Mathematics / Year 8 / Measurement and Geometry / Geometric reasoning

Curriculum content descriptions

Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning (ACMMG202)

Elaborations
  • establishing the properties of squares, rectangles, parallelograms, rhombuses, trapeziums and kites
  • identifying properties related to side lengths, parallel sides, angles, diagonals and symmetry
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Angles,  Congruence (Geometry),  Quadrilaterals

Interactive

The Mathematical Toolkit

A 2D Shapes tool that can be used to create geometric objects such as quadrilaterals, circles, triangles, lines, arcs, rays, segments and vectors on a coordinate grid. Plot and label the vertices to reveal the internal angles, side lengths, area and perimeter, then manipulate the shapes on a grid to transform their shape ...

Interactive

The geometer's warehouse

This web-based, multimedia resource focuses on the geometry of the Stage 4 and Stage 5 Mathematics syllabus. It comprises 70 dynamic html worksheets, each exploring a different outcome in Stage 4 and Stage 5 geometry.

Interactive

Numeracy wrap: Parallelogram peculiarities

Interactive activities that guide students to investigate properties of parallelograms.

Online

reSolve: Quarter Cartons

This lesson challenges students to use algebra and proportional reasoning to investigate how changing the size of a paper square or rectangle impacts the dimensions of a box folded from that paper. Students apply knowledge about nets of 3D objects and explore algebraic relationships through a set of hands-on activities ...

Online

reSolve: Polygon Pieces

This lesson explores the geometry of cutting polygons in different ways and using algebra to express subsequent findings. Students use one straight cut to divide a convex polygon into two new polygons. They make generalisations about the total number of sides of the two new polygons, and about the number of different combinations ...

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 ...

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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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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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.

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

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

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

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 ...

Online

Circles and cylinders: Year 8 – planning tool

This planning resource for Year 8 is for the topic of Circles and cylinders. Students recall and revise circumference, radius and diameter from Year 7. They understand the relationships between these measures and can use relevant formulae to solve problems.

Online

Algorithms: Year 8 – planning tool

This planning resource for Year 8 is for the topic of Algorithms. Students begin to design, create and test algorithms that involve a sequence of steps that identify congruency or similarity of shapes. They describe how algorithms work through classifying and distinguishing between similar and congruent triangles.

Online

Pythagoras and trigonometry: Year 8 – planning tool

This planning resource for Year 8 is for the topic of Pythagoras and trigonometry. Students are introduced to Pythagoras’ theorem to solve problems involving the side lengths of right-angled triangles.

Online

Volume and surface area: Year 8 – planning tool

This planning resource for Year 8 is for the topic of Volume and surface area. Students further develop their understanding of volume and capacity of right prisms by developing formulas, taking measurements and investigating, making approximations and solving problems in many contexts.