6-GM-4-4


6.GM.4.4 Identify and describe the line(s) of symmetry in two-dimensional shapes.

In a Nutshell

A line of symmetry for a two-dimensional shape is a line that divides the shape into two equal halves such that one half can be reflected across the line and matched up exactly with the other half. A two-dimensional shape can have no line of symmetry or at least one line of symmetry that can be a horizontal, vertical or diagonal line. When identifying and describing lines of symmetry for a two-dimensional shape, the number of lines of symmetry and what type of lines of symmetry such as a vertical line of symmetry or horizontal line of symmetry should be given in the description.

Student Actions

Teacher Actions

  • Develop a deep and flexible conceptual understanding of lines of symmetry by exploring different two-dimensional shapes by using mirrors or folding along a line to determine if the line is a line of symmetry for the shape.

  • Develop the ability to make conjectures and generalize patterns by exploring the types of lines of symmetry for different two-dimensional shapes. For example, the number of lines of symmetry will increase by one for a regular polygon as the number of sides increase by one.

  • Develop the ability to communicate mathematically with others through discussion or writing in order to explain why a given line is or is not a line of symmetry for a  given two-dimensional shape.

  • Implement tasks that promote reasoning and problem solving about lines of symmetry by engaging students in exploring two-dimensional shapes that have no line of symmetry and shapes that have one or more lines of symmetry. For example, mirrors or reflective surfaces can be used to explore lines of symmetry.

  • Pose purposeful questions about lines of symmetry, such as “Do all rectangles have the same lines of symmetry? Triangles?” and extend questions to other two-dimensional shapes.

  • Elicit and use evidence of student thinking to assess progress towards understanding why a line for a given shape represents a line of symmetry and adjust instruction to support their understanding.

Key Understandings

Misconceptions

  • A line of symmetry divides a two-dimensional shape into two equal halves such that one half can be reflected across the line and matches up exactly with the other half.

  • A two-dimensional shape can have no lines of symmetry or it could have at least one line of symmetry.

  • Lines of symmetry can be vertical, horizontal, or diagonal lines.

 

 

  • Think a line that divides a two-dimensional shape into two equal halves is a line of symmetry. For example, students may think the diagonal line in the rectangle below is a line of symmetry.

 

 

 

                                                    

  • Think a figure can have only one line of symmetry.

  • Have trouble identifying lines of symmetry that are diagonal lines.

OKMath Framework Introduction

6th Grade Introduction