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!