Two Piece Tangram – version 1

Draw yourself a 4 x 4 square and label it with the correct conventions/notations. Write down all the properties of the square – eg angles, perimeter, area, symmetry etc

Something to help with your explanation and notation Angles: Sum of the exterior angles 3 equal angles each ___degrees No equal angles Opposite angles are equal 4 equal angles each ___degrees Right Angle One pair of equal angles 5 equal angles each___degrees All angles add to 1 pair of opposite angles are equal 6 equal angles each___degrees Alternate angles are equal Sides: One pair of parallel sides Two pairs of parallel sides One pair of adjacent sides are equal Two pairs of adjacent sides are equal No sides are equal 2 sides are equal All sides are equal Two pairs of opposite sides are equal Total number of sides Diagonals: Diagonals cross at right angles Diagonals are of equal length Diagonals bisect each other Shape Names: Triangles Kite Isosceles Rhombus Right Angled Triangle Hexagons Scalene Equilateral Triangle Pentagons Quadrilaterals Regular Square Parallelogram Rectangle Trapeziums Conventions: Use arrows to show lines are parallel Use marks to show lines of equal length Use arcs to show angles are equal Use this to show a right angle Symmetry: Lines of Symmetry Order of Rotational Symmetry

Now mark 3 units along one edge of the square Now mark 3 units along one edge of the square. Draw a line from the furthest vertex to this point. Cut along this line. Write down all the properties of the two shapes (without using any measuring instruments, for those that don’t know Pythagoras or Trig they may have to measure the two pieces). What is special about the triangle? What is the ratio of the two - perimeters, areas? What proportion/fraction is each perimeter and area of the original square?

Join the two shapes together to form other shapes. Write down all the properties of the two shapes & explain/justify how you know these properties (without using any measuring instruments). For the moment without overlaps.

Two Piece Tangram – version 2

Draw yourself a 4 x 4 square and label it with the correct conventions/notations. Write down all the properties of the square – eg angles, perimeter, area, symmetry etc

Now mark 2 units along one edge of the square Now mark 2 units along one edge of the square. Draw a line from the furthest vertex to this point. Cut along this line. Write down all the properties of the two shapes (without using any measuring instruments, for those that don’t know Pythagoras or Trig they may have to measure the two pieces). (If using Pythagoras keep your answer in surd form). What is the ratio of the two - perimeters, areas? What proportion/fraction is each perimeter and area of the original square?

Join the two shapes together to form other shapes. Write down all the properties of the two shapes & explain/justify how you know these properties (without using any measuring instruments). For the moment without overlaps.

Some extra questions to ask of the students – Some may form a right angled triangle with the two shapes. Ask them why it is similar, what the scale factor is, what is the ratio of the perimeters and areas between the small and large triangle? How many Pentagons have you found? What are your rules? Convince someone that you have found them all? How can you classify them? By combing the two shapes how many different angles can you find?

Two Piece Tangram – version 3

For version 3 same as above but use a square of length a. Create a two piece tangram (both shapes must be different) so that there is an angle in the triangle of 300 or 600 or 450. Create a two piece tangram so that one of the shapes tessellates. Write equations for the shapes so that are drawn on a graphics calculator. Overlap the shapes and find out the % that is overlapped. If the starting shape is a rectangle and the sides are in the ratio of 1:2 or 1:√2 or a:b - Create a two piece tangram (both shapes must be different) so that there is an angle in the triangle of 300 or 600 or 450.