1. Problem Statement
This problem is called Slice The Bagel. The problem is to make three cuts to slice a bagel into 12 pieces. The cuts have to be straight but you can stack up or fold the pieces any way you want. The pieces don't have to be the same size
2. Process
I tried to solve the problem by making models with paper. I cut out shapes like bagels and cut them into different pieces. This is called modeling.
I started out by cutting the bagel in half like I was going to put it in the toaster. It looked like:
Then I stacked the halves on top of each other and cut each half into 2 pieces. That gave me 2 x 2 = 4 pieces that looked like this:
The next thing I thought of was stacking up the pieces and cutting through them. But that would only make 4 x 2 = 8 pieces. It didn't work but at least I saw a pattern. I saw that each time I stacked up the pieces and cut them I multiplied the number of pieces. So then I thought what three numbers multiply together to make 12? Well 2 x 2 x 3 = 12, of course.
So if I could divide one piece into three pieces with one cut then I could stack up the four pieces I had and cut them all into three pieces in one swoop. Then came the hard part. How could I cut one of the pieces into 3 pieces? After a little staring I saw the answer:
My Answer
Here's the way I finally sliced the bagel. I took the four "C" shaped pieces that I got from my first two cuts, stacked them up and made one more cut down through them like this:
3. Evaluation
I felt that this problem was fun. I liked the problem because I had a chance of solving the problem using my hands. The hardest part was figuring out how one piece of bagel could be cut into three with a single cut. I learned that math could be fun. I was proud to have solved the problem.
