Multiplication of Fractions (And January's Math Practice of the Month!)

In this "two-for-one" post, I am sharing some videos that I have been experimenting with to assist WCSU teachers as they plan their instruction around multiplication of fractions while simultaneously emphasizing CCSS Math Practice 3 (illustrated at left).

Math Practice 3 states that students must be able to construct viable arguments and critique the reasoning of others.

As you watch the videos, think about how students are being asked to present their arguments and analyze the reasoning of others.

What instructional practices foster growth of this practice?

About the lesson...

Typically, this is a fifth grade concept, however, if students do not have deep conceptual understanding that they can communicate using an area model, we need to "go back to square 1."  For seventh grade students, an excellent place to revisit this concept is between studying probability of compound events and ratios and proportions.



Multiplying Fractions Part 1 addresses the intuitive hook:

Multiplying Fractions Part 2 shows how to bring students from the intuitive level through the concrete model for multiplying (and dividing) fractions emphasizing the importance of dimensionality.  This is some video footage of Katy's sixth grade class at Rumney.

Multiplying Fractions Part 3 shows how to bring students from the concrete model to pictorial and abstract representations of multiplying and dividing fractions.

Here's what Katy's white board looked like at the end of the day:

We did four examples together to model going from the concrete to the pictorial to the symbolic.  Then, students worked though the examples (a through h) on the board at their own pace to practice.  This allowed me to work with individuals without holding up those who were revving their engines.

Katy's students did this work in their math journals.  You could also have students the graphic organizer (included with the "Useful links" below) to record this work (or even have tech savvy kids record it digitally using the template).

Stay tuned!  

My next blog post will include video for Multiplying Fractions Parts 4 and 5 showing:

• How to arrive at a conjecture for multiplying any two fractions, 
• How to extend that idea to address multiplication of mixed numbers,
• Techniques for moving from the abstract symbolic understanding of fractions to being able to communicate deep conceptual understanding using multiple representations, and 
• Applying conceptual understanding to multiple contexts and non-routine problems. 

Useful links:

• Here is the pre-assessment of a student's understanding of fractions as equal parts of a whole (referenced in the first video).
• Here is link to the instructional plan (referenced in the first video) that I have been working on writing up.
• Here is a graphic organizer that students can use to organize their exploratory work.
• Here is an organizer to help students develop the conjecture.