NOTE: The curriculum snippets here may not be uptodate. If you wish to see the current information for the Australian Curriculum for any year level, visit here for English or Maths. Other subjects can also be found at the same website.

Level Description

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 connecting number representations with number sequences, partitioning and combining numbers flexibly, representing unit fractions, using appropriate language to communicate times, and identifying environmental symmetry
Fluency includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing outcomes of chance experiments, interpreting maps and communicating positions
Problem-solving includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of three-dimensional objects and using number properties to continue number patterns
Reasoning includes using generalising from number properties and results of calculations, comparing angles and creating and interpreting variations in the results of data collections and data displays

Number and Algebra

Number and place value

Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051)

Identifying even numbers using skip counting by twos or by grouping even collections of objects in twos
- TUTORIALS/LESSON PLANS
  - Odd and Even – Investigation Lesson Plan – http://www.curriculum.edu.au/verve/_resources/Odd_and_even.pdf
- WORKSHEETS
  - Group in Pairs: Odd & Even – https://www.mathworksheets4kids.com/odd-even/group-pairs1.pdf
  - Grouping Items – https://www.mathworksheets4kids.com/odd-even/grouping1.pdf
  - Odd and Even Numbers Worksheet Collection – https://www.edhelper.com/odd_and_even_numbers.htm
  - Identifying Odd and Even Numbers – https://www.mathworksheets4kids.com/odd-even/identify1.pdf
- VIDEOS
  - Splash ABC – http://splash.abc.net.au/home#!/media/2549569/odd-and-even-numbers
  - Learning Odd and Even Numbers for Kids – https://www.youtube.com/watch?v=uuD5JlrMnAk&t=44s
Explaining why all numbers that end in the digits 0, 2, 4, 6 and 8 are even and that numbers ending in 1, 3, 5, 7 and 9 are odd
- TUTORIALS/LESSON PLANS
  - This is a great set of activities for understanding odd and even numbers. http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.1.1.pdf
- WORKSHEETS
  - Identifying if a Number is Odd or Even – https://www.superteacherworksheets.com/even-odd/even-odd_TWQDM.pdf?up=1466611200
  - Interactive online quiz half way down the page on working out whether a number is odd or even. http://www.aaamath.com/g25a2-evenodd.html
- VIDEOS

Recognise, model, represent and order numbers to at least 10 000 (ACMNA052)

Some general activities for this descriptor.
- TUTORIALS/LESSON PLANS
  - “Students will recognise, model, represent and order four-digit numbers. Students will also add and subtract 1, 10, 100, and 1000 to and from a four-digit number.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.1.2.pdf
Placing four-digit numbers on a number line using an appropriate scale
- TUTORIALS/ACTIVITIES
  - Classroom Ready Activities – https://www.edex.com.au/index.php/downloads/dl/file/id/50/MAV_place_value.pdf
  - Ordering 4 Digit Numbers – http://www.primaryresources.co.uk/maths/mathsB5.htm
  - Estimating the Position and Values of Four Digit Numbers – https://mathsframe.co.uk/en/resources/downloadworksheet?wsid=276&f=Estimate-4-digit-numbers-on-a-number-line.pdf
  - “Students will represent numbers to 1000 on a number line.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.4.2.pdf
- VIDEOS
Reproducing numbers in words using their numerical representations and vice versa
- TUTORIALS
  - Reading and Writing Numbers PowerPoint – http://www.primaryresources.co.uk/maths/powerpoint/Reading_and_Writing_Numbers.ppt
- ACTIVITIES
  - Write Numbers in Words Quiz – https://au.ixl.com/math/year-3/write-numbers-in-words

Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)

Recognising that 10 000 equals 10 thousands, 100 hundreds, 1000 tens and 10 000 ones
- TUTORIALS/ACTIVITIES
  - Students will revise standard partitioning and regrouping of three digit numbers up to and over 1000. http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.1.3.pdf
  - “Students will recognise, model, represent and order four-digit numbers” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.2.2.pdf
  - Also – http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.2.7.pdf
Justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations
- TUTORIALS/ACTIVITIES
  - “Students will partition and regroup numbers into standard place value partitions of thousands, hundreds, tens and ones (using 0 as a place holder).” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.2.3.pdf
  - “Students will partition and regroup numbers into standard and non-standard place value partitions of
    thousands, hundreds, tens and ones.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.3.3.pdf
  - “Students will par–on and regroup three and four digit numbers to assist addition and subtraction.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.4.3.pdf

Recognise and explain the connection between addition and subtraction (ACMNA054)

Demonstrating the connection between addition and subtraction using partitioning or by writing equivalent number sentences
- TUTORIALS/ACTIVITIES
  - “Students will understand inverse relationship between addition and subtraction and recognising patterns in number sequences and describing the rules for these patterns.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.1.4.pdf

Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

Recognising that certain single-digit number combinations always result in the same answer for addition and subtraction, and using this knowledge for addition and subtraction of larger numbers
- TUTORIALS
  - Memorising Number Facts – http://www.helpingwithmath.com/resources/math_facts.htm
  - Students will revise addition and subtraction strategies of counting on, combinations to ten, doubles, near doubles, add ten, and bridge through ten . Students will apply these strategies as well as number chunking to solve addition of two-digit numbers” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.1.5.pdf
- VIDEOS
  - Relating addition and subtraction – https://www.khanacademy.org/math/cc-1st-grade-math/cc-1st-add-subtract/cc-1st-add-subtract-10/v/relating-addition-and-subtraction
Combining knowledge of addition and subtraction facts and partitioning to aid computation (for example 57 + 19 = 57 + 20 – 1)
- TUTORIALS/ACTIVITIES
  - “Students will revise addition and subtraction strategies of counting back, combinations to ten, doubles, near doubles, friendly numbers, and bridge through ten . Students will apply these strategies to subtract 9, 8 and 7 from a given number, and extend this strategy to subtract 90, 80 and 70.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.1.6.pdf
  - “Students will further develop the addition strategy of splitting numbers, using number chunking (expanded numbers) and compensation (rounding and adjusting) to solve addition problems for two digit numbers.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.2.5.pdf
  - “Students will use addition and subtraction facts, friendly numbers and adjustment to solve subtraction problems.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.2.6.pdf
- POSTERS
  - Split Strategy – Addition

Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)

Establishing multiplication facts using number sequences
- TUTORIALS/ACTIVITIES
  - ” Students will use strategies to recall multiplication facts x0, x1, x2 and x10.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.2.4.pdf
  - “Students will have instant recall of multiplication facts 1s, 2s, 5s and 10s.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.3.1.pdf
- THE LIME ZONE TIMES TABLE WEBSITE – CURRENTLY IN TEST MODE .
  - 1’s to 12’s and mixed. Beat the 60 second clock and try to get 100%. http://www.cybecom.com.au/test/

Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057)

Writing simple word problems in numerical form and vice versa
- TUTORIALS/ACTIVITIES
  - How to Write Word Problems in Math – http://sciencing.com/write-word-problems-math-8153161.html
  - “Students will represent and solve problems involving multiplication and division.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.3.4.pdf
  - “Students will represent and solve problems involving multiplication and division.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.4.1.pdf
- WORKSHEETS
  - Number Patterns Worksheet – https://www.superteacherworksheets.com/pattern/number-patterns-basic_TZDZD.pdf?up=1466611200
Using a calculator to check the solution and reasonableness of the answer

Fractions and decimals

Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058)

Partitioning areas, lengths and collections to create halves, thirds, quarters and fifths, such as folding the same sized sheets of paper to illustrate different unit fractions and comparing the number of parts with their sizes
- TUTORIALS/LESSONS
  - Fraction Models – http://www.numeracycontinuum.com/component/content/category/13-aspect-6
- VIDEO
  - Let’s Learn Fractions – https://www.youtube.com/watch?v=n0FZhQ_GkKw
- ACTIVITIES
  - Dividing Shapes into Fractions Worksheet – http://www.primaryresources.co.uk/maths/pdfs/12fracwork.pdf
  - Real World Application using Pikelets and Lamingtons – https://education.nsw.gov.au/content/dam/main-education/teaching-and-learning/student-assessment/media/documents/Fractions-pikelets-and-lamingtons-book.pdf
Locating unit fractions on a number line
- TUTORIAL
  - “Students will represent fifths, quarters, thirds and halves on a number line.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.3.6.pdf
- VIDEO
  - Fractions on a Number Line – https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-fractions-on-the-number-line/v/fractions-on-a-number-line
- ACTIVITIES
  - Identify Unit Fractions on Number Lines – https://www.ixl.com/math/grade-3/identify-unit-fractions-on-number-lines
  - Identify the Fractions Using the Number Line – https://www.mathworksheets4kids.com/number-lines/fractions/proper2.pdf
Recognising that in English the term ‘one third’ is used (order: numerator, denominator) but that in other languages this concept may be expressed as ‘three parts, one of them’ (order: denominator, numerator) for example Japanese

Money and financial mathematics

Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059)

Recognising the relationship between dollars and cents, and that not all countries use these denominations and divisions (for example Japanese Yen)
- TUTORIALS/ACTIVITIES
  - “Students will represent money values in multiple ways, and calculate change from $1.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.1.7.pdf
  - “Students will represent money values in multiple ways, and calculate change from $5” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.3.5.pdf
  - “Students will apply known addiIon strategies to money situations.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.4.4.pdf
- VIDEO
  - Different Currencies – http://splash.abc.net.au/home#!/media/1566328/funny-money

