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Mathematics / Year 8 / Measurement and Geometry / Geometric reasoning

Curriculum content descriptions

Define congruence of plane shapes using transformations (ACMMG200)

Elaborations
  • understanding the properties that determine congruence of triangles and recognising which transformations create congruent figures
  • establishing that two figures are congruent if one shape lies exactly on top of the other after one or more transformations (translation, reflection, rotation), and recognising that the matching sides and the matching angles are equal
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
ScOT terms

Congruence (Geometry)

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 ...

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

TIMES Module 13: Measurement and Geometry: construction - teacher guide

This is a 30-page guide for teachers that explains the central role of construction and presents examples of constructions.

Online

TIMES Module 10: Measurement and Geometry: introduction to measurement - teacher guide

This is a 16-page guide for teachers. It provides an introduction to the initial ideas of measurement, and introduces the measurement of length, area, volume and time.

Interactive

Surface area and volume

This is an interactive resource about investigating the surface areas and volumes of rectangular and triangular prisms. The resource can be used in one of two modes. In the Explore mode, the student can vary the height, width and depth of the prism, and the surface area and volume are calculated automatically. In the Compute ...

Interactive

Area of a parallelogram

This is a Geogebra activity used to teach the area of a parallelogram. Suitable for use with an interactive whiteboard (IWB).

Interactive

Numeracy wrap: It's what's inside that counts

interactive activities that guide students to explore the interior and exterior angle sums of polygons.

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.

Interactive

Syllabus bites – mixing it up

The fifth in a series of Syllabus bites related to transformations on the Cartesian plane. This bite covers combinations (composition) of transformations.

Interactive

Examples of Pythagoras' Theorem Part 2

An animated tutorial demonstrating the application of Pythagoras' theorem through some worked examples, followed by a interactive quiz.

Video

Are plants mathematicians?

Ever noticed that plants are examples of Fibonacci numbers? Watch Vi Hart draw examples of flower petals and leaf growth that follow this pattern. See how plants seem to use Phi (.), the golden ratio. Find out how to make your own 'angle-a-tron' to create interesting petal designs. This is the second in a series of two.

Interactive

Plotting Points in a Quadrant

An animated tutorial demonstrating how to locate and plot points on the Cartesian plane, given coordinates. An interactive quiz is included.

Interactive

The Numberline

An interactive tool that can help students explore a number line, including points representing integers, fractions and decimals

Interactive

Renovate, Calculate!

A student resource that explores the use of mathematics in the trades. Highly interactive investigations into ratio, areas of special quadrilaterals and right-angled trigonometry.

Interactive

Numeracy wrap: Tell me why

Interactive activities that guide students to consider the use and presentation of geometric reasoning.

Interactive

Expressions

An animated tutorial with a focus on collecting 'like' terms to simplify expressions. An interactive quiz is included.

Interactive

Area of a triangle

This is a Geogebra activity used to teach the area of a triangle. Suitable for use with an interactive whiteboard (IWB).

Video

Using Pythagoras' Theorem (Simulation)

An interactive simulation in which students use Pythagoras' theorem can be used to find distances.

Interactive

Syllabus bites – frenzied flipping

This is the second in a series of Syllabus bites related to transformations on the Cartesian plane. This Bite covers reflection of points.

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.