# Australian Curriculum & NSW Syllabus

Here at A Learning Place A Teaching Place, our primary goal is to develop deep mathematical understanding in both teacher and students. As such, we offer mathematical resources that are aligned to the primary school standards and outcomes of the Australian Mathematics Curriculum and NSW Mathematics Syllabus.
Below, you will find all Australian Primary School Curriculum and NSW Syllabus Outcomes as covered in our Teaching Resources. Australian Curriculum content descriptions are in GREEN, NSW Mathematics Syllabus Outcomes are in ORANGE and A Learning Place A Teaching Place levels are in BLACK. Here, you can see how we provide teaching resources aligned to the Australian Curriculum and NSW Mathematics Syllabus.
If you have a question about how our resources align to the Australian Curriculum and NSW Mathematics Syllabus, please do not hesitate to email us at info@alearningplace.com.au today!

ACMNA001 Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point

NSW MAe-4NA Counts to 30, and orders, reads and represents numbers in the range 0 to 20

·  Early Counting and Grouping 1  Count forwards and backwards by ones

·  Early Counting and Grouping 2  Write numerals correctly

·  Early Counting and Grouping 3  Recognise a numeral when its name is spoken, recognise a number when seeing its numeral

ACMNA002 Connect number names, numerals and quantities,  including zero, initially up to 10 and then beyond

NSW MAe-4NA Counts to 30, and orders, reads and represents numbers in the range 0 to 20

·  Early Counting and Grouping 4 Counting items with one-to-one correspondence, last number said is the total

·  Early Counting and Grouping 5  Identify a number by the number before and after, identify the number before and after a number

·  Early Counting and Grouping 6  A number always represents the same amount

·  Early Counting and Grouping 7  Counting forwards is adding 1, counting backwards is taking away 1,

·  Early Counting and Grouping 8  Number after is 1 more, Number before is 1 fewer

·  Early Counting and Grouping 9  Subitise the number in collection without counting

ACMNA289  Compare, order and make correspondences between  collections, initially to 20, and explain reasoning

NSW MAe-4NA Counts to 30, and orders, reads and represents numbers in the range 0 to 20

NSW MAe-6NA groups, shares and counts collections of objects, describes using everyday language, and records using informal methods

·  Early Counting and Grouping 10 Estimate the number in a group, then count using one-to-one correspondence

·  Early Counting and Grouping 11 Identify that numbers are inclusive

·  Early Counting and Grouping 12 Groups with markers and with no markers, compare equal and unequal groups

ACMNA004 Represent practical situations to model addition and  sharing

MAe-5NA combines, separates and compares collections of objects, describes using everyday language, and records using informal methods

·  Early Counting and Grouping 13 Join groups to add, record ‘and’, ‘is’

·  Early Counting and Grouping 14 Taking away to subtract record ‘is’, ‘take away’

·  Early Counting and Grouping 15 Find difference through adding to the smaller group or taking away from the larger group

·  Place Value 1 Partition single-digit numbers, equal not equal Combinations to 10 through partitioning

·  Place Value 2 Placing and counting counters on 10 frames, using 5 as a reference, identifying friends of 10

·  Place Value 3 Partition teen numbers

·  Place Value 5 Friends of 20

NSW MAe-4NA Counts to 30, and orders, reads and represents numbers in the range 0 to 20

·  Place Value 4 Teen numbers are ’10 and…’

·  Money and Financial Mathematics 1 Describe and identify Australian coins

ACMNA016 Recognise and describe one­half as one of two equal parts of  a whole

NSW MAe-7NA Describes two equal parts as halves

·  Fractions and Decimals 1 Halve shapes and lengths, explaining it is half as big / long

ACMNA005 Sort and classify familiar objects and explain the basis  for these classifications. Copy, continue and create  patterns with objects and drawings

NSW MAe-8NA Recognises, describes and continues repeating patterns

·  Patterns and Algebra 1 Identify patterns and the part that repeats

·  Patterns and Algebra 2 Recognise errors in patterns using the part repeats

ACMMG006 Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explaining reasoning in  everyday language

NSW MAe-9MG Describes and compares lengths and distances using everyday language

·  Measurement and Geometry 2 Create / compare lengths, heights, distances

·  Measurement and Geometry 4 Compare lengths, identifying that if A is longer than B, and B is longer than C, then A is also longer than C

NSW MAe-10MG Describes and compares areas using everyday language

·  Measurement and Geometry 10 Compare area by direct comparison

·  Measurement and Geometry 11 Compare 3 areas, identifying if A has a larger area than B, and B has a larger area than C, then A also has a larger area than C

NSW MAe-11MG Describes and compares the capacities of containers and the volumes of objects or substances using everyday language

·  Measurement and Geometry 8 Compare the volumes of objects and the capacities of containers, directly

NSW MAe-12MG Describes and compares the masses of objects using everyday language

·  Measurement and Geometry 12 Compare mass by hefting, describing light and heavy objects

ACMMG007 Compare and order the duration of events using the  everyday language of time

ACMMG008 Connect days of the week to familiar events and actions

NSW  MAe-13MG Sequences events, uses everyday language to describe the durations of events, and reads hour time on clocks

·  Time 1 Name the days of the week, identifying the day before and after and describing events on days

·  Time 2 Sequence events in time using ordinal numbers 1st, 2nd, 3rd…

·  Time 3 Compare and describe long and short time durations

·  Time 4 Investigate time on the hour on analog and digital clocks, describing the direction of hand movement related to sundials

ACMNA009 Sort, describe and name familiar two-­dimensional  shapes and three­dimensional objects in the  environment

NSW MAe-14MG Manipulates, sorts and represents three-dimensional objects and describes them using everyday language

·  Measurement and Geometry 7 Compare three-dimensional objects, describing flat and curved surfaces

