Fractions as Whole Number Multiples
Students will be able to illustrate fractions as products using a number line.
- 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.
Explicit Instruction/Teacher modeling(10 minutes)
- Hand out and preview the Illustrating Whole Number by Fraction Products worksheet.
- Guide your students through the three-step explanation.
Guided Practice(10 minutes)
- Have your students take turns going through the three-step process with exercise #1 ( providing another example).
- Answer any clarifying questions.
Independent working time(10 minutes)
- Release your students to complete the remaining exercises.
- 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.
- 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.
- 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.
Review and closing(10 minutes)
- Review the answers for Illustrating Whole Number by Fraction Products.
- Perform the assessment as a whole class.