Teaching the Common Core Math Standards With Hands-On Activities, Grades 3-5 (32 page)

a.
“Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

b.
“Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.

c.
“Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

d.
“Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.”

Background

A unit fraction is a fraction whose numerator is 1. All fractions whose numerator is larger than 1 can be expressed as either the sum of unit fractions or the sum of other fractions that have the same denominator.

For example,
can be expressed as
or
or
.

Mixed numbers with the same denominator can be added or subtracted by adding or subtracting the numerators, then adding or subtracting the whole numbers, and then simplifying, if necessary.

For example,
.

Mixed numbers with the same denominator can also be added or subtracted by replacing each mixed number with an equivalent fraction, then adding or subtracting the numerators, and then simplifying, if necessary.

For example,
.

(
Note:
Emphasize the term
unit fraction
wherever it is used, to help students learn the terminology.)

Activity 1: Decomposing a Fraction

Students will decompose a fraction into a sum of fractions with the same denominator in six different ways.

Materials

Scissors; reproducible, “Fraction Bars,” for each student.

Procedure

1.
Hand out copies of the reproducible. Explain that it contains several fraction bars.

2.
Explain that students are to cut out all of the fraction bars. They will use the fraction bars to decompose
in six different ways and will then write an equation for each way. Order does not matter, and each fraction should have the same denominator.

Closure

Ask your students what strategies they used to decompose
. Did they use addition? Subtraction? Did they use any other methods?

Answers

Following are six ways to decompose
.
(1)
(2)
(3)
(4)
(5)
(6)