NSW MAe-15MG Manipulates, sorts and describes representations of two-dimensional shapes, including circles, triangles, squares and rectangles, using everyday language

·  Measurement and Geometry 1 Squares, triangles, circles and rectangles

·  Measurement and Geometry 6 Comparing three-dimensional objects and two-dimensional shapes, identifying dimensions and the two-dimensional surfaces of  three-dimensional objects, describing straight lines and corners, and curved lines on two-dimensional shapes

ACMNA010 Describe position and movement

NSW MAe-16MG Describes position and gives and follows simple directions using everyday language

·  Measurement and Geometry 3 Describing the position of an object in relation to another object using positional language

·  Measurement and Geometry 5 Give and follow directions to a place

·  Measurement and Geometry 9 Describing the position of an object in relation to self, giving and following directions to and from self

ACMNA011 Answer yes/no questions to collect information

NSW MAe-17SP Represents data and interprets data displays made from objects

·  Statistics and Probability 1 Asking and answering yes and no questions, recording data in a chart in rows

ACMNA012  Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and  tens starting from zero

ACMNA013 Recognise, model, read, write and order numbers to at least  100. Locate these numbers on a number line

ACMNA014 Count collections to 100 by partitioning numbers using place  value

NSW MA1-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20

·  Addition and Subtraction 1 Counting forwards by 1s is adding 1, recording on a number line

·  Addition and Subtraction 2 Count backwards by 1s is subtracting 1, recording on a number line

·  Place Value 6  Friends of 10 through addition/subtraction/commutativity

·  Place Value 7  Place value of teen numbers

·  Place Value 8  Partition single-digit, teen numbers

·  Place Value 9  Friends of 20

·  Place Value 10  Friends of any decade

·  Place Value 11  Standard/non-standard place value of two-digit numbers, Partition two-digit numbers

ACMNA015 Represent and solve simple addition and subtraction problems using a range of strategies including counting on,  partitioning and rearranging parts

NSW MA1-5NA uses a range of strategies and informal recording methods for addition and subtraction

·  Addition and Subtraction 3 Add and subtract single-digit numbers counting by ones with counters

·  Addition and Subtraction 4 Add and subtract single-digit numbers counting by ones on a number line

·  Addition and Subtraction 6 Add single-digit numbers using place value to bridge 10

·  Addition and Subtraction 7 Subtract single-digit numbers using place value to bridge 10

·  Addition and Subtraction 8 Add/subtract single-digit numbers using place value to bridge 20

NSW MA1-6NA uses a range of mental strategies and concrete materials for multiplication and division

·   Multiplication and Division 1  Divide making ‘groups of’ / ‘equal groups’

·   Multiplication and Division 2  Divide by 2  2 equal groups, number in each group, left over, halves, Divide by 2 groups of 2, number of groups, part left over

·   Multiplication and Division 3 Patterns and Algebra 8 Rhythmic / skip count forwards and backwards by 2s, 5s and 10s naming multiples on a number line and on a hundred chart

·   Multiplication and Division 4 Patterns and Algebra 8  Divide into groups of 2, 5 and 10, and find total using skip and rhythmic counting

ACMNA016 Recognise and describe one­half as one of two equal parts of  a whole.

NSW MA1-7NA represents and models halves, quarters and eighths

·  Fractions and Decimals 2 Halves of shapes and groups

NSW MA1-8NA creates, represents and continues a variety of patterns with numbers and objects

·  Addition and Subtraction 11 Patterns and Algebra 6 Add using associativity

·  Addition and Subtraction 12 Patterns and Algebra 7 Missing and equivalent number sentences

·  Patterns and Algebra 9 Identify odd and even number patterns, recognising when an error occurs

·  Patterns and Algebra 10 Explain even numbers by halving to get a whole number

ACMNA018 Investigate and describe number patterns formed by skip  counting and patterns with objects

NSW MA1-8NA creates, represents and continues a variety of patterns with numbers and objects

·  Patterns and Algebra 3 Identifying part that repeats in a pattern

·   Multiplication and Division 3 Patterns and Algebra 8 Rhythmic / skip count forwards and backwards by 2s, 5s and 10s naming multiples on a number line and on a hundred chart

ACMNA017 Recognise, describe and order Australian coins according to  their value

NSW MA1-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20

·  Money Financial Mathematics 2 Values of Australian coins and notes

·  Money Financial Mathematics 3 Other countries’ coins and notes

ACMMG019 Measure and compare the lengths and capacities of pairs of  objects using uniform informal units

NSW MA1‑9MG measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres

·  Measurement and Geometry 14 Length in multiple / single informal units

NSW MA1‑10MG measures, records, compares and estimates areas using uniform informal units

·  Measurement and Geometry 16 Area in multiple units, square is best

NSW MA1‑11MG measures, records, compares and estimates volumes and capacities using uniform informal units

·  Measurement and Geometry 18 Volume and Capacity multiple units, cube flat surfaced objects, liquid curved surface objects

NSW MA1‑12MG measures, records, compares and estimates the masses of objects using uniform informal units

·  Measurement and Geometry 19 Compare, order mass equal arm balance

ACMMG020 Tell time to the half ­hour

ACMMG021 Describe duration using months, weeks, days and hours

NSW MA1-13MG describes, compares and orders durations of events, and reads half- and quarter-hour time

·    Time 5 Duration of months, seasons, days, hours

·    Time 6 Hand movement on clock, half past

ACMMG022 Recognise and classify familiar two­dimensional shapes and three-dimensional objects using obvious features

NSW MA1‑14MG sorts, describes, represents and recognises familiar three-dimensional objects, including cones, cubes, cylinders, spheres and prisms

·  Measurement and Geometry 17 Three-dimensional objects flat/curved surfaces, lines, edges

