Number
The mathematics curriculum intended by this statement will provide opportunities for students to:
• develop an understanding of numbers, the ways they are represented, and the quantities for which they stand;
• develop accuracy, efficiency, and confidence in calculating — mentally, on paper, and with a calculator;
• develop the ability to estimate and to make approximations, and to be alert to the reasonableness of results and measurements.
Algebra
The mathematics curriculum intended by this statement will provide opportunities for students to:
• recognise patterns and relationships in mathematics and the real world, and be
able to generalise from these;
• develop the ability to think abstractly and to use symbols, notation, and graphs and
diagrams to represent and communicate mathematical relationships, concepts,
and generalisations;
• use algebraic expressions confidently to solve practical problems. / Number and Algebra. Number involves calculating and estimating, using appropriate mental, written, or machine calculation methods in flexible ways. It also involves knowing when it is appropriate to use estimation and being able to discern whether results are reasonable. Algebra involves generalising and representing the patterns and relationships found in numbers, shapes, and measures.
Level 1
Within a range of meaningful contexts, students should be able to: / In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically.
They will solve problems and model situations that require them to:
Exploring number• make up, tell, and record number stories, up to 9, about given objects and sequence pictures;
• form a set of up to 20 objects;
• read and write any 2-digit whole number;
• rote count to at least 50.
Exploring computation and estimation
• make sensible estimates and check the reasonableness of answers;
• model and explain addition calculations with a sum of up to 20;
• using up to 20 objects, model and explain subtraction calculations;
• find, by practical means, one half and one quarter of a shape, and a half of a set of objects.
Exploring patterns and relationships
• make and describe repeating and sequential patterns;
• continue a repeating and sequential pattern;
• illustrate and talk about relationships.
Exploring equations and expressions
• write number sentences, using = , from story contexts. /
Number strategies
NA1-1Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.Number knowledge
NA1-2Know the forward and backward counting sequences of whole numbers to 100.NA1-3Know groupings with five, within ten, and with ten.
Equations and expressions
NA1-4Communicate and explain counting, grouping, and equal-sharing strategies, using words, numbers, and pictures.
Patterns and relationships
NA1-5Generalise that the next counting number gives the result of adding one object to a set and that counting the number of objects in a set tells how many.NA1-6Create and continue sequential patterns.
Level 2
Within a range of meaningful contexts, students should be able to: / In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically.They will solve problems and model situations that require them to:
Exploring number• read any 3-digit whole number;
• explain the meaning of the digits in 2- or 3-digit whole numbers;
• order any set of three or more whole numbers (up to 99);
• write and solve comparison problems;
• write and solve story problems which involve halves, quarters, thirds, and fifths.
Exploring computation and estimation
• make sensible estimates and check the reasonableness of answers;
• recall the basic addition and subtraction facts;
• mentally perform calculations involving addition and subtraction;
• demonstrate the ability to use the multiplication facts;
• write and solve story problems which involve whole numbers, using addition,
subtraction, multiplication, or division;
• write and solve story problems which require a choice of any combination of the four arithmetic operations.
Exploring patterns and relationships
• continue a sequential pattern and describe a rule for this;
• use graphs to illustrate relationships.
Exploring equations and expressions
• use the mathematical symbols =, <, > for the relationships “is equal to”, “is less than”, and “is greater than”. /
Number strategies
NA2-1Use simple additive strategies with whole numbers and fractions.Number knowledge
NA2-2Know forward and backward counting sequences with whole numbers to at least 1000.NA2-3Know the basic addition and subtraction facts.
NA2-4Know how many ones, tens, and hundreds are in whole numbers to at least 1000.
NA2-5Know simple fractions in everyday use.
Equations and expressions
NA2-6Communicate and interpret simple additive strategies, using words, diagrams (pictures), and symbols.Patterns and relationships
NA2-7Generalise that whole numbers can be partitioned in many ways.NA2-8Find rules for the next member in a sequential pattern.
Level 3
Within a range of meaningful contexts, students should be able to: / In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically.
They will solve problems and model situations that require them to:
Exploring number• explain the meaning of the digits in any whole number;
• explain the meaning of the digits in decimal numbers with up to 3 decimal places;
• order decimals with up to 3 decimal places.
Exploring computation and estimation
• make sensible estimates and check the reasonableness of answers;
• recall the basic multiplication facts;
• write and solve problems which involve whole numbers and decimals and which require a choice of one or more of the four arithmetic operations;
• solve practical problems which require finding fractions of whole number and decimal amounts.
Exploring patterns and relationships
• describe in words, rules for continuing number and spatial sequential patterns;
• make up and use a rule to create a sequential pattern;
• state the general rule for a set of similar practical problems;
• use graphs to represent number, or informal, relations.
Exploring equations and expressions
• solve problems of the type □ + 15 = 39 /
Number strategies
NA3-1Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.Number knowledge
NA3-2Know basic multiplication and division facts.NA3-3Know counting sequences for whole numbers.
