# EARLY STAGE ONE MATHS FOCUS

## NUMBERS AND ALGEBRA

## WHOLE NUMBERS

OUTCOME

A student:

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

TEACHING POINT | Students may use incorrect terms since these are frequently heard in everyday language, eg ‘How much did you get?’ rather than ‘How many did you get?’ when referring to a score in a game. To represent the equality of groups, the terms ‘is the same as’ and ‘is equal to’ should be used. In Early Stage 1, the term ‘is the same as’ is emphasised as it is more appropriate for students’ level of conceptual understanding. |

LANGUAGE | Students should be able to communicate using the following language: count forwards, count backwards, number before, number after, more than, less than, zero, ones, groups of ten, tens, is the same as, coins, notes, cents, dollars. |

## Expectations of Attainment

Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point | count forwards to 30 from a given number |

count backwards from a given number in the range 0 to 20 | |

identify the number before and after a given number | |

describe the number before as ‘one less than’ and the number after as ‘one more than’ a given number | |

read and use the ordinal names to at least ‘tenth’ |

Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond | read numbers to at least 20, including zero, and represent these using objects (such as fingers), pictures, words and numerals |

estimate the number of objects in a group of up to 20 objects, and count to check | |

use 5 as a reference in forming numbers from 6 to 10, eg ‘Six is one more than five’ | |

use 10 as a reference in forming numbers from 11 to 20, eg ‘Thirteen is 1 group of ten and 3 ones’ |

Subitise small collections of objects | recognise the number of objects or dots in a pattern of objects or dots instantly, |

instantly recognise (subitise) different arrangements for the same number, eg different representations of five | |

Compare, order and make correspondences between collections, initially to 20, and explain reasoning | count with one-to-one correspondence |

make correspondences between collections, eg ‘I have four counters, you have seven counters. So you have more counters than me’ | |

compare and order numbers and groups of objects | |

use the term ‘is the same as’ to express equality of groups |

Use the language of money | use the language of money in everyday contexts, eg coins, notes, cents, dollars |

recognise that there are different coins and notes in our monetary system |

## ADDITION & SUBTRACTION

OUTCOME

A student:

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

TEACHING POINT | The word ‘difference’ has a specific meaning in this context, referring to the numeric value of the group. In everyday language, it can refer to any attribute. |

LANGUAGE | Students should be able to communicate using the following language: count forwards, combines with, joins, count backwards, take away, how many more, all together, makes. |

## Expectations of Attainment

Represent practical situations to model addition and sharing | combine two or more groups of objects to model addition |

model subtraction by separating and taking away part of a group of objects | |

use concrete materials or fingers to model and solve simple addition and subtraction problems | |

compare two groups of objects to determine ‘how many more’ | |

use visual representations of numbers to assist with addition and subtraction, eg ten frames | |

create and recognise combinations for numbers to at least 10, eg ‘How many more make 10?’ | |

describe the action of combining, separating and comparing using everyday language, eg makes, joins, combines with, and, get, take away, how many more, all together | |

count forwards by ones to add and backwards by ones to subtract | |

record addition and subtraction informally using drawings, words and numerals |

## MULTIPLICATION & DIVISION

OUTCOME

A student:

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

TEACHING POINT There are two forms of division: | Sharing (partitive) – How many in each group? eg ‘If 12 marbles are shared between three students, how many does each get?’ |

Grouping (quotitive) – How many groups are there? eg ‘If I have 12 marbles and each child is to get four, how many children will get marbles?’ |

LANGUAGE | Students should be able to communicate using the following language: group, share, equal. |

## Expectations of Attainment

Investigate and model equal groups | use the term ‘group’ to describe a collection of objects |

use the term ‘sharing’ to describe the distribution of a collection of objects | |

model equal groups | |

recognise groups that are not equal in size | |

group and share concrete materials to solve problems |

## FRACTIONS & DECIMALS

OUTCOME

A student:

