AC9M8M06 Year 8 Mathematics

AC9M8M06 – Year 8 Mathematics: null

Strand

Measurement

Substrand

Measurement

This Content Descriptor from Year 8 Mathematics provides the specific knowledge and skills students should learn. Use it to plan lessons, create learning sequences, and design assessments that align with the Australian Curriculum v9.

Content Descriptor

use Pythagoras’ theorem to solve problems involving the side lengths of right-angled triangles

Elaborations

• discussing and comparing different applications, demonstrations and proofs of Pythagoras’ theorem, from Egypt and Mesopotamia, Greece, India and China with other historical and contemporary applications and proofs
• using Pythagoras’ theorem to determine unknown lengths of sides in right-angled triangles and finding lengths of sides of right-angled triangles in practical applications
• recognising the relationship between the squares of lengths of sides for different types of triangles: right-angled, acute or obtuse
• identifying Pythagorean triples, such as (\(3,4,5\)), (\(5,12,13\)), (\(7, 24, 25\)) and (\(8,15, 17\))
• investigating how Pythagoras' theorem can be applied to determine the distance between two points in the plane, and how this can be used by predictive algorithms to navigate autonomous vehicles

Achievement Standard This Supports

This Content Descriptor contributes to the following Achievement Standard:

Year 8 ASMATY8

Year 8 Mathematics Achievement Standard

By the end of Year 8, students recognise irrational numbers and terminating or recurring decimals. They apply the exponent laws to calculations with numbers involving positive integer exponents. Students solve problems involving the 4 operations with integers and positive rational numbers. They use mathematical modelling to solve practical problems involving ratios, percentages and rates in measurement and financial contexts. Students apply algebraic properties to rearrange, expand and factorise linear expressions. They graph linear relations and solve linear equations with rational solutions and one-variable inequalities, graphically and algebraically. Students use mathematical modelling to solve problems using linear relations, interpreting and reviewing the model in context. They make and test conjectures involving linear relations using digital tools. Students use appropriate metric units when solving measurement problems involving the perimeter and area of composite shapes, and volume of right prisms. They use Pythagoras’ theorem to solve measurement problems involving unknown lengths of right-angle triangles. Students use formulas to solve problems involving the area and circumference of circles. They solve problems of duration involving 12- and 24-hour cycles across multiple time zones. Students use 3 dimensions to locate and describe position. They identify conditions for congruency and similarity in shapes and create and test algorithms designed to test for congruency and similarity. Students apply the properties of quadrilaterals to solve problems. They conduct statistical investigations and explain the implications of obtaining data through sampling. Students analyse and describe the distribution of data. They compare the variation in distributions of random samples of the same and different size from a given population with respect to shape, measures of central tendency and range. Students represent the possible combinations of 2 events with tables and diagrams, and determine related probabilities to solve practical problems. They conduct experiments and simulations using digital tools to determine related probabilities of compound events.