Fraction Goodies

So the kids are feeling pretty good about fractions.....they were so sure they knew all my tricks....but then I threw this at them....

I gave them a 4 x 4 grid and asked them to show me 1/2.

They groaned at this "baby" math....."How easy!"...I heard.....and they got to work.....this is what most of them came up with.   I expected this...a straightforward way to show 1/2.

I had one that was a bit different from the others.....

Everyone felt very good about their fractions.....and in the end...everyone agreed that 1/2 of the grid was 8 squares colored in.....case closed.......

So, I put this up.....and asked....is this half?

The kids with total and complete authority said......NO!......so I put this one up and asked....is this half?

(Sorry, the picture is upside down).....the kids again responded.....No, not half!  No matter how many times I asked them, they insisted the 2 previous pictures couldn't be half........here is what they said...

It doesn't look like a fraction.

The parts have to be touching....

I reminded them what they told me before that 1/2 of 16 was 8....and that in both of these 8 squares are colored in.....but almost all the class was adamant that this was NOT half!

I finally had to cut apart the grid in front of them....and rearrange the squares into a more traditional arrangement.....

Then I moved them around....and said...I still have 8 pink squares, and 8 white squares....am I still showing half?.....

Finally, some light bulbs starting going off....... after much discussion, the class agreed that it doesn't matter how a fraction is arranged....equal is equal....even if it looks different!!!

Equal is equal......

There are still some kids who are really thinking hard about this concept....I expect more and more light bulbs to keep going on as we continue to dive deep into fractions!