# Structure 5.0

●      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 = 2L + 2W, then W = P/2 − L. If A = πr2 then r = √A/π for r > 0).

●      They solve simple equations (for example, 5x + 7 = 23, 1.4x − 1.6 = 8.3, and 4x2 − 3 = 13) using tables, graphs and inverse operations.

●      They recognise and use inequality symbols.

●      They solve simple inequalities such as y ≤ 2x + 4 and decide whether inequalities such as x2 > 2y 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) = 2x − 4, xy = 24, y = 2x and y = x2 − 3 to model various situations.