Getting in Line

To begin the activity, students should trace around the pattern block they are considering so that they can draw in the lines of reflection (mirror lines). For a square, the four lines would be:

Some of the other pattern block shapes are more difficult to analyse (see diagrams in the Answers section).
Some students will draw lines that appear to cut the shape in half but are not lines of reflection symmetry. For example:

Students need to self-check these lines by looking at the whole shape and then comparing it with the image they see when they put a mirror on the mirror line.
Investigating the number of lines of symmetry of a circle is an interesting extension. Some students may colour the whole circle to show that there are so many lines that they couldn’t draw them all.
This is one way of describing infinity.
Finding lines of symmetry for shapes made from a number of pattern blocks is considerably more difficult than for single pattern block shapes. However, the same principles apply (see the diagrams in the Answers section).
The final challenge is to build pattern block shapes with specified numbers of lines of symmetry. In this case, students will need to consider the single pattern block shapes once more. For example, building a pattern with three lines of symmetry will need to be based around a triangle or a hexagon shape. A pattern with four lines of symmetry will need to be based around a square shape. See the Answers section for examples.

Answers to Activities

Activity
1.

2. triangle:

a.  b. 3 mirror lines

rhombus:

a. b. 2 mirror lines

trapezium:

a.         b. 1 mirror line
hexagon:

a. b. 6 mirror lines

3. a. 3 mirror lines

b. 1 mirror line

c. no mirror lines

d. 4 mirror lines

4. Answers will vary. Some examples are:
a.

b.

c.