NA3-4Know how many tenths, tens, hundreds, and thousands are in whole numbers.
NA3-5Know fractions and percentages in everyday use.
Equations and expressions
NA3-6Record and interpret additive and simple multiplicative strategies, using, words, diagrams, and symbols, with an understanding of equality.Patterns and relationships
NA3-7Generalise the properties of addition and subtraction with whole numbers.NA3-8Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns.
Level 4
Within a range of meaningful contexts, students should be able to: / In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically.They will solve problems and model situations that require them to:
Exploring number• explain the meaning of negative numbers;
• explain the meaning and evaluate powers of whole numbers;
• find fractions equivalent to one given;
• express a fraction as a decimal, and vice versa;
• express a decimal as a percentage, and vice versa;
• express quantities as fractions or percentages of a whole.
Exploring computation and estimation
• make sensible estimates and check the reasonableness of answers;
• write and solve problems involving decimal multiplication and division;
• find a given fraction or percentage of a quantity;
• explain satisfactory algorithms for addition, subtraction, and multiplication;
• demonstrate knowledge of the conventions for order of operations.
Exploring patterns and relationships
• find a rule to describe any member of a number sequence and express it in words;
• use a rule to make predictions;
• sketch and interpret graphs on whole number grids which represent simple everyday situations.
Exploring equations and expressions
• find and justify a word formula which represents a given practical situation;
• solve simple linear equations such as 2 □ + 4 = 16. /
Number strategies and knowledge
NA4-1Use a range of multiplicative strategies when operating on whole numbers.NA4-2Understand addition and subtraction of fractions, decimals, and integers.
NA4-3Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
NA4-4Apply simple linear proportions, including ordering fractions.
NA4-5Know the equivalent decimal and percentage forms for everyday fractions.
NA4-6Know the relative size and place value structure of positive and negative integers and decimals to three places.
Equations and expressions
NA4-7Form and solve simple linear equations.Patterns and relationships
NA4-8Generalise properties of multiplication and division with whole numbers.NA4-9Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.
Level 5
Within a range of meaningful contexts, students should be able to: / In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically.They will solve problems and model situations that require them to:
Exploring number• convert numbers expressed in standard form to ordinary form, and vice versa;
• round numbers sensibly;
• express the values of square roots in approximate and exact forms.
Exploring computation and estimation
• make sensible estimates and check the reasonableness of results;
• solve practical problems involving decimals and percentages;
• solve problems involving positive and negative numbers, using practical activities or
models if needed;
• express one quantity as a percentage of another;
• increase and decrease quantities by given percentages, including mark up, discount, and GST;
• share quantities in given ratios.
Exploring patterns and relationships
• generate patterns from a structured situation, find a rule for the general term, and
express it in words and symbols;
• generate a pattern from a rule;
• sketch and interpret graphs which represent everyday situations;
• graph linear rules and interpret the slope and intercepts on an integer co-ordinate
system.
Exploring equations and expressions
• evaluate linear expressions by substitution;
• solve linear equations;
• combine like terms in algebraic expressions;
• simplify algebraic fractions;
• factorise and expand algebraic expressions;
• use equations to represent practical situations. /
Number strategies and knowledge
NA5-1Reason with linear proportions.NA5-2Use prime numbers, common factors and multiples, and powers (including square roots).
NA5-3Understand operations on fractions, decimals, percentages, and integers.
NA5-4Use rates and ratios.
NA5-5Know commonly used fraction, decimal, and percentage conversions.
NA5-6Know and apply standard form, significant figures, rounding, and decimal place value.
Equations and expressions
NA5-7Form and solve linear and simple quadratic equations.Patterns and relationships
NA5-8Generalise the properties of operations with fractional numbers and integers.NA5-9Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.
Level 6
Within a range of meaningful contexts, students should be able to: / In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically.They will solve problems and model situations that require them to:
Exploring computation and estimation• perform basic operations on fractions and mixed numbers;
• classify numbers as whole, integer, rational, or irrational;
• devise a strategy to solve a number problem;
• estimate and calculate answers, making efficient use of a calculator, where appropriate, as part of solving a problem;
• discuss the reasonableness and meaning of the answers obtained in solving a problem.
Exploring patterns and relationships
• form and interpret a graph;
• generate linear and quadratic patterns and find and justify the rule;
• generate a pattern from a rule;
• graph linear, quadratic, and exponential functions, and relations of the form x2 + y2 = r2 and xy = c
Exploring equations and expressions
• form and solve linear equations, simultaneous equations, and simple quadratic equations;
• substitute values into formulae. /
Number strategies and knowledge
NA6-1Apply direct and inverse relationships with linear proportions.NA6-2Extend powers to include integers and fractions.
NA6-3Apply everyday compounding rates.
NA6-4Find optimal solutions, using numerical approaches.
Equations and expressions
NA6-5Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.Patterns and relationships
NA6-6Generalise the properties of operations with rational numbers, including the properties of exponents.NA6-7Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.
NA6-8Relate rate of change to the gradient of a graph.
