Whole Numbers

Addition & Subtraction

Multiplication & Division

Fractions & Decimals

Patterns & Algebra

Whole Numbers

OUTCOME

A student:

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

TEACHER NOTE | Students should be encouraged to develop different counting strategies, eg if they are counting a large number of items, they can count out groups of ten and then count the groups. |

They need to learn correct rounding of numbers based on the convention of rounding up if the last digit is 5 or more and rounding down if the last digit is 4 or less. |

LANGUAGE | Students should be able to communicate using the following language: count forwards, count backwards, number before, number after, more than, less than, number line, number chart, digit, zero, ones, groups of ten, tens, groups of one hundred, hundreds, round to. |

The word ‘and’ is used when reading a number or writing it in words, eg five hundred and sixty-three. |

Develop confidence with number sequences to 100 by ones from any starting point (ACMNA012) | count forwards or backwards by ones, from a given three-digit number |

identify the numbers before and after a given three-digit number | |

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

Recognise, model, represent and order numbers to at least 1000 (ACMNA027) | represent three-digit numbers using objects, pictures, words and numerals |

use the terms ‘more than’ and ‘less than’ to compare numbers | |

arrange numbers of up to three digits in ascending order | |

use number lines and number charts beyond 100 to assist with counting and ordering (Communicating, Problem Solving) | |

give reasons for placing a set of numbers in a particular order (Communicating, Reasoning) |

Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences (ACMNA026) | count forwards and backwards by twos, threes and fives from any starting point |

count forwards and backwards by tens, on and off the decade, with two- and three-digit numbers, eg 40, 30, 20, … (on the decade); 427, 437, 447, … (off the decade) | |

identify number sequences on number charts |

Group, partition and rearrange collections of up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028) | apply an understanding of place value and the role of zero to read, write and order three-digit numbers |

form the largest and smallest number from three given digits (Communicating, Reasoning) | |

recognise the symbols for dollars ($) and cents (c) | |

count and represent large sets of objects by systematically grouping in tens and hundreds | |

use models such as base 10 material, interlocking cubes and bundles of sticks to explain grouping (Communicating, Reasoning) | |

use and explain mental grouping to count and to assist with estimating the number of items in large groups | |

use place value to partition three-digit numbers, eg 326 as 3 groups of one hundred, 2 groups of ten and 6 ones | |

state the place value of digits in numbers of up to three digits, eg ‘In the number 583, the “5” represents 500 or 5 hundreds’ | |

partition three-digit numbers in non-standard forms, eg 326 can be 32 groups of ten and 6 ones | |

round numbers to the nearest hundred | |

estimate, to the nearest hundred, the number of objects in a collection and check by counting, eg show 120 pop sticks and ask students to estimate to the nearest hundred |

Count and order small collections of Australian coins and notes according to their value (ACMNA034) | use the face value of coins and notes to sort, order and count money |

compare Australian coins and notes with those from other countries, eg from students’ cultural backgrounds (Communicating) | |

determine whether there is enough money to buy a particular item (Problem Solving, Reasoning) | |

recognise that there are 100 cents in $1, 200 cents in $2, … | |

identify equivalent values in collections of coins and in collections of notes, eg four $5 notes have the same value as one $20 note |

Addition & Subtraction

OUTCOME

A student:

MA1-5NA: uses a range of strategies and informal recording methods for addition and subtraction involving one- and two-digit numbers

Teaching Point | Some students may need assistance when two tenses are used within the one problem, eg ‘I had six beans and took away four. So, how many do I have now?’ |

The word ‘left’ can be confusing for students, eg ‘There were five children in the room. Three went to lunch. How many are left?’ Is the question asking how many children are remaining in the room, or how many children went to lunch? |

Language | Students should be able to communicate using the following language: plus, add, take away, minus, the difference between, equals, is equal to, empty number line, strategy. |

Strategies | Jump strategy on a number line – an addition or subtraction strategy in which the student places the first number on an empty number line and then counts forward or backwards, first by tens and then by ones, to perform a calculation. (The number of jumps will reduce with increased understanding.) Jump strategy method: eg 46 + 33 Two number lines show different ways of adding numbers using small and large increments. Jump strategy method: eg 79 – 33 |

Split strategy – an addition or subtraction strategy in which the student separates the tens from the units and adds or subtracts each separately before combining to obtain the final answer. Split strategy method: eg 46 + 33 46+33 | |

