AC9M9N01
See also: Learning Areas / Mathematics / Mathematics / Number / Year 9
recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools
Elaborations
- AC9M9N01_E1 - investigating the real number system by representing the relationships between irrationals, rationals, integers and natural numbers and discussing the difference between exact representations and approximate decimal representations of irrational numbers
- AC9M9N01_E2 - using a real number line to indicate the solution interval for inequalities of the form \(ax+b<c\) ; for example, \(2x+7<0\), or of the form \(ax+b>c\); for example, \(1.2x-5.4>10.8\)
- AC9M9N01_E3 - using positive and negative rational numbers to solve problems; for example, for financial planning such as budgeting
- AC9M9N01_E4 - solving problems involving the substitution of real numbers into formulas, understanding that solutions can be represented in exact form or as a decimal approximation, such as calculating the area of a circle using the formula \(A=\mathrm{π}r^2\) and specifying the answer in terms of \(π\) as an exact real number; for example, the circumference of a circle with diameter \(5\) units is \(5\mathrm\pi\) units, and the exact area is \(\mathrm\pi(\frac52)^2=\frac{25}4\mathrm\pi\) square units which rounds to \(19.63\) square units, correct to \(2\) decimal places
- AC9M9N01_E5 - investigating the position of rational and irrational numbers on the real number line, using geometric constructions to locate rational numbers and square roots on a number line; for example, \(\sqrt2\) is located at the intersection of an arc and the number line, where the radius of the arc is the length of the diagonal of a one-unit square
Achievement Standard Components
- ASMAT901 - By the end of Year 9, students recognise and use rational and irrational numbers to solve problems.