Patterns and Algebra

Describe, continue, and create number patterns resulting from performing addition or subtraction (ACMNA60)

Identifying and writing the rules for number patterns
- TUTORIAL/ACTIVITIES
  - Finding a Rule of a Sequence – https://www.mathsisfun.com/algebra/sequences-finding-rule.html
  - Number Patterns using the Think Aloud and Other Rules – https://education.nsw.gov.au/teaching-and-learning/student-assessment/smart-teaching-strategies/numeracy/number-and-algebra/algebraic-techniques/number-patterns
- VIDEO
  - Practice Finding Patterns in Numbers – https://www.youtube.com/watch?v=l-6uEtTBH7g
Describing a rule for a number pattern, then creating the pattern
- TUTORIAL/ACTIVITIES
  - Talking about Patterns and Algebra (various levels) – https://education.nsw.gov.au/teaching-and-learning/student-assessment/smart-teaching-strategies/numeracy/number-and-algebra/patterns-and-algebra
  - “Students will copy, con1nue, create and describe patterns with numbers and identify missing elements.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.2.1.pdf

Measurement and Geometry

Using units of measurement

Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

Recognising the importance of using common units of measurement
- TUTORIALS
  - Measurement Information – https://nzmaths.co.nz/measurement-information
  - Why Do We Have Units of Measurement – http://www.mathworksheetscenter.com/mathtips/unitsofmeasurement.html
- WORKSHEETS
  - Choosing the Best Units of Measurement worksheet – http://www.mathworksheetscenter.com/mathtips/unitsofmeasurement.html
- VIDEOS
  - Introduction to Measurement – https://www.youtube.com/watch?v=Iu6YaZoh4ec
Recognising and using centimetres and metres, grams and kilograms, and millilitres and litres
- TUTORIALS
  - Converting Metric Units Slideshow – https://www.slideshare.net/bigpassy/converting-metric-units
  - “Students will measure objects using metric units of metre, kilogram and litre. Students will use comparative language to describe the measures.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.1.8.pdf
  - “Students will measure objects using metric units of centimetre and metre, kilogram and gram, and litre and millilitre. Students will use comparative language to describe these measures.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.3.7.pdf

Tell time to the minute and investigate the relationship between units of time (ACMMG062)

Recognising there are 60 minutes in an hour and 60 seconds in a minute
- TUTORIALS
  - Analog and Digital Time – https://www.education.nsw.gov.au/teaching-and-learning/student-assessment/smart-teaching-strategies/numeracy/measurement-geometry/time/stage-2-analog-digital-time
  - “Students will measure and compare the duration of an activity, comparing relationship between seconds, minutes and hours. Students will read from and record times on digital and analogue clocks at five minute intervals.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.1.9.pdf
  - “Students will construct a digital clock and show analogue time in a digital representation. Students will read from and record times on digital and analogue clocks to and from the hour.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.4.7.pdf
- VIDEOS
  - Time: “Seconds, Minutes and Hours” by StoryBots – https://www.youtube.com/watch?v=gEStq1e1Qrc
- WORKSHEETS
  - Estimating Time – https://www.mathworksheets4kids.com/estimation/time/units1.pdf

Shape

Make models of three-dimensional objects and describe key features (ACMMG063)

Exploring the creation of three-dimensional objects using origami, including prisms and pyramids
- TUTORIALS
  - 3D Space and Geometry – https://education.nsw.gov.au/teaching-and-learning/student-assessment/smart-teaching-strategies/numeracy/measurement-geometry/space-and-geometry-3d/Stage-3-space-and-geometry-3D
  - Constructing Pyramids and Prisms – https://education.nsw.gov.au/teaching-and-learning/student-assessment/smart-teaching-strategies/numeracy/measurement-geometry/space-and-geometry-3d/stage-3-3d-space-constructing-prisms-and-pyramids
  - “Learners will describe the features and construct nets of three-dimensional objects.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.2.8.pdf
  - “Students will describe the features of three-dimensional objects, and create three-dimensional models.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.4.6.pdf
- VIDEO
  - 3D Shape Nets – https://www.youtube.com/watch?v=SwDjm6Ra1W4
- ACTIVITIES
  - Identify Nets of 3D Shapes – https://www.mathworksheets4kids.com/solid-shapes/net-shape1.pdf
  - Match 3D Shapes to Their Nets – https://www.mathworksheets4kids.com/solid-shapes/net-matching1.pdf
  - Printable 3D Nets to Cut and Fold – http://www.greatmathsteachingideas.com/wp-content/uploads/2012/03/Making-3D-Shapes.pdf

