Guided Lessons
Learning Library

# Fractions as Whole Number Multiples

Teach your students to use number lines to illustrate fractions as products, specifically where one factor is a fraction and one fraction is a whole number.

No standards associated with this content.

No standards associated with this content.

Which set of standards are you looking for?

Students will be able to illustrate fractions as products using a number line.

(5 minutes)
• Call out the following equation to your students (pausing at "equals..."), as you write: “ ⅕ + ⅕ + ⅕ = ⅗.”
• Ask your students to join in while you continue aloud writing, “⅓ + ⅓ =...” (wait for “two-thirds!”)
• Presents one more, “⅛ + ⅛ + ⅛ + ⅛ = …”(“four eighths!”)
• Ask your students to consider this: What clues do you see in each equation that gives hints to what the sums might be? Have them think, pair and share with a partner.
• Have students share as a whole class and note any academic language and terms for future reference.
• Point out to your students that in each of the opening examples, a sum of unit fractions can be written as a product of a whole number and a fraction. For example:
• ⅕ + ⅕ + ⅕ = ⅗ is expressed as 3 x ⅕ = ⅗
• ⅓ + ⅓ = ⅔ is expressed as 2 x ⅓ = ⅔
• ⅛ + ⅛ + ⅛ + ⅛ = 4/8 is 4 x ⅛ = 4/8
• Draw the connection to the transitive property of equality (which comes up in algebra, but is nicely illustrated here: If ⅕ + ⅕ + ⅕ = ⅗ and 3 x ⅕ = ⅗, then ⅕ + ⅕ + ⅕ = 3 x ⅕ . This will be illustrated throughout today’s lesson.
• Summarize by sharing with your class: You can write any fraction as a product of a whole number and a fraction in three steps. You can even illustrate it on a number line, which is what this lesson is all about.
(10 minutes)
• Hand out and preview the Illustrating Whole Number by Fraction Products worksheet.
• Guide your students through the three-step explanation.
(10 minutes)
• Have your students take turns going through the three-step process with exercise #1 ( providing another example).
(10 minutes)
• Release your students to complete the remaining exercises.

Support

• For practice, provide several fractions as exercises for writing number sentences where one factor is a whole number and the other is a unit fraction.
• Print out a sheet of open number lines for students to practice illustrating number sentences where one factor is a unit fraction and the other is a whole number.

Enrichment

• Pose challenge exercises that include improper fractions and mixed numbers.
• A computer with Internet access and a projector makes for a great set-up to display student assignments, examples and answers.
(5 minutes)
• Divide your students into four groups and assign each group a number (1-4).
• Assign each group a corresponding task:
• Tell the whole number factor.
• Tell the unit fraction factor.
• Tell the Sum of Unit Fractions sentence. Give a brief explanation of how it would be illustrated on a number line.
• Hold up a fraction and call on each group to share their assigned task.
(10 minutes)
• Review the answers for Illustrating Whole Number by Fraction Products.
• Perform the assessment as a whole class.