Mr Duey, everyone's favourite rapping maths teacher
Take the top number, divide it by the bottom number
This was one of the BIG IDEAS I wanted to get across. It is really important, particularly when introducing "unit fractions" - those with 1 in the numerator.
Here's is what we did. I have included some of the questions and discussion points that we encountered along the way in brackets:
Step 1 - Get some coloured cardboard or paper and cut it into long, thin strips.
Step 2 - Fold the strip in half. (Q. How many different ways can you do this? - A. Infinite) I was hoping they would do it the easy way, as shown in the picture, but I was prepared for those divergent thinkers who wanted to try something different, like a diagonal fold etc.
So, 1 divided by 2 = 1/2 (top number divided by the bottom number, like Mr Duey said)
Step 3 - Fold it in half again. (Hmm, half of a half is a quarter; there's 2 quarters in a half)
Step 4 - Fold it in half a third time to make eighths. (So, how many eighths in a whole? in a half? in a quarter?)
Step 5 - Unfold the shape and cut along each fold line. (How many pieces will you end up with? How many cuts do you need to make?)
Step 6 - Swap one piece with someone who has a different colour. (What fraction do you have now that is a different colour? What fraction is the original colour?)
Step 7 - Now swap 2 more pieces with the same person. (What fraction now is the original colour? the new colour? Which is biggest? Which is smallest? What happens to the fraction when the numerator gets bigger? What happens to the fraction when the numerator gets smaller?)
So what?This is all pretty basic stuff. Yep, we cut up some paper and had a bit of a play. So what?
Well, I wanted to get the kids tho articulate their observations about what they could see in front of them. I find this produces some good insights into what they are thinking. So we went on to....
Step 8 - Now write 2 statements about this arrangement you have in front of you.
And here's a selection of what the kids wrote:
3/8 of my shape is pink.
More than half of my shape is blue.
5/8 of my shape is blue.
3/8 < 5/8
5/8 is more than 3/8
5 eighths are red and the rest is blue.
Less than half of my shape is green.
1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = 1
3/8 and 5/8 = 8/8
There are 3 blue eighths.
My shape is 8/8.
All the pieces are equal.
3/8 is equal to 6/16.
3/8 < 7/8