Loci and constructions
Collection of secondary mathematics resources covering loci and construction.
Loci and Constructions
This resource consists of 12 instant maths ideas, ideal for use as starter questions, extension question or probing questions to assess understanding, providing students with the opportunity to explore loci and constructions using physical activities, by solving problems such as the goat and the shed problem, drawing an ellipse, accurate triangles, polygons and constructions using a compass and a straight edge.
Loci
This interactive excel file allows students to investigate loci. Each of the interactive sheets enables students to see random points on or near the locus and how the locus is constructed. Loci include the locus of points equidistant from a point, from a line segment and from two lines.
There are also eight sheets of questions on loci and related topics which may be duplicated for classroom use.
Constructions and Loci
This MEP resource from CIMT is taken from text book 9B which covers the mathematics scheme of work for the second half of year 9.
Constructions and loci begins with a recap of different types of angle; angles on a straight line, vertically opposite, supplementary, corresponding, alternate and a recap of scale drawing before moving on to constructions; perpendicular bisector, angle bisector and triangles. The topic concludes with look at simple loci.
Loci
• Loci - kinds of loci (using rich collaborative tasks)
• Loci - distinguishing loci based on their conditions (using rich collaborative tasks)
• Loci using learners as points (using co-operative small group work)
• Loci - from diagrams to conditions (using rich collaborative tasks)
• Loci - imaginary movements (using rich collaborative tasks)
• 2D construction with loci (using rich collaborative tasks
Constructions
This resource from Defence Dynamics looks at the military’s historical (and current) use of constructions and mathematical accuracy in warfare and peacetime defence.
Students are asked to draw constructions to represent how the military target hostile forces, stressing the importance of accuracy in calculations which consider projected paths. They will need to be able to construct scale drawings, an angle bisector, a perpendicular bisector, a triangle and a variety of loci.
Triangle Construction
This resource, from the Association of Teachers of Mathematics (ATM) publication ‘We Can Work It Out’, is a group problem-solving activity in which each student in the group is given a number of the twelve information cards. Students are responsible for introducing the information contained on their cards at an appropriate time in the problem solving process.
Triangle construction requires students to use the information gained from the cards to make an accurate drawing of a triangle. Students will need to be familiar with angle and triangle terminology, symmetry, divisibility facts, factors, multiples and fractions in order to solve the problem.
Geometry: Construction Proof
This resource consists of two interactive Virtual Textbook excel files dealing with some aspects of construction and geometric proof.
Perpendicular Bisectors and Geometry: Construction, Proof
Geometrical Properties of Lines, Angles and Polygons
Geometry resource package from the National STEM Learning Centre from the secondary mathematics webpage.
Locus Mystery
This resource written by Shirley Fall focuses on constructing loci. There are eighteen cards with statements about an area of land centred on a four-sided field reputed once to have belonged to a notorious highwayman. Students are asked to discuss in groups and use the cards to construct the diagram and hence solve the puzzle of where to dig for the treasure
