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Thursday, April 3, 2014

What Size Cookie Would You Like?

Stop at the store and buy a package or two of those chewy Chips Ahoy and don't forget to bring a knife. This has got to be my favorite way to introduce fractions.  I've taught fractions before at higher grade levels but have only been teaching them for a few years in first grade. These young mathematicians have no concept of what a fraction is, so it makes this introduction all the more fun and important because I want to do something that really sticks in their brains.
I started our math lesson by having everyone sign up for the size of cookie they would like. Some years I have everyone on the one-eighth but this year one of these young mathematicians was trying hard to convince everyone that he has a fraction place mat and he is sure one-half is bigger. Some believe him but most see that 8 and sign up for one-eighth anyways. Now comes the fun.  I pull out a cookie and place it under the document camera as I explain that I need to cut the cookie into 8 equal parts so everyone can have one-eighth. As soon as I start cutting, these mathematicians are beginning to groan. One-eighth is so small they say. But I give everyone exactly what they signed up for and start on cutting a cookie into fourths. The students who signed up for one-fourth are excited knowing they get more but they quickly realize that one-half would be better.

By this point my students know they don't want to cut the cookie into more pieces and they are starting to understand the meaning of a fraction. We end by dividing all the cookies that are left over and eating them too.  We'll wait for another day to talk about dividing sandwiches. Fractions just go so well with food!

Today we started back up our introduction into fractions by discussing what we already know about fractions.
Our list included 3 things:
1. Fractions have to be equal parts.
2. The number on the top tells how many you get.
3. The number on the bottom tells how many parts there are.
Wow! This is getting close to using numerator and denominator. We aren't there and we won't even go there this year but these 6 & 7 year old mathematicians are coming pretty close on their own. So the problem for today is to discover how many ways you can divide a sandwich into two equal parts. I had a stack of 4-inch papers already cut and ready for them. It didn't take long for them to come up with a way and soon everyone had discovered these two ways.

We glued them down and labeled the fractions before I asked if they were sure there were no other possibilities. Everyone agreed there were only two ways until I asked again. Then some students started to waiver. So I pushed a little more and made everyone who was sure there were only two ways stand up. Four hesitant boys stood up and showed some visible relief when I announced I couldn't find another way either. Then we changed the problem to dividing a sandwich into fourths. I made sure to use the words fourth and quarter interchangeably. Right away everyone wanted to make sure they found all of the ways. Someone quickly blurted out that there were only two ways with the half, so there must be four ways for the fourth. I kept my smile to myself and let them go forward with a vengeance trying to find a fourth way. They were determined to find it.

 It took a while before they gave up on discovering a fourth possibility and conceded that there are only three ways to divide the sandwich. We even had a sixth grade student come in, take one look at what we had discovered and claim there was another way. We gave her a few minutes to show us but my students were pretty proud when they proved her wrong. So we labeled our fractions and looked back over our work. We talked about the importance of having equal parts and were just cleaning up when I overheard my favorite quote of the day, "My mom didn't even know we could do fractions."
I think we have laid the foundation for a good, strong understanding of fractions. A little more practice in our math centers with making pictures using whole circles, half circles and quarter circles should be perfect for giving them a little independent practice with the concept of fractions.

This was a great multi-day introduction but if you teach something a little higher than first, you should head over to Beyond Traditional Math to look at how she introduces fractions to third graders. Homemade brownies? Mmm mmm mmm! But beware in my class we won't choose an eighth of a brownie, we know better now.

Beyond Traditional Math

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