Decomposing Fractions: Using Visual Models and Equations

This lesson teaches how fractions with numerators greater than one can be decomposed into a sum of fractions with common denominators. Using visual fraction models and equations, students learn that fractions represent parts of a whole, a set, or a value on a number line. The lesson explains the roles of numerators and denominators and demonstrates how to decompose fractions like 3/8 and 5/6 into sums of smaller fractions. Visual models are used to reinforce the concept that fractions can be broken down into smaller parts, and the lesson concludes with a summary of these ideas.

What does the numerator in a fraction represent?

• The total number of parts in the whole

• The number of shaded parts in a visual model

• The number of parts in a set

• The number of parts that make up the whole

What does the denominator in a fraction indicate?

• The number of shaded parts

• The total number of parts in the whole

• The number of parts in a set

• The number of parts that are not shaded

How can the fraction 3/8 be expressed as a sum of smaller fractions?

• 1/8 + 1/8 + 1/8

• 1/4 + 1/4 + 1/4

• 1/3 + 1/3 + 1/3

• 1/8 + 1/8 + 1/4

What is the sum of the smaller fractional parts that make up 5/6?

• 1/6 + 1/6 + 1/6 + 1/6 + 1/6

• 1/3 + 1/3 + 1/3

• 1/5 + 1/5 + 1/5 + 1/5 + 1/5

• 1/6 + 1/6 + 1/6 + 1/6

Which visual model matches the equation for the fraction 5/6?

• A model with 2 shaded parts out of 6

• A model with 5 shaded parts out of 6

• A model with 4 shaded parts out of 6

• A model with 3 shaded parts out of 6