This is day 1 of multiplication of fraction by a fraction and I can already see this will dramatically increase my blogging! So much to write about (for reflection, excitement and possibly confusion). With the implementation of CCSS this year, this is new in the Investigations curriculum and I am finding some things I love about it already and some things I am struggling with just a bit.
Before this lesson, students have worked in the context of a bike race of “x” number of miles and found a fraction of the race various bikers have completed. Looked like this:
This lesson went very smoothly and I found it was more of a struggle to have them model what was happening on the fraction bar since finding the fraction of the whole number was an action they could do mentally. To some, it seemed like an unnecessary step and to be honest, I wavered between unnecessary and yet completely necessary to make their thinking visual. I knew how important it would be in fraction x fraction, so I made them construct the model of what was happening in the story.
Today we started fraction of a fraction. It incorporates the same visual image of the fraction bar, so I love that continuation from previous lessons. It did lack a context, which at first bothered me but as we continued working, and heard the discussions, I moved past that. Tomorrow, I am actually going to have them come up with a story to go along with a few problems to see if they can contextualize the math they are doing. We started with a fraction of a half and then a fraction of a third, writing the expressions (some equations) as we went:
Of course, you always have the students who fly through the work and finish early as I am walking around and having discussions with the students who need some extra help, so I asked those who finished early to think about the denominator each time. Why is the product’s denominator changing from the denominators of the factors? Did you have an idea what the denominator would be before you used the fraction bar? There thoughts were so interesting:
I am thinking this will be one of MANY multiplication and division of fraction posts! I am just amazed at the ease the students work with the fraction bars and I like what Investigations has done thus far with these lessons. One tweak I would like made would be the directions…students are asked to “stripe 1/2 of the shaded portion” and it is becoming a tongue-twister for me 🙂 I keep saying shaded when I mean striped, minor detail but they keep correcting me!
These conversations are so rich and valuable for this understanding that it blows my mind that a teacher could just say “multiply the numerators. multiply the denominators. That is multiplication of fractions.” If I had learned fractions this way, it would have all made SO much more sense!
To be continued…