NSW MA1‑15MG manipulates, sorts, represents, describes and explores two-dimensional shapes, including quadrilaterals, pentagons, hexagons and octagons

·  Measurement and Geometry 13 Two-dimensional shapes, lines, sides

ACMMG023 Give and follow directions to familiar locations

NSW MA1‑16MG represents and describes the positions of objects in everyday situations and on maps

·  Measurement and Geometry 15 Position and Directions

ACMSP262 Choose simple questions and gather responses

ACMSP263 Represent data with objects and drawings where one object or drawing represents one data value. Describe the displays

NSW MA1-17SP gathers and organises data, displays data in lists, tables and picture graphs, and interprets the results

·  Statistics and Probability 3 Collect and represent data in pictures and objects

·  Statistics and Probability 4 Interpret picture graphs chance language

ACMSP024 Identify outcomes of familiar events involving chance and describe them using everyday language such as ‘will happen’, ‘won’t happen’ or ‘might happen’

NSW MA1-18SP recognises and describes the element of chance in everyday events

·  Statistics and Probability 2 Chance outcomes of familiar events

ACMNA027 Recognise, model, represent and order numbers to at  least 1000

ACMNA028  Group, partition and rearrange collections up to 1000 in  hundreds, tens and ones to facilitate more efficient  counting

NSW MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers

·  Place Value 12 Count forwards and backwards by 10s on and off the decade

·  Place Value 13 Partition tens numbers

·  Place Value 14 Identify friends of any 100, through addition and subtraction

·  Place Value 15 Explain standard and non-standard place value of three-digit numbers grouping flexibly in hundreds, tens and ones, read and order three-digit numbers on a number line and hundred charts, partition three-digit numbers using standard and non-standard place value and non-place value

·  Place Value 16 Patterns and Algebra 12 Count forwards and backwards by 100s, 10s and 1s on and off the hundred and decade from three-digit numbers

ACMNA034 Count and order small collections of Australian coins and  notes according to their value

·  Money Financial Mathematics 4 Recognise that there 100 cents in \$1, 200 cents in \$2

·  Money Financial Mathematics 5 Count and order small collections of coins and notes according to their value

·  Money Financial Mathematics 6 Make given amounts in multiple ways using coins and notes.

·  Addition and Subtraction 18 Money Financial Mathematics 7 Add and subtract coins and notes, count change

·  Multiplication and Division 6 Money Financial Mathematics 8 Make given amounts in multiple ways using coins and notes

ACMNA029 Explore the connection between addition and subtraction

ACMNA030 Solve simple addition and subtraction problems using a  range of efficient mental and written strategies

ACMNA036 Solve problems by using number sentences for addition or  subtraction

NSW MA1-5NA uses a range of strategies and informal recording methods for addition and subtraction

·  Addition and Subtraction 13 Add and subtract 2 tens numbers, including on a hundreds chart, counting forwards and backwards by 10s on the decade

·  Addition and Subtraction 14 Add and subtract a tens number by partitioning the tens number

·  Addition and Subtraction 15 Add and subtract a ten numbers to and from two-digit numbers, counting forwards and backwards by 10s off the decade

·  Addition and Subtraction 16 Add and subtract a tens number and a two-digit number by partitioning the tens number.

·  Addition and Subtraction 17  Add / subtract 2-digit numbers by partitioning

·  Addition and Subtraction 19 Patterns and Algebra 13  Relationship between addition and subtraction to see difference in three ways and to complete missing number sentences

·  Addition and Subtraction 20 Patterns and Algebra 14  Solve problems involving addition or subtraction, representing a word problem as a number sentence and writing a word problem to represent a number sentence

ACMNA031 Recognise and represent multiplication as repeated  addition, groups and arrays

ACMNA032 Recognise and represent division as grouping into equal  sets and solve simple problems using these  representations

NSW MA1-6NA uses a range of mental strategies and concrete materials for multiplication and division

·  Multiplication and Division 5 Divide array, describe multiplication, skip count / number rows, number in each row, multiply / divide repeated add / subtract, divide ‘groups of …’ count groups, / ‘… equal groups’ count counters, any part remaining

·  Multiplication and Division 7 Divide by making ‘groups of …’ and count groups, and making ‘… equal groups’ and count counters in each group, divide into ‘groups of …’ and ‘… equal groups’ and describe part left over

·  Multiplication and Division 8 Divide ‘groups of 4’ / ‘4 equal groups’  quarters, number of groups / in each group, any remaining

ACMNA033 Recognise and interpret common uses of halves, quarters  and eighths of shapes and collections

NSW MA1-7NA represents and models halves, quarters and eighths

·  Fractions and Decimals 3 Quarter shapes by quartering and by halving a half,

·  Fractions and Decimals 4 Quarter groups by quartering and by halving a half,

·  Fractions and Decimals 5 Eighth shapes by eighthing, by halving a quarter and by quartering a half

·  Fractions and Decimals 6 Eighth groups by eighthing, by halving a quarter and by quartering a half

ACMNA026  Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any  starting point, then moving to other sequences

ACMNA035 Describe patterns with numbers and identify missing  elements

NSW MA1-8NA creates, represents and continues a variety of patterns with numbers and objects

·  Patterns and Algebra 11 Describe patterns that increase and decrease by adding and subtracting 10

ACMNA037 Compare and order several shapes and objects based on length, area, volume and capacity using appropriate  uniform informal units

NSW MA1 9MG measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres

·  Measurement and Geometry 21 Make tape measure using informal units and using centimetres, measure using metres and centimetres

NSW MA1 10MG measures, records, compares and estimates areas using uniform informal units

·  Measurement and Geometry 23 Measure area using uniform informal square units arranged in a grid, (array)

NSW MA1 11MG measures, records, compares and estimates volumes and capacities using uniform informal units