Inverse strategy – a subtraction strategy in which the student adds forward from the smaller number to obtain the larger number, and so obtains the answer to the subtraction calculation. Inverse strategy method: eg 65 – 37 start at 37 An inverse operation is an operation that reverses the effect of the original operation. Addition and subtraction are inverse operations; multiplication and division are inverse operations. |

Explore the connection between addition and subtraction | use concrete materials to model how addition and subtraction are inverse operations |

use related addition and subtraction number facts to at least 20, eg 15 + 3 = 18, so 18 – 3 = 15 and 18 – 15 = 3 |

Solve simple addition and subtraction problems using a range of efficient mental and written strategies | use and record a range of mental strategies to solve addition and subtraction problems involving two-digit numbers, including: |

the jump strategy on an empty number line | |

the split strategy, eg record how the answer to 37 + 45 was obtained using the split strategy 30+40=70 7+5=12 so 70+12=82 | |

an inverse strategy to change a subtraction into an addition, eg 54 – 38: start at 38, adding 2 makes 40, then adding 10 makes 50, then adding 4 makes 54, and so the answer is 2 + 10 + 4 = 16 | |

select and use a variety of strategies to solve addition and subtraction problems involving one- and two-digit numbers | |

perform simple calculations with money, eg buying items from a class shop and giving change (Problem Solving) | |

check solutions using a different strategy (Problem Solving) | |

recognise which strategies are more efficient and explain why (Communicating, Reasoning) | |

explain or demonstrate how an answer was obtained for addition and subtraction problems, eg show how the answer to 15 + 8 was obtained using a jump strategy on an empty number line (Communicating, Reasoning) |

Multiplication & Division

OUTCOME

A student:

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

TEACHING POINTS | After students have divided a quantity into equal groups (eg they have divided 12 into groups of four), the process can be reversed by combining the groups, thus linking multiplication and division. |

When sharing a collection of objects into two, four or eight groups, students may describe the number of objects in each group as being one-half, one-quarter or one-eighth, respectively, of the whole collection. | |

An array is one of several different arrangements that can be used to model multiplicative situations involving whole numbers. It is made by arranging a set of objects, such as counters, into columns and rows. Each column must contain the same number of objects as the other columns, and each row must contain the same number of objects as the other rows. | |

Formal writing of number sentences for multiplication and division, including the use of the symbols × and ÷, is not introduced until Stage 2. |

STRATEGIES | 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?’ This form of division relates to repeated subtraction, 12 – 4 – 4 – 4 = 0, so three children will get four marbles each. |

LANGUAGE | Students should be able to communicate using the following language: add, take away, group, row, column, array, number of rows, number of columns, number in each row, number in each column, total, equal, is the same as, shared between, shared equally, part left over, empty number line, number chart. |

The term ‘row’ refers to a horizontal grouping, and the term ‘column’ refers to a vertical grouping. | |

Refer also to language in Stage One 1 Multiplication and Division |

Recognise and represent multiplication as repeated addition, groups and arrays | model multiplication as repeated addition, eg 3 groups of 4 is the same as 4 + 4 + 4 |

– find the total number of objects by placing them into equal-sized groups and using repeated addition (Problem Solving) | |

– use empty number lines and number charts to record repeated addition, eg (Communicating) | |

– explore the use of repeated addition to count in practical situations, eg counting stock on a farm (Problem Solving) | |

recognise when items have been arranged into groups, eg ‘I can see two groups of three pencils’ | |

use concrete materials to model multiplication as equal ‘groups’ and by forming an array of equal ‘rows’ or equal ‘columns’, eg | |

– describe collections of objects as ‘groups of’, ‘rows of’ and ‘columns of’ (Communicating) | |

– determine and distinguish between the ‘number of rows/columns’ and the ‘number in each row/column’ when describing collections of objects (Communicating) | |

– recognise practical examples of arrays, such as seedling trays or vegetable gardens (Reasoning) | |

model the commutative property of multiplication, eg ‘3 groups of 2 is the same as 2 groups of 3’ |

Represent division as grouping into equal sets and solve simple problems using these representations | model division by sharing a collection of objects equally into a given number of groups, and by sharing equally into a given number of rows or columns in an array, eg determine the number each person receives when 10 objects are shared between two people |

