Level Description
The proficiency strands understanding, fluency, problemsolving 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
 Problemsolving includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of threedimensional 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/oddeven/grouppairs1.pdf
 Grouping Items – https://www.mathworksheets4kids.com/oddeven/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/oddeven/identify1.pdf
 VIDEOS
 Splash ABC – http://splash.abc.net.au/home#!/media/2549569/oddandevennumbers
 Learning Odd and Even Numbers for Kids – https://www.youtube.com/watch?v=uuD5JlrMnAk&t=44s
 TUTORIALS/LESSON PLANS
 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/evenodd/evenodd_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/g25a2evenodd.html
 VIDEOS
 TUTORIALS/LESSON PLANS
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 fourdigit numbers. Students will also add and subtract 1, 10, 100, and 1000 to and from a fourdigit number.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.1.2.pdf
 TUTORIALS/LESSON PLANS
 Placing fourdigit 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=Estimate4digitnumbersonanumberline.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
 TUTORIALS/ACTIVITIES
 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/year3/writenumbersinwords
 TUTORIALS
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 fourdigit 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
 TUTORIALS/ACTIVITIES
 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 nonstandard 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
 TUTORIALS/ACTIVITIES
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
 TUTORIALS/ACTIVITIES
Recall addition facts for singledigit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)
 Recognising that certain singledigit 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 twodigit 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/cc1stgrademath/cc1staddsubtract/cc1staddsubtract10/v/relatingadditionandsubtraction

 TUTORIALS
 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
 TUTORIALS/ACTIVITIES
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/
 TUTORIALS/ACTIVITIES
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/writewordproblemsmath8153161.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/numberpatternsbasic_TZDZD.pdf?up=1466611200
 TUTORIALS/ACTIVITIES
 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/13aspect6
 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/maineducation/teachingandlearning/studentassessment/media/documents/Fractionspikeletsandlamingtonsbook.pdf
 TUTORIALS/LESSONS
 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
 ACTIVITIES
 Identify Unit Fractions on Number Lines – https://www.ixl.com/math/grade3/identifyunitfractionsonnumberlines
 Identify the Fractions Using the Number Line – https://www.mathworksheets4kids.com/numberlines/fractions/proper2.pdf
 TUTORIAL
 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/funnymoney
 TUTORIALS/ACTIVITIES
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/sequencesfindingrule.html
 Number Patterns using the Think Aloud and Other Rules – https://education.nsw.gov.au/teachingandlearning/studentassessment/smartteachingstrategies/numeracy/numberandalgebra/algebraictechniques/numberpatterns
 VIDEO
 Practice Finding Patterns in Numbers – https://www.youtube.com/watch?v=l6uEtTBH7g
 TUTORIAL/ACTIVITIES
 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/teachingandlearning/studentassessment/smartteachingstrategies/numeracy/numberandalgebra/patternsandalgebra
 “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
 TUTORIAL/ACTIVITIES
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/measurementinformation
 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
 TUTORIALS
 Recognising and using centimetres and metres, grams and kilograms, and millilitres and litres
 TUTORIALS
 Converting Metric Units Slideshow – https://www.slideshare.net/bigpassy/convertingmetricunits
 “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
 TUTORIALS
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/teachingandlearning/studentassessment/smartteachingstrategies/numeracy/measurementgeometry/time/stage2analogdigitaltime
 “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
 TUTORIALS
Shape
Make models of threedimensional objects and describe key features (ACMMG063)
 Exploring the creation of threedimensional objects using origami, including prisms and pyramids
 TUTORIALS
 3D Space and Geometry – https://education.nsw.gov.au/teachingandlearning/studentassessment/smartteachingstrategies/numeracy/measurementgeometry/spaceandgeometry3d/Stage3spaceandgeometry3D
 Constructing Pyramids and Prisms – https://education.nsw.gov.au/teachingandlearning/studentassessment/smartteachingstrategies/numeracy/measurementgeometry/spaceandgeometry3d/stage33dspaceconstructingprismsandpyramids
 “Learners will describe the features and construct nets of threedimensional objects.” http://www.cnscurric.catholic.edu.au/uploads/1/0/3/9/10391716/mag_3.2.8.pdf
 “Students will describe the features of threedimensional objects, and create threedimensional 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/solidshapes/netshape1.pdf
 Match 3D Shapes to Their Nets – https://www.mathworksheets4kids.com/solidshapes/netmatching1.pdf
 Printable 3D Nets to Cut and Fold – http://www.greatmathsteachingideas.com/wpcontent/uploads/2012/03/Making3DShapes.pdf
 TUTORIALS
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/clocksangles.html
 TUTORIALS/LESSON PLANS
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/introducingmappingskillslessonyear234/
 TUTORIALS
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
 “Students will investigate objects and shapes that are symmetrical and non symmetrical. They will
 TUTORIALS/LESSONS PLANS
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/chanceandprobability
 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_13.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
 TUTORIALS
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
 ACTIVITIES
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/years34dataandstatistics
 ACTIVITIES
 TUTORIALS
 Collecting data to investigate features in the natural environment
 ACTIVITIES
 Data Collection and Graphing – https://www.ala.org.au/classroomexercises/activity1datacollectionandgraphing/
 Graphing and Finding Probability of Environments – https://www.ala.org.au/classroomexercises/activity3graphingandprobability/
 ACTIVITIES
Interpret and compare data displays (ACMSP070)
 Comparing various studentgenerated 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
 “Students will compare various student generated data representation and describe their similarities and
 ACTIVITIES/LESSONS
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 singledigit 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 threedimensional objects. Students conduct chance experiments and list possible outcomes. They conduct simple data investigations for categorical variables.
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