·  Measurement and Geometry 26 Make a measuring device using liquid informal units to measure capacities of containers with curved surfaces, make models using cubes to volume in cubes, compare volumes by displacement

ACMNA038 Compare masses of objects using balance scales

NSW MA1 12MG measures, records, compares and estimates the masses of objects using uniform informal units

·  Measurement and Geometry 28 Measure mass using uniform informal units on an equal arm balance

ACMNA039 Tell time to the quarter ­hour, using the language of ‘past’  and ‘to’

NSW MA1 13MG describes, compares and orders durations of events, and reads half- and quarter-hour time

·  Time 7 Estimate and measure duration of time using informal units

·  Time 9 Experience activities that take an hour, half, quarter, one minute, few seconds

·  Time 10 Tell time to quarter to and past hour analog and digital clocks, linked to fractions ‘half’ and ‘quarter’

ACMNA040 Name and order months and seasons

ACMNA041 Use a calendar to identify the date and determine the  number of days in each month

·  Time 8 Use a simple calendar to estimate and measure the number of months, weeks and days till an event

ACMNA042 Describe and draw two-dimensional shapes, with and without digital technologies

ACMNA045 Investigate the effect of one ­step slides and flips with and  without digital technologies

ACMNA046 Identify and describe half and quarter turns

NSW MA1 15MG manipulates, sorts, represents, describes and explores two-dimensional shapes, including quadrilaterals, pentagons, hexagons and octagons

·  Measurement and Geometry 20 Regular / irregular two-dimensional shapes, vertices, straight, curved, vertical, horizontal, parallel lines

·  Measurement and Geometry 27 Describe one-step slides, flips, full, half, quarter turns

ACMNA043 Describe the features of three-­dimensional objects

NSW MA1 14MG sorts, describes, represents and recognises familiar three-dimensional objects, including cones, cubes, cylinders, spheres and prisms

·  Measurement and Geometry 24 Distinguish between three-dimensional objects and two-dimensional shapes, identifying dimensions, flat surfaces of three-dimensional objects are two-dimensional shapes

·  Measurement and Geometry 25 Sort, describe and classify a three-dimensional object by its features on seeing them, and from a description of its features.

ACMNA044 Interpret simple maps of familiar locations and identify the  relative positions of key features

NSW MA1 16MG represents and describes the positions of objects in everyday situations and on maps

·  Measurement and Geometry 22 Interpret simple maps of familiar spaces and describe the position of objects and features

ACMNA047 Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or  ‘impossible’

ACMNA048 Identify a question of interest based on one categorical  variable. Gather data relevant to the question

ACMNA049 Collect, check and classify data

ACMNA050 Create displays of data using lists, table and picture  graphs and interpret them

NSW MA1 17SP gathers and organises data, displays data in lists, tables and picture graphs, and interprets the results

NSW MA1 18SP recognises and describes the element of chance in everyday events

·  Statistics and Probability 5 Describe likelihood using chance language

·  Statistics and Probability 6 Collect data using tally marks, display data in lists, tables and picture graphs using a base line and one-to-one correspondence., comparing the usefulness of different types of data displays

·  Statistics and Probability 7 Interpret lists, tables and picture graphs by asking questions about data, including using the language of chance, and using the data to answer the questions

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

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

NSW MA2-4NA applies place value to order, read and represent numbers of up to five digits

·  Place Value 17 Patterns and Algebra 16 Count by 1s, 10s, 100s and 1000s, over 1000s, Standard and non-standard place value of four-digit numbers

·  Place Value 18 Multiplicative place value of whole numbers to ten-thousands by multiplying and dividing by 10

ACMNA054 Recognise and explain the connection  between addition and subtraction

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

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

NSW MA2-5NA uses mental and written strategies for addition and subtraction involving two-, three-, four- and five-digit numbers

·  Addition and Subtraction 21 Add and subtract three- and four-digit numbers using place value

·  Addition and Subtraction 23, Money and Financial Maths 9  Add and subtract money, rounding to the nearest 5c, and give change

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

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

NSW MA2-6NA uses mental and informal written strategies for multiplication and division

·  Multiplication and Division 9 Multiplication and division by 10 using multiplicative place value

·  Multiplication and Division 10, Patterns and Algebra 18  Multiplication and division by 2 using properties and relationships, relating division to fractions

·  Multiplication and Division 11, Patterns and Algebra 18  Multiplication and division by 4 using properties and relationships, relating division to fractions

·  Multiplication and Division 12, Patterns and Algebra 18  Multiplication and division by 3 using properties and relationships, relating division to fractions

·  Multiplication and Division 13, Patterns and Algebra 18  Multiplication and division by 5 using properties and relationships, relating division to fractions

ACMNA058 Model and represent unit fractions and their multiples to a  complete whole

NSW MA2-7NA represents, models and compares commonly used fractions and decimals

·  Fractions and Decimals 7 Role of the denominators 2, 4, 3, 5, 8, 10, as the number of parts we have divided by

·  Fractions and Decimals 8 Multiplicative relationships between fractions while building a fraction wall.

