Constructing loci
I can construct a set of points that satisfy a set of conditions.
Constructing loci
I can construct a set of points that satisfy a set of conditions.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- Constructing a set of points a set distance from a given point produces a circle
- A compass should be used for this construction
- The point could be the vertex of a shape or contained within a shape
- A ruler should be used to indicate two points that are a set distance from a line
- The end points of the line should have a compass used to indicate the distance from the point
Keywords
Locus/Loci - A locus is a set of points that satisfy a given set of conditions. Multiple sets of points are referred to as loci.
Circle - A circle is a locus of points that are equidistant from a fixed point. This fixed point is the centre of the circle and the distance from the centre to the locus of points is the radius of the circle.
Common misconception
Pupils may think that the locus of a line is a rectangle.
Choose the vertices of their rectangle and ask if they are the same distance from the line as another point. Link to Pythagoras' theorem if necessary to highlight that the diagonal length will be longer.
To help you plan your year 11 maths lesson on: Constructing loci, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Constructing loci, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Loci and construction unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Equipment
Ruler, pair of compasses, pencil
Licence
Lesson video
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Starter quiz
6 Questions
Finding all possible positions for a vertex when drawing a 2nd side
Drawing an angle to show what direction a side takes
Drawing the first side of a triangle
RHS
SAS
SSA
ASA
SSS
Use a ruler to draw side PQ.
Set compasses to 7 cm and draw a circle centre Q.
Draw a ray line at angle of 45° at P.
Mark R at the point(s) where the ray and circle meet.
Add the line(s) RQ to complete the triangle(s).
Exit quiz
6 Questions
