Home → Curriculum Hub → Maths Lessons → Schemes of Work → Three-Year GCSE Higher → Constructions
This Higher GCSE scheme of work unit covers constructions in Year 9. It is three hours: an angle bisector, then a locus as a region, then a path that is equidistant from two lines or two points.
Students have to leave every compass arc in place, because those marks are the working. That habit is what later scale- drawing, bearings and Higher locus exam items all expect.
A student who has secured this unit:
Students should be secure with the following before beginning this unit.
A bisector is built from two equal-radius arcs. Rubbing those marks out hides the evidence that the line is equidistant from the two sides.
A locus can be a set of points, a path, or a region. ‘At least 2 cm from a point’ is a disc; ‘nearer to A than B’ is a half-plane bounded by the perpendicular bisector.
The angle bisector is the set of points equidistant from the two arms. The perpendicular bisector is the set equidistant from the two endpoints.
A freehand diagram with the given lengths and the required region labelled stops students opening the compasses on the wrong rule.
| Misconception | Teaching focus |
|---|---|
| Letting the compass hinge slip, then treating the ragged arc as accurate. | Lock the hinge, hold the spike still, and turn the page for the first three arcs. |
| Erasing the construction marks so the line looks ‘clean’. | Tell the class the arcs are the method and will lose a mark if they vanish. |
| Reaching for a protractor to ‘check’ a bisector instead of trusting the equal arcs. | Put the protractors away for these three hours and keep only compasses and a straight edge. |
| Shading the far side of a ‘nearer to A’ boundary. | Pick a test point in each region and measure to A and to B before the pencil is shaded. |
| Using an angle bisector when the rule is equal distance from two points. | Ask ‘two sides or two ends?’ and only then choose the instrument pair. |
Every lesson in this unit is already built. A Mr Mathematics membership gives you the presentation, worksheet, question generator and video tutorial for all 3 lessons, alongside the full Key Stage 3, GCSE, IGCSE and A-Level libraries.
A school membership covers every teacher in your department, so the whole scheme of work is resourced from one subscription.
Students learn how to construct angle bisectors using a pair of compasses and a straight edge.
Later, students use equilateral triangles to construct 30° and 45° angles as learning progresses.
Students learn how to construct the locus of a region by considering loci about a point and line.
Later, as learning progresses, students consider combinations of loci to identify more complex regions.
Students learn to construct angles and perpendicular bisectors to identify given points.
Later, as learning progresses they solve more complex problems involving multiple loci and bisectors.
Students revise how to construct the locus of a line and about a point to solve various geometry problems.
Later, as learning progresses, they consider the angle and perpendicular bisectors.
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