Fractions as Whole Number Multiples

Introduction

• 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.