Tuesday 28 September 2010

Factor caterpillars

1. Choose a start number. Find the factors of the number..
e.g. 16. Factors are 1,2,4,8,16
2. Add up the PROPER Factors of the number.
e.g. 1+2+4+8=15.

Repeat for 15.
Factors are 1,3,5,15.
1+3+5=9.

Factors of 9 are 1,3,9
1+3=4

Factors of 4 are 1,2,4
1+2=3

Factors of 3 are 1,3 (3 is prime as it has two factors).

1=1 So stop here.

If you write each number in your chain on a circle of card, you can make lovely caterpillars.

Good questions. Whixh numbers under 100 make the longest chain.
Which numbers are boring! (Primes)
Why are square numbers interesting here?
What is special about powers of 2 to start?
What is really special about 6 and 28!
Try 220!

FULL PAGE LINK


Here are some pictures...
One of them includes what happens when you start at 30 ...



Monday 13 September 2010

Difference of 4


This is one of my favoruite early lessons, and really lends itself to mixed ability Y7. I'm posting it in response to the mathchat discussion tonight.

Start with a 2x2 grid, and put numbers in the spaces...

Having done this, drawe a few arrows, and do some times tables...

Followed by some adding...











Then, simply - the difference between 46 and 64 is 18.

Questions you can ask...

"Can you choose numbers that give you a difference of 4"

"What happens if you use the same numbers, in a different order"

"What happens if you add 1 to every number"

"Are there any differences you cannot make"

"what happens if you put numbers in in a pattern - 2,4,6,8, etc"

"Is there more than 1 way to make a difference of 4?"

....

It is a lot of fun (and I take no original credit for the lesson. Picked it up on my PGCE many moons ago (OK - 1995/96!)