– describe the part left over when a collection cannot be shared equally into a given number of groups/rows/columns (Communicating, Problem Solving, Reasoning) | |

model division by sharing a collection of objects into groups of a given size, and by arranging it into rows or columns of a given size in an array, eg determine the number of columns in an array when 20 objects are arranged into rows of four | |

– describe the part left over when a collection cannot be distributed equally using the given group/row/column size, eg when 14 objects are arranged into rows of five, there are two rows of five and four objects left over (Communicating, Problem Solving, Reasoning) | |

model division as repeated subtraction | |

– use an empty number line to record repeated subtraction (Communicating) | |

– explore the use of repeated subtraction to share in practical situations, eg share 20 stickers between five people (Problem Solving) | |

solve multiplication and division problems using objects, diagrams, imagery and actions | |

– support answers by demonstrating how an answer was obtained (Communicating) | |

– recognise which strategy worked and which did not work and explain why (Communicating, Reasoning) | |

record answers to multiplication and division problems using drawings, words and numerals, eg ‘two rows of five make ten’, ‘2 rows of 5 is 10’ |

Fractions & Decimals

OUTCOME

A student:

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

TEACHING POINT | In Stage 1, the term ‘three-quarters’ may be used to name the remaining parts after one-quarter has been identified. |

LANGUAGE | Students should be able to communicate using the following language: whole, part, equal parts, half, quarter, eighth, one-half, one-quarter, one-eighth, halve (verb). |

Recognise and interpret common uses of halves, quarters and eighths of shapes and collections | use concrete materials to model a half, a quarter or an eighth of a whole object, eg divide a piece of ribbon into quarters |

– create quarters by halving one-half, eg ‘I halved my paper then halved it again and now I have quarters’ (Communicating, Problem Solving) | |

– describe the equal parts of a whole object, eg ‘I folded my paper into eight equal parts and now I have eighths’ (Communicating) | |

– discuss why 1/8 is less than 1/4, eg if a cake is shared among eight people, the slices are smaller than if the cake is shared among four people (Communicating, Reasoning) | |

recognise that fractions refer to equal parts of a whole, eg all four quarters of an object are the same size | |

– visualise fractions that are equal parts of a whole, eg ‘Imagine where you would cut the rectangle before cutting it’ (Problem Solving) | |

recognise when objects and shapes have been shared into halves, quarters or eighths | |

record equal parts of whole objects and shapes, and the relationship of the parts to the whole, using pictures and the fraction notation for half (1/2), quarter (1/4) and eighth (1/8), eg | |

use concrete materials to model a half, a quarter or an eighth of a collection, eg | |

– describe equal parts of a collection of objects, eg ‘I have quarters because the four parts have the same number of counters’ (Communicating) | |

recognise when a collection has been shared into halves, quarters or eighths | |

record equal parts of a collection, and the relationship of the parts to the whole, using pictures and the fraction notation for half (1/2), quarter (1/4) and eighth (1/8) | |

use fraction language in a variety of everyday contexts, eg the half-hour, one-quarter of the class |

Patterns & Algebra

OUTCOME

A student:

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

TEACHING POINT | In Stage 1, describing number relationships and making generalisations should be encouraged when appropriate. |

LANGUAGE | Students should be able to communicate using the following language: pattern, missing number, number sentence. |

Describe patterns with numbers and identify missing elements | describe a number pattern in words, eg ‘It goes up by threes’ |

determine a missing number in a number pattern, eg 3, 7, 11, __, 19, 23, 27 | |

– describe how the missing number in a number pattern was determined (Communicating, Reasoning) | |

– check solutions when determining missing numbers in number patterns by repeating the process (Reasoning) |

Solve problems by using number sentences for addition or subtraction | Complete number sentences involving one operation of addition or subtraction by calculating the missing number, eg find _ so that 5+_=13 or 15−_=9 |

– make connections between addition and related subtraction facts to at least 20 (Reasoning) | |

– describe how a missing number in a number sentence was calculated (Communicating, Reasoning) | |

solve problems involving addition or subtraction by using number sentences | |

– represent a word problem as a number sentence (Communicating, Problem Solving) | |

– pose a word problem to represent a number sentence (Communicating, Problem Solving) |

Length

Area

Volume & Capacity

Mass

Time

3D Space

2D Space

Position

Length

OUTCOME

A student:

