People normally draw factor trees like this:

This isn't right in three ways:

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

You can see a bigger version here.

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

This isn't right in three ways:

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

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:

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

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

Mr. Gregg,

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These are great. I love your colourful factor forest and clever monsters!

ReplyDeleteI really like the images you have created your students. Congratulations!

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