Shapes and Designs: Rotational Symmetry
Interactive Sketchpad Exploration
LESSON
CORRESPONDENCE
Investigation 5.1 & 5.2
INTRODUCTION
This Sketchpad lesson allows students to make shapes rotate around a
center point by the angle of rotation of their choice. This allows them to
investigate the rotational symmetries that a variety of shapes possess.
Paired with a worksheet, students make estimates on Sketchpad of the
number of degrees of rotation needed to rotate a shape back onto itself.
They can then check their answers on Sketchpad as they watch their
shape rotate and compare it to the original. Shapes include: equilateral
triangles, isosceles triangles, a star, and quadrilaterals like a square,
rectangle, and parallelogram.
KEY VOCABULARY
ANGLE: the opening between two straight lines that meet at a vertex,
measured in degrees. In a polygon, its inner angles formed from its
segments are usually referred to as its “angles.”
DEGREE: A unit of measure of angles equal to 1/360th of a complete
circle. A 90° angle has ninety of these 1/360th angles, forming a right
angle or 1/4 of a circle.
ROTATIONAL SYMMETRY: What a figure has if it can be rotated by
an angle less than 360°, about a central point, and still look the same.
EQUILATERAL TRIANGLE: A triangle with all three sides the same
length.
ISOSCELES TRIANGLE: A triangle with two sides the same length.
SCALENE TRIANGLE: A triangle with no sides the same length.
QUADRILATERAL: Any polygon with four sides.
LAUNCH
Begin by telling students they will be using Sketchpad to help them
figure out how to make shapes have a perfect match. Open the sketch
and show the students how to rotate the given shape: double-click on
the parameter “angle= ” at the top and a box will pop up. Enter a value,
such as 90° (the students might propose one) and press OK. Press the
button Rotate from noon.
Likely, the students will not have selected 120° or 240° and the triangles
will not match. Discuss how the red arc relates to the angle value that
was chosen. Tell the students they will be trying to make the triangle,
and other shapes, match. Before the students begin, you might ask them
what will happen if they choose an angle greater than 360°. The
worksheet provides further guidance.
Teacher’s Notes 1
© 2005 KCP Technologies
Shapes and Designs: Rotational Symmetry
EXPLORE
As you walk around the class:
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Make sure students are comfortable with the notion of angle.
Emphasize the vocabulary of equilateral, isosceles, and scalene
triangles.
Push the students to explore all the possibilities of symmetry
and not to stop when they find just one. For example, the star
has SIX symmetries in multiples of 60°. A student may find
that 120° works, and 180°, but make sure they find the “in
between” angles.
As you interact with students working on the activity, probe
whether students understand that the shapes are rotating
around a center point.
SUMMARIZE
With at least 10 minutes remaining in the class, bring the students back
together for a class discussion. Ask the students which shape had the
most rotational symmetries, which has the least, and why. Ask them to
come up with a couple other examples of shapes that have no rotational
symmetries, and more than 3 rotational symmetries. During this
discussion, listen for the ways that students use the word angle, since
this is often a difficult concept for them. For an interesting extension:
ask students about the rotational symmetries of the circle!
Teacher Notes 2
© 2005 KCP Technologies