Math Background

Lesson: Comparing and Ordering Fractions
Introducing the Concept

Use models and diagrams to introduce this concept. Relate comparing and ordering fractions to comparing and ordering whole numbers, but don't overlook the added complication of the denominator.

Materials: student-made fraction kits, colored pencils or markers

Preparation: Provide each student with twelve pieces of precut wax-paper squares or cut 6-inch squares of tracing paper (they must be able to see through it).

Prerequisite Skills and Concepts: Students should be able to compare and order whole numbers. They should have a good grasp of what a fraction is and what its parts represent, and they should be able to write equivalent fractions.

  • Say: Take one of your paper squares and carefully fold it in half. Color one of the parts.
  • Ask: What part of your square is colored? What part is not colored?
    (one-half, one-half)

    Work with students to fold and color all of the remaining squares.

    paper squares
    paper squares
  • Ask: What does one square represent?
    Students should recognize that one square is one whole.
  • Say: Hold up any square that you folded into four segments.
  • Ask: What does one segment represent?
    Students should identify one segment of the four equal-size segments as representing one-fourth.
  • Ask: If you're holding the fourths square in which you colored in two segments, what does the colored part represent?
    Students should easily see that they colored two fourths.
  • Say: Place your two-fourths square over your one-half square.
  • Ask: How do the fractions compare?
    Students should notice that since the same portion of each square is colored in, one-half equals two-fourths.
  • Say: Place your two-fourths square over your four-eighths square.
  • Ask: How do the fractions compare?
    Students should notice that since the same portion of each square is colored in, two-fourths equals four-eighths.

    Continue in this way, helping students to compare by using words such as greater than and less than as well as equal to and not equal to. Do this orally until students are comfortable with the language, and then remind them of the symbols they used to represent these comparisons when they were working with whole numbers.

  • Say: Mix up your fraction squares. Take the first four squares from the top of your stack and put the rest out of the way. Put the squares in order from least amount colored to greatest amount colored.
  • Ask: Can you write the names of your fractions from least to greatest?
    This should be an easy task. If it is not, find some time later to work with any student who is having trouble.
  • Ask: Can you use your fraction squares to help you put the fractions in order from least to greatest? three-fourths, five-eighths, three-eighths

    Students should be able to pick out the appropriate models visually and use them to order the fractions.


Houghton Mifflin Math Grade 4