·  Fractions and Decimals 9 Non-unit fractions and the role of numerator as the number of parts we are concerned with

·  Fractions and Decimals 10 Locate fractions on a number line and identify that  2/2, 3/3, 4/4, 10/10, 5/5, 8/8 = 1 including on a number line

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

ACMNA060 Describe, continue, and create number  patterns resulting from performing addition or  subtraction

NSW MA2-8NA generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values

·  Patterns and Algebra 15 Explain even and odd numbers

·  Addition and Subtraction 22, Patterns and Algebra 19  Missing and equivalent number sentences, explaining equality and the relationship between addition and subtraction

·  Patterns and Algebra 16 Patterns adding and subtracting 1000s, 100s, 10s and 1s

·  Patterns and Algebra 17 Rule for number pattern, then create the pattern

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

NSW MA2 9MG measures, records, compares and estimates lengths, distances and perimeters in metres, centimetres and millimetres, and measures, compares and records temperatures

·  Measurement and Geometry 30 Metric length units metre, (decimetre), centimetre, millimetre, explaining the relationship to multiplicative place value

NSW MA2 10MG measures, records, compares and estimates areas using square centimetres and square metres

·  Measurement and Geometry 33 Measure area using square metre, (square decimetre), square centimetre, (square millimetre), identifying length units have been turned into squares by extending into second dimension

NSW MA2 11MG measures, records, compares and estimates volumes and capacities using litres, millilitres and cubic centimetres

·  Measurement and Geometry 35 Metric volume and capacity units, litre, (decilitre), centilitre, millilitre, explaining the relationship to multiplicative place value measure volume and capacity using cubic metre, (cubic decimetre), cubic centimetre, (cubic millimetre), identifying area units have been turned into cubes by extending into third dimension

NSW MA2 12MG measures, records, compares and estimates the masses of objects using kilograms and grams

·  Measurement and Geometry 36 Metric mass units, kilogram, (hectogram, decagram), gram, explaining the relationship to multiplicative place value

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

NSW MA2 13MG reads and records time in one-minute intervals and converts between hours, minutes and seconds

·  Time 11 Tell time to the minute on digital and analog clocks and record both

NSW MA2 15MG manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features

·  Measurement and Geometry 29 Regular and irregular triangles, identifying the 3 straight lines that meet at vertices as sides, symmetry and rigidity

·  Measurement and Geometry 32 Regular and irregular quadrilaterals, identifying the 4 straight lines that meet at vertices as sides, special quadrilaterals, angles

ACMMG063 Make models of three ­dimensional objects  and describe key features

ACMMG066 Identify symmetry in the environment

NSW MA2 15MG makes, compares, sketches and names three-dimensional objects, including prisms, pyramids, cylinders, cones and spheres, and describes their features

·  Measurement and Geometry 34 Prisms and pyramids, identifying  3 dimensions, flat surfaces with straight lines that meet at vertices as edges and faces, deconstructing nets, describing angles, vertical, horizontal and parallel lines, and symmetry

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

NSW MA2 16MG identifies, describes, compares and classifies angles

·  Measurement and Geometry 31 Angles as the amount of turn, identifying the vertex and arms, angles as the relative slant of two arms that meet at a vertex, compare angles as less than, equal to, greater than right angle

·  Time 12 Analog clock time, including the angles created through hand movement

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

NSW MA2 17MG uses simple maps and grids to represent position and follow routes, including using compass directions

·  Measurement and Geometry 37 Interpret, draw, simple grid maps with alpha-numeric grid references

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

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

ACMSP069 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

ACMSP070 Interpret and compare data displays

NSW MA2 18SP selects appropriate methods to collect data, and constructs, compares, interprets and evaluates data displays, including tables, picture graphs and column graphs

NSW MA2 19SP describes and compares chance events in social and experimental contexts

·  Statistics and Probability 8 Collect data, record in picture graphs and simple column graphs

·  Statistics and Probability 9 Interpret and compare data displays, including making statements using the language of chance

·  Statistics and Probability 10 Refine questions to collect data that may be easily recorded in categories, recording in lists, picture graphs, simple column graphs, with and without technology, compare child-generated data representations, describing similarities and differences

·  Statistics and Probability 11 Conduct repeated trials of chance experiments, identifying possible outcomes, recording results in lists, tables and column graphs, and explaining variation in results

ACMNA072  Recognise, represent and order numbers to at least tens of  thousands

ACMNA073  Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

ACMNA079  Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation

NSW  MA2-4NA applies place value to order, read and represent numbers of up to five digits

MA2-7NA represents, models and compares commonly used fractions and decimals

·  Place Value 19 Patterns and Algebra 20 Patterns adding / subtracting 1000s, 100s, 10s, 1s, Count, standard/non-standard place value, five-digit

·  Place Value 20 Fractions and Decimals 11 Multiplicative place value, to tenths, expressing as decimal and fraction

·  Place Value 21 Fractions and Decimals 12 Multiplicative place value, to hundredths, expressing as decimal and fraction

·  Place Value 22 Fractions Decimals 16 Money and Financial Mathematics 11 money to 2 decimal places, cents fraction of a dollar

·  Fractions Decimals 17  Round a number with one or two decimal places to the nearest whole number

·  Place Value 23 Round a number with one or two decimal places to the nearest whole number

ACMNA080  Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies

ACMNA083  Use equivalent number sentences involving addition and  subtraction to find unknown quantities

MA2-5NA uses mental and written strategies for addition and subtraction involving two-, three-, four- and five-digit numbers

·  Addition and Subtraction 24 Money and Financial Mathematics 10 Add and subtract five-digit numbers, including as money, using properties and relationships

·  Addition and Subtraction 27 Patterns and Algebra 24 Record number sentences to represent additive problems, to find unknown quantities.

