● At Level 5 students identify collections of numbers as subsets of natural numbers, integers, rational numbers and real numbers.

● They use venn diagrams and tree diagrams to show the relationships of intersection, union, inclusion (subset) and complement between the sets.

● They list the elements of the set of all subsets (power set) of a given finite set and comprehend the partial-order relationship between these subsets with respect to inclusion (for example, given the set {*a*, *b*, *c*} the corresponding power set is {Ø, {*a*}, {*b*}, {*c*}, {*a*, *b*}, {*b*, *c*}, {*a*, *c*}, {*a*, *b*, *c*}}.)

● They test the validity of statements formed by the use of the connectives *and, or, not,* and the quantifiers *none*, *some* and *all*, (for example, ‘*some* natural numbers can be expressed as the sum of two squares’).

● They apply these to the specification of sets defined in terms of one or two attributes, and to searches in data-bases.

● Students apply the commutative, associative, and distributive properties in mental and written computation (for example, 24 × 60 can be calculated as 20 × 60 + 4 × 60 or as 12 × 12 × 10).

● They use exponent laws for multiplication and division of power terms (for example 23 × 25 = 28, 20 = 1, 23 ÷ 25 = 2−2, (52)3 = 56 and (3 × 4)2 = 32 × 42).

● Students generalise from perfect square and difference of two square number patterns(for example, 252 = (20 + 5)2 = 400 + 2 × (100) + 25 = 625. And 35 × 25 = (30 + 5) (30 − 5) = 900 − 25 = 875)

● Students recognise and apply simple geometric transformations of the plane such as translation, reflection, rotation and dilation and combinations of the above, including their inverses.

● They identify the identity element and inverse of rational numbers for the operations of addition and multiplication (for example, 1/2 + −1/2 = 0 and 2/3 × 3/2 = 1).

● Students use inverses to rearrange simple mensuration formulas, and to find equivalent algebraic expressions (for example, if *P* = 2*L* + 2*W*, then *W* = *P*/2 − L. If *A* = *πr*2 then *r* = √*A*/*π* for *r* > 0).

● They solve simple equations (for example, 5*x* + 7 = 23, 1.4*x* − 1.6 = 8.3, and 4*x*2 − 3 = 13) using tables, graphs and inverse operations.

● They recognise and use inequality symbols.

● They solve simple inequalities such as *y* ≤ 2*x* + 4 and decide whether inequalities such as *x*2 > 2*y* are satisfied or not for specific values of *x* and *y*.

● Students identify a function as a one-to-one correspondence or a many-to-one correspondence between two sets.

● They represent a function by a table of values, a graph, and by a rule.

● They describe and specify the independent variable of a function and its domain , and the dependent variable and its range.

● They construct tables of values and graphs for linear functions. They use linear and other functions such as *f*(*x*) = 2*x* − 4, *xy* = 24, *y* = 2*x* and *y* = *x*2 − 3 to model various situations.