November 09, 2012
Expert Corner: Building Understanding of Fractions
Thom O'Brien has been with ExploreLearning for ten years in a variety of roles, including working with teachers to integrate Gizmos into more effective teaching in math and science. Thom has a Master's degree in Instructional Mathematics and he taught 7th grade math before joining EL.
For many teachers and students, fractions are a struggle. It’s a topic that comes around every year, but how can you present fractions to your students so that they really “get” them?
ExploreLearning offers several Gizmos designed to help students build real understanding of fractions. Two of our most popular are the Fraction Artist Gizmos 1 & 2. (The difference between the two is the Lesson Materials: the first is introductory, while the second provides more challenge.)
Both Fraction Artist Gizmos provide students with a blank canvas, which they can divide up and “paint,” loosely modeled after the style of artist Piet Mondrian.
For example, you or your students could make a painting like the one to the right. You could then ask students, “What fraction of this painting is red?” This is a good “fraction basics” question. To answer, students need to see two things. First, the painting is divided into 3 equal-sized pieces, so the denominator of the fraction needs to be a 3. Secondly, there is one red piece, so the numerator is 1. Putting it together, this painting is 1/3 red.
Students can continue dividing the painting up, and adding other colors to it. (And as they do, the fraction questions can get a little more interesting.) For example, suppose students divide the red section again (divide 1/3 into thirds), and then add some yellow, as shown to the right. So, here’s a new question: “How much of this painting is yellow?”
In fact, the painting is 1/9 yellow. Could your students explain why? The Gizmo’s “Inspect sections” feature can help illustrate why. (Note the blue overlay in the 3rd image to the right.)
Mathematically, what this shows is that 1/3 of 1/3 is 1/9, or in other words, 1/3 • 1/3 = 1/9. (This is a nice way to provide some understanding behind the oft-quoted saying, “’of’ means multiply.”
You could also ask students, “How much of the painting is red now?” The answer is 2/9. Each red section is one ninth (1/9), so two of them is two ninths (2/9). In other words, 1/9 + 1/9 = 2/9. (You can find answers like this in the Gizmo by using the “Inspect colors” option.) This helps illustrate why, when adding fractions, numerators get added but denominators do not.
So in this short “mini-lesson,” we’ve touched on at least four important fraction concepts – the meaning of the numerator, the meaning of the denominator, multiplying fractions, and adding fractions. (And obviously, we’ve only barely scratched the surface of what’s possible. There are plenty of other ideas in the Lesson Materials.) Not bad for a fun, simple painting Gizmo!