| Original Problem: | Draw two straight lines that cross each other once, touch opposite sides of the rectangle, and form four sections that each contain the same number of dots. |
1. Problem Statement
This problem is called Parting The Dots. The problem starts with a rectangle with many dots drawn in it. The problem is to draw two straight lines that, go over each other once, touch opposite sides of the rectangle, and make four divisions that each have the same number of dots.
2. Process
I tried to solve the problem by drawing different lines through the rectangle and counting the dots on either side. This is the guess and check method. The first thing I did was draw a line lengthwise, about in the middle of the rectangle.
I counted the dots. One side had eleven dots, the other side had nine dots. Then I added up the number of dots. I got twenty dots in all. That meant there would have to be ten dots on each side after the first cut. By moving my first line a little bit I split the rectangle in halves with ten dots on each side. It looked like this.
Then, to speed things up, I got a ruler. I used the ruler to try out different lines without having to draw and erase them. I tried to split the rectangle a second time in two ways. The first time I got six and four dots in two of the divisions. This looked like:
I moved the ruler a little to add one more dot to the division with four in it. That gave me six and five dots in the divisions.
Finally I moved the line a little way again to put it in between the first two lines and got my answer.
My Answer
This is my solution.
3. Evaluation
I felt this problem was hard. I liked using dots and fractions. The hardest part was splitting the rectangle in fourths with an equal number. I didn't learn anything. I'm proud I found a solution.
