The proficiency strands understanding, fluency, problem-solving and reasoning are an integral part of mathematics content across the three content strands: number and algebra, measurement and geometry, and statistics and probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. The achievement standards reflect the content and encompass the proficiencies.
At this year level:
- understanding includes making connections between representations of numbers, partitioning and combining numbers flexibly, extending place value to decimals, using appropriate language to communicate times and describing properties of symmetrical shapes.
- fluency includes recalling multiplication tables, communicating sequences of simple fractions, using instruments to measure accurately, creating patterns with shapes and their transformations and collecting and recording data.
- problem-solving includes formulating, modelling and recording authentic situations involving operations, comparing large numbers with each other, comparing time durations and using properties of numbers to continue patterns.
- reasoning includes using generalising from number properties and results of calculations, deriving strategies for unfamiliar multiplication and division tasks, comparing angles, communicating information using graphical displays and evaluating the appropriateness of different displays.
Number and Algebra
Investigate and use the properties of odd and even numbers - ACMNA071
- using the four operations with pairs of odd or even numbers or one odd and one even number, then using the relationships established to check the accuracy of calculations.
Recognise, represent and order numbers to at least tens of thousands - ACMNA072
- reproducing five-digit numbers in words using their numerical representations, and vice versa
Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems - ACMNA073
- recognising and demonstrating that the place-value pattern is built on the operations of multiplication or division of tens.
Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 - ACMNA074
- recognising that number sequences can be extended indefinitely and determining any patterns in the sequences.
Recall multiplication facts up to 10 × 10 and related division facts - ACMNA075
- using known multiplication facts to calculate related division facts.
Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder - ACMNA076
- using known facts and strategies, such as commutativity, doubling and halving for multiplication, and connecting division to multiplication when there is no remainder.
Investigate equivalent fractions used in contexts - ACMNA077
- exploring the relationship between families of fractions (halves, quarters and eighths or thirds and sixths) by folding a series of paper strips to construct a fraction wall.
Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line - ACMNA078
- converting mixed numbers to improper fractions and vice versa
- investigating the use of fractions and sharing as a way of managing Country: for example taking no more than half the eggs from a nest to protect future bird populations.
Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation - ACMNA079
- using division by 10 to extend the place-value system.
- using knowledge of fractions to establish equivalences between fractions and decimal notation.
Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies - ACMNA080
- recognizing that not all countries use dollars and cents, eg India uses rupees.
- carrying out calculations in another currency as well as in dollars and cents and identifying both as decimal systems.
Explore and describe number patterns resulting from performing multiplication - ACMNA081
- identifying examples of number patterns in everyday life
Solve word problems by using number sentences involving multiplication or division where there is no remainder - ACMNA082
- representing a word problem as a number sentence
- writing a word problem using a given number sentence
Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction - ACMNA083
- writing number sentences to represent and answer questions such as: ‘When a number is added to 23 the answer is the same as 57 minus 19. What is the number?’
- using partitioning to find unknown quantities in number sentences.
Measurement & Geometry
Use scaled instruments to measure and compare lengths, masses, capacities and temperatures - ACMMG084
- reading and interpreting the graduated scales on a range of measuring instruments to the nearest graduation
Compare objects using familiar metric units of area and volume - ACMMG290
- comparing areas using grid paper
- comparing volume using centicubes.
- recognising that metric units are not the only units used throughout the world, for example measuring the area of floor space using tatami mats (Japan), using squares for room and house area (Australia)
Convert between units of time - ACMMG085
- identifying and using the correct operation for converting units of time
Use ‘am’ and ‘pm’ notation and solve simple time problems - ACMMG086
- calculating the time spent at school during a normal school day.
- calculating the time required to travel between two locations.
- determining arrival time given departure time
Compare the areas of regular and irregular shapes by informal means - ACMMG087
- comparing areas using metric units, such as counting the number of square centimetres required to cover two areas by overlaying the areas with a grid of centimetre squares.
Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies - ACMMG088
Identifying common two-dimensional shapes that are part of a composite shape by re-creating it from these shapes.
- creating a two- dimensional shapes from verbal or written instructions.
Use simple scales, legends and directions to interpret information contained in basic maps - ACMMG090
- identifying the scale used on maps of cities and rural areas in Australia and a city in Indonesia and describing the difference.
- using directions to find features on a map.
Create symmetrical patterns, pictures and shapes with and without digital technologies - ACMMG091
- using stimulus materials such as the motifs in Central Asian textiles, Tibetan artefacts, Indian lotus designs and symmetry in Yolngu or Central and Western Desert art
Compare angles and classify them as equal to, greater than, or less than, a right angle - ACMMG089
- creating angles and comparing them to a right angle using digital technologies
STATISTICS & PROBABILITY
Describe possible everyday events and order their chances of occurring - ACMSP092
- using lists of events familiar to students and ordering them from ‘least likely’ to ‘most likely’ to occur.
Identify everyday events where one cannot happen if the other happens - ACMSP093
- using examples such as weather, which cannot be dry and wet at the same time.
Identify events where the chance of one will not be affected by the occurrence of the other - ACMSP094
- explaining why the probability of a new baby being either a boy or a girl does not depend on the sex of the previous baby.
Select and trial methods for data collection, including survey questions and recording sheets - ACMSP095
- comparing the effectiveness of different methods of collecting data
- choosing the most effective way to collect data for a given investigation
Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values - ACMSP096
- exploring ways of presenting data and showing the results of investigations
- investigating data displays using many-to-one correspondence
Evaluate the effectiveness of different displays in illustrating data features including variability - ACMSP097
- interpreting data representations in the media and other forums in which symbols represent more than one data value.
- suggesting questions that can be answered by a given data display and using the display to answer questions.
By the end of Year 4, students choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to two decimal places. Students solve simple purchasing problems. They identify and explain strategies for finding unknown quantities in number sentences. They describe number patterns resulting from multiplication. Students compare areas of regular and irregular shapes using informal units. They solve problems involving time duration. They interpret information contained in maps. Students identify dependent and independent events. They describe different methods for data collection and representation and evaluate their effectiveness.
Students use the properties of odd and even numbers. They recall multiplication facts to 10 x 10 and related division facts. Students locate familiar fractions on a number line. They continue number sequences involving multiples of single digit numbers. Students use scaled instruments to measure temperatures, lengths, shapes and objects. They convert between units of time. Students create symmetrical shapes and patterns. They classify angles in relation to a right angle. Students list the probabilities of everyday events. They construct data displays from given or collected data.