Lesson 8

Are All Pieces Created Equal?

Lesson Purpose

The purpose of this lesson is for students to understand that equal pieces of an identical whole do not need to be the same shape.

Lesson Narrative

In previous lessons, students learned that when they partition circles and rectangles into halves, thirds, or fourths, each piece must be equal. To this point, they have determined whether the pieces are equal by cutting out pieces and physically matching them and by visually inspecting whether the pieces appear to be the same equal-size shape. 

In this lesson, students learn that halves, thirds, and fourths of the same whole can be different shapes or have different attributes. For example, they recognize that a square is partitioned into fourths, whether it is partitioned into equal-size triangles or equal-size squares.

ADiagram. Square partitioned into four equal parts. One part shaded.

BDiagram. Square partitioned into four equal parts. One part shaded.

By the end of the lesson, students realize that as long as the shapes are partitioned into the same number of equal pieces, the pieces will have the same name and have the same size. 

  • Representation
  • MLR2

Learning Goals

Teacher Facing

  • Partition circles and rectangles into halves, thirds, and fourths in different ways.
  • Recognize halves, thirds, and fourths of rectangles and circles.

Student Facing

  • Let’s make halves, thirds, and fourths in different ways.

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 did you say, do, or ask during the lesson synthesis that helped students be clear on the learning of the day? How did previewing the cool-down of the lesson before you started teaching today allow you to help students synthesize their learning?

Suggested Centers

  • How Are They the Same? (1–5), Stage 2: Grade 2 Shapes (Addressing)
  • Which One? (K–5), Stage 3: Grade 2 Shapes (Addressing)

Print Formatted Materials

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