This year's Forest of Factors

Following on from last year's post Important Factors, and after our work finding prime numbers with Cuisenaire rods and in the playground, Year 4 had a go at making prime factor trees this year. Here's our Forest of Factors:

See more on the Year 4 blog

Our trees made a really big Forest of Factors display for the primary corridor. As the Year 2 and Year 3 children are passing it regularly, it was a good idea to explain the display to them. We did it without using the words "factor", "multiple" or "prime" so that it would be easier for them to understand:

 "Hello everyone. This is our Forest of Factors."

"1, 2, 3, 4.... 40"

"What do you notice about our pictures?"

"Number 1 is my bird. It's different to all the other numbers. If you times something by 1 it just stays the same number."

"So 1 is special, and we don't think about it with our trees and mushrooms. It's just flying up in the sky!"

"Some of the numbers are simple trees. Look at 38. 38 is 19 times 2, so we've given it two branches that finish with flowers."

"Ten is five times two."

"26 is 13 times 2."

"These ones had just two branches and two flowers."

"But some of the trees have more flowers. Like 12, and 32."

"With the mushrooms there's no two numbers that you can times together to make that number."

"Can you see a number that is a mushroom?"

"So that's our Forest of Factors. We hope you understand it a bit better now."

Finding prime numbers in Year 4

In Year 4 we've been looking at prime numbers this week.

Some of us have been out in the playground, using the hundred square there:

Here's a how we did it:

Later we had a go in the classroom, using a photo of the hundred square (16 colour bitmap format):

and, on Paint, filling he numbers in the 5, 3, 7 and 2 times table with colour:

And there we have it: the grey ones (except for 1) are the prime numbers!

(also blogged on the Year 4 blog)

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".

Thank you Monsieur Cuisenaire!

In Year 5 we've been getting some of the classic bits of maths equipment off the shelves and dusting them down. Things like the cuisenaire rods, invented by the Belgian teacher Georges Cuisenaire in 1931 and recommended to the world by Caleb Gattegno in the 1950s. They seem to get talked about less these days, as a Google Ngram check shows:

But even if they're less fashionable, it's still worth seeing what they can do...

In Year 5 at IST we used them to investigate the "walls" of numbers. So, with ten for instance, what layers of the wall can you make out of just one colour? In this case there's the orange ten itself, the yellow fives, the red twos and the wood-coloured ones. The layers, of course, are the factors of the number. And it soon becomes apparent that some numbers only have themselves and one as factors: the prime numbers.
In fact using the cuisenaire rods now makes more sense than it did in the past. You can easily make a record of what you've done with the rods online. The cuisenarie environment here does the job very well.

If you're at IST you can see a video of some of the Year 5 children explaining prime numbers using the cuisenaire rods as examples here (you'll need to sign in to your Google Apps account).

As a footnote, it's fascinating watching how Caleb Gattegno used Cuisenaire rods in this film of a model lesson from 1961: