Teaching Models


A fraction can be used to represent a part of a whole or part of a group or collection of things. For example, a whole circle can be divided into four equal parts and the fraction three-fourths used to represent three of four equal parts. Children should be reminded that the parts into which the whole is divided must be of equal size.

A fraction can be defined formally as a number that can be expressed in the form a over b, where b ≠ 0, a is the numerator, and b is the denominator. The denominator of a fraction cannot equal zero.

A unit fraction is a fraction with a numerator of 1 (for example, one-half, one-third, one-fourth, one over n). The definition of a unit fraction one over n is to take one unit and divide it into n equal pieces. One of these smaller pieces is the amount represented by the unit fraction.

The fraction m over n can represent the quotient of m and n or m ÷ n. If the fraction m over n is defined in terms of the unit fraction one over n, the fraction m over n means m unit fractions of one over n. If m = n, then m over n = 1.

Comparing Fractions
At this grade level, the comparing and ordering of fractions is limited to unit fractions, and pictures are provided to aid a child in deciding which of two fractions is the greater or lesser. For unit fractions, one over a > one over b if and only if a < b. For example, one-third > one-fourth because 3 < 4.

Children learn that a fractional part of a number, such as one-third of 6, can be found by separating the group of six into the same number of equal groups as the denominator of the fraction, which is 3 in this case, and then counting the number in 1 group, which is 2. So one-third of 6 is 2.

2 is one-third of 6.

Teaching Model 9.4: Comparing Fractions

Houghton Mifflin Math Grade 2