Why do this problem?
This problem gives students the opportunity to derive the various properties of quadrilaterals whilst reinforcing the importance of using appropriate language and terminology. These may include angle rules, identifying parallel lines and symmetry which could lead to solving more complex questions. Along the way, the challenges will provoke some insightful discussion linking together different geometrical ideas.
Possible approach
The task could be used when students are not yet familiar with these quadrilaterals (they can be labelled ah). They should be familiar with right angles, parallel lines and symmetry. Pupils could play the game in pairs or begin as a whole class against the teacher. They should hone their strategies in pairs or small groups, which will involve defining each shape based upon its characteristics. Encourage the use of mathematical language.
You might want to move on to the questions to consider at the bottom of the problem.
The task could also be used as a wholeclass plenary exercise. The teacher can think of a quadrilateral and the teacher can select students to ask questions. Praise should be given to pupils who use the correct mathematical language.
It may be useful to print and cut out the shapes so that students can label and group them more easily. Alternatively, the quadrilaterals could be displayed on the board. The learners thinking may be brought together by groups of students presenting their findings, for instance posters of their flow charts. There is also room for a wholeclass discussion using the key questions for prompts to extend their ideas further.
Encourage pupils to play the game without using the handout. Can they remember the shapes and their properties without looking at them?
Key questions
Possible support
Initially, the students could be prompted to note the properties of each quadrilateral under given headings after being taught the relevant concepts. An activity whereby students fill in a table could be useful (see below for example). This could be followed by a grouping exercise to sort the shapes providing a starting point as to how they can be distinguished from one another.
Shape 
# of right angles 
# of pairs of parallel lines 
# lines of symmetry 
# sides of equal length 
Isosceles Trapezium 




Rectangle 




Kite 




Rhombus 




Parallelogram 




Square 




Trapezium 




Arrowhead 




Additionally, the students could each be given a single shape to work with and tasked with labelling various features. They could compare this with their peers to initiate collaboration.
Possible extension
Can you invent a game with more shapes, where you can always identify your friend's shape in four questions? What is the maximum number of shapes you could have in such a game?