Structure

knowledge of the effect of multiplying by ten on the location of the decimal point in a number use of lists, venn diagrams and grids to record items that have a certain attribute selection of a sample from a population recognition that one set is or is not a subset of another use of ‘=’ to indicate equivalence or the result of a computation variation of order and grouping of addition (commutative and associative property) to facilitate computations; for example, 3 + 5 + 7 + 5 = 3 + 7 + 5 + 5 =10 +10= 20 specification of all possible outcomes of a simple chance event construction of number sentences calculations using notation such as ‘3 + 5 − 2 =’ use of distributive property in calculations; for example, 6 × 37 = 6 × 30 + 6 × 7 construction of lists, venn diagrams and grids to be used for recording combinations of two attributes • **Continuum links** • Properties of Operations || **3.25** conversion between venn diagrams and karnaugh maps as representations of relationships between two sets recognition and completion of patterns formed by constant addition or subtraction use of add and subtract as inverse operations to solve simple word equations such as ‘I am thinking of a number. If I add 6 I get 18, what number did I start with?’ use of trial and error to find a missing number in a number sentence; for example, 4 × ? + 6 = 22 use of language to describe change in everyday items or attributes whose value varies over time incorporation of tables of information relating pairs of everyday variables sorting of sequences into certain types (constant addition, constant multiplication, fibonacci, square, triangular) use of division and multiplication as inverses; for example, multiplication by 25 can be carried out as ‘multiplication by 100 followed by division by 4’ consistent and correct use of conventions for order of operations construction of diagrams illustrating the possible relationship between two sets and the truth of statements involving the words all, some or none construction of number patterns and tables of values from an equation or a recurrence relation recognition that a given number pattern can be represented by an apparently unrelated equation and recurrence relation; for example, 5, 9, 13 … represented by ‘multiply position in the pattern (first, second, third ...) by 4 and add 1’ and ‘start with 5 then repeatedly add 4 to the previous term’ understanding of zero and its characteristic of not having a multiplicative inverse, and the consequences of attempting division by zero
 * **Progressing towards level 3** || **Progressing towards level 4** || **Progressing towards level 5** || **Progressing towards level 6** ||
 * **2.25**
 * 2.5 **
 * 2.75**
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 * 3.75**

• Rules for Sequences • Equivalence in number sentences || **4.25** use of inverse and identity when subtracting and dividing rational numbers identification of domain and range; independent and dependent variable and their role in graphing representation of data by plotting points in the first quadrant and explanation of key features collection and classification of sets of data as either linear or non-linear depending on whether the slope is constant interpretation of a letter as a symbol for any one of a set of numbers and use in symbolic description of relationships use of inequality, equality, approximately equal and not equal, including in symbolic expressions translation from verbal description to algebraic representation, and of the structure of algebraic expressions; for example, if $500 is shared between n people, each receives 500/n solution of simple linear equations using tables, graphs and inverse operations (backtracking) representation of inequalities as parts of the number line; for example, x < −5 translation between symbolic rules, patterns and tables for linear functions lists of sets in the power set of a given set and knowledge that the total number of set equals 2n for n elements in the given set solution of equations such as x² = 17 as required in measurement situations; for example, using pythagoras theorem graphical representation of simple inequalities such as y ≤ 2x + 4 selection of a type of function (linear, exponential, quadratic) to match a set of data translation between forms (table, graph, rule, recurrence relation) of representation of a function
 * • Continuum links**
 * 4.5**
 * 4.75**


 * • Continuum links**

• Structure of algebraic expressions

• Manipulating symbols || **5.25** relationships between two sets using a venn diagram, tree diagram and karnaugh map factorisation of algebraic expressions by extracting a common factor solution of equations by graphical methods identification of linear, quadratic and exponential functions by table, rule and graph in the first quadrant knowledge of the quantities represented by the constants m and c in the equation y = mx + c expression of the relationship between sets using membership, ∈, complement, ′, intersection, ∩, union, ∪, and subset, ⊂, for up to two sets representation of numbers in a geometric sequence (constant multiple, constant percentage change) as an exponential function knowledge of the relationship between geometrical and algebraic forms for transformations expansion of products of algebraic factors, for example, (2x + 1)(x − 5) = 2x² − 9x − 5 equivalence between algebraic forms; for example, polynomial, factorised and turning point form of quadratics use of inverse operations to re-arrange formulas to change the subject of a formula expression of irrational numbers in both exact and approximate form factorisation of simple quadratic expressions and use of the null factor law for solution of equations testing of sequences by calculating first difference, second difference or ratio between consecutive terms to determine existence of linear, quadratic and exponential functions formulation of pairs of simultaneous equations and their graphical solution representation of algebraic models for sets of data using technology
 * 5.5**
 * 5.75**

Exponential functions || || Maths Tasks || Maths Tasks || Pre test Post test** ||  ||   ||   || Type in the content of your page here.
 * • Continuum links**
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