MAe-7NA: describes two equal parts as halves

TEACHING POINT | In everyday usage, the term ‘half’ is sometimes used to mean one of two parts and not necessarily two equal parts, eg ‘I’ll have the biggest half’. It is important to model and reinforce the language of ‘two equal parts’ when describing half. |

LANGUAGE | Students should be able to communicate using the following language: whole, part, equal parts, half, halves. |

## Expectations of Attainment

Establish the concept of one-half | share an object by dividing it into two equal parts, eg cutting a piece of ribbon into halves |

recognise that halves are two equal parts | |

recognise when two parts are not halves of one whole | |

use the term ‘half’ accurately in everyday situations | |

record halves of objects using drawings | |

recognise halves can be different shapes |

## PATTERNS & ALGEBRA

OUTCOME

A student:

MAe-8NA: recognises, describes and continues repeating patterns

TEACHING POINT There are two forms of division: | Sharing (partitive) – How many in each group? eg ‘If 12 marbles are shared between three students, how many does each get?’ |

Grouping (quotitive) – How many groups are there? eg ‘If I have 12 marbles and each child is to get four, how many children will get marbles?’ |

LANGUAGE | Students should be able to communicate using the following language: group, share, equal. |

## Expectations of Attainment

Investigate and model equal groups | use the term ‘group’ to describe a collection of objects |

use the term ‘sharing’ to describe the distribution of a collection of objects | |

model equal groups | |

recognise groups that are not equal in size | |

group and share concrete materials to solve problems |

Record grouping and sharing using informal methods | label the number of objects in a group |

record grouping and sharing informally using pictures, words and numerals |

## MEASUREMENT AND GEOMETRY

## LENGTH

OUTCOME

A student:

MAe-9MG: describes and compares lengths and distances using everyday language

TEACHING POINT | When students are asked to compare the lengths of two objects of equal length and can consistently say that the objects are equal in length though their relative positions have been altered, they are |

This is an important concept and develops over time. | |

Once students can compare two lengths, they should then be given the opportunity to order three or more lengths. This process requires students to understand that if A is longer than B, and B is longer than C, then A is longer than C. | |

Once students can compare two lengths, they should then be given the opportunity to order three or more lengths. This process requires students to understand that if A is longer than B, and B is longer than C, then A is longer than C. | |

Length and distance are distinct concepts. The term ‘length’ is generally used to describe a measure from end to end of a drawn interval, a two-dimensional shape or a three-dimensional object. The term ‘distance’ is generally used to describe the lineal space between two things, places or points. Activities should focus on both concepts. |

LANGUAGE | Students should be able to communicate using the following language: length, end, end-to-end, side-by-side, long, longer than, longest, short, shorter than, shortest, high, higher than, highest, tall, taller than, tallest, low, lower than, lowest, the same as, near, nearer, far, further, close, closer. |

## Expectations of Attainment

Use direct and indirect comparisons to decide which is longer, and explain their reasoning using everyday language (ACMMG006) | identify the attribute of ‘length’ as the measure of an object from end to end |

make and sort long and short constructions from concrete materials | |

use everyday language to describe length, eg long, short, high, tall, low | |

use everyday language to describe distance, eg near, far, nearer, further, closer | |

use comparative language to describe length, eg longer, higher, taller than, shortest, lower than, longest, the same as | |

compare lengths directly by placing objects side-by-side and aligning the ends | |

compare lengths indirectly by copying a length, eg using the same strip of paper to compare lengths | |

record length comparisons informally by drawing, tracing, or cutting and pasting, and by using words and numerals |

## AREA

OUTCOME

A student:

MAe-10MG: describes and compares areas using everyday language

TEACHING POINT | The attribute of area is the amount of surface (either flat or curved) and can be measured in square units, eg square centimetres (cm2), square metres (m2). |

In Early Stage 1, students develop an awareness of the attribute of area and some of the language used to describe area. They develop an awareness of the attribute of area through covering activities, through colouring in, and as comparisons of area are made. | |

