Unit 5: Constructing triangles and quadrilaterals
Planning guidance
Unit objectives
Within this unit, students will learn to:
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Measure and draw angles
Identify and name angles
Define triangles and quadrilaterals
Draw a triangle given two sides and one angle
Draw a triangle given one side and two angles
Draw a triangle given three sides
Draw a square given one side
Draw a rectangle given its length and width
Draw a rhombus given one side and one angle
Draw a parallelogram given two adjacent sides and an angle
Draw a trapezium given two adjacent sides and two angles
Identify types of angles produced by parallel lines
Find unknown angles
Having covered types of angle, triangle and quadrilateral in Year 7, these topics will be consolidated and
built on within the tasks involving construction of triangles and quadrilaterals. Teachers may choose to
spend additional time with students ensuring competency at measure (angles and length), practising the
constructions and using angle properties to find missing angles in various shapes.
This unit should take three weeks. There are three key sections to this unit. Within each section there
are a number of department tasks to be completed collaboratively. These tasks should form the starting
point of planning lessons and are designed to encourage debate and discussion amongst teachers. As this
topic involved use of precision equipment, it would be worthwhile discussing how tasks can be used in
lessons and how competency in using equipment can be developed.
Suggested Structure
The actual number of lessons spent on each section will depend on the individual class and the number of
lessons available to teachers. We suggest the following based on a total of 9, 12 or 15 lessons over the
three weeks:
Section
Constructing Triangles
Constructing Quadrilaterals
Properties of angles in parallel lines
9 lessons
3
2
4
12 lessons
4
3
5
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15 lessons
4
4
7
Constructing triangles
Objectives
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Measure and draw angles
Identify and name angles
Define triangles
Recognise the properties of triangles
Recognise impossible triangles
Draw a triangle given two sides and one angle
Draw a triangle given one side and two angles
Draw a triangle given three sides
In this unit students work to develop their knowledge of angle facts as well as refining their construction
skills and their skills in using mathematical equipment accurately. Since this is a three week unit, enough
time should be given to ensuring students feel confident in using protractors and pairs of compasses.
When working on the construction of triangles, students have the chance to revisit types of triangles and
triangle properties and should be encouraged to explore the minimum information needed to construct a
triangle. In addition, there is an emphasis on use of technical notation for equal length lines and parallel
lines.
To really extend students and to encourage them to think carefully about the properties of triangles
rather by considering impossible triangles and thinking about what conditions are needed for a triangle to
be ‘possible’.
For further guidance, including the Department Tasks for this section, click Constructing triangles under
Planning resources on the main page for this unit.
Constructing quadrilaterals
Objectives:
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Use coordinates
Measure and draw angles
Identify and name angles
Define quadrilaterals
Recognise the properties of quadrilaterals
Draw a square given one side
Draw a rectangle given its length and width
Draw a rhombus given one side and one angle
Draw a parallelogram given two adjacent sides and an angle
Draw a trapezium given two adjacent sides and two angles
For this section, students extend their skills to looking at quadrilaterals. Again, names and properties of
the shapes should be considered and students should be confident in identifying quadrilaterals and
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deciding what makes ‘a square a square’ etc. In the same way as working with triangles, students then
spend time constructing shapes accurately, each time considering whether shapes are possible to
construct and what the minimum require information is. Considering different orientations is extremely
important.
Excellent group or pair tasks can be implemented through asking students to challenge each other with
construction questions and also by asking those more confident in their skills (especially in using pairs of
compasses and protractors) to support their peers.
For further guidance, including the Department Tasks for this section, click Constructing quadrilaterals
under Planning resources on the main page for this unit.
Angles in parallel lines
Objectives:
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Measure and draw angles
Identify and name angles
Identify types of angles produced by parallel lines
Find the values of unknown angles
Having worked with triangles and quadrilaterals and discussed some angle properties, students will spend
the last week of this unit looking at angles in parallel lines. There is ample opportunity to explore and
investigate angle properties and consolidate measuring angles skills.
Throughout the unit we encourage using the correct technical terminology for angle relationships and
correct notation in diagrams.
There is emphasis here on developing reasoning skills (which would work well as talk tasks and group
work), but some teachers may wish to encourage students to develop their written skills in this unit.
For further guidance, including the Department Tasks for this section, click angles in parallel lines under
Planning resources on the main page for this unit.
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