Using Models to Teach Fraction Understanding: 5 Essential Components

1. Introduce multiple models for the same fraction. For example, the money model is commonly used for ¼ because of student’s familiarity with the coin and the fact that four quarters make a dollar. However, the clock model is also a good model for ¼ since we often refer to “quarter after 5”, or “quarter to 2”. It is important that students don’t get stuck using only one model for a given fraction. Having multiple models at their disposal will help the flexibility of their thinking and allow them to switch models if needed. Otherwise, we run the risk of students not being able to understand fractions like 1/3 or 1/8 because they don’t “fit” in a given model. Students should be encouraged to move among different representations of a given fraction, identify equivalence, and determine which model(s) are the most useful in a given context. One way to help students achieve this is playing a matching game with different representations of the same fraction.
2. Encourage students to think flexibly about “the whole”. When working with the set model, students see that ¼ looks different in a set of 4 items than it does in a set of 12 items. In the earlier grades, encouraging students to experiment with different wholes will better prepare them to see fractions as operators (1/3 of 15 is not the same as 1/3 of 90) in later grades.
3. Allow students to explore fractions as more than just “a part of a whole”. As students progress through the years, it becomes increasingly important that they are able to recognize fractions as division, ratios, and comparisons. Using flexibility in language and how we discuss fractions helps students do the same. Instead of always referring to ¼ as “1 part of a whole with four pieces”, refer to it in multiple ways like “1 divided by 4” or “1 red crayon to 4 crayons in total”.
4. Give students practice with decomposing fractions. For example, ¾ is the same as ¼ + ¼ + ¼ which is also the same as ½ + ¼. This will ensure that students will be more successful in problem solving with fractions (for example, ¾ + ½ becomes easier to see as ½ + ¼ + ½, which in turn is ½ + ½ + ¼, and students know that ½ + ½ is a whole, and there is ¼ left over.
5. Estimate! When introducing new fractions that are unfamiliar to students, help them rely on benchmarks (0, ½, and 1). Students develop a sense of magnitude for the fractions that will help them visualize what a fraction like 7/8 looks like (a little less than 1). See the Spin to Win game on Mathwire for an example of a game students can play. Moving forward, students who have a solid ability to estimate are more likely to be able to estimate sums and differences of fractions.

For further suggestions on teaching fractions visit the Rational Number Project.

http://www.cehd.umn.edu/ci/rationalnumberproject/default.html

Elizabeth Masalsky is a 6th, 7th, and 8th grade mathematics teacher at Battery Park City School in Manhattan. She has a post-baccalaureate in mathematics from Brandeis University and her master’s in secondary math education from Bard College. Elizabeth is a Math for America Master Teacher and continues her professional development through workshops with Math for America, Metamorphosis and Math in the City.