Year 11 - Maths
Problem solving with loci and constructions
Loci and construction
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils construct triangles and construct diagrams following specific restrictions using their knowledge of loci and their work on constructions.
Lesson Summary
You will learn to use your knowledge of loci and constructions to solve problems.
Key Notes
- Your knowledge of loci can be applied to your knowledge of bearings
- Your knowledge of loci can be used to help solve area problems
Vocabulary To Learn
- 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 Mistakes To Avoid
- Pupils may not consider that, in some contexts (e.g. a corded lawnmower), the shape of the locus will include sectors of different radii, if a shape/object is creating a barrier.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Your knowledge of loci can be applied to your knowledge of bearings. Your knowledge of loci can be used to help solve area problems.
2. Use this key word in a maths sentence and explain it clearly. '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. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may not consider that, in some contexts (e.g. a corded lawnmower), the shape of the locus will include sectors of different radii, if a shape/object is creating a barrier. Correction: Have pupils consider the impact of going around the corner of a shape.
More Lessons In This Unit
- Advanced problem solving with loci and constructions Study Guide
- Applying constructions to loci problems Study Guide
- Checking and securing understanding of bisecting an angle Study Guide
- Checking and securing understanding of constructing a perpendicular to a given line through a point Study Guide
- Checking and securing understanding of constructing the perpendicular bisector of a line segment Study Guide
- Constructing a right-angled triangle given the length of the hypotenuse and one other side length Study Guide
- Constructing a triangle given three side lengths using compasses Study Guide
- Constructing a triangle given two angles and the side length between them Study Guide
- Constructing a triangle given two side lengths and an angle not between them Study Guide
- Constructing a triangle given two side lengths and the angle between them using a compass Study Guide
- Constructing angles of 90° and 45° Study Guide
- Constructing loci Study Guide
- Solving loci problems in context Study Guide
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