Technology 2

Today's challenge was to build a structure which could launch (and steer) a marble towards a target 3 metres away.
The teams only had sheets of newsprint paper to use to create the ramp, plus sellotape. It had to be portable and free standing (they couldn't support it themselves).
All the teams managed the task really well, so accuracy was the testing point. They got 5 points for shooting past the drink bottle (3 metres away), and 10 points for actually hitting it.
There was a tie for first place (with 25 points from three goes):
The team of Danielle, Alena and Stacey, plus the team of Isaac, Aleks and Millie.

Technology 1

Today's challenge was to create a launcher for a table tennis ball with a selection of materials... 2 rubber bands, 6 sheets of paper, 4 straws, 4 ice block stocks, and sellotape. Not all the materials had to be used.
Not all the groups managed to finish, the task, but it was a great activity for practising our team work and for focusing on time management.

Pixar in a Box 2

Today we continued our study of Pixar, and found out more about how this amazing company is able to create such fun and cool new virtual worlds for us every time they release a new movie.
Lesson 2: Crowds
When the designers were planning Wall-e, they wanted him to go from a world where there was only one robot - himself on Earth - to a place where there were hundreds of different robots, all with their own jobs and purposes.
The designers were tasked with creating all these different robots, but instead of inventing a thousand different robots form scratch, they simply used the branch of mathematics known as "combinatorics" to create a few different heads, a few bodies, a few arms, etc, and mixed and matched them.
We also had a design task to carry out or ourselves. The challenge was to create 1000 different dinosaurs by using a limited number of body parts (head, tail, arms, legs and body) - preferably fewer than 25. In the end we worked out that 21 or 24 different body parts is the answer, and we designed what they might look like.
Here's the maths:
2 x 5 x 10 x 5 x 2 = 1000 (24 body parts)
or
4 x 5 x 5 x 2 x 5 = 1000 (21 body parts)

Pixar in a Box 1

The Khan Academy have joined forces with Pixar (the awesome company that brought us films like Toy Story, Brave and Inside Out) to create a series of lessons which combine maths and animation. Through these lessons we are able to learn about some of the techniques the animators use in order to make their films. Plus we're also able to catch a glimpse of what goes on in an enormous company such as Pixar, where so many employees with distinct skills are working together towards a common goal.
Lesson 1: Environment Modelling
This series looked at Brave. One of the challenges when the animators made Brave was creating so much grass which moved in natural ways. We learned how parabolic arcs helped the designers to make single blades of grass, and how they were animated in order to move naturally.

Maths Investigation 3

The Locker Problem
Imagine this: there are 1000 students at a school, each with a locker, which is shut. At the start of the day, the first student comes into school and opens all of the lockers.
Then the second student comes in and touches locker numbers 2, 4, 6, 8 etc... if it's shut, he opens it, if it's open he shuts it.
The third student comes in and touches numbers 3, 6, 9, 12... etc. (If it's shut she opens it, if it's open she shuts it.)
It carries on all day. The students come in, and starting with their own locker, they touch the ones which are multiples of their number.

The challenge is figuring out what state the lockers are in by the end of the day.

PHEW!

There are a couple of things to think about when tackling this problem...
1. Downsize the issue. 1000 is a big number. Try it out with 20 lockers and see if a pattern starts emerging which you can extrapolate.
2. Think about what happens to a specific locker. How many times will locker number 1 be touched? How many times will locker number 21 be touched?

It wasn't long before a few of the students in the group realised that this problem has a lot to do with square numbers - such as 1, 4, 9, 16, and so on. When you write down the factors of each locker number you will realise why.

Maths Investigation 2

Today we looked at a bit of Geometry.
Firstly Polygons: How many diagonal lines are there inside polyhedral shapes? And is there a general rule? Can the number be predicted?
We found that for a four-sided shape the total is 2, five-sided it's 5, six-sided it's 9, seven-sided it's 14, and eight-sided it's 20. So obviously the number of diagonals increases. To find a rule, we looked carefully at each corner, and we found it useful to notice, for every shape, how many diagonals came from each corner.
In the end we did come up with a rule, and used it to predict that the number of diagonals in a 100-sided shape is 4850 (phew!).
Here's our rule, where "s" means the number of sides on the shape:
(s-3) x s / 2. We checked it and it works for all the smaller shapes, so we think it will work for the larger ones too.

Then we had some time to work with Polyhedra. We looked at three nets and noticed that although they are all called pyramids, they were quite different. We folded and made the shapes, then designed our own nets which were made from at least three different 2D shapes.

Maths Investigation 1

Today we worked on a couple of maths investigations that gave us a bit of brain drain.

Firstly, the Corner to Corner counter game... on a 3x3 grid, how many moves does it take to get the red counter from the top right corner to the (empty) bottom left?

We found that the shortest number of moves is 13, and then tried out the game with a 2x2, 4x4 and 5x5 grid. We charted our progress and a pattern emerged. We found that every time a new grid was used the number of moves increased by 8.
We worked toward finding a rule for the pattern.

Lastly we investigated Ninety degree Spirolaterals. This is the pattern for drawing a 3- spirolateral: 1 + 2 + 3 + 1 + 2 + 3 etc. You draw for one square, then turn ninety degrees, draw two squares, turn ninety, draw three squares, turn ninety, and start again at one. We found that some spirolaterals come round to the start, and others (like the four) do not. They continue on indefinitely.