ACMNA076  Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder

ACMNA075  Recall multiplication facts up to 10 × 10 and related division  facts

ACMNA082  Solve word problems by using number sentences involving  multiplication or division where there is no remainder

MA2-6NA uses mental and informal written strategies for multiplication and division

·  Multiplication and Division 14 Patterns and Algebra 18 Multiplication and division by 9 using properties and relationships, relating division to fractions

·  Multiplication and Division 15 Patterns and Algebra 18 Multiplication and division by 6 using properties and relationships, relating division to fractions

·  Multiplication and Division 16 Patterns and Algebra 18 Multiplication and division by 8 using properties and relationships, relating division to fractions

·  Multiplication and Division 17 Patterns and Algebra 18 Multiplication and division by 7 using properties and relationships, relating division to fractions

·  Multiplication and Division 19 Patterns and Algebra 25 Solve word problems using number sentences involving multiplication and division

ACMNA077  Investigate equivalent fractions used in contexts

ACMNA078  Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line

MA2-7NA represents, models and compares commonly used fractions and decimals

·  Fractions and Decimals 13 Equivalent fractions using concrete material and the relationship between numerator and denominator

·  Fractions and Decimals 14 Equivalent fractions on a number line

ACMNA071  Investigate and use the properties of odd and even numbers

ACMNA074  Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9

ACMNA081  Explore and describe number patterns resulting from  performing multiplication

NSW  MA2-8NA generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values

·  Addition and Subtraction 25 Patterns and Algebra 21 Add and subtract combinations of odd and even numbers, using the results to check calculations

·  Patterns and Algebra 23 Patterns involving skip counting multiples, naming terms, identifying the rule using multiplication / division

·  Multiplication and Division 18 Patterns involving skip counting multiples, naming terms, identifying the rule using multiplication / division

·  Patterns and Algebra 22 Addition and Subtraction 26 Fractions and Decimals 15 Number patterns, adding and subtracting fractions

ACMMG084  Use scaled instruments to measure and compare lengths, masses, capacities and temperatures

NSW  MA2-9MG measures, records, compares and estimates lengths, distances and perimeters in metres, centimetres and millimetres, and measures, compares and records temperatures

·  Measurement and Geometry 39 Measure and convert metric length units, using fractions and multiplicative place value to hundredths

·  Measurement and Geometry 46 Temperature on a scale thermometer

ACMMG290 Compare objects using familiar metric units of area and  volume

ACMMG087 Compare the areas of regular and irregular shapes by  informal means

NSW  MA2-10MG measures, records, compares and estimates areas using square centimetres and square metres

·  Measurement and Geometry 42 Measure the area of non-rectangular shapes in square centimetres and square metres

NSW  MA2-11MG measures, records, compares and estimates volumes and capacities using litres, millilitres and cubic centimetres

·  Measurement and Geometry 45 Millilitres using scale on measuring container, converting between millilitres and litres, measuring water displaced as volume

NSW  MA2-12MG measures, records, compares and estimates the masses of objects using kilograms and grams

·  Measurement and Geometry 47 Mass in grams and kilograms using a set of scales, converting between grams and kilograms, grams and a fraction of a kilogram

ACMMG085  Convert between units of time

ACMMG086  Use am and pm notation and solve simple time problems

NSW  MA2-13MG reads and records time in one-minute intervals and converts between hours, minutes and seconds

·  Time 13 Time using ‘am’ and ‘pm’

·  Time 14 Convert between units of time

·  Time 15 Interpret simple calendars, timetables, timelines

ACMMG088  Compare and describe two dimensional shapes that result  from combining and splitting common shapes, with and  without the use of digital technologies

ACMMG091  Create symmetrical patterns, pictures and shapes with and  without digital technologies

NSW  MA2-15MG manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features

·  Measurement and Geometry 41 Create two-dimensional shapes by combining and splitting

·  Measurement and Geometry 38 Create designs by reflecting, translating and rotating shapes, identifying symmetry and tessellation

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

NSW MA2-14MG makes, compares, sketches and names three-dimensional objects, including prisms, pyramids, cylinders, cones and spheres, and describes their features

Measurement and Geometry 44 Sketch the vertices, edges and faces of prisms and pyramids, cylinders and cones, and cube models using perspective, top, front, back and side view

ACMMG089  Compare angles and classify them as equal to, greater than  or less than a right angle

NSW  MA2-16MG identifies, describes, compares and classifies angles

·  Measurement and Geometry 40 Use angle testers, to test angles with 2 lines, 1 line as less than, larger than or a right angle

ACMMG090  Use simple scales, legends and directions to interpret  information contained in basic maps

NSW  MA2-17MG uses simple maps and grids to represent position and follow routes, including using compass directions

·  Measurement and Geometry 43 Use a key, compass, grid references, angles, scale distances on an alpha-numeric grid map

ACMSP092 Describe possible everyday events and order their chances  of occurring

ACMSP093 Identify everyday events where one cannot happen if the  other happens

ACMSP094 Identify events where the chance of one will not be affected  by the occurrence of the other

NSW  MA2-19SP describes and compares chance events in social and experimental contexts

·  Statistics and Probability 14 Order chance, chance affecting chance

ACMSP095 Select and trial methods for data collection, including survey  questions and recording sheets

ACMSP096 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

ACMSP097 Evaluate the effectiveness of different displays in illustrating  data features including variability

NSW  MA2-18SP selects appropriate methods to collect data, and constructs, compares, interprets and evaluates data displays, including tables, picture graphs and column graphs

·  Statistics and Probability 12 Trial and evaluate methods for collecting data, selecting the most effective method for a given investigation, including 2 way tables and one-to-many correspondence, evaluating the effectiveness of different displays of the same data.

·  Statistics and Probability 13 Ask questions about data in a display, including using the language of chance, and use the data to answer the questions..

