![3-ways-to-rotate-a-shape](https://lindsaybowden.com/wp-content/uploads/2020/01/3-ways-to-rotate-a-shape-683x1024.png)
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](https://lindsaybowden.com/wp-content/uploads/2020/01/rotate-shapes-1024x1024.png)
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](https://lindsaybowden.com/wp-content/uploads/2020/01/method1step2-300x300.jpg)
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](https://lindsaybowden.com/wp-content/uploads/2020/01/method1step3-300x300.jpg)
Next, write down the coordinates of your new shape.
![free-geometry-worksheets](https://lindsaybowden.com/wp-content/uploads/2020/01/method1step4-300x300.jpg)
Finally, remove the patty paper and graph your image.
![](https://lindsaybowden.com/wp-content/uploads/2020/01/method1step6-300x300.jpg)
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](https://lindsaybowden.com/wp-content/uploads/2020/01/rotation-coordinate-rules-1024x1024.png)
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.
![](https://lindsaybowden.com/wp-content/uploads/2020/01/method2-300x300.jpg)
Next, write the coordinates of your pre-image.
![rotating-a-shape](https://lindsaybowden.com/wp-content/uploads/2020/01/method2step1-300x300.jpg)
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](https://lindsaybowden.com/wp-content/uploads/2020/01/method2step2-300x300.jpg)
Finally, graph the coordinates for your image.
![shape-rotations](https://lindsaybowden.com/wp-content/uploads/2020/01/method2step3-300x300.jpg)
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.
![](https://lindsaybowden.com/wp-content/uploads/2020/01/four-quadrants-1024x1024.png)
First, write down the coordinate rule and the coordinates of your pre-image.
![](https://lindsaybowden.com/wp-content/uploads/2020/01/method3step1-300x300.jpg)
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](https://lindsaybowden.com/wp-content/uploads/2020/01/method3step2-300x300.jpg)
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](https://lindsaybowden.com/wp-content/uploads/2020/01/method3step4-300x300.jpg)
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](https://lindsaybowden.com/wp-content/uploads/2020/01/method3step5-300x300.jpg)
I hope you liked these 3 strategies for rotating a shape!
Would any of these methods help you with rotations? Let me know below!
You may also like:
- 13 Free Math Worksheets and Activities
- How I Teach Proofs
- First Day of Geometry Free Activity
Head to LindsayBowden.com/Training to sign up for my FREE training on creating engaging math resources!
![rotate-a-shape](https://lindsaybowden.com/wp-content/uploads/2020/01/rotate-a-shape.png)