4 mistakes learners make with rotation, each one named and explained.
A rotation needs a centre, an angle and a direction. All three, every time.
360 degrees is offered for a rotation that visibly changed the orientation.
360 is the number most attached to turning, and it is the one that comes first.
Question. A shape turned upside down
A common answer. 360 degrees
The answer. 180 degrees
Why. 360 degrees would return the shape exactly to where it started.
If the picture changed, the rotation cannot be a full turn.
A shape turned upside down is described as a 90 degree rotation.
90 degrees is the rotation practised most often, so it is the one that comes to mind.
Question. A shape turned upside down about its centre
A common answer. 90 degrees
The answer. 180 degrees
Why. A quarter turn puts the shape on its side; upside down is half a turn.
Rotate a book on the desk. A quarter turn and a half turn look nothing alike.
A clockwise rotation is carried out anticlockwise.
Positive is the mathematical convention for anticlockwise, which is the opposite of a clock.
Question. (1, 3) rotated 90 degrees clockwise about the origin
A common answer. (-3, 1)
The answer. (3, -1)
Why. Clockwise takes a point above the origin round to the right.
Turn the page. Physically rotating a rough sketch settles the direction in a second.
A 90 degree rotation swaps the two coordinates and leaves both positive.
Swapping is the visible half of the rule and the sign is the half that is easy to lose.
Question. (1, 3) rotated 90 degrees clockwise
A common answer. (3, 1)
The answer. (3, -1)
Why. The point moves into a different quadrant, so one coordinate has to change sign.
Sketch it. If your answer is in the same quadrant, the rotation has not happened.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.