Assessment Strategies: What and How?

Course(s): Year 10 (Stage 5.1) KLA RE ENG MA SCI HSIE PDHP CA TAS LOTE  E

Unit of Work: Review of Space & Geometry Indicative Hours: 15 h Term: 3 Weeks: 7 to 10 Unit Description:

This topic gets covered in Stage 4. Its inclusion at this juncture is to review basic concepts and practise essential skills in preparation for the School Certificate Examination.

The study of solid shapes imparts basic understanding of their dimensions that is an essential requirement in the Measurement strand. Also students of Design & Technology and Art may apply skills developed in this topic, when they prepare diagrams, sketches and/or drawings for the making of models or products; and students of Science will find this topic useful when drawing and building models of crystals.

The study of angles is the introduction to Deductive Geometry where students are required to support statements with reasons. A sound understanding of this basic topic facilitates a better application of geometrical concepts to solve problems and theorems at a later stage.

The sequential build-up of geometrical concepts requires students to study triangles and basic quadrilaterals and utilise geometrical instruments to construct these shapes according to stipulated parameters. The properties of special quadrilaterals are important in Measurement. For example, the perpendicularity of the diagonals of a rhombus and a kite allow a rectangle of twice the size to be constructed around them, leading to formulae for finding area. At this Stage, the treatment of triangles and quadrilaterals is still informal, with students consolidating their understandings of different triangles and quadrilaterals and being able to identify them from their properties.

Similarity is linked with ratio in the Number strand and with map work in Geography. Similar and congruent figures are embedded in a variety of designs (eg tapa cloth, Aboriginal designs, Indonesian ikat designs, Islamic designs, designs used in ancient Egypt and Persia, window lattice, woven mats and baskets).

Syllabus outcomes for each course:

SGS 4.1: Describes and sketches three-dimensional solids including polyhedra, and classifies them in terms of their properties.

SGS 4.2: Identifies and names angles formed by the intersection of straight lines, including those related to transversals on sets of parallel lines, and makes use of the relationships between them.

SGS 4.3: Classifies, constructs, and determines the properties of triangles and quadrilaterals.

SGS 4.4: Identifies congruent and similar two-dimensional figures stating the relevant conditions.

1 Resources:

Mathematics Syllabus Years 7 – 10, 2003 New Century Mathematics Year 10 (Stage 5.1) – Chapter 6 CD-ROM included with textbook Hotmaths website

If this unit of work is course specific skip to page 3

2 Phase 1:

Properties of Solids Teaching Strategies Registration Assessment  Describing solids in terms of their  Demonstrate the describe solids in terms of their geometric Strategies: what geometric properties properties number of faces, shape of faces number and and how? number of faces type of congruent faces number of vertices number of shape of faces edges convex or non-convex  Teacher in-class number and type of congruent faces  Identify the pairs of parallel flat faces of a solid. observation number of vertices number of edges  Demonstrate if two straight edges of a solid are  Questioning convex or non-convex intersecting, parallel or skew  Identifying any pairs of parallel flat faces  Participation of a solid  Explain the meaning of uniform cross- section  Determining if two straight edges of a  Written assessment  Classify solids on the basis of their properties. solid are intersecting, parallel or skew task  Determining if a solid has a uniform  Explain the meaning of Polyhedron. cross-section  Classifying solids on the basis of their  Explain the different properties. properties A polyhedron is a solid whose faces  Interpret and make models from isometric drawings are all flat.  Recognise solids with uniform and non-uniform cross- A prism has a uniform polygonal sections cross-section.  Analyse three-dimensional structures in the environment to A cylinder has a uniform circular explain why they may be particular shapes eg buildings, cross-section. packaging A pyramid has a polygonal base and  Visualise and name a common solid given its net one further vertex (the apex).  Recognise whether a diagram is a net of a solid A cone has a circular base and an apex.  Identify parallel, perpendicular and skew lines in the All points on the surface of a sphere environment are a fixed distance from its centre.  Identifying right prisms and cylinders and oblique prisms and cylinders  Identifying right pyramids and cones and oblique pyramids and cones  Sketching on isometric grid paper shapes built with cubes 3  Representing three-dimensional objects in two dimensions from different views  Confirming, for various convex polyhedra, Euler’s formula

F + V = E + 2 relating the number of faces (F), the number of vertices (V) and the number of edges (E)  Exploring the history of Platonic solids and how to make them  Making models of polyhedra

Phase 2:

