Rotational symmetry 1/2


Each pupil should choose two sheets of origami paper. Both sheets will be folded in all of the activities.

It is suggested that this topic should be given in two lessons.


A discussion question: What polygon shape is your sheet? Explain.


Answer: The sheet is a square shape having 4 equal length sides and 4 right angles.


A discussion question: Is it possible to fold the 2 square sheets into 4 congruent squares using only 2 folds? Explain.

The pupils should give an explanation why the 4 squares are congruent.


Answer 1: In order to obtain the 4 congruent squares the sheets were folded on opposite sides. With the next fold once again the smaller opposite sides were folded and the sheets were opened out.

The pupils should give an explanation why the 4 squares are congruent.


Answer 2: Shapes are congruent when it is possible to completely cover each shape with the other.


Folding instructions: Cut the square sheets into 4 smaller squares.

If the cutting process is difficult for some pupils it is suggested that the teacher should have ready cut squares.


Folding instructions: In the next stage of folding use only 2 cut squares.


Folding instructions: Fold opposite sides of both squares.


Folding instructions: Fold opposite shorter sides of the rectangles.


Folding instructions: Fold the parallel longer sides to each other on both rectangles.Open the 2 rectangles.


Instructions: Mark the point of intersection for the two lines of reflective symmetry. Put the rectangles on to each other, choose a common vertex and mark these vertices.


A discussion question: After putting the rectangles on to each other and marking the common vertex and point of intersection put a pencil or pen on the point of intersection turn the top rectangle around until you finish a complete rotation. How many times during the rotation of the rectangle did the two rectangles cover each other exactly? Explain.


Answer: During the process of one complete rotation the top rectangle covered the other rectangle two times. A rectangle has rotational symmetry of Order 2.


Folding instructions: Open the two rectangles to the original square shape.


Folding instructions: Fold two opposite vertices on both squares.


Folding instructions: Fold as shown.


Folding instructions: On both sheets fold the right angled vertex into a small triangle.


Folding instructions: Turn over both shapes.


Folding instructions: Fold and open on both sheets as shown.


Folding instructions: Turn over both shapes.


Folding instructions: On another small square fold two opposite parallel sides into a rectangle.


Folding instructions: Fold the marked vertex backwards and put your folded rectangle inside the head of the puppy.
 Lesson Aims
 Identify two shapes as congruent after a rotation.
 Identify which shapes are congruent as a result of reflective or rotational symmetry or both.
 Identify the shapes with rotational symmetry of various orders.
 Identify using activities to identify propeties of symmetry in different shapes.
 Model name
A puppy
 Lesson structure
According to the curriculum.
 Lesson content
The folding process at different stages enables the pupil to learn about the concept of rotational symmetry together with the concept of reflective symmetry (not formal definitions). On completing the final surprising model the pupil can revise previously learnt concepts and review the new concepts that have been learnt in this lesson.
 Prior knowledge
The concepts of polygon and reflective symmetry.
 Materials
Origami square sheets 15 cm/15 cm and markers.