*Contributor: Marlene Vogel. Lesson ID: 10623*

What if a triangle looked in a mirror? What if it slid across the room? Learn how congruent shapes can transform. You'll complete interactive online and hands-on activities AND create your own dance!

categories

subject

Math

learning style

Kinesthetic, Visual

personality style

Golden Retriever

Grade Level

Intermediate (3-5)

Lesson Type

Dig Deeper

**The Shapes Family **

Once upon a time, there was a family who had a mother (triangle), a father (square), and three pairs of congruent twins. One pair of congruent twins were squares. Another pair of congruent twins were triangles. The third pair of congruent twins were circles. Their family portrait is above.

This family is very unique! Not only does this family have 3 pairs of congruent twins, but each set of twins has a special talent. Mr. and Mrs. Shape, in hopes of keeping their children physically fit, bought a coordinate plane for the children to play on outside. The children took turns playing on the coordinate plane, one set of twins at a time. After a while, Mr. and Mrs. Shape began to notice that each set of twins could perform geometric transformations. One set of twins could perform a translation; one set could perform a reflection; and one set could perform a rotation!

**Vocabulary** All definitions can be found at A Maths Dictionary For Kids Quick Reference:

- congruent
- coordinate plane
- dilation
- perpendicular
- reflection
- rotation
- transformation
- translation
- x-axis
- y-axis

**Visual examples of the vocabulary** (Optional: Older or more advanced students can draw their own visual examples of the vocabulary)

*congruent*:

Not*congruent*:*coordinate plane*:*dilation*:*perpendicular*: Refer to the visual example of the coordinate plane. Notice that the two red lines form a cross. This is an example of perpendicular lines.*reflection*:*rotation*:*transformation*: View the visual examples for dilation, reflection, rotation, and translation.*translation*:*x-axis*and*y-axis*: (Note: The x-axis is the red line, and the y-axis is the blue line.)

Congruent shapes are shapes that are identical to each other. They are the same size and the same shape.

The neat thing about congruent shapes is that they can go through what are called transformations. From the vocabulary and definitions above, you now know that transformations in shapes include dilations, reflections, rotations, and translations.

You are now going to work on some activities to help you understand reflections, rotations, and translations. You will *not* work on any activities that involve *dilations*. Dilations are part of transformations in geometry; however, dilations change the size of one of the shapes in a pair. Once the size of the shape is changed, the shapes are no longer considered *congruent*. This lesson focuses on transformations with *congruent* shapes.

It’s time to become familiar with a *coordinate plane*. A coordinate plane is also called a *graph*. It has 2 axes. One is called the x-axis, and one is called the y-axis. Below is a picture of a coordinate plane:

In this example, the x-axis is the green line, and the y-axis is the orange line. The x-axis is always the line in a coordinate plane that goes from left to right. The y-axis in a coordinate plane is always the line that goes up and down. An easy way to remember which line is the x-axis and which line is the y-axis is to pretend the lines are a person. When the person is sleeping he is lying down (like the x-axis). When the person is awake, he stands and yawns (like the y-axis). The y in yawn can help you remember that the y-axis is the one going up and down.

Complete the following activity to become more familiar with a coordinate plane and how shapes are reflected, rotated, and translated:

- Get a piece of graph paper, a ruler, and some colored pencils. Draw your own coordinate plane. You may want to use two different colors for the x-axis and y-axis until you can remember them better. Label each of the lines just like the picture below:
- Print the
**Shapes Template**from the Downloadable Resources in the right-hand sidebar. - Cut out the shapes.
- Trace and cut out each shape twice on construction paper. Use the same color for each shape, but different colors from shape to shape. (For example, make two red triangles, two pink hearts, two blue circles, etc.)

Before moving on in this activity, you need to make sure that you understand each transformation you are going to perform on the coordinate plane with your shapes.

The first transformation you want to try on your coordinate plane is *reflection*.

- Place your shapes on your coordinate plane, so that they look like they are looking in a mirror.
- To help you understand the transformation of reflection you need to take a moment and go to a mirror in your house. Take a pencil with you. Stand in front of the mirror, and hold the pencil up with your right hand. Look at yourself in the mirror. This is your reflection. You need to do the same with two of the same shapes on your coordinate plane.
- When you reflect a shape on a coordinate plane, you are flipping that shape. Whichever axis you choose to flip your shape over can be your “mirror line."
- Choose two of the same shape, and show reflection on your coordinate plane. Since both of the shapes are the same size and the same color, you may want to put a design on each shape to help show reflection. Look at the picture below to see how to do this:
- As you can see in my example, I chose to use two red triangles to show reflection. I put a star in one corner of each triangle to help show that the triangles are being reflected or flipped. I chose my y-axis as my mirror line. You can choose either axis as your mirror line.
- Once you have completed setting up your shapes on your coordinate plane, use some glue to keep them in place.
- Make sure that you label your graph paper with the word "reflection."

Now take a moment to make sure you understand the transformation of *rotation*.

- When shapes are rotated, they are moved around a central point. One way to help understand this is to take out a piece of loose leaf paper that has holes in the margin.
- Place the piece of paper on the table in front of you, and put your finger over one of the holes. See the picture below to see how this looks:
- Keep that finger in place, and use your other hand to move the paper. Look at the picture below to see how to do this:
- You have just rotated your paper! Your finger acts as the central point, and you moved your paper from a vertical position (up and down) to a horizontal position (left to right).
- You will need to get a clean piece of graph paper, and make another coordinate plane; so that you can show the transformation of rotation. Make this second coordinate plane exactly like the first one.
- Choose two of the same shapes to use in this part of the activity.
- Take one shape, place it on your coordinate plane, and glue it into place.
- Take the second shape, and place it right next to the one you just glued.
- Again, you may want to draw a design on both of your shapes; so that you can show one of the shapes was rotated. I chose to draw an arrow on each of my squares.
- Place one finger on one place where your two shapes are touching.
- Using your other hand, rotate the shape that is not glued.
- Once you get the shape rotated, glue it into place.
- Make sure you write the word "rotation" on your coordinate graph (See picture below).

For the final part of this activity, you will make a third picture showing the transformation of *translation*.

- You will need to make one last coordinate plane that looks exactly like the first two.
- When you are translating a shape, you are simply sliding the shape. You do not need to flip it like you did in reflection or turn it like you did in rotation.
- A fun way to understand the transformation of translation is to use two coins (make sure they are the same) and a piece of loose leaf paper.
- Take your ruler and a colored pencil, and draw a line down the middle of your loose leaf paper.
- Stack your two coins, one on top of the other, on one side of the line.
- To translate the top coin, simply put your finger on the top coin and slide it to the other side of the line. You have just translated the top coin!
- Once you have finished making your coordinate plane, choose two of the same shape.
- Choose a place on your coordinate plane to glue one of your shapes.
- Once the first shape is glued, place the second shape on top of it.
- Put your finger on the second shape, and slide it to another place on your coordinate plane.
- Glue the second shape on the coordinate plane.
- Again, you may want to put a design inside your shapes; so that you can show that the shapes were translated and not reflected or rotated. I chose to use circles as my shapes and hearts as my designs. The hearts show that I did not flip or rotate my circle because they are facing the same way in each circle.
- Make sure you write the word "translation" on your coordinate graph (See picture below).

Now you have three pictures showing examples of transformations in geometry!

You may want to hang them somewhere in your learning space so that you can look at them as reminders if you need them.

In the *Got It?* section of this lesson, you will work on hands-on and online activities to make sure you understand the concept and idea of transformation in geometry! BTW, dance time is coming up soon!

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