Day 4:

Symmetry

Part 2

AKS: 4MA.E.8 identify and draw geometric objects, classify polygons based on properties, and solve problems involving area and perimeter of rectangular figures.

Learning Targets: I can draw lines of symmetry in two-dimensional figures.

I can identify lines of symmetry in two-dimensional figures.

Activating Strategy

What Do You Notice? What Do You Wonder?

Mini-Lesson

We have learned how to identify and draw points, lines, line segments, rays, angles (right, acute, obtuse), perpendicular lines, and parallel lines.

Today, we will continue learning about lines of symmetry. We will learn how to identify and draw lines of symmetry in two-dimensional figures and describe how these shapes are symmetrical.

Listen as I think aloud...

Mathematicians, if a two-dimensional shape can be partitioned on a line so that the two halves match exactly, then it is said to have a line of symmetry. A two-dimensional shape or figure may even have multiple lines of symmetry.

Let's take a look at this scenario:

Lily drew three triangles. Lily says that all triangles have at least one line of symmetry. Her friend Molly disagreed and said that some triangles do not have a line of symmetry. Who do you agree with and why? Draw all possible lines of symmetry on each of Lily’s triangles to support your mathematical thinking.

I know that in order to have a line of symmetry, I have to be able to partition the shape in half and have a mirror or exact image on each side of the partition.

Let’s consider the first triangle. Can I divide it into two halves, each part being an exact mirror image?

Let’s place the georeflector mirror on the triangle to see if there is a line of symmetry. If I can see the same shape or a mirror image as I look through the georeflector mirror, I have identified a line of symmetry.

Watch as I model how to use the Georeflector Mirror tool to show the two halves are mirror images of each other.

Place the beveled edge of the Georeflector Mirror pointed down and toward you.
Position the tool on the line of symmetry in the figure, image, or object.
Reflections appear on the other side. Each half should match the reflection of the other half.

Directions: To find the line of reflection (symmetry), move the Georeflector Mirror to a position/location where both sides of the two-dimensional figure perfectly reflect each other. Trace a line with a pencil where the beveled edge meets the paper.

Let's discuss how to identify all lines of symmetry in the equilateral triangle. Rotate the triangle or the georeflector mirror to identify the other two lines of symmetry in the equilateral triangle. See the image below with the three lines of symmetry identified and drawn.

Let’s consider a different triangle. Let’s observe this triangle and determine if there are any lines of symmetry.

As I place the georeflector mirror on the triangle, I notice if any reflections demonstrate a mirror image. I can see that there is not an exact line of symmetry in this triangle. I did not see the same image reflected or shown as I rotated the georeflector mirror.

I cannot find a line of symmetry for this triangle. This tells me that not every shape or figure may have a line of symmetry.

I will model how to find one line of symmetry in Triangle 3 using the georeflector mirrors and draw the line of symmetry. Now, let’s look back at the original problem. Lily said all triangles have at least one line of symmetry, but Molly disagreed. I noticed that I had to agree with either Lily or Molly. I am going to write my answer.

I agree with Molly. Not all triangles will have a line of symmetry. To have a line of symmetry, the shape, or in this case, the triangle must have the exact image when folded in half. The second triangle does not have a line of symmetry. Therefore, Lily is incorrect in her thinking.

Watch a learning video:

Guided Practice

Mathematicians, it is your turn to try! Explore this scenario.

How many lines of symmetry, if any, do the triangles below have? Justify your math thinking by drawing the lines of symmetry.

Before going to rotations, complete the following:

Today, we explored 2-dimensional figures to determine if the figures have lines of symmetry using a georeflector mirror. Remember, for a 2D figure to have a line of symmetry, the shape or figure must contain two halves that are mirror images or match exactly. As we end our math learning today, I want you to answer the following question.

How many lines of symmetry does the shape have, if any?

Draw the lines of symmetry to justify your mathematical thinking.

Independent Task

1. FRECKLE - Complete THREE Freckle Assignments each week. DUE FRIDAY. Your HIGHEST score in Targeted Practice is your weekly math grade - Click HERE for Freckle website

GRADED Targeted Practice - Current skill (5 questions; Score Goal=80% or higher)
Fact Practice - Multiplication Fact Practice
Adaptive Practice - At YOUR level

2. iREADY Math - Complete 30 minutes at your level each week

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