AC9M10SP02 Year 10 Mathematics

AC9M10SP02 – Year 10 Mathematics: null

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This Content Descriptor from Year 10 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

interpret networks and network diagrams used to represent relationships in practical situations and describe connectedness

Elaborations

• investigating how networks and network diagrams can be used to model authentic situations, recognising what real world quantity is represented by the nodes (vertices), and what real world quantity is represented by the links between them (edges)
• investigating the use of graphs to represent a network, analysing connectedness; for example, investigating the “The Seven Bridges of Königsberg” problem
• investigating how polyhedra can be represented as a network using edges, vertices, interior and exterior faces; representing the number of edges, vertices and faces in a table and demonstrating how Euler’s formula \(F + V = E + 2\) applies
• investigating how a social network, intranet, local area network (LAN), electrical wiring or wireless network of a home can be represented as a network diagram to specify relationships; for example, using network diagrams to investigate practical problems involving connections, power overload or the need for routers
• investigating the use of networks to represent authentic situations; for example, rail or air travel between or within London, Paris, Hong Kong; a food web representing a simple eco-system; metabolic networks and other chemical or biological structures
• representing First Nations Australians’ kinship systems using network diagrams and exploring the significance of relationships to Country/Place

Achievement Standard This Supports

This Content Descriptor contributes to the following Achievement Standard:

Year 10 ASMATY10

Year 10 Mathematics Achievement Standard

By the end of Year 10, students recognise the effect of approximations of real numbers in repeated calculations. They use mathematical modelling to solve problems involving growth and decay in financial and other applied situations, applying linear, quadratic and exponential functions as appropriate, and solve related equations, numerically and graphically. Students make and test conjectures involving functions and relations using digital tools. They solve problems involving simultaneous linear equations and linear inequalities in 2 variables graphically and justify solutions. Students interpret and use logarithmic scales representing small or large quantities or change in applied contexts. They solve measurement problems involving surface area and volume of composite objects. Students apply Pythagoras’ theorem and trigonometry to solve practical problems involving right-angled triangles. They identify the impact of measurement errors on the accuracy of results. Students use mathematical modelling to solve practical problems involving proportion and scaling, evaluating and modifying models, and reporting assumptions, methods and findings. They use deductive reasoning, theorems and algorithms to solve spatial problems. Students interpret networks used to represent practical situations and describe connectedness. They plan and conduct statistical investigations involving bivariate data. Students represent the distribution of data involving 2 variables, using tables and scatter plots, and comment on possible association. They analyse inferences and conclusions in the media, noting potential sources of bias. Students compare the distribution of continuous numerical data, using various displays, and discuss distributions in terms of centre, spread, shape and outliers. They apply conditional probability to solve problems involving compound events. Students design and conduct simulations involving conditional probability, using digital tools.