Fractions, which are usually taught in fifth or sixth grade, are a challenge for many students. So in middle school, we find many students that have difficulty with fractions. My school's RTI (Response to Intervention) time was recently designated as a time to work on fractions with both seventh and eighth graders. So today I started with two new groups to focus on fractions. My sixth period group was with seven eighth graders and the seventh period group was with eight (very energetic) seventh grade boys.
I was keenly aware that I was starting an instructional unit with students I hadn't worked with before and that I needed some way to get their attention, yet establish some limits. I continue to look for hand-on visual models to explain mathematical concepts that I am trying to get accross.
When the seven students came into the room, I had two large cookies on the side table. (I made these chocolate chip cookies from one mix, pressing half the dough into the bottom of an eight-inch round cake pan.) Of course their attention was mine right away! I told the students the problem that we would work on later. There were two large cookies and they needed to figure out a way to share them evenly. I quoted what my mother used to say,"If you can't share them, share and share alike, then nobody gets any!" I told them we had some drills to do first, but they should be thinking about this problem.
After the drills, which then went quite smoothly, we came back to the cookie problem. Two large cookies split among seven people seemed to be quite a problem for them. The first idea was that they would share a part with me and cut each cookie into eight parts. I declined and they worried out loud about a cook that wouldn't eat her own cooking! After explaining diabetes limitations, I told them if they could come up with the fraction that each person would get, I could help them know how to cut the cookies. I gave them a hint: when I was a kid and Grandma gave us a bag of candy, we divied it out by saying "One for you, one for you..." until they were all given out. I asked them how they would have to cut the cookies so they could divy them out evenly. They knew it would have to be in sevenths. And they realized they would each get a part from both cookies. So they would be eating 2/7 of a cookie. I then got out my protractor and a piece of paper. They knew that there are 360 degrees in a circle, so we figured that 1/7 of a circle was about 51 degrees. I made a 51 degree paper wedge to use as a cutting guide. After sanitizing their hands they cut the cookies perfectly!
While they were munching on pie-shaped cookie pieces I explained that we had divided two cookies by seven people and each got to have 2/7. The line in a fraction means "divided by" in this kind of problem. I had another similar word problem printed out that I put on a clip easel.
"Camp Winnetaka has 300 campers. The chef made 90 extra-large pizzas. If the pizzas are shared equally among the campers, how much will each camper get?" By referring back to the cookie problem, students were able to see that 90 pizzas were being divided by 300 people. So each one would get 90/300. I told them that it wasn't likely that the chef would cut each of those pizzas into 300 tiny pieces and then let each camper go and get one piece from each pizza. They realized the need to reduce and we were able to spend the rest of the period working with individual white boards on reducing fractions, improper fractions and mixed numbers. (Each camper got 3/10 of a pizza.)
The seventh grade group had to split three cookies among eight people. They came up with two solutions which caused a bit of an argument until I stepped in. The first proposal was to cut each cookie into eight pieces and everyone would get three. The second solution was to cut two cookies into four pieces and give everyone one piece, then to cut the last cookie into eight pieces and give everyone one of those. It was a great time to point out that both would be the same amount.
At the end of the period, I asked them to individually write a few sentences about how they thought they were doing with the skills we had worked on today. I listed them on the board: word problems dividing food among people, reducing fractions, changing improper fractions to mixed numbers and back. The students were honest and most expressed that there was something in the class that had helped them today, especially with that type of fraction word problem. I thoroughly enjoyed teaching these classes and am looking forward to Wednesday when I see them again!
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