AC9M9N01 Year 9 Mathematics

Content descriptor recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools

Elaborations

• • Elaboration 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
• • Elaboration 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
• • Elaboration using positive and negative rational numbers to solve problems; for example, for financial planning such as budgeting
• • Elaboration 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(5/2)^2=25/4\mathrm\pi square units which rounds to 19.63 square units, correct to 2 decimal places
• • Elaboration 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