New
New
Year 7

Introduction to rotations

I can understand the nature of rotations and appreciate what changes and what is invariant.

New
New
Year 7

Introduction to rotations

I can understand the nature of rotations and appreciate what changes and what is invariant.

Lesson details

Key learning points

1. The length of the lines do not change when rotated
2. The angles inside an object do not change when rotated
3. When an object is rotated, its image is congruent
4. Unless a full rotation occurs, the object and its image will not have the same orientation

Common misconception

After an object has been rotated, the orientation stays the same if the image looks the same.

This is only true if the object is rotated through 360°. Otherwise, the orientation is different as each vertex is in a different position.

Keywords

• Rotation - The rotation of an object is the turning of an object by a fixed amount and around a fixed point (called the centre of rotation).

In Task B question 3, it is important for the projection to have 16:9 aspect ratio for the measurements to be consistent, or for the question to be printed for students to measure with a ruler.
Teacher tip

Equipment

Pen or pencil, ruler, protractor.

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Starter quiz

6 Questions

Q1.
What is 360 - 90?
170
250
260
280
Q2.
is the process by which an object is changed into its image by moving, sliding, turning, flipping or stretching.
Correct Answer: Transformation, transformation, transform, Transform
Q3.
When a vertex is labelled $$E^{\prime}$$, it means the __________ of E.
object
orientation
position
transformation
Q4.
What does the term "invariant property" mean?
A shape that hasn't changed location after a translation has been applied.
Correct answer: A property of a mathematical object that hasn't changed after a transformation.
A property of a mathematical object that has changed after a transformation.
A property of a vertex that moves after a transformation.
Q5.
Which properties are invariant when an object is translated?
Correct answer: length of a side
Correct answer: size of an angle
position
Q6.
Which of these shows an arrow that has been turned round?
Correct Answer: An image in a quiz

Exit quiz

6 Questions

Q1.
In which direction will this vehicle be facing when it is rotated so its wheels touch the road?
left
Q2.
Which of these objects, when rotated by a quarter-turn, will fit into the space in this shape to complete a rectangle?
A
C
D
Q3.
Complete this sentence: "When an object is rotated, the lengths of its sides are invariant. This means the lengths of the sides remain ."
Correct Answer: the same, exactly the same, same, identical, unchanged
Q4.
Sam transforms an object and its orientation changes. Which of these describes why the orientation has changed?
The object hasn't been rotated to become its image.
The object has been translated right to become its image.
Correct answer: The object has been rotated through a half turn to become its image.
Orientation always changes when objects are translated.
Correct answer: Orientation always changes when objects are rotated by less than a full turn.
Q5.
Which of these is a rotation of this object?
Image 1