on the Olympics, we decided to run a relay race around part of our school grounds to see which team was fastest.  We have four house teams, Emerald, Ruby, Sapphire and Topaz.  Each student ran the 360m course and 'tagged' the next member of their team.  Individual times were recorded by hand using digital stopwatches.  Two teams ran at a time so that the others could do the timing.

However, despite our organisation, one person's time was not recorded.  In addition, the teams that didn't have 5 members had to have someone run twice which resulted in a much slower time.  This then led to thinking about what we should do to put this right.  Should we run again another day, or could we use mathematics to come up with a solution?  

So our problem is this, how do we make it fair for the teams with 4 members to compete with a team of 5?

As if by magic, a right angle appeared...

Year 5 looked at a certain kind of triangle. It's one inside a circle where the long side of the triangle is the diameter of the circle. The opposite corner is on the circle too.

At first we looked at these triangles on a big scale. The school pitch, like every football pitch, has a very convenient circle, with a straight line right through its middle. If that line is the long side of a triangle, what angle would the opposite corner have?



Next we used a pair of compasses and a ruler to recreate the situation:

We've also started using GeoGebra  in Year 5. It's great for showing how the angle is always 90°:

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com I didn't take it on to this with Year 5, but there is a fairly simple proof that this will be always the case...

Hexagonal Tiling

Trying Some Tiling

On a recent trip to Barcelona, I thought these lovely hexagonal Antoni Gaudi tiles in La Perdrera would generate some tiling investigations.

Reproductions are also used on the pavements of the city centre.
On returning to school I showed this photo to my students and we discussed the tiles, their shape and design and wondered if we could make some of our own that fitted together in the same way.  We noticed that 3 different ideas centred on alternate vertices which when they were put together made 3 different yet complete designs.  The bottom left tile bothered us somewhat though, as it didn't seem to fit the pattern.  Would ours do the same?  
So we investigated, first for a homework and then with the help of the photocopier and some good old cutting and sticking.  More of an art activity than maths, it could be argued, but the end results were very satisfying and made a stunning display.

First, some that didn't follow the above pattern:  

Then, others that did!

The bottom left tile on the original didn't bother us any longer!  Well done Year 6!