Halving Paper

Students alway love to fold paper in half. They somehow understand that this creates a fraction of 1/2 even at the preschool level. But what happens when they fold it in half again? It creates four equal rectangles or a fraction of 1/4. What if they keep going?

I challenged them to think about how many times we could fold a piece of regular paper (8.5 by 11) in half. They first guessed 10+, then I had them do two folds. They immediately revised their guesses to 5-8. The actual number for a child is 6 and for the strongest human only 7 times to a fraction of 1/128th. We tried it with larger paper and were only able to obtain an 8th fold. We did it with a Mathlete Dollar and only achieved six folds. 

I had them use the attached pdf which showed them the fractions they created after each fold. 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, and finally 1/128. I had them open the paper and count the sections. Very quickly, they realized that the denominators (we did not focus on that word yet, just "the bottom of the fraction") were the doubling numbers they learned the previous week. They loved making that connection. The larger the bottom number, the smaller the fraction.

Then I had them fold the pdf paper. Next, I had them do it with the same paper with no fractions listed and they had to write the fractions with each fold. They should attempt this with your help during the week many times. I want them to "feel" the fractions.

Then we had them work with paper that was gridded with 1/2, 1/4, 1/8, 1/16, 1/32, 1/64. I had them shade in several of the sections and then list this as the top of the fraction and give the resulting fraction. For example, with the 1/16 paper, they might have shaded in 3 of the 16ths and then wrote the fraction 3/16 and circle it. I told them to do this many times during the week and use color to make the fractions come alive.

I would love it if they came to class next week with dozens of pages of these fractions.