Mathematics / Year 8 / Measurement and Geometry / Geometric reasoning

Curriculum content descriptions

Develop the conditions for congruence of triangles (ACMMG201)

Elaborations
  • investigating the minimal conditions needed for the unique construction of triangles, leading to the establishment of the conditions for congruence (SSS, SAS, ASA and RHS)
  • solving problems using the properties of congruent figures
  • constructing triangles using the conditions for congruence
General capabilities
  • Numeracy Numeracy
ScOT terms

Congruence (Geometry),  Triangles (Shapes)

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Geometric reasoning - congruence

This is a website designed for both teachers and students that introduces congruence of shapes in the plane through transformations. In particular, transformations, translations, reflections in an axis and rotations of multiples of 90 degrees are used to define congruence and to identify congruent shapes. The four congruence ...

Online

reSolve: Mechanical Linkages: Quadrilaterals

This series of six lessons explores geometry using real world contexts focussed on the dynamics of linkages and moving joints of everyday tools and objects. Students use physical models and computer simulations, the lessons move from a view of geometry as a study static diagrams to encompass movement. Each lesson is outlined ...

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Making triangles

In this lesson, students study the concept of triangle inequality, which determines if three positive numbers can serve as the side lengths of a triangle. Students experiment with various combinations of three natural numbers. They investigate whether these numbers can form a triangle and classify and construct the corresponding ...

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8Sp02A Similarity - Ochre Education

This four lesson unit of work focuses on similarity in geometry. Students define similarity of shapes in terms of dilations; determine if shapes are similar by using dilations and isomorphic transformations, check if corresponding angles are congruent and the ratios of corresponding side lengths are the same; define similarity ...

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8Sp01A Congruence - Ochre Education

This eight lesson unit of work focuses on congruence. Students explore the congruence of lengths, angles, and shapes, determine the congruence of triangles and shapes using appropriate tests including with algorithms and determine the size of unknown corresponding parts and finally solve problems involving congruence through ...

Downloadable

Geometry: Foundation to Year 9

This comprehensive resource describes the progression of geometric reasoning. The resource demonstrates examples of relevant teaching strategies, investigations, activity plans and connected concepts in geometry including teaching and cultural implications.

Online

Shapes and objects: Year 8 – planning tool

This planning resource for Year 8 is for the topic of Shapes and objects. Students begin to explore geometric properties and proof. They identify the properties of quadrilaterals based on transformation, angles, parallel sides, side lengths, diagonals and symmetry.

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8M07A Volume and capacity - Ochre Education

This four lesson unit of work focuses on volume and capacity. Students convert between volume units using the cube of the length conversion, convert between volume and capacity; calculate the volume and capacity of prisms with cross-sections that are triangular, quadrilateral, or irregular shapes; and investigate a rich ...

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8M06A Area and surface area - Ochre Education

This seven lesson unit of work focuses on area and surface area. Students convert between area units, determine the area of trapezia, kites, and rhombi, determine lengths from areas and areas from lengths, determine the areas of circles and parts of circles, determine and estimate the areas of irregular and composite shapes ...

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8M04A Length - Ochre Education

This lesson focuses on the lengths of paths and perimeters of shapes. Students determine the perimeter of composite shapes with circles, semicircles and quadrants using Pythagoras’ theorem and unit conversion. The unit includes a slide show for structuring presentation of the unit, student tasks including supplementary ...

Interactive

Syllabus bites – turbo turning

The fourth in a series of Syllabus bites related to transformations on the Cartesian plane. This Bite covers rotation of points.

Online

TIMES Module 17: Measurement and Geometry: the circle - teacher guide

This is a 15-page guide for teachers. In the module the formulas for finding the circumference and area of a circle are introduced. The history and significance of the number pi is also included in this module.

Interactive

Syllabus bites – flipping and sliding

This is the third in a series of Syllabus bites related to transformations on the Cartesian plane. Students further their understanding of translation and reflection and explore relationships between these two transformations.

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The Geometry and Algebra of Honeycomb - Calculate

This integrated unit of work explores the amazing structures of honeycomb by examining the properties of regular and irregular polygons and polyhedra. Students then move on to solve problems using geometric and algebraic reasoning.

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8M03A Pythagoras' theorem - Ochre Education

This unit of work focuses on Pythagoras' theorem. Students define and identify the hypotenuse of a right-angled triangle as being the longest side and opposite the right angle and the perpendicular sides as being the shorter two sides and adjacent to the right angle; define Pythagoras' theorem in words and symbols; use ...

Downloadable

How many in the queue?

Students use visualising and movement activities to develop an understanding of the relationship between variables.

Downloadable

Measurement: Foundation to Year 9

This comprehensive resource describes the progression of measurement ideas. The resource demonstrates examples of relevant teaching strategies, investigations, activity plans and connected concepts in measurement including teaching and cultural implications.

Online

Graphs: Year 8 – planning tool

This planning resource for Year 8 is for the topic of Graphs. Students explore linear relationships in the context of the Cartesian plane using digital tools. Students will then go on to find the rule for a linear relationship and solve linear equations, both graphically and algebraically.

Online

Area and perimeter: Year 8 – planning tool

This planning resource for Year 8 is for the topic of Area and perimeter. Students build on their knowledge of the area and perimeter of rectangles, parallelograms and triangles to rhombi, kites and trapezia. They identify and use the formulae for these to solve problems.

Online

Position and location: Year 8 – planning tool

This planning resource for Year 8 is for the topic of Position and location. Students work with 3D objects that can be located on the x, y, z planes, allowing students to extend their thinking away from flat objects on a 2D plane, to objects with volume that have a position in space with (x, y, z) coordinates. Students ...