# Multiplying Fractions via Area

Nicora has a great post on multiplying fractions, check it out here.  This is something similar that I end up reviewing with my 8th graders.  She was wondering about what I have found so here it is….

I start with AREA, Chris(@trianglemancsd) may call it an array, whatever works.  I started approaching multiplication this way since they are pounded with Area problems in 7th grade.  The concept and procedure is ingrained and ready to be built upon.

I start with a multiplication problem I am pretty confident all of my students will know, such as 3×5.  Students will quickly tell me it is 15.  I ask how they can represent that math question and answer, and I get a variety of methods.  I will get at least one student who shows me an area problem.  I pick that example and we talk about area and what it means, how to represent it and I ask them to draw a diagram on graph paper showing it.  This is what I get:

This is exactly what I want to see, even though I kinda manipulated the students into showing me a representation I want to build upon.  I then ask them to show me representations of 3 and 5 using the graph paper grid, and then I create the following construction to connect to their previous representation of  3×5.

This is not a big stretch from what they already do and know, so I have them practice it a bit and come up with new problems in order to try and stump their friends or even me.  Students try and get tricky, and at least one will introduce the idea of fractions into the mix.  Once again, they are leading their learning where I would like them to go.