Day 3:

Symmetry

Part 1

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 about the way each structure is built?
How does the left side compare to the right side of each structure?
What do you notice about the size and shape of the windows in each structure?
Which structure looks more balanced? Explain.
What are some other examples of real-life objects that have left and right or top and bottom matching parts?

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 learn that some two-dimensional figures have an attribute called line symmetry. We will also 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:

A figure has line symmetry if it can be folded over a line so that its two halves match exactly. This line is called a line of symmetry.

A line of symmetry divides a figure into two congruent parts that are mirror images of each other. A figure is symmetrical if it has a line of symmetry.

Some figures are not symmetrical and do not have any lines of symmetry.

Other figures are symmetrical and may contain one or more lines of symmetry.

How can we determine if a line of symmetry can be drawn on a two-dimensional figure to divide it into matching parts?

Let’s examine this two-dimensional figure and identify and draw at least one line of symmetry within it.

I can fold this paper square to discover if it has a line of symmetry. When I fold the square into two equal parts, the parts must match exactly. Each half should be a mirror image of the other.

Let’s fold the square vertically, matching the two halves and seeing that both parts are exactly the same. Trace each line of symmetry using a different color crayon.

Draw a line segment on the fold. This is a vertical line of symmetry within the square.

I can verify and check if this is a true line of symmetry by using the Georeflector Mirror. If one half of the square matches the other half, it is symmetrical. The first line of symmetry is shown with a red line.

I wonder if it’s possible to fold the square in a different direction and find another line of symmetry. Let’s fold this square horizontally.

When I fold this square horizontally, the two halves match. They are mirror images of each other, exactly the same shape and size.

Draw a line segment on the fold. This is a horizontal line of symmetry within the rectangle. The second line of symmetry is shown with a purple line.

I can verify and check if this is a true line of symmetry by using the Georeflector Mirror. If the reflection of the top half of the square matches that of the bottom half, then it is symmetrical.

I wonder if there are any more lines of symmetry...

Wow! I can fold this square diagonally, too. When I fold this square diagonally, the two halves match. I can see that both halves are exactly the same shape and size—mirror images of each other.

Draw a line segment on the fold from corner to corner. This is a diagonal line of symmetry within the square.

I can verify and check if this is a true line of symmetry by using the Georeflector MIrror. If the two halves of the square match or reflect each other, then the square is symmetrical.

I can also fold this square along the opposite diagonal. The two halves of the square match or reflect each other perfectly.

The third line of symmetry is shown with a green line.

The fourth line of symmetry is shown with a blue line.

Wow! This square has 4 lines of symmetry!

Watch a learning video:

Guided Practice

Mathematicians, it’s your turn to give it a go! I will provide you with a rectangular blank index card, a marker, and a Mira tool. With your math partner, fold the index card (rectangle) to determine if there is a line of symmetry. Use the Mira tool to verify or confirm the line of symmetry you identified is accurate.

If you identify and draw a line of symmetry, challenge yourself to locate one or two more lines of symmetry.

You must:

Fold the index card in half and determine if the two halves match exactly.
Demonstrate that the fold is a line of symmetry if the two halves match precisely and are mirror images of each other.
Draw a line on the crease/fold and may also use the Georeflector mirrors to explore line symmetry further.

As you work in collaborative groups, I want you to think about what you learned today as you worked with different shapes to determine if each had a symmetry line. You may fold the two-dimensional figures and use your Georeflector Mirror to determine the lines of symmetry in each shape.

Today, we explored different two-dimensional figures and determined whether each figure has at least one line of symmetry. Remember, for a shape to have a line of symmetry, the figure can be folded on a line so that the two halves match exactly or are mirror images of each other.

To complete our math learning today, I want you to answer the following question:

Which shape does NOT have a line of symmetry?

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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