Max Maths, Year 5, Learn together, Reflective and rotational symmetry in regular polygons (1)

In a mathematics lesson for Year 5, students explore the concepts of reflective and rotational symmetry within regular polygons. Regular polygons are shapes with equal sides and angles, and they often exhibit interesting symmetrical properties. For instance, an equilateral triangle, which has three equal sides, also boasts three lines of symmetry. Each line of symmetry divides the triangle into two identical halves, demonstrating its reflective symmetry. Furthermore, this triangle has rotational symmetry of order 3, meaning that it can be rotated around its center in increments that are fractions of a full circle (in this case, 120 degrees) and still look the same three times in one full rotation.

Similarly, a square, with its four equal sides, has four lines of reflective symmetry. Each line cuts the square into two mirror-image parts. In terms of rotational symmetry, a square has an order of 4, indicating that it can be turned to four different positions around its central point and still appear unchanged each time, at every 90-degree turn. Moving on to a regular pentagon with five equal sides, it naturally has five lines of reflective symmetry. The pentagon also demonstrates rotational symmetry of order 5, allowing it to be rotated in 72-degree intervals around its center and maintain its original shape throughout five distinct orientations within a full 360-degree rotation.