Rotate Shapes Around a Vertex & Rotational Symmetry Worksheet for 11-Year-Olds

Instructions

Welcome to the world of spins and turns! In this worksheet, we will explore two cool concepts: rotation and rotational symmetry.

• Rotation: This is when we turn a shape around a fixed point, called the center of rotation or a vertex. We can rotate shapes by a certain number of degrees (like 90°, 180°, or 270°) and in a certain direction (clockwise, like a clock's hands, or counter-clockwise, the opposite way).
• Rotational Symmetry: A shape has rotational symmetry if it looks exactly the same after being rotated less than a full 360° turn. The order of rotational symmetry is the number of times a shape looks identical during one full 360° rotation.

Read each question carefully and write your answers in the space provided. Have fun!

Part 1: Objective Questions

For this section, choose the best answer or fill in the blank.

1. A full turn is a rotation of ______ degrees.
2. A 180° rotation is also known as a:
   A) Quarter turn
   B) Half turn
   C) Full turn
   D) No turn
3. True or False: A 90° clockwise rotation is the same as a 270° counter-clockwise rotation.
4. The fixed point that a shape turns around is called the ______ of rotation.
5. What is the order of rotational symmetry for a square?
   A) 1
   B) 2
   C) 4
   D) 8
6. A rotation in the opposite direction of a clock's hands is called ______-clockwise.
7. True or False: A rectangle has an order of rotational symmetry of 4.
8. Which of these shapes has an infinite order of rotational symmetry?
   A) Square
   B) Star
   C) Circle
   D) Triangle
9. An equilateral triangle (all sides equal) has an order of rotational symmetry of ______.
10. If a shape's angle of rotation is 60°, what is its order of rotational symmetry?
    A) 3
    B) 4
    C) 5
    D) 6
11. Imagine a plus sign (+). What is its order of rotational symmetry?
12. True or False: Every shape has a rotational symmetry of at least order 1.
13. A regular pentagon (5 equal sides) has an order of rotational symmetry of ______.
14. What is the smallest angle you need to rotate a regular octagon (8 equal sides) for it to look the same?
    A) 90°
    B) 60°
    C) 45°
    D) 30°
15. Which of these capital letters has rotational symmetry?
    A) F
    B) R
    C) A
    D) H
16. A parallelogram that is not a rectangle has an order of rotational symmetry of ______.
17. A scalene triangle (no equal sides) has an order of rotational symmetry of ______.
18. Imagine a standard stop sign (an octagon). If the word "STOP" is at the top, where is the word after a 180° rotation?
    A) At the top
    B) At the bottom, but upside down
    C) On the right side
    D) On the left side
19. A shape that only looks like its original self after a full 360° turn has an order of rotational symmetry of ______.
20. True or False: A 90° turn is also called a quarter turn.

Part 2: Subjective Questions

For this section, think carefully and write a full answer explaining your reasoning.

1. Describe what happens when you rotate a rectangle 90° clockwise around its center point. Does it look the same as when it started? Explain.

2. Explain the difference between rotational symmetry and reflective (line) symmetry. You can use a square as an example.

3. List three capital letters of the alphabet that have an order of rotational symmetry of 2.

4. A windmill has 4 identical blades. What is its order of rotational symmetry and its angle of rotation? Explain how you found the angle.

5. Can a triangle have an order of rotational symmetry of 2? Explain why or why not.

6. Imagine a shape that you rotate 180° and it looks exactly the same. What can you say about this shape? Give an example of such a shape.

7. A shape has an order of rotational symmetry of 6. What are all the angles of rotation (less than 360°) where the shape will look identical to its starting position?

8. Why does a circle have an "infinite" order of rotational symmetry?

9. Describe a simple shape that has NO rotational symmetry (order 1). Then, describe how you could change it to give it rotational symmetry of order 2.

10. If you rotate a shape 270° clockwise, what is the equivalent rotation in the counter-clockwise direction? Explain your thinking.

Answer Key

Part 1: Objective Questions

1. 360
2. B) Half turn
3. True
4. center
5. C) 4
6. counter
7. False (Its order is 2)
8. C) Circle
9. 3
10. D) 6 (because 360 / 60 = 6)
11. 4
12. True
13. 5
14. C) 45° (because 360 / 8 = 45)
15. D) H (Others with rotational symmetry include I, N, O, S, X, Z)
16. 2
17. 1
18. B) At the bottom, but upside down
19. 1
20. True

Part 2: Subjective Questions

(Note: Student answers may vary slightly but should reflect these key ideas.)

1. When you rotate a rectangle 90° clockwise, it will be standing "tall" instead of "wide" (or vice versa). It does not look the same as when it started. It only looks the same after a 180° rotation.

2. Rotational symmetry is when a shape looks the same after being turned around a central point. A square looks the same after a 90°, 180°, and 270° turn. Reflective symmetry is when you can fold a shape along a line (the line of symmetry) and both halves match perfectly. A square has 4 lines of symmetry.

3. Examples include: H, I, N, O, S, X, Z. (Student only needs to list three).

4. Its order of rotational symmetry is 4 because there are 4 identical blades. The angle of rotation is 90°. You find this by dividing a full circle (360°) by the order (4), so 360 / 4 = 90°.

5. No, a triangle cannot have an order of rotational symmetry of 2. To have an order of 2, it would need to look the same after a 180° turn. If you turn a triangle 180°, its vertex will point in the opposite direction, so it cannot look the same. A triangle can have an order of 1 (scalene) or 3 (equilateral).

6. You can say that the shape has a "point symmetry" or an order of rotational symmetry of at least 2. It means that for every point on the shape, there is a corresponding point directly opposite the center of rotation. Examples: a rectangle, a parallelogram, an oval, or the letter S.

7. The angles are multiples of its angle of rotation (360 / 6 = 60°). The angles would be: 60°, 120°, 180°, 240°, and 300°.

8. A circle has infinite order because it has no vertices or distinct sides. No matter what tiny angle you rotate it by (e.g., 1°, 0.5°, 0.001°), it will always look exactly the same. Therefore, there are an infinite number of times it looks the same in a full 360° turn.

9. A simple shape with no rotational symmetry (order 1) is a scalene triangle or the letter 'J'. To give it order 2, you could take the letter 'J', then rotate it 180° and attach it to the original 'J' at the center point. This would create a new shape that looks the same after a 180° turn.

10. A 270° clockwise rotation is the same as a 90° counter-clockwise rotation. A full circle is 360°. If you turn 270° in one direction, the remaining turn to get back to the start is 360° - 270° = 90°. So, a turn of 270° one way is the same as a turn of 90° the other way.