The Australian Curriculum places a very heavy focus on deep-level understanding and mathematical reasoning. This means that students can no longer simply answer routine mathematical questions that look exactly the same as those they have seen before. These type of questions do not require deep-level understanding, logical reasoning, problem-solving or analytical thinking, but instead use only recall of memorised formulae or algorithms without any challenging thinking on the part of the student. The skills of mathematics are encompassed in the Proficiency Strands.

These changes mean that most maths classrooms need to change, and change significantly.

In many traditional mathematics classrooms teachers present an algorithm or formula to students, demonstrate how it works and explain its use, and then give students routine questions to practice until they have the new method memorised. In this environment there is almost never “*inquiry and active participation in challenging and engaging experiences*”, and it is therefore impossible to meet the new requirements.

The new requirements are best met though student inquiry and active participation in a problem-based teaching environment. Problem-based mathematics engages students through challenging, insightful problems, and leads them through the process of experimenting to develop new mathematical understanding by focusing on fundamental mathematical principles and patterns.

Download a free Australian Curriculum Preparation Pack here.

- Problem-based teaching is essential for the curriculum, so what does it look like?
- How Back-to-Front Maths works
- Getting started
- Free Stuff

**Content that students cover in each year:**

{filelink=3}

### Year 1:

- count, read, write, model and order numbers to 100
- count in 2s, 5s and 10s from zero
- add and subtract single-digit numbers using simple strategies (e.g. count on, partition, rearrange parts)
- recognise coins
- describe “one half”
- use informal units to measure and order length and capacity
- tell the time using half hours, and describe time duration in months, weeks, days and hours
- recognise common 2D shapes and 3D objects and describe them using terms such as corners, edges and faces
- give and interpret simple directions to familiar places indicating both the direction and the distance (e.g. using terms such as clockwise, anticlockwise, forwards, backwards, under, further)
- describe events using the terms will happen, won’t happen and might happen
- collect responses, and represent these using drawings or objects

{filelink=1}**Year 1 Alignment Table**

{filelink=2}**Year 1 Term Planner**

### Year 2:

- count, read, write, model and order numbers to 1000 and partition numbers to 1000 using hundreds, tens and ones
- count forwards and backwards in 2s, 3s, 5s and 10s from any starting point
- add and subtract simple numbers using strategies such as building to 10, tens facts, doubles, turn arounds, adding ten, ten frames and twenty frames
- represent multiplication as groups, arrays and repeated addition, represent division as grouping equal sets
- recognise and count coins and notes
- recognise and describe halves, quarters and eighths of objects and collections
- use uniform informal units to measure, compare and order objects according to length, area, volume, mass and capacity
- tell the time using quarter hours, including “to” and “past”
- Name and order the seasons and months, and connect these to the seasons used by Aboriginal people. Use a calendar.
- draw common 2D shapes and describe 3D objects using terms such as corners, edges and faces
- interpret simple maps and directions to familiar places
- investigate single-step flips and slides, and identify half and quarter turns
- describe events as likely, unlikely, certain and impossible
- collect data, and make lists, tables and picture graphs

{filelink=4}**Year 2 Alignment Table**

{filelink=5}**Year 2 Term Planner**

### Year 3:

- count, read, write, model and order numbers to 10 000 and partition numbers to 10 000 using hundreds, tens and ones
- identify odd and even numbers
- identify, complete and make number patterns using addition and subtraction
- recall addition and subtraction facts for single-digit numbers
- add and subtract numbers using regrouping
- recall multiplication and division facts for 2s, 3s, 5s and 10s
- represent and solve problems using any one of the four operations
- represent amounts of money in different ways, and count change to 5 cents
- recognise and describe multiple halves, thirds, quarters, fifths and eighths up to one whole
- use metric units to measure, compare and order objects according to length, mass and capacity
- tell the time using minutes, explore time units connections (e.g. 60 seconds in a minute)
- model and describe 3D objects
- interpret and make simple grid maps
- describe angles and compare their sizes using ‘turns’ language
- identify symmetry
- conduct chance experiments describe results
- identify questions and collect data
- organise data and make and interpret lists, tables, picture graphs and simple column graphs

