recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers with and without using digital tools
Elaborations
investigating the real number system by representing the relationships between irrational numbers, rational numbers, integers and natural numbers and discussing the difference between exact representations and approximate decimal representations of irrational numbers
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 formax+b>c , for example, 1.2x-5.4>10.8
using positive and negative rational numbers to solve problems, for example, for financial planning such as budgeting
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=πr2 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 5π units, and the exact area is π(52)2=254π square units, which rounds to 19.63 square units, correct to 2 decimal places
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, 2 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
Code
VC2M9N01
Curriculum resources and support
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