# Discovering Numerator and Denominator with a Pan of Brownies

The way to a child’s stomach heart brain is most definitely with sweet treats. While I don’t like to sugar up my students, I do like when they can connect math to the real world.  That was exactly my mission when I brought in a pan of brownies.

If all else fails, capture their interest with food!

So far at this point, we had examined the definition of a fraction, and thought about things that come in halves and quarters.  It was time to move into some more new vocabulary, the numerator and denominator of a fraction.

In came the pan of brownies.  I brought it over to a large rectangle table and had them all gather around me.  As they were salivating I asked them how I could split this pan into fractions so that we’d all get an equal amount.  I asked them to draw what that looked like in their math journals knowing that we had 25 students in the room.  This was easier said than done.

For some reason, a bunch of them abandoned the hard work we’ve done with arrays, and started drawing diagonals and squiggly lines all over their papers.  It was like they heard the word “fraction” and felt they needed to abandon everything they knew for this brand new concept.

*Sigh*

Then, I asked them to start sharing solutions, and we started to get somewhere. Arrays popped up on the chalkboard, 2 x 13 arrays (“I didn’t want to leave the teacher out!”), a 5×5 array and a 3 x 10 array.  I asked them which one would get them the best deal.

The settled on the 2 x 13 model so that I could get a brownie (how kind!).  That was when I began cutting.  I handed out the first one and asked them to think about what fraction of the brownie pan they were getting. That was when I introduced the fraction in number form and explained the difference between the numerator and denominator. The numerator was the number of pieces they were going to get to eat, and the denominator was the total pieces in the pan. For example (Hint: This is not the actual pan of brownies I used, since the cuts became VERY small and very messy…they were super gooey! So…I had to whip up another batch tonight for this picture, YUM!):

The numerator and denominator suddenly became clear!

They didn’t REALLY get it though, until the last person got their brownie. At that moment, I gave her my piece, telling her how proud I was that she was so patient to wait and be last. That was when the numerator part really sunk in, because I announced that she was getting 2/26 of the brownie, while everyone else only got 1/26. It was a lesson in patience as well as a lesson in math.

It was a pretty sweet mini lesson!