ACMNA106 Create simple financial plans

NSW MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers

·  Money and Financial Mathematics 12 Financial plans, budgets, GST, invoices, receipts

ACMNA099 Use estimation and rounding to check the  reasonableness of answers to calculations

ACMNA291 Use efficient mental and written strategies and apply  appropriate digital technologies to solve problems

NSW MA3-5NA selects and applies appropriate strategies for addition and subtraction with counting numbers of any size

·  Addition and Subtraction 3 – 24 Add / subtract single-digit to 5-digit numbers

ACMNA098  Identify and describe factors and multiples of whole  numbers and use them to solve problems

ACMNA099 Use estimation and rounding to check the reasonableness of answers to calculations

ACMNA100 Solve problems involving multiplication of large  numbers by one-­ or two-­digit numbers using efficient  mental, written strategies and appropriate digital  technologies

ACMNA101 Solve problems involving division by a one digit  number, including those that result in a remainder

ACMNA121 Use equivalent number sentences involving  multiplication and division to find unknown quantities

NSW MA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

·  Multiplication and Division 20 Highest common factor

·  Multiplication and Division 21, Patterns and Algebra 26 Equivalent division calculations result if both numbers are divided by the same factor

·  Multiplication and Division 22 Divisibility Tests

·  Multiplication and Division 23 Fractions and Decimals 20 Division with remainders divided to create fractions

·  Multiplication and Division 24 Multiply 2-digit numbers, mental strategies

·  Fractions and Decimals 19 Role of vinculum as meaning divided by

ACMNA104 Recognise that the place value system can be extended beyond hundredths

ACMNA105 Compare, order and represent decimals

NSW MA3-7NA compares, orders and calculates with fractions, decimals and percentages

·  Fractions and Decimals 18, Place Value 24 Multiplicative place value, to hundredths, multiplying / dividing by 10, 100, 1000, as decimal and fraction

·  Fractions and Decimals 19, Place Value 25 Multiplicative, standard / non-standard thousandths

ACMNA102 Compare and order common unit fractions and  locate and represent them on a number line

ACMNA103 Investigate strategies to solve problems involving  addition and subtraction of fractions with the same  denominator

·  Fractions and Decimals 22 Place Value 26 Order fractions and decimals on a number line

·  Fractions and Decimals 23 Addition and Subtraction 29 Add / subtract fractions same denominator

ACMNA107 Describe, continue and create patterns with  fractions, decimals and whole numbers resulting  from addition and subtraction

NSW MA3-8NA analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane

·  Fractions and Decimals 24 Place Value 27 Patterns and Algebra 27 Number patterns fractions, decimals, whole numbers

ACMMG108 Choose appropriate units of measurement for  length, area, volume, capacity and mass

ACMMG109 Calculate the perimeter and area of rectangles using  familiar metric units

NSW MA3 9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length

·  Measurement and Geometry 51 Kilometres, multiplicative place value, convert between units, compare metric system / imperial system length

NSW MA3 10MG selects and uses the appropriate unit to calculate areas, including areas of squares, rectangles and triangles

·  Measurement and Geometry 52 Hectares, square kilometres, compare metric system / imperial system area

NSW MA3 11MG selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities, and converts between units of capacity

·  Measurement and Geometry 55 Cubic metres, compare metric / imperial system volume capacity

NSW MA3 12MG selects and uses the appropriate unit and device to measure the masses of objects, and converts between units of mass

·  Measurement and Geometry 57 Mass tonnes, multiplicative place value, convert, compare metric / imperial system mass, gross mass and net mass

ACMMG110 Compare 12­ and 24 hour time systems and convert  between them

NSW MA3 13MG uses 24-hour time and am and pm notation in real-life situations, and constructs timelines

·  Time 16 Duration stop watch, start and finish time

·  Time 17 Convert between 12 and 24 hour time

ACMMG111 Connect three ­dimensional objects with their nets  and other two­-dimensional representations

NSW MA3 14MG identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views

·  Measurement and Geometry 54 Properties prisms and pyramids, bases, faces shape, sections / cross-sections uniform / non-uniform

·  Measurement and Geometry 56 Draw prisms / pyramids, nets

ACMMG114 Describe translations, reflections and rotations of  two­ dimensional shapes. Identify line and rotational  symmetries

ACMMG115 Apply the enlargement transformation to familiar two  dimensional shapes and explore the properties of  the resulting image compared with the original

NSW MA3 15MG manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties

·  Measurement and Geometry 50 Rotational symmetry, translations, reflections

·  Measurement and Geometry 49 Angle / side properties two-dimensiomal shapes, enlarge, similar

ACMMG112 Estimate, measure and compare angles using  degrees. Construct angles using a protractor

NSW MA3 16MG measures and constructs angles, and applies angle relationships to find unknown angles

·  Measurement and Geometry 48 Angles in degrees with a protractor

ACMMG113 Use a grid reference system to describe locations.  Describe routes using landmarks and directional  language

NSW MA3 17MG locates and describes position on maps using a grid-reference system

·  Measurement and Geometry 53 Use legend / key, compass, scale, alpha-numeric grid references to locate features and describe routes

ACMSP116 List outcomes of chance experiments involving  equally likely outcomes and represent probabilities  of those outcomes using fractions

ACMSP117 Recognise that probabilities range from 0 to 1

ACMSP118 Pose questions and collect categorical or numerical  data by observation or survey

ACMSP120 Describe and interpret different data sets in context

NSW MA3 18SP uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables

·  Statistics and Probability 15 Column / line graphs, dot plots, tables, decisions

ACMSP119 List outcomes of chance experiments involving  equally likely outcomes and represent probabilities  of those outcomes using fractions

NSW MA3 19SP conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes

·  Statistics and Probability 16 Chance experiments, probabilities using fractions, identifying the sum equals 1

ACMNA124  Investigate everyday situations that use  integers. Locate and represent these  numbers on a number line

NSW MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers

·  Fractions and Decimals 25 Place Value 28 Multiplicative, standard and non standard place value of numbers of any size

·  Addition and Subtraction 32 Patterns and Algebra 30 Additive problems involving negative numbers

ACMNA123  Select and apply efficient mental and written  strategies and appropriate digital  technologies to solve problems involving all  four operations with whole numbers

NSW MA3-5NA selects and applies appropriate strategies for addition and subtraction with counting numbers of any size

·  Addition and Subtraction 3 – 28 Add / subtract single-digit to 5-digit numbers, solving problems (weekly)

ACMNA129  Multiply decimals by whole numbers and  perform divisions by non- zero whole numbers where the results are terminating decimals, with and without digital technologies

