AC9M8M07 Year 8 Mathematics

AC9M8M07 – 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 mathematical modelling to solve practical problems involving ratios and rates, including financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model

Elaborations

• modelling and solving problems related to situations such as scales on maps and plans, the mixing of chemicals or ingredients, or calculating magnification factors applying relevant ratios and proportions
• modelling problems involving converting money amounts using different exchange rates and applying them when planning and budgeting for overseas travel
• modelling situations involving financial contexts; for example, income tax, using taxation rates on annual income, comparing different taxation brackets and rates of pay; comparing the benefits of different phone plans using different call rates and associated fees to determine the best plan
• modelling situations involving the use of ratios in radiocarbon dating methods, including the ratio of carbon-\(14\) to carbon-\(12\) isotopes in organisms, to measure dates of First Peoples of Australia’s habitation on the Australian continent
• modelling situations involving ratio and its application in the making of string and cordage by First Nations Australians, including the ratio of length to the mass of a rope, the strength of the ply in proportion to a rope’s pulling force, and the proportion of fibre for the length of string required

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.