Saturday, May 25, 2013

Interactive Math Journal: Fractions of Fractions

I've been promising my kids all year that I was going to teach them how to multiply fractions, and now with only 5 teaching days left, I can finally get to it.  Thursday, I introduced the lesson by giving each student multiple half sheets of paper.  Our first task was to find what 1/2 of 1/2 was.  We folded the paper in half vertically, colored half with one color crayon, then folded it in half horizontally and colored that half with a different color crayon.  The piece that had the two overlapping colors showed us what 1/2 of 1/2 was, or 1/4.  We then did the same activity again, but this time wondering what 1/2 of 1/3 was.  I kept recording our findings on the board.  At one point, I heard a gasp from Abbie.  She looked at me excitedly and kind of started bouncing in her seat.  I knew she had discovered something, but I asked her to hold on to her thoughts just a little longer.  As we kept going with the paper, I heard more and more gasps and "oh!!!!!" coming from the class.  I could tell some kids were getting frustrated that the others were discovering something they were not, so I finally let Abbie tell us what she first discovered.  Of course, she saw that we were making arrays with our papers, and noticed that all we had to do was multiply the denominators.  It was a different student that noticed that in each of our examples, the numerators were also multiplied.  It was an exciting moment for the class!! 

Then, someone raised their hand and asked, "Are we going to put this in our notebooks?"  To be honest, I hadn't thought of that, but they had such a great idea!  They actually wanted to add to their notebooks on their own!  YIPEE!!!  Since this activity took so long, we had to wait a day to enter it into our notebooks, but that gave me a chance to type up some blank rectangles to record our drawings in.  Here is the end result: 

This student chose pink and yellow to color with, so the overlapping piece is orange and shows the end result!

This student showed that 1/2 is shaded in yellow, while 3/4 is in pink.  The orange shows that 1/2 of 3/4 is 3/12!

This time, we included a "What I know" and "What I learned" section.  It should be on the left hand page, but oh well.  We are still learning!

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