Probability Scales

Following from some of our work on Probability, year 7 students have been having some fun putting events on probability scales! It's a lovely activity because making decisions about how likely things are to happen inevitably leads to some kind of numerical or fractional reasoning! This is being posted from an iPhone as a kind of test, but we will add a gallery when we can.

Guess whats in the bag!

Probability in year 7 - So we put 15 different coloured sweets in a bag and then pulled 1 out at random and noted the colour and then put it back. We repeated this exercise a number of times and got the tally chart above. Each student was allowed 2 guesses at the contents of the bag with the first successful guess winning the sweets! The challenge was 'what' to guess and 'when' to guess! Guess early and you get the first chance at winning the sweets, but you have less information to help you. Wait too long and somebody might get there first. Some tricky decisions! The whole point is of course that the more times you repeat the experiment, the more likely the tally chart is to show the right proportions. What colour do you think the sweets were? Could there be a purple one in there somewhere? Are there definitely more greens? We had a lot of fun. These and similar games for playing with this idea are published here - Guess my colour, Roll'em and In a spin.

Coming up...

This is just a short entry to show some things that are coming up with my classes next week in mathematics here at the International School of Toulouse!

Year 7s are getting stuck in to a new unit on probability (link for IST members). There is lots of game playing and experimenting planned as we try and challenge our intuition with some good logical reasoning!


Year 10s will be looking in depth, backwards and forwards at percentages. We will have some fun looking at percentages in the media and trying to get to the bottom of the headlines like 'Jedi Knights are the worlds fastest growing religion.'


Year 11s will continue their work on a statistical analysis of UK number singles using this 'NumberOnes' activity that includes a cool database of the whole history of number one singles, how long they were at number one, how long the songs are and what decade the songs were released in. There are some great patterns emerging!

Year 12 Maths Studies students will be revisiting right angled trigonometry and using dynamic geometry software to build their own 'trig ratio calculator'. This, in an attempt to see how trig ratios arise from naturally observed phenomena!


Year 13 Maths Studies students are moving on from sets and logic to probability. ( I love how year 13 are studying the same topic as year 7) We will try and marry what we know about tree diagrams, and , or etc with the work we have done on sets and logic, starting with this 'Probability Trees' activity.

Making 3D shapes!

This is a display made by year 10 students learning about the surface area and volume of prisms, cones and spheres! This quickly moves from cuboids that are quite approachable to shapes with curved surface areas likes cones and spheres. We had particularly good fun making cones (follow link for more details). The challenge was to make a cone with a base radius of 10cm and a perpendicular height of 24 cm. Students were given an A2 piece of card and those measurements. Firstly they had to figure out what the net of a cone looks like then figure out what the measurements needed to be to make sure the cone met its requirements! There is no substitute for having to build shapes from nets to help understand how the net relates to the shape. By mistake, one group made a fabulous 'Bar of Gold' shape which is a truncated rectangular based pyramid. Anyone know another name? Some students discovered 'antiprisms' and one group made a beautiful shape that we dont yet know the name of - see the picture below. A special mention is reserved for the students who printed the proof of the surface area of a cone on the T-Shirt (one for the display and one for me)! Great, practical, investigative fun all round!

The unnamed shape!

Some more photos of our display below.

Optimal Cuboid

Year 7 students had fun with this idea last week. We have been exploring the idea that there are different nets for a cube and going on to look at the nets of cuboids and the ideas of surface area and volume. So students were given a piece of A4 card and asked to draw the net, cut out and build a cube 5cm x 5cm x 5cm. Then with the remaining card they have to build the biggest cuboid they can. There was lots of thinking about this to do before they cut anything out! How do I draw the net of the cube that leaves me the most card left over? How can I make the cuboid as big as possible? What does 'big' mean in this context? How can we decide who is the winner? Who has built the biggest cuboid? Fun was had, cuboids were created and thinking was done!

More can be read about the thinking behind this activity here!

Mobius Mess

A small group of year 6 and 7 students gathered after school today to make a proper 'Mobius Mess'. With paper scissors and glue, we explored all the different features of the wonderfulMobius Strip. How many faces does it have? How many edges? What if you twist it twice? Three times? What if you cut them all in half along their length, what happens then? It would be great to write all about that, but that would spoil the fun for those of you that havent tried it. There are lots of sites out there on this topic and we used this one to get us started. We made some a bit likethese too! There are lots of surprises and fascinating things going on! We recomend you try yourselves, but the video below might give you a quick overview and you might understand how we made such a 'Mobius Mess!'

Posted by Jim Noble, Curriculum leader for secondary mathematics, International School of Toulouse, www.intst.eu, Co-author www.teachmaths-inthinking.co.uk

     

The Big Breakfast Venn

It started out as a simple idea. IB Maths studies students drew a giant Venn diagram on the playground with chalk to do a survey of what people had for breakfast. They stood where they belonged in the diagram and they drew little stick figures of themselves to serve as a record. At break we invited other staff and students to put themselves in the diagram, then lots of classes from the primary school came over and before we knew it we had created 'The Big Breakfast Venn'. The drawings got more and more elaborate with the art department steeling the show! It was a simple idea just to play with different sections of a Venn diagram before going on to some more complicated problems and it turned in to a great whole school activity. Hopefully below you can see some of the great pictures we got to keep a record!

Posted by Jim Noble, Curriculum leader for secondary mathematics, International School of Toulouse, www.intst.eu, Co-author www.teachmaths-inthinking.co.uk