Tak-tiles

by Jessica

Tak-tiles are something that primary children can handle too (although most of the resources on the Web are secondary-oriented). With them algebra makes immediate sense, and they look good too.

We borrowed these ones from secondary,

Tak-tiles

but the shapes on the bottom right are a little tricky so we started with something simpler, a sort of puzzle on a special kind of grid:

First we named the basic areas (not shapes). No sooner had we named c than Sophie observed that a is made up of b and c. 

Harry put it as equation: 

b + c = a

So, armed with this, we were able to describe all the areas in our puzzle with abcs.
The blue rectangle on the right for instance is two of the a-squares, to be written 2a.

Someone noticed that sometimes you could describe an area in more than one way, for instance with the red shape on the left of the puzzle:

it's b + c, but it could be written more simply as just a.

So we got creating, filling the empty grid to make our designs:

The only rule was that everything had to be made up of abcs. There were to be no other-shaped bits that couldn't be broken up into as or bs or cs.
Here's some of our work:

The next thing to do was to start describing shapes in terms of area using abcs.
Millie's M for instance, we worked out to be 6a + 4b.

There's lots more. What would be the area of Max's green dragon be?
And then more tricky questions. Someone objected that those white "eye shapes" in Max's design aren't allowed. But when we thought carefully about it we realised we could describe it with the abcs.

You could easily have a go at creating a design yourself. Just click on the blank grid and download it. Then open it in Paint or whatever colouring-in program you prefer - and go.)

by Amandine

Important factors

People normally draw factor trees like this:

This isn't right in three ways:

1. First of all, it should be a tree that goes up and actually looks like a tree.
2. As the prime factors are so important, they should stand out.
3. And  - the trees should be a bit more beautiful than this.

We started off in Year 5 looking at factors using the Cuisenaire rods, to make the factor walls of numbers. This makes what a factor is so clear:

Then we drew some different factor trees to investigate the question "What different factor trees can you make for 96?" -

 

 

 

 

 

Next, we thought about what mathematical questions about prime numbers we could investigate. Here are some of them:

Ella-May - Do all numbers have a two and a three as one of their prime factors?

Mr Gregg - Are there any other numbers less than 100 with six prime factors?

Sophie - Would an odd number have as many prime factors as an even number?

William - Do bigger numbers have more prime factors?

Harry - Do bigger numbers have bigger prime factors?

Some children suggested we make a huge forest of trees for lots of numbers. Here's part of it:

You can see a bigger version here.

At the same time we played a game, Ocean of Primes, adapted from the nrich Factor Track:

(You can get this as a Word document here. Best to scale it up to A3 when you print it.)

To round off this term's work on factorisation we looked at a great book, Richard Evan Schwartz's You Can Count on Monsters. 

In this book, all the prime numbers are monsters with particular shapes:

Two

Three

Five

Seven

Other numbers have designs made up of these ones. For instance, here's 14:

14 has 7 and 2 as prime factors, so they're in the picture

We had a good look at the book and the poster:

After we'd absorbed what was going on, we created some of our own in a similar style:

Each has the prime factors of the number illustrated:

Anna: 24 has the prime factors 3, 2, 2 and 2

Emily: 104 has 13, 2, 2 and 2 as prime factors

Sophie: The prime factors of 144 are 3, 2, 2, 3, 2, 2

UPDATE - FEBRUARY 2016 - THOUGHT FLOWERS

Read how two artists transformed our factor trees into "thought flowers".

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!