3 Ways to Rotate a Shape

3-ways-to-rotate-a-shape

These 3 methods to rotate a shape were super helpful for my students!

Rotating a shape can be a difficult concept for both students and teachers. After seeing my students struggle with this topic, I came up with a few strategies to make rotations easier. 

These 3 strategies work with different levels of learners. I encourage you to try all 3!

 

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1. Use Patty Paper

Patty paper or wax paper is useful for so many math concepts! I always had plenty of patty paper in my classroom. This is the patty paper I use from Amazon.  I love using patty paper to rotate a shape because it helps visual learners “see” the rotation before actual graphing it. 

rotate-shapes

For this method, you will place the patty paper over the graph and trace the shape. You will also plot the origin (0,0) on your patty paper. 

rotate-a-shape

Next, rotate the patty paper. For this example, I wanted to rotate 90 degrees clockwise. So, I turned the patty paper one quarter turn to the right. Make sure you keep the origin on the patty paper lined up with the origin on your graph.

rotating-a-shape

Next, write down the coordinates of your new shape.

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Finally, remove the patty paper and graph your image. 

2. Use Coordinate Rules

Coordinate rules are a great tool for transformations. There are three coordinate rules for rotating about the origin. 

Using the coordinate rules to rotate a shape are great if your students aren’t allowed to use patty paper on the test. Check out the rules below. 

rotation-coordinate-rules

The first step for using coordinate rules to rotate a shape is to write the coordinate rule on your paper. For this example, I wrote the coordinate rule for 180 degrees. 

Next, write the coordinates of your pre-image. 

rotating-a-shape

Then, use the coordinate rule to get the coordinates for your image.

For 180 degrees, the rule is (-x, -y). This means to change the signs of both the x value and the y value.

BE CAREFUL: The negative DOES NOT mean that the number must be negative. It means change the sign. So, if my pre-image coordinates are negative, they will change to positive. 

rotate-about-the-origin

Finally, graph the coordinates for your image. 

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3. Use the Quadrants

This method is a variation of method #2. It’s my favorite method! It uses the four quadrants of the graph to rotate the shape. 

First, write down the coordinate rule and the coordinates of your pre-image.

Next, determine what quadrant your image should be after the rotation.

In this example, the pre-image is in the second quadrant. If I rotate 90 degrees clockwise, the shape will be in the first quadrant. Rotating 180 degrees, will put the shape in the fourth quadrant. If I rotate 270 degrees, the shape will be in the third quadrant.

So, all points should be in the third quadrant. 

rotation-coordinate-rules

The quadrant tells you what the signs should be for all of your coordinates. In the third quadrant, the signs are (- , -).

All of my coordinates for my image will have those signs. 

geometry-lessons

Finally, look back at the coordinate rule. For 270 degrees (and for 90 degrees), the rule tells me to switch the x and y values. 

Since I already have my signs, I just need to switch the x and y values. So, since point W is (-4, 5), then W’ will be (-5, -4).

Do that for all the coordinates. Then graph your image. 

rotate-shapes

I hope you liked these 3 strategies for rotating a shape! 

Would any of these methods help you with rotations? Let me know below!

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rotate-a-shape

Lindsay

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