{filelink=6}**Year 3 Alignment Table**

{filelink=7}**Year 3 Term Planner**

#### Year 4:

- count, read, write, model and order numbers to 100 000 and partition numbers to 100 000 using hundreds, tens and ones
- identify odd and even numbers
- identify, complete and make number patterns using multiplication
- recall multiplication and division facts to 10 x 10
- represent and solve problems using any one of the four operations (no remainders for division)
- represent purchases using money, including in another currency
- investigate equivalent fractions
- count halves, thirds and quarters to more than a whole, including mixed numbers
- introduce tenths and hundredths using decimal notation and connect these to fractions
- measure length, mass, capacity and temperature on instruments with scales
- use metric units for area and volume, including comparing the area of regular and irregular 2D shapes
- convert between time units, and solve time problems including using am and pm
- describe compare 2D shape combinations
- interpret and make simple grid maps using scales, directions and legends
- describe angles as smaller to, equal to, or greater than a right angle
- create symmetrical patterns
- order chance events, and describe their effect on other chance events
- choose data collection methods
- organise data and make and interpret tables, picture graphs and column graphs, and evaluate the effectiveness of displays

{filelink=8}**Year 4 Alignment Table**

{filelink=9}**Year 4 Term Planner**

### Year 5:

- identify multiples and factors
- multiply large numbers by one or two digit numbers
- divide by single digits, with remainders
- represent and solve problems and use estimation and rounding
- make simple budgets
- order fractions
- add and subtract fractions with the same denominators
- introduce thousandths using decimal notation and order decimal numbers
- make patterns using fractions, decimals and whole numbers
- choose units to measure length, area, mass, capacity and volume
- calculate area of rectangles
- convert between 12 and 24 hour time
- use nets and other 2D representations for 3D objects
- use grid references for directions and locations
- construct, measure and describe angles using degrees
- translate, reflect, rotate and enlarge 2D shapes, and identify symmetry (line and rotational)
- represent outcomes of events with “equal chances” using fractions between 0 and 1
- pose questions and collect data that can be grouped using categories or numerical means
- make and interpret tables, column graphs and dot plots, and describe sets of data within the one context

{filelink=10}**Year 5 Alignment Table**

{filelink=11}**Year 5 Term Planner**

### Year 6:

- identify and describe prime, composite, square and triangular numbers
- solve problems using all four operations with whole numbers
- introduce negative numbers
- add and subtract decimal numbers
- multiply whole numbers by decimals, divide numbers with terminating decimals, including by powers of 10
- add and subtract fractions with related denominators
- find a fraction of another quantity (whole numbers only)
- convert between equivalent fractions, decimals and percentages
- use percentage to investigate discounts (10%, 25% and 50%)
- use order of operations and brackets
- use decimal numbers with the metric system of measurement
- convert between units for length, mass and capacity
- connect volume and capacity
- investigate perimeter and area of shapes
- interpret timetables
- make prisms and pyramids
- define angle types (acute, obtuse, right, reflex) using degrees
- investigate angles on a straight line, angles at a point and vertically opposite angles and use these to find unknown angles
- combine translations, reflections and rotations of 2D shapes
- introduce Cartesian coordinate system
- represent probabilities using fractions, decimals and percentages, and compare expected frequencies with observed frequencies in experiments
- interpret and compare data sources (including secondary data)
- make and side-by-side column graphs, pie charts and dot plots with one-to-many correspondence

{filelink=12}**Year 6 Alignment Table**

{filelink=13}**Year 6 Term Planner**

### Year 7:

- investigate index notation, powers and square roots for perfect squares
- solve problems using the associative, commutative and distributive laws
- compare, order, add and subtract using negative numbers
- add and subtract fractions with unrelated denominators
- multiply and divide fractions and decimals
- round decimal numbers
- convert between equivalent fractions, decimals and percentages
- add and subtract fractions with related denominators
- express one quantity as a fraction or percentage of another, and find a fraction or percentage of another number
- use simple ratios
- calculate best buys and discounts
- use letters to represent variables in algebraic equations
- substitute values in for the variables in algebraic equations
- use order of operations and brackets with algebraic equations
- plot points on the Cartesian plane using tables of values using all four quadrants
- graph and solve simple linear equations from realistic situations
- find areas of rectangles, triangles and parallelograms using formulae
- find volumes of rectangular prisms and cubes using formulae
- draw combined prisms and pyramids
- investigate parallel lines, and the corresponding, alternate and cointerior angles formed when a set of parallel lines is crossed by a transversal
- classify triangles and quadrilaterals according to their properties, and explore the relationships between the sum of their angles
- translate, reflect and rotate of 2D shapes by multiples of 90
^{o}on the Cartesian plane, and identify line and rotational symmetry - list sample space, and assign probabilities between 0 and 1
- investigate large-count or continuous data
- make and interpret stem and leaf plots and dot plots
- calculate the mean, median, mode and range for a data set, and compare these measures

{filelink=14}**Year 7 Alignment Table**

{filelink=15}**Year 7 Term Planner**