K–10Mathematics K–10 Syllabus

Implementation for K–2 from 2023 and 3–10 from 2024

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Content

Early Stage 1

Stage 1

Stage 2

Stage 3

Stage 4

Stage 5

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Teaching advice

Examples

Indices C (Path)

MAO-WM-01
develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly
MA5-IND-P-02
describes and performs operations with surds and fractional indices (Path: Adv)

Indices C (Path)

Stn (Standard), Adv (Advanced) and Ext (Extension) have been used to suggest paths for related Stage 6 courses.

Describe surds

Describe a real number as a number that can be represented by a point on the number line
Examine the differences between rational and irrational numbers and recognise that all rational and irrational numbers are real
Convert between recurring decimals and their fractional form using digital tools
Describe the term surd as referring to irrational expressions of the form $\sqrt[n]{x}$ where $x$ is a rational number and $n$ is an integer such that $n \geq 2$ , and $x > 0$ when $n$ is even
Recognise that a surd is an exact value that can be approximated by a rounded decimal
Demonstrate that $\sqrt{x}$ is undefined for $x < 0$ and that $\sqrt{x} = 0$ when $x = 0$ using digital tools
Describe $\sqrt{x}$ as the positive square root of $x$ for $x > 0$ and $\sqrt{0} = 0$

Apply knowledge of surds to solve problems

Establish and apply the following results for $x > 0$ and $y > 0$ : ${(\sqrt{x})}^{2} = x = \sqrt{x^{2}}$ , $\sqrt{x y} = \sqrt{x} \times \sqrt{y}$ and $\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}$
Apply the 4 operations to simplify expressions involving surds
Expand and simplify expressions involving surds
Rationalise the denominators of surds of the form $\frac{a \sqrt{b}}{c \sqrt{d}}$

Describe and use fractional indices

Apply index laws to describe fractional indices as: $a^{\frac{1}{n}} = \sqrt[n]{a}$ and $a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = {(\sqrt[n]{a})}^{m}$
Translate expressions in surd form to expressions in index form and vice versa
Evaluate numerical expressions involving fractional indices including using digital tools

Related files

Life Skills