YEAR 7 MATHS FOCUS
MEASUREMENT AND GEOMETRY
GEOMETRICAL SHAPES
OUTCOME
A student:
MA4-17MG:
- classifies, describes and uses the properties of triangles and quadrilaterals, and determines congruent triangles to find unknown side lengths and angles
TEACHING POINTS | The properties of special quadrilaterals are important in the Measurement and Geometry strand. For example, the perpendicularity of the diagonals of a rhombus and a kite allows a rectangle of twice the size to be constructed around them, leading to formulas for finding area. |
| In Stage 4, the treatment of triangles and quadrilaterals is still informal, with students consolidating their understanding of different triangles and quadrilaterals and being able to identify them from their properties. | |
| Students who recognise class inclusivity and minimum requirements for definitions may address this Stage 4 content concurrently with content in Stage 5 Properties of Geometrical Figures, where properties of triangles and quadrilaterals are deduced from formal definitions. | |
| Students should give reasons orally and in written form for their findings and answers. For some students, formal setting out could be introduced. | |
| A range of examples of the various triangles and quadrilaterals should be given, including quadrilaterals containing a reflex angle and figures presented in different orientations. | |
| Dynamic geometry software and prepared applets are useful tools for investigating properties of geometrical figures. |
| RELEVANCE | In geometry, students study two-dimensional shapes, three-dimensional objects, and position, before moving on to the study and application of angle relationships and the properties of geometrical figures. As the focus moves to relationships and properties, students learn to analyse geometry problems. They develop geometric and deductive reasoning skills, as well as problem-solving skills. Students also develop an understanding that geometry is linked to measurement and is very important in the work of architects, engineers, designers, builders, physicists, land surveyors, etc. However, they also learn that geometry is common and important in everyday situations, including in nature, sports, buildings, astronomy, art, etc. |
| LANGUAGE | In Stage 4, students should use full sentences to describe the properties of plane shapes, eg ‘The diagonals of a parallelogram bisect each other’. Students may not realise that in this context, the word ‘the’ implies ‘all’ and so this should be made explicit. Using the full name of the quadrilateral when describing its properties should assist students in remembering the geometrical properties of each particular shape. Students in Stage 4 should write geometrical reasons without the use of abbreviations to assist them in learning new terminology, and in understanding and retaining geometrical concepts. This syllabus uses the phrase ‘line(s) of symmetry’, although ‘axis/axes of symmetry’ may also be used. ‘Scalene’ is derived from the Greek word skalenos, meaning ‘uneven’. ‘Isosceles’ is derived from the Greek words isos, meaning ‘equals’, and skelos, meaning ‘leg’. ‘Equilateral’ is derived from the Latin words aequus, meaning ‘equal’, and latus, meaning ‘side’. ‘Equiangular’ is derived from aequus and another Latin word, angulus, meaning ‘corner’. |
Expectations of Attainment
Classify triangles according to their side and angle properties and describe quadrilaterals
| label and name triangles (eg triangle ABC or ΔABC) and quadrilaterals (eg ABCD) in text and on diagrams |
| use the common conventions to mark equal intervals on diagrams | |
recognise and classify types of triangles on the basis of their properties (acute-angled triangles, right-angled triangles, obtuse-angled triangles, equilateral triangles, isosceles triangles and scalene triangles)
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distinguish between convex and non-convex quadrilaterals (the diagonals of a convex quadrilateral lie inside the figure) | |
investigate the properties of special quadrilaterals (parallelograms, rectangles, rhombuses, squares, trapeziums and kites), including whether:Literacy Critical and creative thinking
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classify special quadrilaterals on the basis of their propertiesLiteracy Critical and creative thinking
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| Identify line and rotational symmetries (ACMMG181) | investigate and determine lines (axes) of symmetry and the order of rotational symmetry of polygons, including the special quadrilateralsCritical and creative thinking Literacy
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| investigate the line and rotational symmetries of circles and of diagrams involving circles, such as a sector or a circle with a marked chord or tangent | |
| identify line and rotational symmetries in pictures and diagrams, eg artistic and cultural designs |
| Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral (ACMMG166) | justify informally that the interior angle sum of a triangle is 180°, and that any exterior angle equals the sum of the two interior opposite anglesLiteracy Critical and creative thinking
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| use the angle sum of a triangle to establish that the angle sum of a quadrilateral is 360° | |
| use the angle sum results for triangles and quadrilaterals to determine unknown angles in triangles and quadrilaterals, giving reasons |
| Use the properties of special triangles and quadrilaterals to solve simple numerical problems with appropriate reasoning | find unknown sides and angles embedded in diagrams, using the properties of special triangles and quadrilaterals, giving reasonsCritical and creative thinking
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