Applying constructions to loci problems
Lesson details
Learning outcome
I can apply the rules for constructing angle and line bisectors to loci problems.
Key learning points
- The perpendicular bisector of a line segment divides the line segment into two equal parts
- The perpendicular bisector is the same distance from each end point of the line segment
- If you only had the two end points, the perpendicular bisector would still be the same distance from each point
- The bisector of an angle divides the angle into two equal parts.
Keywords
Bisect - To bisect means to cut or divide an object into two equal parts.
Loci - A locus is a set of points that satisfy a given set of conditions. Multiple sets of points are referred to as loci.
Equidistant - Points A and B are equidistant from a third point C if the distance AC is equal to the distance BC.
Common misconception
Pupils may believe that there is only one point which is equidistant from two points.
Highlight that forming any isosceles triangle will mean that that the point is equidistant from both points.
Teacher tip
If space allows, you may want to consider getting the pupils to place themselves equidistant from two 'cones' or two walls. Alternatively the use of counters can allow pupils to really consider the points in which satisfy the condition.
Equipment
Ruler, pair of compasses, pencil
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.A __________ is a set of points that satisfy a given set of conditions.
Q2.Which diagram shows the locus of points 3 metres or less from point A?
Q3.Which diagram shows the locus of points more than 3 metres from point A?
Q4.Which diagram shows the locus of points 6 cm from the line segment AB?
Q5.Which diagram shows the locus of points less than 6 cm from the line segment AB?
Q6.Alex stands somewhere in his garden. Alex is less than 5 m from the house and more than 6 m from the tap. He is within 3 m of the tree. Alex is standing in region .
Assessment exit quiz
6 Questions
Q1.Which diagram shows a perpendicular bisector?
Q2.Alex places two cones, A and B, on the ground. Which of these points are equidistant from A and B?
Q3.Which of these points are closer to TU than they are to ST?
Q4.Jacob wants to find all the points that are the same distance from LM as they are from MN. What construction should he use?
Q5.Which region is illustrated on this diagram?
Q6.Select the region which matches this description: closer to AB than BC and closer to CD than AD .
To help you plan your 11 maths lesson on: Applying constructions to loci problems, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your 11 maths lesson on: Applying constructions to loci problems, 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.