How to teach algorithms for geometric problems
Year 7 to Year 10 (ages 12 to 16)
An algorithm is a precise, step-by-step procedure for solving a problem. In geometry, algorithms describe how to sort shapes by their properties, test whether two shapes are congruent, carry out a construction, or solve a spatial problem, always in the same reliable order.
How to teach it
- Start with a familiar sorting task (e.g. sort shapes by number of sides) and write down the exact steps used, in order.
- Introduce a congruence-testing algorithm: measure all three sides of each triangle, then compare the two sets for an exact match (SSS).
- Use a flowchart to show decision points explicitly, e.g. 'do all three sides match? yes -> congruent, no -> not congruent'.
- Emphasise that a good algorithm gives the SAME correct answer every time it is followed, with no guesswork.
- Practise writing an algorithm for a new problem (e.g. classifying a quadrilateral) before checking it against a worked example.
Common mistakes
- Skipping or reordering steps because a shortcut 'looks' right for one example.
- Writing an algorithm with a missing decision point, so it cannot handle every case.
- Assuming an algorithm that works for one type of shape automatically works for all shapes.
- Describing what the algorithm's GOAL is, rather than the actual step-by-step procedure to get there.
Frequently asked questions
What is an algorithm in geometry?
A precise, step-by-step set of instructions for solving a geometric problem, such as checking whether two shapes are congruent, or carrying out a construction. Following the same steps in order always gives the same, correct result.
Why does the ORDER of steps matter in a geometric algorithm?
Following steps out of order can give a wrong or inconsistent answer. A congruence-checking algorithm, for example, must compare the right pairs of sides and angles in a fixed order, not a random one.
What is a flowchart used for?
A flowchart shows the steps and decision points of an algorithm visually, using boxes and arrows, making the logic easy to follow and check for gaps.
What year are algorithms for geometric problems taught?
In the Australian Curriculum this spans Year 7 to Year 10: sorting shapes by algorithm at Year 7 (AC9M7SP04), congruence algorithms at Year 8 (AC9M8SP04), construction algorithms at Year 9 (AC9M9SP03), and general spatial-problem algorithms at Year 10 (AC9M10SP03).
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.