ACMNA130  Multiply and divide decimals by powers of 10

NSW MA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

·  Multiplication and Division 25 Fractions and Decimals 26 Place Value 29 Multiply / divide decimals 1000ths by whole numbers and powers of 10, record remainders fractions / decimals when dividing by 10

ACMNA134  Explore the use of brackets and order of  operations to write number sentences

·  Multiplication and Division 9 – 17, 19, 22, 24 Multiply / divide by 10, 2, 4, 3, 5, 9, 6, 8, 7, multiply 2-digit, solve problems (weekly)

·  Addition and Subtraction 33 Multiplication and Division 29 Patterns and Algebra 31 Order of operations / grouping symbols

ACMNA122  Identify and describe properties of prime,  composite, square and triangular numbers

·  Multiplication and Division 27 Patterns and Algebra 29 Identify and explain square and triangular numbers

·  Multiplication and Division 28 Patterns and Algebra 32 Prime and composite numbers, composite numbers are products of prime factors, using prime factors to simplify calculations

ACMNA125  Compare fractions with related  denominators and locate and represent  them on a number line

ACMNA126  Solve problems involving addition and  subtraction of fractions with the same or  related denominators

NSW MA3-7NA compares, orders and calculates with fractions, decimals and percentages

·  Fractions and Decimals 33 Addition and Subtraction 30 Add and subtract fractions with related denominators mental

ACMNA127  Find a simple fraction of a quantity where the  result is a whole number, with and without  digital technologies

NSW MA3-6NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

·  Fractions and Decimals 27 Multiplication and Division 28 Division is multiplication by a fraction

ACMNA128  Add and subtract decimals, with and without  digital technologies, and use estimation and  rounding to check the reasonableness of  answers

·  Fractions and Decimals 28 Fractions in their simplest form by dividing numerator and denominator by their highest common factor

·  Fractions and Decimals 32 Place Value 32 Addition and Subtraction 29 Add and subtract decimals using place value

ACMNA131  Make connections between equivalent  fractions, decimals and percentages

ACMNA132  Investigate and calculate percentage  discounts of 10%, 25% and 50% on sale  items, with and without digital technologies

·  Fractions and Decimals 29 Percentages as hundredths

·  Fractions and Decimals 30 Money and Financial Mathematics 13 Percentage discount

ACMNA133  Continue and create sequences involving  whole numbers, fractions and decimals.  Describe the rule used to create the sequence

NSW MA3-8NA analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane

·  Fractions and Decimals 34 Patterns and Algebra 28 Place Value 31 Addition and Subtraction 31 Patterns of whole numbers, fractions and decimals in table, describe rule

ACMMG143  Introduce the Cartesian coordinate system  using all four quadrants

·  Measurement and Geometry 62 Cartesian plane, describe location / construct shapes

ACMMG135  Connect decimal representations to the  metric system

ACMMG136  Convert between common metric units of  length, mass and capacity

NSW MA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length

·  Measurement and Geometry 59 Convert between metric length units using multiplicative place value

ACMMG137  Solve problems involving the comparison of  lengths and areas using appropriate units

NSW MA3-10MG selects and uses the appropriate unit to calculate areas, including areas of squares, rectangles and triangles

·  Measurement and Geometry 60 Different perimeters / same area, same perimeter / different areas

ACMMG138  Connect volume and capacity and their units  of measurement

NSW MA3-11MG selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities, and converts between units of capacity

·  Measurement and Geometry 64 Relate cubic / liquid units millilitre / cubic centimetre, convert liquid units multiplicative place value, compare metric / imperial cubic / liquid units

NSW MA3-12MG selects and uses the appropriate unit and device to measure the masses of objects, and converts between units of mass

·  Measurement and Geometry 67 Relate liquid units / mass units – litre / kilogram, convert mass units multiplicative place value

ACMMG139  Interpret and use timetables

NSW MA3-13MG uses 24-hour time and am and pm notation in real-life situations, and constructs timelines

·  Time 18 Timelines using scale

·  Time 19 Timetables, plan trips and daily activities

ACMMG140  Construct simple prisms and pyramids

NSW MA3-14MG identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views

·  Measurement and Geometry 63 Prisms and pyramids nets, cubes, skeletal, drawings

ACMMG142  Investigate combinations of translations, reflections and rotations, with and without  the use of digital technologies

NSW MA3-15MG manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties

·  Measurement and Geometry 61 Combinations translation, reflection, rotation

·  Measurement and Geometry 58 Diagonals, axes of symmetry

·  Measurement and Geometry 65 Parts of circles

ACMMG141  Investigate, with and without digital  technologies, angles on a straight line,  angles at a point and vertically opposite  angles. Use results to find unknown angles

NSW MA3-16MG measures and constructs angles, and applies angle relationships to find unknown angles

·  Measurement and Geometry 66 Right, acute, obtuse, straight, reflex, revolution, angles on a straight line and at a point, vertically opposite angles, equal size, use to find unknown angles

ACMSP147  Interpret and compare a range of data  displays, including side-­by-­side column graphs for two- categorical variables

ACMSP148  Interpret secondary data presented in digital  media and elsewhere

NSW MA3-18SP uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables

·  Statistics and Probability 19 Two-way tables and side-by-side column graphs, identifying intended message and potentially misleading

ACMSP144  Describe probabilities using fractions,  decimals and percentages

ACMSP145  Conduct chance experiments with both  small and large numbers of trials using  appropriate digital technologies

ACMSP146  Compare observed frequencies across  experiments with expected frequencies

NSW MA3-18SP conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes

·  Statistics and Probability 17 Trials, predict frequencies

·  Statistics and Probability 18 Fractions and Decimals 31 Place Value 30 Evaluate games of chance, describing probabilities using fractions, decimals and percentages, including on a number line