Myths about teaching can hold you back
- Year 11•
- Higher
Advanced problem solving with loci and constructions
I can use my knowledge of loci and constructions to solve problems.
- Year 11•
- Higher
Advanced problem solving with loci and constructions
I can use my knowledge of loci and constructions to solve problems.
Lesson details
Key learning points
- Your knowledge of loci can be applied to your knowledge of bearings
- Your knowledge of loci can be used to help solve area problems
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.
Bearing - A bearing is an angle measured in degrees from North in the clockwise direction and written with three figures. E.g. an angle of 82° is written as 082°.
Area - The area is the size of the surface and states the number of unit squares needed to completely cover that surface.
Common misconception
Pupils may give an angle rather than a bearing.
Remind pupils that a bearing is an angle, measured clockwise from North and given as three figures.
To help you plan your year 11 maths lesson on: Advanced problem solving with loci and constructions, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Advanced problem solving with loci and constructions, 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
Protractor, pair of compasses, ruler, pencil
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.The of points equidistant from another point can be represented by a circle.
Q2.A goat is tied to a railing by a 2 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 security 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. Any ship must stay 10 metres of more away from each rock. Which locus shows that are 10 metres away from rock S? (A, C have radii of 10 m).
Q5.Sam’s family want to move to a house that is further than 7 km from a factory at P, but also still at most 3 km from the river. Sam's family should move to region .
Q6.Two mobile phone masts (X and Y) can broadcast their signal to a maximum of 24 km. The further away from the mast, the weaker the signal is. Which points will not receive a signal from either mast?
Assessment exit quiz
6 Questions
Q1.A is an angle measured in degrees from North in the clockwise direction and written with three figures.
Q2.A boat (B) leaves a port (P) on a bearing of 051° at a speed of 20 km/h. The boat has been travelling for 3 hours and minutes.
Q3.Three sensors are set up for security. Sensor 1 has a range 15 m, sensor 2 has a range 12 m and sensor 3 has a range 20 m. All 3 sensors are activated. The intruder is likely to be in region .
Q4.A ship, S, needs to pass through a point that is midway between two buoys. Which construction can be used to determine the point that the ship must pass through?
Q5.A ship, S, needs to pass through a point that is midway between two buoys. What bearing should the ship sail on?
Q6.A rear windscreen wiper cleans only part of the glass. The wiper blade is 24 cm long and pivots 160° from the horizontal. The area of the window that is cleaned by the blade is π cm².
