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".