Monday, February 10, 2014

Visual Fraction Models for Multiplication

One of the newest (and often most difficult) elements of Common Core is using visual models to show mathematical thinking.  In 5th grade, this is an element in both decimals and fractions that can often be difficult for students because it's completely different from what they're comfortable with.  They've always been used to "finding the answer" and now they are asked to "show how you can find it" or "show what that looks like".

I have a great product to help teach this:  Multiplying Fractions Packet - With Visual Models
As I moved into multiplying fractions last week with my students, I started out with multiplying fractions by whole numbers with visual models.

My students receive an information page with the steps for creating a model for multiplying fractions by whole numbers.  Next, they are given the outline of the visual models and have practice problems to try on their own.  They fill in the models to match the problem and find their answer.  (See example below)
Next, I challenge my students to create the models on their own.  They are given additional problems and the space to draw their models.  The difficult part of this is organizing their models neatly, so using a ruler is definitely a good idea for them.
The next mini-lesson I introduce is multiplying fractions by fractions.  This was slightly more difficult for my students because the models are more confusing.  They need to create the fraction model for one fraction, and then split that fraction up in the opposite direction to shade in the other fraction across.  (As you can tell, this is very difficult to explain!!)

I tell them that when you multiply fractions, you are taking a fraction OF another fraction and ultimately the fraction will become smaller.  Here is what it looks like:
The first fraction is shaded in columns, and the second fraction is shaded in rows.  I like my kids to use two primary colors (one for each fraction) so that they can easily see the area where they overlap.  The green becomes the numerator and the entire model is their denominator.

Once they are given the models for practice, they are then given a page in which they have to create their own models.  A few of my students asked if they could have some graph paper to help them create neater models and I was able to find a website that had printable graph paper that worked out perfectly.  
Once I teach the visual models, I then teach my students the "quick and easy" way of simply multiplying across, and then work on word problems.  

All of the mini-lessons shown above, along with word problem practice and a comprehensive quiz on all of these skills can be found HERE in my Multiplying Fractions Packet.

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