Year 6 Maths: Rotation

What is Rotation?

Hello, Year 6! Today, we’re going to learn about rotation. Rotation means turning a shape around a fixed point, which we call the centre of rotation. Imagine turning a steering wheel or spinning a top—that’s what rotation is!

Key Rules of Rotation

1. Centre of Rotation: This is the point around which the shape rotates. You can choose any point, but common points are the corners of the shape or the origin (0,0) on a grid.
2. Angle of Rotation: This tells us how far to turn the shape. We usually measure the angle in degrees (°). Common angles are:
   • 90°: A quarter turn.
   • 180°: A half turn.
   • 270°: Three-quarters of a turn.
   • 360°: A full turn.
3. Direction of Rotation: We can rotate shapes in two directions:
   • Clockwise: Turn to the right, like the hands of a clock.
   • Anticlockwise (or Counterclockwise): Turn to the left.

Visualising Rotation

Let’s think about a square. If we rotate it 90° clockwise around its centre, it will still look the same but in a different position.

Examples of Rotation

• Example 1: Rotate the point (2, 3) 90° clockwise around the origin (0, 0).
  • New coordinates: (3, -2)
• Example 2: Rotate the triangle ABC, with vertices A(1, 1), B(1, 4), C(4, 1) 180° anticlockwise around the origin.
  • New coordinates: A(-1, -1), B(-1, -4), C(-4, -1)

Tips and Tricks

• Use a Grid: When you’re unsure about where a point will go after rotation, drawing it on graph paper can help.
• Count Squares: If rotating on a grid, count how many squares you move to find the new position.
• Practice with Shapes: Draw different shapes and practice rotating them. It makes it easier to understand!

Questions on Rotation

Easy Level Questions

1. What does rotation mean?
2. What is the centre of rotation?
3. How many degrees are in a full rotation?
4. What direction do we rotate in a clockwise direction?
5. What is 90° clockwise rotation?
6. If you rotate a point 180°, what happens to its position?
7. Name a common angle used for rotation.
8. What does anticlockwise mean?
9. Can you rotate a shape around any point?
10. What happens to a square when you rotate it 360°?

Medium Level Questions

11. Rotate the point (2, 2) 90° clockwise around the origin. What are the new coordinates?
12. What is the new position of the point (3, 4) after a 180° rotation?
13. If you rotate a triangle 90° anticlockwise, what happens to its orientation?
14. Rotate the point (1, -1) 270° clockwise. Where does it land?
15. How do you rotate a shape around a point that is not the origin?
16. What is the new position of (5, 5) after a 90° rotation?
17. If we rotate a shape 180°, how does it compare to its original position?
18. Rotate the point (-2, 1) 90° clockwise. What are the new coordinates?
19. How many degrees do we need to rotate to get the same position?
20. Can you rotate a shape without changing its size? Why or why not?

Hard Level Questions

21. Rotate the triangle with vertices A(2, 3), B(5, 3), C(3, 6) 90° anticlockwise around the origin. What are the new coordinates?
22. If a rectangle is rotated 180°, how do the corners change?
23. What is the new position of the point (-4, 2) after rotating 270° clockwise?
24. How does the angle of rotation affect the final position of a shape?
25. If you rotate a shape 90°, can you rotate it back to the original position? How?
26. Rotate the point (0, 5) 180° around the origin. What are the coordinates?
27. If you rotate (3, -2) 90° clockwise, what will be the coordinates?
28. Explain how to find the new position of a shape when rotated by 270° anticlockwise.
29. How would you describe the movement of a point that has been rotated 90° clockwise?
30. What happens to a circle when it undergoes a rotation?

Answers and Explanations

Easy Level Answers

1. Turning a shape around a point.
2. The point the shape turns around.
3. 360°.
4. Turning to the right.
5. A quarter turn.
6. It moves to the opposite position.
7. 90°.
8. Turning to the left.
9. Yes, but it’s easier with certain points.
10. It stays in the same place.

Medium Level Answers

11. (2, -2).
12. (-2, -4).
13. It changes direction but keeps the same shape.
14. (-1, -3).
15. Use the distance from the shape to the point to rotate.
16. (5, -5).
17. It flips over to the opposite side.
18. (1, -2).
19. 360°.
20. Yes, rotation changes position but not size.

Hard Level Answers

21. A'(-3, -2), B'(-3, -5), C'(-6, -3).
22. The corners switch places, but the shape stays the same.
23. (2, -4).
24. Different angles change the final orientation of the shape.
25. Yes, by rotating back the same amount.
26. (0, -5).
27. (-2, 3).
28. Count squares from the centre to find the new position.
29. It moves in a circular path around the centre.
30. It stays the same; every point on the circle moves equally.

I hope you enjoyed learning about rotation! Practice makes perfect, so keep rotating those shapes!