Let's investigate

This sheet of paper has been folded once.
The shape is cut out as shown.
Describe the final shape you would get if you opened it out.
How many lines of symmetry will it have?

1) Copy the diagram. Reflect the shape in the mirror line.

2) The diagram shows a shaded square on a grid.
Draw a similar grid and shade in three more squares so the design is symmetrical about both mirror lines.

3) The line AB is a reflection of the line CD in a mirror line.

Draw the diagram and mark in the mirror line. 
List all the points with whole number co-ordinates that lie on the mirror line.
What do you notice about the co-ordinates of these points?

4) The diagram shows three squares on a co-ordinate grid.

Decide where to place two more squares to make the pattern symmetrical about the mirror line.
What are the co-ordinates of the vertices of the two squares?

5) (a) Draw a grid with x and y axes from $-4$ to $+4$.
Join the point $(-4,4)$ to the origin $(0,0)$.
Reflect this line in the y-axis, then reflect the line and its image in the x-axis.
What mathematical sign have you made?
(b) Write instructions to make an addition sign using a line and reflecting it in different ways.