Solving loci problems in context
Lesson details
Learning outcome
I can solve problems involving a combination of loci.
Key learning points
- Loci problems involve performing various constructions
- The problem asks for these constructions within the context of the question
- All construction lines should be left on the diagram to show your working
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.
Perpendicular - Two lines are perpendicular if they meet at right angles.
Bisect - To bisect means to cut or divide an object into two equal parts.
Common misconception
Pupils may erase their construction marks.
Remind pupils that they should always leave their construction marks on their diagrams but encourage them not to press to hard with their pencils.
Teacher tip
Have pupils design their own loci problems, where multiple different constructions are needed.
Equipment
Pair of compasses, ruler, protractor, pencil
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Which diagram shows an angle bisector?
Q2.Aisha places two cones, A and B, on the ground. Which of these points are closer to A than they are to B?
Q3.Which of these points are equidistant from ST and TU?
Q4.Izzy wants to find all the points that are the same distance from LM as they are from MN. What construction should she use?
Q5.Which region is illustrated on this diagram?
Q6.Select the region which matches this description: closer to AD than CD and closer to AB than BC.
Assessment exit quiz
6 Questions
Q1.The locus of points equidistant from another point can be represented by a .
Q2.A goat is tied to a railing by a 1.5 metre long rope. There is a barn near the railing. Which of these shows the locus of points the goat can walk to?
Q3.A door-bell camera (S) can film any object up to 5 metres away. It can only film in locations that it can see in a straight line. Which construction shows the locus of locations the camera can film?
Q4.This map shows two rocks, P and S, out at sea. A swimmer swims so that they are always the same distance from each rock. Which locus shows the swimmer's route?
Q5.Izzy’s grandma wants to move to a house that is within 7 km of Izzy’s house at P, but also still at most 3 km from the river. Izzy's grandma should move to region .
Q6.Aisha wants to work out whether point P is closer to point A or point B. What construction should Aisha use?
To help you plan your 11 maths lesson on: Solving loci problems in context, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your 11 maths lesson on: Solving loci problems in context, 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.