Prime Factor Trees.

A visual way to teach the concept of prime factorization is my literally creating a factor tree. My students absolutely loved this activity and it made an awesome display for a bulletin board.

Materials (per group or person)
1 12x18 sheet of sky blue construction paper
1 12x 18 sheet of brown construction paper
2 half sheets or one whole of 2 different greens
markers
numbers to be factored written on 3x5 cards.

Multiplying Fractions.

Again the credit is not mine. :) But some fun stuff!!

irageo : Was thinking about multiplications, too.
irageo : Might be easiest to start with something like 1/x * 1/y
irageo : 1/3 times 1/2... 1/6
irageo : 1/2 times 1/2... 1/4
irageo : 1/4 times 1/3... 1/12
irageo : 3/4 times 1/3... Well, 3/4 is just 3 1/4's, isn't it? 3* 1/4.
irageo : so 3/4 times 1/3 must be 3 times as much as 1/4 times 1/3...
irageo : 3/12
irageo : 1/4 times 2/3...
irageo : Well, 2/3 is 2 1/3's... 2* 1/3, right?
irageo : So 1/4 times 2/3 must be twice as much as 1/4 times 1/3...
irageo : 2/12!
irageo : Now... the tricky bit...
irageo : 3/4 times 2/3!
irageo : I wonder if there's any pattern here... some shortcut we could take...
irageo : I'd do a few problems the long way around first, though
irageo : Let them try and work out the "shortcut" themselves
kaspirant: I did that the other day with borrowing fractions...they were so amazed when i showed them the shortcut. I love doing that.
irageo : But here's the thing
irageo : about shortcuts
irageo : Unless you know WHY they work, it's worse than not having it at all.
kaspirant: Right and the reason that it is necessary to teach 'the long way' to understanding first.

Dividing Fractions.

I can't take credit for this. But I was amazed!!

irageo : Hey there. How was fractions?
kaspirant: Actually turned out better than I expected. Nice when the kids surprise me that way
irageo : I was thinking this morning about dividing fractions
irageo : and how to introduce it
kaspirant: /ponder
irageo : What's 2/2?
kaspirant: *sadly you just lost half my class*
irageo : One, very good. What's 5/5?
irageo : One again, excellent. What's 6/6?
irageo : What's 5384/5384?
kaspirant: we did that today ... hehe...only it was more like this…
irageo : It's all one. Anything divided by itself is one.
irageo : So, what's 1/2 divided by 1/2? That's one, too!
irageo : What's 2*1?
irageo : Two, right! What's 5*1?
irageo : 5, excellent! What's 5384*1?
irageo : Multiplying by one gives you exactly the same thing you started with!
irageo : Now, a bit of magic:
irageo : 4/5 divided by 2/3. That looks tough
irageo : But wait, magic!
irageo : Multiply by one... and it doesn't change
irageo : But we're going to multiply by one in a special way.
irageo : What's 8/8? One!
What's 17/17? One!
What's 3/2 divided by 3/2?...
irageo : It's ONE!
irageo : So we can multiply (4/5)/(2/3) by (3/2)/(3/2) and still get the same thing, right?
kaspirant: *realizes that the best thing right now is to listen... listens intently, grinning*
irageo : So we multiply the top... 4/5 times 3/2 is 12/10...
irageo : And multiply the bottom... 2/3 times 3/2 is 6/6... Hey!
irageo : 6/6 is what?
irageo : It's one!
irageo : What happens when we divide by one?
irageo : It stays the same!
irageo : So, 12/10 divided by one is...
irageo : 12/10!
irageo : And then you reduce, blah blah...
irageo : Magic!
kaspirant: Magic!!
irageo : How's that sound?