Lesson 4

Division Situations

Lesson Purpose

The purpose of this lesson is for students to solve division problems when the quotient is a fraction or mixed number.

Lesson Narrative

In previous lessons students solved equal sharing problems involving division of whole numbers with answers in the form of mixed numbers and fractions using diagrams. They noticed patterns and made generalizations about the relationship between the expression \(a \div b\) and the fraction \(\frac{a}{b}\) for specific values of \(a\) and \(b\). Students have observed that the numerator of the fraction is the number of objects being shared, while the denominator is the number of equal shares. This lesson brings all of these ideas together through contexts, equations, and diagrams. Students continue to notice patterns across these contexts and build flexibility with interpreting fractions in terms of division by creating their own situations. Fluently moving between representations gives students the ability to choose an appropriate representation to solve a problem (MP1).

Consider what division situations students or their families might be familiar with. Measurement contexts often present situations when division results in a fraction or mixed number. For example, making something with fabric, dividing large amounts of food in to smaller containers, or measuring and cutting wood for a project.

  • Engagement
  • Representation

Learning Goals

Teacher Facing

  • Solve problems involving division of whole numbers leading to answers in the form of fractions.

Student Facing

  • Let’s solve and represent division problems.

Required Preparation

CCSS Standards


Lesson Timeline

Warm-up 10 min
Activity 1 20 min
Activity 2 15 min
Lesson Synthesis 10 min
Cool-down 5 min

Teacher Reflection Questions

What strategies are students using to divide numbers that result in a quotient that is a fraction or mixed number? What questions have you asked that encourage students to see the relationship between the dividend and the numerator and the divisor and the denominator?

Suggested Centers

  • Rolling for Fractions (3–5), Stage 3: Divide Whole Numbers (Addressing)
  • Target Measurements (2–5), Stage 4: Degrees (Supporting)

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