Fawn Nguyen Rocks with Fraction Division

Ms. Win does it again! I’ve decided that Fawn Nguyen is my most favorite math teacher that I’ve never met! I look forward to meeting her and many other admired math bloggers at Math Twitter Camp 2013 in Philly at the end of July.

In this blog post, she presents a very conceptual way for students to visualize division of fractions.� I’ve tried different approaches using the area model, but none have touched this one for it’s efficiency.� Here’s why it’s better than what I’ve done in the past:

• She uses graph paper, so the area models are neat.
• She has students sketch the area model for both the dividend and the divisor.
• She uses color to differentiate between the dividend and the divisor.
• She gently leads students to discover that the dimensions of each whole are the most efficient when students use the two numbers that are� (1) the denominator of the dividend and (2) the denominator of the divisor.
• She starts off simply and then gradually shows all cases such as mixed numbers, and finally a larger fraction dividing into a smaller fraction, resulting in a quotient that is a fraction less than one (this example is added in the comments).
• She encourages students to check their answer using an online calculator with a fraction mode.

Here’s a peak at her first example, which asks students to divide 3/4 by 2/3:  Although this lesson doesn’t show it, her comments indicate that she eventually introduces students to short cut numerical methods, first using common denominator and even perhaps (egads!) common numerator a la Chrisopher Danielson’s post, and finally showing the traditional invert and multiply algorithm that is easy and efficient, but leads to zero conceptual understanding.� However, after students have seen the concept unfold visually, at least the students have a chance of remembering the conceptual reasoning of fraction division.

If you were to poll students, or adults that are not math teachers, and ask them WHY 8 divided by 4 is 2, I bet that they would be able to explain it satisfactorily.� However, if you were to ask the same group (and even some adults that ARE math teachers)� and asked them WHY 3/4 divided by 2/3 is 1 and 1/8, I can almost guarantee a pained, puzzled expression.

Thanks, Fawn and Christopher, for adding to the conversation!

Both Fawn’s blog and Christopher’s blog can be subscribed to via email.� I highly recommend that you follow them for some great mathematical instructional ideas.

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