Level 7
Within a range of meaningful contexts, students should be able to: / In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically.
They will solve problems and model situations that require them to:
Exploring patterns and relationships• use sequences and series to model real problems and interpret their solutions;
• describe and use arithmetic or geometric sequences or series in common situations;
• model a variety of situations, using graphs;
• sketch graphs and investigate the graph of a function, using a calculator and plotting points if necessary;
• use graphical methods to investigate a pattern in data and, where appropriate,
identify its algebraic form;
• find by inspection, and interpret, maxima, minima, points of inflection, asymptotes, and discontinuities for given graphs;
• describe the relationship between members of families of curves in terms of transformations.
Exploring equations and expressions
• write appropriate equation(s) or inequation(s) to describe a practical situation;
• choose suitable strategies (graphic, numeric, algebraic, and trigonometric) for finding solutions to equations or inequations, and interpret the results;
• carry out appropriate manipulation and simplification of algebraic expressions. /
Patterns and relationships
M7-1Apply co-ordinate geometry techniques to points and lines.M7-2Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs.
M7-3Use arithmetic and geometric sequences and series.
M7-4Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions.
M7-5Choose appropriate networks to find optimal solutions.
Equations and expressions
M7-6Manipulate rational, exponential, and logarithmic algebraic expressions.M7-7Form and use linear, quadratic, and simple trigonometric equations.
M7-8Form and use pairs of simultaneous equations, one of which may be non-linear.
Level 8
Within a range of meaningful contexts, students should be able to: / In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically.They will solve problems and model situations that require them to:
Exploring patterns and relationships• use sequences and series to model real or simulated situations and interpret the findings;
• investigate and interpret convergence of sequences and series;
• choose and carry out appropriate manipulation and graphical representation of complex numbers;
• model real and simulated situations, using linear programming techniques, and obtain and interpret optimal solutions;
• use graphical techniques to explore and illustrate y = xa, y = ax + b
cx + d and piece-wise functions;
• choose an appropriate model for real data, including the use of log-log and semi-log
techniques, and analyse and interpret the results;
• sketch the graphs of inverse and/or reciprocal functions and explain relationships
between them and the original functions.
Exploring equations and expressions
• investigate and find numbers of arrangements and selections from a number of objects;
• expand and use binomial expressions for small positive integral exponents;
• use simultaneous equations to model real and simulated situations, and interpret their solutions in a given context;
• use appropriate numerical methods and technology to solve non-linear equations;
• use and prove the factor and remainder theorems;
• solve any quadratic equation and equations of the form zn = a (for n a positive integer) and z = r cisø
• carry out the manipulation necessary to use trigonometric expressions in other areas of mathematics;
• find solutions, including the general solution, for trigonometric equations. /
Patterns and relationships
M8-1Apply the geometry of conic sections.M8-2Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions.
M8-3Use permutations and combinations.
M8-4Use curve fitting, log modelling, and linear programming techniques.
M8-5Develop network diagrams to find optimal solutions, including critical paths.
Equations and expressions
M8-6Manipulate trigonometric expressions.M8-7Form and use trigonometric, polynomial, and other non-linear equations.
M8-8Form and use systems of simultaneous equations, including three linear equations and three variables, and interpret the solutions in context.
M8-9Manipulate complex numbers and present them graphically.
Only in old / In both / Only In new
1
2
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4
5
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7
8
NUMBER STRATEGIES AND KNOWLEDGE
3 / 4 / 5 / 6
Number strategies
NA3-1Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.Number knowledge
NA3-2Know basic multiplication and division facts.NA3-3Know counting sequences for whole numbers.
NA3-4Know how many tenths, tens, hundreds, and thousands are in whole numbers.
NA3-5Know fractions and percentages in everyday use. / NA4-1Use a range of multiplicative strategies when operating on whole numbers.
NA4-2Understand addition and subtraction of fractions, decimals, and integers.
NA4-3Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
NA4-4Apply simple linear proportions, including ordering fractions.
NA4-5Know the equivalent decimal and percentage forms for everyday fractions.
NA4-6Know the relative size and place value structure of positive and negative integers and decimals to three places. / NA5-1Reason with linear proportions.
NA5-2Use prime numbers, common factors and multiples, and powers (including square roots).
NA5-3Understand operations on fractions, decimals, percentages, and integers.
NA5-4Use rates and ratios.
NA5-5Know commonly used fraction, decimal, and percentage conversions.
NA5-6Know and apply standard form, significant figures, rounding, and decimal place value. / NA6-1Apply direct and inverse relationships with linear proportions.
NA6-2Extend powers to include integers and fractions.
NA6-3Apply everyday compounding rates.
NA6-4Find optimal solutions, using numerical approaches.
EQUATIONS AND EXPRESSIONS
3 / 4 / 5 / 6
NA3-6Record and interpret additive and simple multiplicative strategies, using, words, diagrams, and symbols, with an understanding of equality. / NA4-7Form and solve simple linear equations. / NA5-7Form and solve linear and simple quadratic equations. / NA6-5Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.