Teaching the Common Core Math Standards With Hands-On Activities, Grades 3-5 (13 page)

Number and Operations—Fractions: 3.NF.3

“Develop understanding of fractions as numbers.”

3. “Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

a.
“Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

b.
“Recognize and generate simple equivalent fractions, e.g.,
Explain why the fractions are equivalent, e.g., by using a visual fraction model.

c.
“Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

d.
“Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols
or
and justify the conclusions, e.g., by using a visual fraction model.”

Background

Fractions may be expressed in many forms. Two common forms are equivalent fractions (fractions that have the same value) and whole numbers (which can be written as a fraction with 1 as the denominator).

If two fractions have the same numerator, the fraction that has the larger denominator has the smaller value. For example,
is less than
Given two pies of equal size, cut one into thirds and the other into halves. It is clear that a piece that is
of the original pie is smaller than a piece that is
of the original pie.

If two fractions have the same denominator and different numerators, the fraction with the larger numerator has the larger value. The fraction with the larger numerator represents more of the equal parts. For example,
has a greater value than
because 7 parts, each part being
are larger than 5 parts, each being

Activity 1: Squares and Fractions

Working in pairs or groups of three, students will cut out four squares and arrange them so that equivalent values correspond to form a large square.