September 18, 2017
By Byron Delcomb

Lesson plan

Fractions as Whole Number Multiples

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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).
  • Answer any clarifying questions.
(10 minutes)
  • Release your students to complete the remaining exercises.


  • For practise, 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 practise illustrating number sentences where one factor is a unit fraction and the other is a whole number.


  • 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.

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