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

Teaching Points | Students should be given opportunities to apply their understanding of measurement, gained through experiences with the use of uniform informal units, to experiences with the use of the centimetre and metre. They could make a measuring device using uniform informal units before using a ruler, eg using a length of 10 connecting cubes. This would assist students in understanding that the distances between marks on a ruler represent unit lengths and that the marks indicate the endpoints of each unit. |

When recording measurements, a space should be left between the number and the abbreviated unit, eg 3 cm, not 3cm. |

Language | Students should be able to communicate using the following language: length, distance, straight line, curved line, metre, centimetre, measure, estimate. |

Compare and order several shapes and objects based on length, using appropriate uniform informal units (ACMMG037) | relate the term ‘length’ to the longest dimension when referring to an object |

make and use a tape measure calibrated in uniform informal units, eg calibrate a paper strip using footprints as a repeated unit | |

– use computer software to draw a line and use a simple graphic as a uniform informal unit to measure its length (Communicating) | |

compare and order two or more shapes or objects according to their lengths using an appropriate uniform informal unit | |

– compare the lengths of two or more objects that cannot be moved or aligned (Reasoning) | |

record length comparisons informally using drawings, numerals and words, and by referring to the uniform informal unit used |

Recognise and use formal units to measure the lengths of objects | recognise the need for formal units to measure lengths and distances |

use the metre as a unit to measure lengths and distances to the nearest metre or half-metre | |

– explain and model, using concrete materials, that a metre-length can be a straight line or a curved line (Communicating, Reasoning) | |

record lengths and distances using the abbreviation for metres (m) | |

estimate lengths and distances to the nearest metre and check by measuring | |

recognise the need for a formal unit smaller than the metre | |

recognise that there are 100 centimetres in one metre, ie 100 centimetres = 1 metre | |

use the centimetre as a unit to measure lengths to the nearest centimetre, using a device with 1 cm markings, eg use a paper strip of length 10 cm | |

record lengths and distances using the abbreviation for centimetres (cm) | |

estimate lengths and distances to the nearest centimetre and check by measuring |

Area

OUTCOME

A student:

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

TEACHING POINTS | In Stage 1, measuring the areas of objects using informal units enables students to develop some key understandings of measurement. These include repeatedly placing units so that there are no gaps or overlaps and understanding that the units must be equal in size. Covering surfaces with a range of informal units should assist students in understanding that some units tessellate and are therefore more suitable for measuring area. |

When students understand why tessellating units are important, they should be encouraged to make, draw and describe the spatial structure (grid). Students should develop procedures for counting tile or grid units so that no units are missed or counted twice. | |

Students should also be encouraged to identify and use efficient strategies for counting, eg using repeated addition, rhythmic counting or skip counting. | |

It is important that students have had some measurement experiences before being asked to estimate areas, and that a variety of estimation strategies is taught. |

LANGUAGE | Students should be able to communicate using the following language: area, surface, measure, grid, row, column. |

Compare and order several shapes and objects based on area using appropriate uniform informal units (ACMMG037) | draw the spatial structure (grid) of repeated units covering a surface |

– explain the structure of the unit tessellation in terms of rows and columns (Communicating) | |

compare and order the areas of two or more surfaces that cannot be moved, or superimposed, by measuring in uniform informal units | |

– predict the larger of two or more areas and check by measuring (Reasoning) | |

record comparisons of area informally using drawings, numerals and words, and by referring to the uniform informal unit used |

Volume & Capacity

OUTCOME

A student:

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

Teaching Points | The order in which volume and capacity appear in the content is not necessarily indicative of the order in which they should be taught. |

Calibrating a container using uniform informal units is a precursor to students using measuring cylinders calibrated in formal units (litres and millilitres) at a later stage. | |

An object displaces its own volume when totally submerged. | |

Refer also to background information in Volume and Capacity Year 1 |

Language | Students should be able to communicate using the following language: capacity, container, volume, measure. |

Compare and order several objects based on volume and capacity using appropriate uniform informal units (ACMMG037) | make and use a measuring device for capacity calibrated in uniform informal units, eg calibrate a bottle by adding cups of water and marking the new level as each cup is added |

compare and order the capacities of two or more containers by measuring each container in uniform informal units | |

compare and order the volumes of two or more models by counting the number of blocks used in each model | |