Students should be given opportunities to compare: two similar shapes of different areas where one fits inside the boundary of the other; two different-shaped areas where one can be placed on top of the other; two shapes where one shape can be cut up and pasted onto the other. | |

Once students can compare two areas, they should then be given the opportunity to order three or more areas. This process requires students to understand that if A is larger than B, and B is larger than C, then A is larger than C. |

LANGUAGE | Students should be able to communicate using the following language: area, surface, closed shape, inside, outside, bigger than, smaller than, the same as. |

Superimposing – the comparison of areas by placing one area on top of another. | |

Superpositioning – the comparison of areas by aligning the edges (or corners) of two areas when one is placed on top of the other. |

## EXPECTATIONS OF ATTAINMENT

Use direct comparison to decide which shape has a larger area and explain their reasoning using everyday language | identify the attribute of ‘area’ as the measure of the amount of surface |

cover surfaces completely with smaller shapes | |

make closed shapes and describe the area of each shape | |

use everyday language to describe area, eg surface, inside, outside | |

use comparative language to describe area, eg bigger than, smaller than, the same as | |

compare two areas directly, eg superimposing or superpositioning two surfaces | |

record area comparisons informally by drawing, tracing, or cutting and pasting, and by using numerals and words |

## VOLUME & CAPACITY

OUTCOME

A student:

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

TEACHING POINT | The term ‘big’ is often used by students to describe a variety of attributes. Depending on the context, it could mean long, tall, heavy, etc. It is important to model with students more precise language to describe volume and capacity. |

LANGUAGE | Students should be able to communicate using the following language: capacity, container, liquid, full, empty, about half-full, volume, space, has more, has less, will hold more, will hold less, takes up more space. |

## EXPECTATIONS OF ATTAINMENT

Use direct and indirect comparisons to decide which holds more, and explain their reasoning using everyday language | identify the attribute of ‘capacity’ as the amount of liquid a container can hold |

fill and empty containers using materials such as water and sand | |

use the terms ‘full’, ’empty’ and ‘about half-full’ | |

compare the capacities of two containers directly by filling one and pouring into the other | |

compare the capacities of two containers indirectly by pouring their contents into two other identical containers and observing the level reached by each | |

establish that containers of different shapes may have the same capacity, eg a tall narrow container may hold the same amount as a short wide container | |

identify the attribute of ‘volume’ as the amount of space an object or substance occupies | |

stack and pack blocks into defined spaces, eg boxes | |

compare the volumes of two objects made from blocks or connecting cubes directly by deconstructing one object and using its parts to construct a copy of the other object | |

compare the volumes of two piles of material directly by filling two identical containers, eg ‘This pile of rice has a larger volume as it takes up more space in the container’ | |

compare the volumes of two objects by observing the amount of space each occupies, eg a garbage truck takes up more space than a car | |

use comparative language to describe volume and capacity, eg has more, has less, will hold more, will hold less, takes up more space | |

record volume and capacity comparisons informally using drawings, numerals and words |

## MASS

OUTCOME

A student:

MAe-12MG: describes and compares the masses of objects using everyday language

TEACHING POINT | As the terms ‘weigh’ and ‘weight’ are common in everyday usage, they can be accepted in student language should they arise. Weight is a force that changes with gravity, while mass remains constant. |

Hefting’ is testing the weight of an object by lifting and balancing it. Where possible, students can compare the weights of two objects by using their bodies to balance each object, eg holding one object in each hand. |

LANGUAGE | Students should be able to communicate using the following language: mass, matter, heavy, heavier, heaviest, light, lighter, lightest, about the same as, hard to push, hard to pull. |

