Area Model for Multiplying Fractions by Fractions

This model should be familiar to the students from our work with multiplying decimals.  Here is a screenshot from today:

Steps:

1. The first factor: Divide the square vertically by the second denominator (5), label the fraction at the bottom (4/5), and shade the fraction with the lighter of your 2 colors.

2. The second factor: Divide the square horizontally by the first denominator (6), label the fraction on the left (1/6), and shade only the intersection of the of the both factors with the second color.

3. Finding the product: The double-shaded region represents the product (4/30). The denominator of the product is the total number of cells, shaded and unshaded (30). 

** Sometimes students shade the entire second factor, all the way across, in step 2, before finding the intersection. While this is not incorrect, I have found that it can sometimes be more confusing.

Another problem:

* For this problem, we started by shading 4/5. Since multiplication is commutative, it does matter which factor you start with..