Monday, August 26, 2013

180- Day 5 Connecting methods for dividing fractions

First of all, I am still over-planning for my lessons.  I'm so used to planning for a 90 minute block instead of a 47 minute period.  I've been starting each class with Estimate180, which is fantastic!  Totally zero entry for the kids and fun!  It is turning out to be perfect for the beginning of class- takes just a few minutes so I can take attendance and maybe glance around for homework.  One class is just obsessed with Mr. Stadel though...they want to know where the pictures were taken, whether the picture is of his house/yard/etc, and one even asked if he was my brother :)

Today we did a little bit more exploring with dividing fractions and unit rate...worked on connecting the graphing method we did yesterday to the standard algorithm for dividing fractions.  I used 4 divided by 1/3 so we were doing a lot of circling of groups and they were happy for a more efficient method.

I've been using kind of an exit ticket in the INB each day...depending on where we get to it either ends the period or starts the next day.  Here's the example from today...I wanted students to summarize what they learned about unit rate and dividing fractions in order to compare two dripping buckets.  I had them use both the graphing method and the standard algorithm- from here they will be able to choose whatever method they find most efficient for any given problem.

Friday, August 23, 2013

180- Day Four- Visual Graph Paper Method for Dividing Fractions
In 7.RP.a.1, students need to be able to calculate unit rate, including rates that have complex fractions.  I tried a method for dividing fractions using graph paper that I found at Fawn Nyugen's site.  Definitely great for my visual learners.  Through the process I found students really just had trouble understanding whether the quotient should be a number greater than 1 or a number less than one, so that became our focus.  By drawing out the fractions using the same wholes, they could see which was larger.  I kept coming back this similar to a "10/2" problem, which is more than 1, or a "2/10" problem, which is less than one.  I did really like the method though!

Some of my not so very visual students did really struggle with it.  Common misconceptions:  When students created the rectangles to represent the fractions some of them really struggled to draw an accurate representation of the fraction.  For example, if they chose a 4x5 rectangle because they were trying to model 4ths and 5ths, when they tried to shade 3/4 they would shade 3 sets of 4 squares rather than 3 rows out of the  4 rows in their rectangle.