4 Teaching Strategies Angles at a Point  Explain and demonstrate the labeling and naming of points,  Labelling and naming points, lines and lines and intervals intervals using capital letters  Labelling the vertex and arms of an  Demonstrate and give examples of labeling vertices and angle with capital letters arms of angles with capital letters  Labelling and naming angles using A Demonstrate the different ways of labeling angles and XYZ notation   Using the common conventions to  Demonstrate the common conventions indicating right indicate right angles and equal angles on angles and equal angles on diagrams diagrams  Identifying and naming adjacent angles  Demonstrate and explain how to identify and name (two angles with a common vertex and a adjacent, vertically opposite angles, straight angles and common arm), vertically opposite angles, angles of complete revolution straight angles and angles of complete revolution, embedded in a diagram  Explain the use of the words ‘complementary’ and  Using the words ‘complementary’ and ‘supplementary’ when describing angles ‘supplementary’ for angles adding to 90º  Demonstrate the use of equality of vertically opposite and 180º respectively, and the terms angles. ‘complement’ and ‘supplement’  Establishing and using the equality of  Recognise and explain why adjacent angles adding to 90º vertically opposite angles form a right angle  Recognise and explain why adjacent angles adding to 180º form a straight angle  Recognise and explain why adjacent angles adding to 360º form a complete revolution  Find the unknown angle in a diagram using angle results, giving reasons

Phase 3:

Angles Associated with Transversals Teaching Strategies  Identifying and naming a pair of parallel  Revision of parallel lines. lines and a transversal  Identify parallel and perpendicular lines in the class  Using common symbols for ‘is parallel to’ environment e.g., opposite sides of the white board are ( ) and ‘is perpendicular to’ () parallel but the adjacent sides are perpendicular and so on. 5  Using the common conventions to Explain the common conventions. indicate parallel lines on diagrams  Identifying, naming and measuring the  Use diagrams to explain the different types of angles in alternate angle pairs, the corresponding parallel lines.(corresponding, alternate and co-interior angle pairs and the co-interior angle angles) pairs for two lines cut by a transversal  Revision of complementary and supplementary angles.  Recognising the equal and supplementary angles formed when a  Demonstrate and explain how to find the value of the pair of parallel lines are cut by a unknown angle by using the properties of two-dimensional transversal shapes and parallel lines results.  Using angle properties to identify parallel lines  Apply angle results to construct a pair of parallel lines using  Using angle relationships to find a ruler and a protractor, a ruler and a set square, or a ruler unknown angles in diagrams and a pair of compasses  Apply angle and parallel line results to determine properties of two-dimensional shapes such as the square, rectangle, parallelogram, rhombus and trapezium  Identify parallel and perpendicular lines in the environment  Construct a pair of perpendicular lines using a ruler and a protractor, a ruler and a set square, or a ruler and a pair of compasses  Use dynamic geometry software to investigate angle relationships

Phase 4:

Notation Teaching Strategies  Labelling and naming triangles (eg ABC)  Demonstrate the ability to label triangles and quadrilaterals. and quadrilaterals (eg ABCD) in text and on diagrams  Demonstrate the common conventions to mark equal  Using the common conventions to mark intervals on diagrams equal intervals on diagrams  Demonstrate how to classify triangles on the basis of their Triangles properties (acute-angled triangles, right angled triangles,  Recognising and classifying types of obtuse-angled triangles, scalene triangles, isosceles triangles on the basis of their properties triangles and equilateral triangles) (acute-angled triangles, right-angled triangles, obtuse-angled triangles, 6 scalene triangles, isosceles triangles and  Demonstrate how to construct triangles using geometrical equilateral triangles) instruments, given different information eg the lengths of all  Constructing various types of triangles sides, two sides and the included angle, and two angles using geometrical instruments, given and one side different information e.g., the lengths of all sides, two sides  Students verify by paper folding or cutting, and testing by and the included angle, and two angles measuring, that the interior angle sum of a triangle is 180º, and one side and that any exterior angle equals the sum of the two  Justifying informally by paper folding or interior opposite angles cutting, and testing by measuring, that  Sketch and label triangles from a given verbal description the interior angle sum of a triangle is  Describe a sketch in sufficient detail for it to be drawn 180º, and that any exterior angle equals the sum of the two interior opposite  Recognise that a given triangle may belong to more than angles one class  Recognise that the longest side of a triangle is always  Using a parallel line construction, to opposite the largest angle prove that the interior angle sum of a triangle is 180º  Recognise and explain why two sides of a triangle must together be longer than the third side  Proving, using a parallel line  Recognise special types of triangles and quadrilaterals construction, that any exterior angle of a embedded in composite figures or drawn in various triangle is equal to the sum of the two orientations interior opposite angles  Determine if particular triangles and quadrilaterals have line and/or rotational symmetry  Apply geometrical facts, properties and relationships to solve numerical problems such as finding unknown sides and angles in diagrams  Justify their solutions to problems by giving reasons using their own words

Phase 5:

