Diagonals of a Quadrilateral
| Grade | Work Samples |
|---|---|
| End of Stage 4 (end of Year 8) | |
| Grade B | Chris Kendall Lesley Reese Ali |
| Grade C | Pat Jessie |
| Grade D | Rania Taylor Cameron |
| Grade E | Bobby |
- New Work Samples
- Morgan
Description of activity
If the diagonals of a quadrilateral bisect each other, what type of quadrilateral could it be? Give reasons for your answer and illustrate by drawing diagrams.
Is there more than one type of quadrilateral in which the diagonals bisect each other?
What conclusions can you make?
Context
Space and Geometry, Working Mathematically
This assessment activity could be presented to students during a unit on Two-dimensional Space where students have been investigating the properties of quadrilaterals, including their diagonals. This task could be used as an initial Working Mathematically investigation or later in the unit to identify depth of knowledge and understanding.
Areas for Assessment
Outcomes
Properties of Geometrical Figures (SGS4.3)
Classifies, constructs, and determines the properties of triangles and quadrilaterals
Applying Strategies (WMS4.2)
Analyses a mathematical or real-life situation, solving problems using technology where appropriate
Communicating (WMS4.3)
Uses mathematical terminology and notation, algebraic symbols, diagrams, text and tables to communicate mathematical ideas
Reasoning (WMS4.4)
Identifies relationships and the strengths and weaknesses of different strategies and solutions, giving reasons
Reflecting (WMS4.5)
Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Stage 4 content
Criteria for assessing learning
(These criteria would normally be communicated to students with the activity.)
Students will be assessed on their ability to:
- demonstrate knowledge and understanding of the nature of different quadrilaterals
- draw a valid conclusion about the diagonals of quadrilaterals
- communicate mathematical ideas.
Possible prompts to assist student engagement
- Do you remember what ‘bisect’ means?
- Have you tried drawing the diagonals first, and then drawing the quadrilateral?
- Can you find some other types of quadrilaterals in which the diagonals bisect each other?
- What types of quadrilaterals result if we place other conditions on the diagonals, eg ‘What if the diagonals are equal in length?’, ‘What if the diagonals bisect each other at right-angles?’
Suggested materials
Pen and paper, ruler, scissors and paper to make shapes