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Loci and construction

Loci and construction

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Why this why now

This unit follows from vectors where pupils revisited and enhanced their understanding of shape and space. We link that knowledge to this unit as well as building from proof and trigonometry to construct accurate and specific shapes and diagrams.

Prior knowledge requirements

  • Use compass and straightedge accurately
  • Understand perpendicular and angle bisectors
  • Apply basic properties of geometric figures

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Why this why now

This unit follows from vectors where pupils revisited and enhanced their understanding of shape and space. We link that knowledge to this unit as well as building from proof and trigonometry to construct accurate and specific shapes and diagrams.

Prior knowledge requirements

  • Use compass and straightedge accurately
  • Understand perpendicular and angle bisectors
  • Apply basic properties of geometric figures

Loci and construction

In this unit, pupils construct triangles and construct diagrams following specific restrictions using their knowledge of loci and their work on constructions.

13 lessons in unit

  1. 1

    Checking and securing understanding of constructing the perpendicular bisector of a line segment

    I can use the properties of a rhombus to construct a perpendicular bisector of a line segment.
  2. 2

    Checking and securing understanding of constructing a perpendicular to a given line through a point

    I can use the properties of a rhombus to construct a perpendicular to a given line through a given point.
  3. 3

    Checking and securing understanding of bisecting an angle

    I can use the properties of a rhombus to construct an angle bisector.
  4. 4

    Constructing angles of 90° and 45°

    I can construct angles of 90° and 45°.
  5. 5

    Constructing a triangle given three side lengths using compasses

    I can construct a triangle given the three required side lengths.
  6. 6

    Constructing a triangle given two side lengths and the angle between them using a compass

    I can construct a triangle given two of the required side lengths and the size of the angle between them.
  7. 7

    Constructing a triangle given two angles and the side length between them

    I can construct a triangle given two angles and the side length between them.
  8. 8

    Constructing a right-angled triangle given the length of the hypotenuse and one other side length

    I can construct a right-angled triangle given the length of the hypotenuse and one other side length.
  9. 9

    Constructing a triangle given two side lengths and an angle not between them

    I can construct a triangle from two side lengths and an angle not between them.
  10. 10

    Constructing loci

    I can construct a set of points that satisfy a set of conditions.
  11. 11

    Applying constructions to loci problems

    I can apply the rules for constructing angle and line bisectors to loci problems.
  12. 12

    Solving loci problems in context

    I can solve problems involving a combination of loci.
  13. 13

    Problem solving with loci and constructions

    I can use my knowledge of loci and constructions to solve problems.

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