Activity
# Symmetry activities: Math

## Tactile activities to help blind and low vision students understand and identify shapes that are symmetrical.

The first post, Create matching symmetrical shapes activity: Popsicle math, is geared for young students with hands-on activities using foam shapes and popsicle sticks to create a simple mirror image. In this post, students will learn more about symmetry and how to identify if a cutout image is symmetrical.

The basic definition of **symmetry**: Symmetry is when an object looks the exact same on one side as the other. To see if an object is symmetrical, draw a line of symmetry or a line dividing an object to show a perfect match on each side.

The basic definition of **Line of Symmetry**: A line of symmetry is the line that divides a shape or an object into two identical parts.

**Asymmetrical** means an object or shape that has two sides that do not match or that are not the same.

In geometry,** symmetry** means that one shape is identical to the other shape when it is moved, rotated or flipped. For two objects to be symmetrical, they must be the same size and shape, with one object having a different orientation from the first. If you can draw a line directly through the center or axis of a shape, so that either side of the line is a reflection of the other, then it is symmetrical.

In geometry, **reflection** is the mirror image of a figure over a line (drawn or imaginary). Also known as “flip” or “mirrored”. The object maintains the same size and shape.

In geometry, a **flip** is a motion in geometry in which an object is turned over a straight line to form a mirror image.

In geometry,** rotation** is when an object is turned clockwise or counter clockwise around a given point. Rotations can be represented on a graph or by simply using a pair of coordinate points.

Here are several hands-on symmetry activities for the whole class to enjoy!

- Using a sheet of construction paper, cut out 4 squares.
- Ask the student to fold the first square in half so that the corner line up exactly. (The folded shape will be a rectangle.)
- Open the square. There should now be an indention where the square was folded in half. This indented line is the line of symmetry. Both sides of the line are exactly the same and the shape is called symmetrical.
- Give the student another construction paper square. Fold it a different way so that each section is exactly the same.
- Hint, the folded shape will be a triangle.

- Continue to each of the 4 squares a different way.

A square with dotted lines indicated the four different ways to fold the square:

- Fold in half from top to bottom (creates a long rectangle)
- Fold in half from left to right (creates a tall rectangle)
- Fold the top left corner to the bottom right corner (creates a triangle with the point facing the bottom right)
- Fold the top right corner to the bottom left corner (creates a triangle with the point facing the bottom left)

Download the square shape to use as a template or to run through a tactile graphics machine (PIAF or Swell machine).

- Using construction paper, cut out two X-shapes.
- Note: The X shape below is wider at the bottom than at the top.

- Fold the X in half to make a line of symmetry where both sides are exactly the same.
- What happens when you fold the shape so that the top folds to the bottom? Is this X symmetrical when folded this way?
- If desired, cut out another X that has the same width for each “leg” and repeat the activity. Why is this X symmetrical when folded right/left and when folded up/down?

X shape where the bottom is wider than the top:

Download the X shape to use as a template or to run through a tactile graphics machine (PIAF or Swell machine).

- Using construction paper, cut out 2 odd shapes.
- Fold the shape left/right. Is it symmetrical? Why or why not?
- Fold the shape top/bottom. Is it symmetrical? Why or why not?
- Can the shape be folded diagonally to make it symmetrical?

Odd shape:

Download the odd shape to use as a template or to run through a tactile graphics machine (PIAF or Swell machine).

Ask the student to create an odd shape by taking a sheet of construction paper and randomly cut out an **odd** shape. Do you think the shape is symmetrical? Check to see if the cut out shape is symmetrical by folding the shape paper in half. (It’s probably not a symmetrical shape!)

Now, ask the student to make a symmetrical shape. Take a sheet of construction paper and fold it in half. Ask the student to cut out an odd shape by starting from the fold and ending on the fold. Remove the section that has been cut out. Open the construction paper. Is the shape symmetrical?

How a symmetry worksheet be modified for a student who is blind or low vision? Below is a worksheet with common shapes. Once a student has learned to identify symmetrical shapes by folding the cutout image, the next step is to identify symmetrical shapes using raised line tactile graphics. This worksheet is an example symmetry worksheet; each shape has a dotted line of symmetry down the center of the shape. There are 3 rows of 5 basic shapes. Download the symmetry shapes worksheet to use as a template or to run through a tactile graphics machine (PIAF or Swell machine).

Download the symmetry worksheet here.

You can make your own symmetry worksheet using free “symmetry shapes” clip art images.

Images of flowers, human and animal faces, butterflies and buildings are often used for examples of more advanced symmetrical images.

Example: Taj Mahal outline drawing

Download the Taj Mahal outline drawing here.

How does symmetry concepts apply to math?

Young students learn to identify what shapes are the same and what shapes are different.

Symmetry for first grade: An object or shape is equal on both sides. Symmetry is defined for both regular and irregular shapes.

Symmetry for 3rd grade math includes learning that a shape that has symmetry if it can be divided by a line so that each half is a mirror image of the other.

According to the National Council of Teachers of mathematics, students in grades 3-5 should be able to apply transformations and use symmetry to analyze mathematical situations, including sliding, flipping and turning two dimensional shapes.

Geometry in 4th grade Common Core (4.G.A.3) “Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts.”

Algebra: A symmetrical graph is said to be symmetric about the x-axis if whenever (a,b) is on the graph, then so is (a,-b).

Graphed image with points at 0,0 -2,2 and -4,4.

High School Geometry: The concepts of congruence, similarity and symmetry can be understood from the perspective of geometric transformation. (From Common Core)

Creating tactile graphics images Part 5: Shapes (Part 1 in this series)

By Diane Brauner

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