## EXPECTATIONS OF ATTAINMENT

Use direct and indirect comparisons to decide which is heavier, and explain their reasoning using everyday language (ACMMG006) | identify the attribute of ‘mass’ as the amount of matter in an object |

use everyday language to describe objects in terms of their mass, eg heavy, light, hard to push, hard to pull | |

use comparative language to describe mass, eg heavier, lighter, heaviest, lightest | |

compare and describe two masses, such as by pushing or pulling | |

compare two masses directly by hefting, eg ‘This toy feels heavier than that one’ | |

record comparisons of mass informally using drawings, numerals and words |

## TIME

OUTCOME

A student:

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

TEACHING POINT | The words ‘long’ and ‘short’ can be confusing to students who have only experienced these words in terms of length measurement. Students will need experience with these words in both length and time contexts. |

LANGUAGE | Students should be able to communicate using the following language: daytime, night-time, yesterday, today, tomorrow, before, after, next, a long time, a short time, week, days, weekdays, weekend days, time, morning, afternoon, clock, analog, digital, hands (of a clock), o’clock. |

## EXPECTATIONS OF ATTAINMENT

Compare and order the duration of events using the everyday language of time (ACMMG007) | use terms such as ‘daytime’, ‘night-time’, ‘yesterday’, ‘today’, ‘tomorrow’, ‘before’, ‘after’, ‘next’, ‘morning’ and ‘afternoon’ |

sequence events in time | |

compare the duration of two events using everyday language, eg ‘It takes me longer to eat my lunch than it does to clean my teeth’ |

Connect days of the week to familiar events and actions (ACMMG008) | recall that there are seven days in a week |

name and order the days of the week | |

classify weekdays and weekend days | |

relate events to a particular day or time of day, eg ‘Assembly is on Tuesday’, ‘We come to school in the morning’ |

Tell time on the hour on analog and digital clocks | read analog and digital clocks to the hour using the term ‘o’clock’ |

describe the position of the hands on an analog clock when reading hour time |

## THREE-DIMENSIONAL SPACE

OUTCOME

A student:

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

TEACHING POINT | The term ‘shape’ refers to a two-dimensional figure. The term ‘object’ refers to a three-dimensional figure. |

Manipulation of a variety of real objects and shapes is crucial to the development of appropriate levels of imagery, language and representation. | |

Local landmarks include buildings, rivers, rock formations and bridges, as well as Aboriginal landmarks. Aboriginal landmarks may include contemporary landmarks and local points of interest. Local Aboriginal communities and education consultants can provide examples |

LANGUAGE | Students should be able to communicate using the following language: object, shape, size, curved, flat, pointy, round, roll, slide, stack. |

## EXPECTATIONS OF ATTAINMENT

Sort, describe and name familiar three-dimensional objects in the environment (ACMMG009) | describe the features of familiar three-dimensional objects, such as local landmarks including Aboriginal landmarks, using everyday language, eg flat, round, curved |

sort three-dimensional objects and explain the attributes used to sort them, eg colour, size, shape, function | |

recognise and use informal names for three-dimensional objects, eg box, ball | |

manipulate and describe a variety of objects found in the environment | |

predict and describe the movement of objects, eg ‘This will roll because it is round’ | |

make models using a variety of three-dimensional objects and describe the models, eg ‘I made a model of a person using a ball and some blocks’ |

## TWO-DIMENSIONAL SPACE

OUTCOME

A student:

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

TEACHING POINT | It is important that students experience shapes that are represented in a variety of ways, eg ‘tall skinny’ triangles, ‘short fat’ triangles, right-angled triangles presented in different orientations and of different sizes, and shapes that are represented using a variety of materials, eg paint, images on the computer, string. Manipulation of a variety of real objects and shapes is crucial to the development of appropriate levels of language and representation. |

In Early Stage 1, it is important that teachers present students with both regular and irregular shapes (regular shapes have all sides and all angles equal). However, students are not expected to use the terms ‘regular’ and ‘irregular’ themselves. | |

Students should be given time to explore materials in order to represent shapes by tearing, painting, drawing, writing, or cutting and pasting. |

