Lesson 2

Representations of Fractions (Part 2)

Lesson Purpose

The purpose of this lesson is for students to make sense of non-unit fractions (including those greater than 1) that have denominators 2, 3, 4, 5, 6, 8, 10, and 12.

Lesson Narrative

In the previous lesson, students made sense of the meaning of numerator and denominator in unit fractions. They identified fractions represented by diagrams, and partitioned diagrams to represent given fractions. In this lesson, they reason in similar ways—using numerical and visual representations—about non-unit fractions and fractions that are greater than 1.

Students are reminded of what they learned in grade 3: that a non-unit fraction \(\frac{a}{b}\) can be understood as \(a\) parts of a unit fraction \(\frac{1}{b}\), and that fractions with different numerators and denominators can be equivalent. Unlike in grade 3, the denominators they see here now include 5, 10, and 12.

As in the previous lesson, rulers can be provided to help students draw, extend, or align partition lines, but should not be used to measure the location of a fraction on any diagram.

  • Representation
  • MLR2

Learning Goals

Teacher Facing

  • Make sense of the numerator and denominator of unit fractions that have denominators 2, 3, 4, 5, 6, 8, 10, and 12.
  • Use diagrams to represent fractions.

Student Facing

  • Let’s name some other fractions and represent them with diagrams.

Required Materials

Required Preparation

Activity 2:

  • Each student needs access to their fraction strips from a previous lesson. 

CCSS Standards

Building On

Building Towards

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

Who participated in math class today? What assumptions are you making about those who did not participate? How can you leverage each of your students’ ideas to support them in being seen and heard in tomorrow’s math class?

Suggested Centers

  • Get Your Numbers in Order (1–5), Stage 3: Denominators 2, 3, 4, or 6 (Addressing)
  • Mystery Number (1–4), Stage 3: Fractions with Denominators 2, 3, 4, 6 (Supporting)

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