Geometric reasoning

Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064)

Opening doors partially and fully and comparing the size of the angles create
Recognising that analogue clocks use the turning of arms to indicate time, and comparing the size of angles between the arms for familiar times
- TUTORIALS/LESSON PLANS
  - “Identify, compare and describe angles in practical situations.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.4.5.pdf
  - Angles between clock arms – https://www.mathsisfun.com/activity/clocks-angles.html

Location and transformation

Create and interpret simple grid maps to show position and pathways (ACMMG065)

Creating a map of the classroom or playground
- TUTORIALS
  - Introducing Mapping Skills – https://www.australiancurriculumlessons.com.au/2013/08/17/introducing-mapping-skills-lesson-year-234/

Identify symmetry in the environment (ACMMG066)

Identifying symmetry in Aboriginal rock carvings or art
Identifying symmetry in the natural and built environment
- TUTORIALS/LESSONS PLANS
  - “Students will investigate objects and shapes that are symmetrical and non symmetrical. They will
    determine where the line symmetry lies for these Shapes.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.4.8.pdf

Statistics and Probability

Chance

Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067)

Conducting repeated trials of chance experiments such as tossing a coin or drawing a ball from a bag and identifying the variations between trials
- TUTORIALS
  - Chance and Probability Tutorials, games and worksheets – http://splash.abc.net.au/home#!/topic/494566/chance-and-probability
  - Probability – https://www.mathsisfun.com/data/probability.html
- VIDEOS
  - Probability Lesson – https://www.youtube.com/watch?v=ihH7ZXemEdI
- WORKSHEETS
  - Chance Worksheet – https://www.ezymathtutoring.com.au/Worksheets/Year%203%20Chance%20Worksheet.pdf
  - Chance Experiments and Variation in Results – http://amsi.org.au/teacher_modules/Chance_years_1-3.html#Year_3_Chance%20experiments_and_variation_in_results
- ACTIVITIES
  - “Students will record an expected outcome and an actual result for a coin toss chance experiment, identifying variations in results over repeated experiments.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.2.9.pdf
  - “Students will conduct chance experiments to examine and compare different chance situations, using the language of chance such as, more likely, less likely and equal chance. Students will then predict which one is more likely to generate a specific event.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.4.9.pdf

Data representation and interpretation

Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068)

Refining questions and planning investigations that involve collecting data, and carrying out the investigation (for example narrowing the focus of a question such as ‘which is the most popular breakfast cereal?’ to ‘which is the most popular breakfast cereal among Year 3 students in our class?’)
- ACTIVITIES
  - “Students will identify and clarify questions about data collection and identify recording methods for the data. Students will then create, interpret and compare displays, reflecting on the both the information gathered and the type of display used.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/m

Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies (ACMSP069)

Exploring meaningful and increasingly efficient ways to record data, and representing and reporting the results of investigations
- TUTORIALS
  - Collecting and Recording Data – https://www.bbc.co.uk/education/topics/z3nygk7
  - Representing Data – https://www.bbc.co.uk/bitesize/guides/zrg4jxs/revision/1
  - Data and Statistics – https://www.stem.org.uk/resources/community/collection/12744/years-3-4-data-and-statistics
- ACTIVITIES
  - Data – http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.2.10.pdf
Collecting data to investigate features in the natural environment
- ACTIVITIES
  - Data Collection and Graphing – https://www.ala.org.au/classroom-exercises/activity-1-data-collection-and-graphing/
  - Graphing and Finding Probability of Environments – https://www.ala.org.au/classroom-exercises/activity-3-graphing-and-probability/

Interpret and compare data displays (ACMSP070)

Comparing various student-generated data representations and describing their similarities and differences
- ACTIVITIES/LESSONS
  - “Students will compare various student generated data representation and describe their similarities and
    differences. Students will be introduced to the mathematical term, variation.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.3.10.pdf

Mathematics Achievement Standard

By the end of Year 3, students recognise the connection between addition and subtraction and solve problems using efficient strategies for multiplication. They model and represent unit fractions. They represent money values in various ways. Students identify symmetry in the environment. They match positions on maps with given information. Students recognise angles in real situations. They interpret and compare data displays.

Students count to and from 10 000. They classify numbers as either odd or even. They recall addition and multiplication facts for single-digit numbers. Students correctly count out change from financial transactions. They continue number patterns involving addition and subtraction. Students use metric units for length, mass and capacity. They tell time to the nearest minute. Students make models of three-dimensional objects. Students conduct chance experiments and list possible outcomes. They conduct simple data investigations for categorical variables.