LANGUAGE | Students should be able to communicate using the following language: shape, circle, triangle, square, rectangle, features, side, straight line, curved line, open line, closed shape. |

## EXPECTATIONS OF ATTAINMENT

Sort, describe and name familiar two-dimensional shapes in the environment (ACMMG009) | identify, represent and name circles, triangles, squares and rectangles presented in different orientations, eg |

sort two-dimensional shapes according to features such as size and shape | |

manipulate circles, triangles, squares and rectangles, and describe their features using everyday language, eg ‘A square has four sides’ | |

make representations of two-dimensional shapes using a variety of materials, including paint, paper, body movements and computer drawing tools | |

draw a two-dimensional shape by tracing around one face of a three-dimensional object | |

identify and draw straight and curved lines | |

compare and describe closed shapes and open lines | |

draw closed two-dimensional shapes without tracing |

## POSITION

OUTCOME

A student:

MAe-16MG: describes position and gives and follows simple directions using everyday language

TEACHING POINT | There are two main ideas for students in Early Stage 1: following an instruction to position an object or themselves, and describing the relative position of an object or themselves. Some students may be able to describe the position of an object in relation to themselves, but not in relation to another object. |

In Early Stage 1, students use the terms ‘left’ and ‘right’ to describe position in relation to themselves. They are not expected to use the terms ‘left’ and ‘right’ to describe the position of an object from the perspective of a person facing in the opposite direction until Stage 1. |

LANGUAGE | Students should be able to communicate using the following language: position, between, next to, behind, inside, outside, left, right, directions. |

## EXPECTATIONS OF ATTAINMENT

Describe position and movement | give and follow simple directions to position an object or themselves, eg ‘Put the blue teddy in the circle’ |

describe the position of an object in relation to themselves using everyday language, such as ‘between’, ‘next to’, ‘behind’ or ‘inside’, eg ‘The table is behind me’ | |

describe the position of an object in relation to another object using everyday language, such as ‘between’, ‘next to’, ‘behind’ or ‘inside’, eg ‘The book is inside the box’ | |

describe the positions of objects in relation to themselves using the terms ‘left’ and ‘right’, eg ‘The tree is on my right’ |

## DATA

OUTCOME

A student:

MAe-17SP: represents data and interprets data displays made from objects

TEACHING POINT | In Early Stage 1, students collect information about themselves and their environment with teacher assistance. They use actual objects as data and group these objects into a data display. |

LANGUAGE | Students should be able to communicate using the following language: information, collect, group, display, objects. |

## EXPECTATIONS OF ATTAINMENT

Answer yes/no questions to collect information (ACMSP011) | collect information about themselves and their environment, including by asking and answering yes/no questions |

Organise objects into simple data displays and interpret the displays | group objects according to characteristics to form a simple data display, eg sort blocks or counters according to colour |

arrange objects in rows or columns according to characteristics to form a data display, eg arrange lunchboxes in columns according to colour | |

interpret information presented in a display of objects to answer questions, eg ‘How many children in our class have red pencil cases?’ |

## STATISTICS AND PROBABILITY

## DATA

OUTCOME

A student:

MAe-17SP: represents data and interprets data displays made from objects

TEACHING POINT | In Early Stage 1, students collect information about themselves and their environment with teacher assistance. They use actual objects as data and group these objects into a data display. |

LANGUAGE | Students should be able to communicate using the following language: information, collect, group, display, objects. |

## EXPECTATIONS OF ATTAINMENT

Answer yes/no questions to collect information (ACMSP011) | collect information about themselves and their environment, including by asking and answering yes/no questions |

Organise objects into simple data displays and interpret the displays | group objects according to characteristics to form a simple data display, eg sort blocks or counters according to colour |

arrange objects in rows or columns according to characteristics to form a data display, eg arrange lunchboxes in columns according to colour | |

interpret information presented in a display of objects to answer questions, eg ‘How many children in our class have red pencil cases?’ |