Teaching Models

Work With Fractions

Comparing and Ordering Fractions
At this grade level, comparing and ordering fractions is limited to unit fractions or to fractions with a common denominator. Many students may need to use pictures to compare and order fractions. For unit fractions, one over a > one over b if and only if a < b. For example, one-third > one-fourth because 3 < 4. To compare fractions with a common denominator, a over c > b over c if and only if a > b. For example, which is greater, three-sevenths or four-sevenths? Since 4 unit fractions of one-seventh are greater than 3 unit fractions of one-seventh, four-sevenths is greater than three-sevenths.

Equivalent Fractions
Two fractions a over b and c over d are equivalent if there exists a number m such that [ m × a over m × b ] = c over d. For example, the fact that [2 × three-halves × 4] = six-eighths implies that three-fourths is equivalent to six-eighths.

Equivalent fractions can be modeled by using a picture in which there are two ways of representing the same “part of the whole.” The fact that three-fourths is equivalent to six-eighths can be shown as follows.

The word of is often used to pose problems involving the multiplication of a whole number by a fraction. At this level, students have not yet learned to multiply fractions. However the phrase “one-third of 6” can be modeled in terms of a group of 6 objects that is separated into 3 smaller groups, each of which has 2 objects.

Addition and Subtraction of Fractions
To add or subtract fractions with like denominators, find the sum or difference of the numerators and keep the common denominator. Answers should be expressed in simplest form.

For example, in three-fourths + two-fourths three unit fractions of one-fourth are added to two unit fractions of one-fourth. The sum equals five unit fractions of one-fourth. So the answer is five-fourths, or 1one-fourth. In three-fourthsone-fourth , one unit fraction of one-fourth is subtracted from three unit fractions of one-fourth. The result is two unit fractions of one-fourth. So the answer is two-fourths, or one-half.


Teaching Model 19.1: Compare Fractions


Houghton Mifflin Math Grade 3