AC9M8M05 Year 8 Mathematics

AC9M8M05 – 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

recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure

Elaborations

• identifying examples of rates in the real world, including constant rates, rate of pay, cost per kilogram, recipes, simple interest and average rates
• applying rates to solve problems involving the conversion between different units of measure; for example, using a conversion rate to convert distances from miles into kilometres; using currency exchange rates to determine the price of items
• applying rates to calculate solutions to problems in different contexts; for example, required run rates in cricket, dilution of concentrated chemicals and comparing the petrol consumption rates of different vehicles
• using taxation tables to calculate an individual's annual income tax
• investigating the application of rates in First Nation Australians’ land management practices, including the rate of fire spread under different environmental conditions such as fuel types, wind speed, temperature and relative humidity; the conservation of water by First Nations Australians by estimating rates of water evaporation based on surface area and climatic conditions

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.