Comparing+Fractions+with+Different+Denominators

Comparing Fractions with Different Denominators
The purpose of this activity is to describe and illustrate how to teach what it means to find a common denominator. The activity may be useful when students have difficulty comparing fractions with different denominators.

Problem: A student does not know how to compare two fractions with different denominators (e.g., 1/3 and 3/5).

Step One: Ask the student what we need to know in order to compare two fractions. If the student replies that we need to have a common group, then ask, "what size should the group be?" If the student replies, "I don't know" (or something like that), provide examples of two different groups.

For example, illustrate 1/3 of a large circle and 3/5 of a smaller square.

Or, illustrate 1/3 of a yardstick and 3/5 of a ruler.

Ask, "what is the problem with trying to compare parts of different wholes?" Appropriate responses may include, "it doesn't make sense to compare parts of different groups", "the wholes need to be the same in order to compare parts."

Step Two: Encourage students to develop and test a rule for comparing things (including fractions). What idea does the rule need to communicate? In this case, we want a rule that communicates the need for a common unit or criteria upon which two or more items can be compared.

Step Three: Ask students to work on the [|Fractions-Comparing] applet to model what it means to compare fractions with different denominators.

As an assessment, ask students to describe and illustrate what it means to find a common denominator. Appropriate responses might include: "finding a whole unit that can be split into equivalent parts", or "finding parts of one whole that are equal to parts of other wholes".