Quadrilaterals Teaching Strategies  Distinguishing between convex and non-  Sketch and label quadrilaterals from a given verbal convex quadrilaterals (the diagonals of a description convex quadrilateral lie inside the figure)  Bisect an angle by applying geometrical properties e.g.,  Establishing that the angle sum of a constructing a rhombus 7 quadrilateral is 360º  Bisect an interval by applying geometrical properties e.g.,  Constructing various types of constructing a rhombus quadrilaterals  Draw a perpendicular to a line from a point on the line by  Investigating the properties of special applying geometrical properties e.g., constructing an quadrilaterals (trapeziums, kites, isosceles triangle parallelograms, rectangles, squares and  Draw a perpendicular to a line from a point off the line by rhombuses) by using symmetry, paper applying geometrical properties e.g., constructing a folding, measurement and/or applying rhombus geometrical reasoning Properties to be  Use ruler and compasses to construct angles of 60º and considered include : 120º by applying geometrical properties e.g., constructing opposite sides parallel an equilateral triangle opposite sides equal  Explain with the help of examples the difference between adjacent sides perpendicular convex and non-convex quadrilaterals. opposite angles equal  Explain the sum of the angles of a quadrilateral. diagonals equal in length diagonals bisect each other  Explain the different properties of quadrilaterals. diagonals bisect each other at right angles diagonals bisect the angles of the quadrilateral  Investigating the line symmetries and the order of rotational symmetry of the special quadrilaterals  Classifying special quadrilaterals on the basis of their properties

Phase 6:

Circles Teaching Strategies  Identifying and naming parts of the circle  Explain that a circle consists of all points that are a given and related lines, including arc, tangent distance from the centre and how this relates to the use of and chord a pair of compasses  Investigating the line symmetries and the  Use dynamic geometry software to investigate the rotational symmetry of circles and of properties of geometrical figures diagrams involving circles, such as a sector and a circle with a chord or tangent 8 Phase 7:

Congruence Teaching Strategies  Identifying congruent figures by  Explain the meaning of the word congruent by superimposing them through a superimposing objects. combination of rotations, reflections and translations  Give class examples of congruent shapes by using diagrams, drawing found in media, design work etc.  Matching sides and angles of two congruent polygons  Also write the matching sides and vertices.  Naming the vertices in matching order when using the symbol º in a  Demonstrate and explain the four tests of congruency by congruence statement means of diagrams.  Drawing congruent figures using  Students can cut out different shapes and test congruency geometrical instruments by placing them on top of each other.  Determining the condition for two circles to be congruent (equal radii)  Explain the difference between congruence and similarity.  Recognise congruent figures in tessellations, art and design work

Phase 8:

Similarity Teaching Strategies  Using the term ‘similar’ for any two  Demonstrate and explain the use of similar figures in figures that have the same shape but not finding lengths in the environment where it is impractical to necessarily the same size measure directly eg heights of trees, buildings.  Matching the sides and angles of similar  Using scale factor demonstrate how to draw similar figures figures (by enlarging or reducing the diagram)  Naming the vertices in matching order when using the symbol lll in a similarity  Explain similarity by enlarging cartoons and pictures and statement hence demonstrate how to find the scale factor.  Determining that shape, angle size and  Demonstrate and explain by means of examples how to 9 the ratio of matching sides are preserved match the sides and angles of similar figures. Use in similar figures enlargement or reduction factor to find the dimensions of  Determining the scale factor for a pair of similar figures. similar polygons  Explain how to construct similar figures using geometrical  Determining the scale factor for a pair of instruments. circles  Calculating dimensions of similar figures  Interpret and use scales in photographs, plans and using the enlargement or reduction factor drawings found in the media and/or other learning areas  Choosing an appropriate scale in order  Enlarge diagrams such as cartoons and pictures to enlarge or reduce a diagram  Constructing scale drawings  Apply similarity to finding lengths in the environment where it is impractical to measure directly eg heights of trees,  Drawing similar figures using geometrical buildings instruments  Apply geometrical facts, properties and relationships to solve problems such as finding unknown sides and angles in diagrams  Justify their solutions to problems by giving reasons using their own words  Recognise that area, length of matching sides and angle sizes are preserved in congruent figures  Recognise that shape, angle size and the ratio of matching sides are preserved in similar figures  Recognise that similar and congruent figures are used in specific designs, architecture and art work eg works by Escher, Vasarely and Mondrian; or landscaping in European formal gardens  Find examples of similar and congruent figures embedded in designs from many cultures and historical periods  Use dynamic geometry software to investigate the properties of geometrical figures

10 REGISTRATION & TEACHER EVALUATION

Date Unit of Work was Started: ______Date Unit of Work was Completed: ______

It is confirmed that the outcomes ticked () above have been completed.

Supporting Students with Special Needs

Students with Special Needs Targeted Outcomes for these Accommodations/ Special Provisions Organised in Class Students Adaptations (if applicable) (if different to rest of class) (as necessary)

11 Comments Teaching Strategies and Applications, noting any additional ones

Use of resources

Need for extra resources

Student response (Students’ attitude to the Unit)

Appropriateness and Achievement of Outcomes

Timing and placement of topic

Depth of coverage

Alterations made to cater for range of abilities in the class

Further points for improvement

Name of Teacher: ______Date: ______

Signature: ______