14-NelsonMathGr6-Chap14 7/20/05 3:45 PM Page 422
CHAPTER 14
You will need
3
Rotational Symmetry
Goal
• pattern blocks
• scissors
• tracing paper
Determine whether and how a shape can be
turned to fit on itself.
Li Ming is putting the cover back on a box.
many ways can Li Ming fit the cover back
? How
on the box?
Li Ming’s lid
I’ll try rotating a block that is the same shape
as the lid.
I trace the square block.
Then I put a sticker at the
top left corner of the block
to keep track of the rotations.
I draw a black dot for the
centre of rotation.
I predict that when I rotate the block around its centre,
I will be able to fit the block inside the tracing four different
ways, and then the sticker will return to the top left.
I test my prediction by rotating the block until it fits the tracing.
centre of
rotation
I rotate the block again until it fits the tracing again.
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I repeat the rotations until
the sticker returns to the
original position.
I know the square has done one complete rotation
around its centre because the sticker is back to the
top left corner.
The square can fit on itself four times during one
complete rotation. My prediction was correct.
The square has order of rotational symmetry of 4.
I can fit the lid on the top of the box four ways with
a different side at the front each time.
Reflecting
1. How did putting a sticker at one of the corners of
the block help keep track of the rotation?
2. Which of these lids has rotational symmetry?
What is the order of that symmetry?
rotational symmetry
A shape that can fit
on itself exactly more
than once in one
complete rotation has
rotational symmetry.
order of rotational
symmetry
The number of times a
shape will fit on itself
exactly during one
complete rotation
Communication Tip
A shape that can fit
on itself only once
during one complete
rotation has no
rotational symmetry,
but we say that it has
order of rotational
symmetry 1.
Checking
3. a) Predict the order of rotational symmetry for this shape.
b) Determine the order of rotational symmetry for this shape.
c) Compare the result with your prediction.
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Practising
4. a) Trace and cut out the pinwheel.
b) Predict the order of rotational symmetry for the pinwheel.
c) Check your prediction by determining the order of
rotational symmetry for the pinwheel.
5. a) Predict the order of rotational symmetry for these shapes.
b) Check your prediction.
6. a) Predict the order of rotational symmetry of these
triangles. Explain each prediction.
b) Check your predictions.
c) Compare the results with your predictions.
A
B
C
7. a) Sort the shapes into those with rotational symmetry and
those without. Use a Venn diagram.
b) For each shape, list its order of rotational symmetry.
C
B
A
F
D
E
G
8. a) Can a polygon with no sides of equal length have
rotational symmetry? Explain.
b) Does every polygon with at least two sides of equal
length have rotational symmetry? Explain.
c) Why is a circle the shape with the most rotational
symmetry?
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