– recognise that models with different appearances may have the same volume (Reasoning) | |

compare and order the volumes of two or more objects by marking the change in water level when each is submerged | |

– recognise that changing the shape of an object does not change the amount of water it displaces (Reasoning) | |

record volume and capacity comparisons informally using drawings, numerals and words, and by referring to the uniform informal unit used |

Mass

OUTCOME

A student:

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

TEACHING POINTS | In Stage 1, measuring mass using informal units enables students to develop some key understandings of measurement. These include: repeatedly using a unit as a measuring device; selecting an appropriate unit for a specific task; appreciating that a common informal unit is necessary for comparing the masses of objects; understanding that some units are unsatisfactory because they are not uniform, eg pebbles. |

Students should appreciate that the pan balance has two functions: comparing the masses of two objects and measuring the mass of an object by using a unit repeatedly as a measuring device | |

When students realise that changing the shape of an object does not alter its mass, they are said to conserve the property of mass |

LANGUAGE | Students should be able to communicate using the following language: mass, heavier, lighter, about the same as, pan balance, (level) balance, measure, estimate. ‘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. |

Compare the masses of objects using balance scales | compare and order the masses of two or more objects by hefting and check using a pan balance |

recognise that mass is conserved, eg the mass of a lump of plasticine remains constant regardless of the shape it is moulded into or whether it is divided up into smaller pieces | |

use uniform informal units to measure the mass of an object by counting the number of units needed to obtain a level balance on a pan balance | |

– select an appropriate uniform informal unit to measure the mass of an object and justify the choice (Problem Solving | |

– explain the relationship between the mass of a unit and the number of units needed, eg more toothpicks than pop sticks will be needed to balance the object (Communicating, Reasoning) | |

record masses by referring to the number and type of uniform informal unit used | |

compare two or more objects according to their masses using appropriate uniform informal units | |

record comparisons of mass informally using drawings, numerals and words, and by referring to the uniform informal units used | |

find differences in mass by measuring and comparing, eg ‘The pencil has a mass equal to three blocks and a pair of plastic scissors has a mass of six blocks, so the scissors are three blocks heavier than the pencil’ | |

– predict whether the number of units will be more or less when a different unit is used, eg ‘I will need more pop sticks than blocks as the pop sticks are lighter than the blocks’ (Reasoning) | |

– solve problems involving mass (Problem Solving) | |

estimate mass by referring to the number and type of uniform informal unit used and check by measuring |

Time

OUTCOME

A student:

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

Teaching Points | ‘Timing’ and ‘telling time’ are two different notions. The first relates to the duration of time and the second is ‘dial reading’. Both, however, assist students in understanding the passage of time and its measurement. ## DurationIt is important in Stage 1 that students develop a sense of one hour, one minute and one second through practical experiences, rather than simply recalling that there are 60 minutes in an hour. ## Telling TimeIn Stage 1, ‘telling time’ focuses on reading the half-hour on both analog and digital clocks. An important understanding is that when the minute hand shows the half-hour, the hour hand is always halfway between two hour-markers. Students need to be aware that there is always more than one way of expressing a particular time, eg |

In Aboriginal communities, calendars may vary in accordance with local seasonal and environmental changes, such as the flowering of plants and the migration patterns of animals, or according to significant events in the local community. Consult with local communities regarding specific local perspectives. |

Language | Students should be able to communicate using the following language: calendar, week, days, date, month, time, clock, analog, digital, hour hand, minute hand, clockwise, numeral, hour, minute, second, o’clock, half past, quarter past, quarter to. The terms ‘hour hand’ and ‘minute hand’, rather than ‘big hand’ and ‘little hand’, should be used to promote understanding of their respective functions. |

Tell time to the quarter-hour using the language of ‘past’ and ‘to’ (ACMMG039) | read analog and digital clocks to the quarter-hour using the terms ‘past’ and ‘to’, eg ‘It is a quarter past three’, ‘It is a quarter to four’ |

describe the position of the hands on a clock for quarter past and quarter to | |

– describe the hands on a clock as turning in a ‘clockwise’ direction (Communicating) | |

– associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes and with the terms ‘quarter past’, ‘half past’ and ‘quarter to’, respectively (Communicating) | |

identify which hour has just passed when the hour hand is not pointing to a numeral | |

record quarter-past and quarter-to time on analog and digital clocks |

3D Space

OUTCOME

A student:

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

Teaching Points | In Stage 1, students begin to explore three-dimensional objects in greater detail. They continue to describe the objects using their own language and are introduced to some formal language. Developing and retaining mental images of objects is an important skill for these students. Manipulation of a variety of real three-dimensional objects and two-dimensional shapes in the classroom, the playground and outside the school is crucial to the development of appropriate levels of language and representation. |

A cube is a special prism in which all faces are squares. In Stage 1, students do not need to be made aware of this classification. |

Language | Students should be able to communicate using the following language: object, shape, two-dimensional shape (2D shape), three-dimensional object (3D object), cone, cube, cylinder, sphere, prism, surface, flat surface, curved surface, face, edge, vertex (vertices). The term ‘vertex’ (plural: vertices) refers to the point where three or more faces of a three-dimensional object meet (or where two straight sides of a two-dimensional shape meet). In geometry, the term ‘edge’ refers to the interval (straight line) formed where two faces of a three-dimensional object meet. |

Describe the features of three-dimensional objects (ACMMG043) | use the terms ‘flat surface’, ‘curved surface’, ‘face’, ‘edge’ and ‘vertex’ appropriately when describing three-dimensional objects |

– describe the number of flat surfaces, curved surfaces, faces, edges and vertices of three-dimensional objects using materials, pictures and actions, eg ‘A cylinder has two flat surfaces, one curved surface, no faces, no edges and no vertices’, ‘This prism has 5 faces, 9 edges and 6 vertices’ (Communicating) | |

distinguish between objects, which are ‘three-dimensional’ (3D), and shapes, which are ‘two-dimensional’ (2D), and describe the differences informally, eg ‘This is a two-dimensional shape because it is flat’ | |

– relate the terms ‘two-dimensional’ and ‘three-dimensional’ to their use in everyday situations, eg a photograph is two-dimensional and a sculpture is three-dimensional (Communicating, Reasoning) | |

recognise that flat surfaces of three-dimensional objects are two-dimensional shapes and name the shapes of these surfaces | |

sort three-dimensional objects according to particular attributes, eg the shape of the surfaces | |

– explain the attribute or multiple attributes used when sorting three-dimensional objects (Communicating, Reasoning) | |

represent three-dimensional objects, including landmarks, by making simple models or by drawing or painting | |

– choose a variety of materials to represent three-dimensional objects, including digital technologies (Communicating) | |

– explain or demonstrate how a simple model was made (Communicating, Reasoning) |

2D Space

OUTCOME

A student:

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

TEACHING POINTS | In Stage 1, students need to have experiences involving directions and turning. Discussions about what represents a ‘full-turn’, a ‘half-turn’ and a ‘quarter-turn’ will be necessary. Relating this information to students physically may be helpful, eg by playing games such as ‘Simon Says’ with Simon saying to make turns. |

Digital technologies such as computer drawing tools may use the terms ‘move’, ‘rotate’ and ‘flip horizontal’, or various other terms, to describe transformations. The icons for these functions may assist students in locating the required transformations. |

LANGUAGE | Students should be able to communicate using the following language: shape, two-dimensional shape (2D shape), circle, triangle, quadrilateral, square, rectangle, pentagon, hexagon, octagon, orientation, features, symmetry, slide, flip, turn, full-turn, half-turn, quarter-turn, clockwise, anti-clockwise. |

In Stage 1, students refer to the transformations of shapes using the terms ‘slide’, ‘flip’ and ‘turn’. While in Stage 2, students are expected to use the terms ‘translate’, ‘reflect’ and ‘rotate’, respectively. | |

Linking the vocabulary of half-turns and quarter-turns to students’ experiences with clocks may be of benefit. | |

A shape is said to have line symmetry if matching parts are produced when it is folded along a line of symmetry. Each part represents the ‘mirror image’ of the other. |

Identify and describe half-turns and quarter-turns (ACMMG046) | identify full-, half- and quarter-turns of a single shape and use the terms ‘turn’, ‘full-turn’, ‘half-turn’ and ‘quarter-turn’ to describe the movement of the shape |

identify and describe amounts of turn using the terms ‘clockwise’ and ‘anti-clockwise’ | |

perform full-, half- and quarter-turns with a single shape | |

– recognise that turning a shape does not change its size or features (Reasoning) | |

– describe the result of a turn of a shape, eg ‘When the shape does a half-turn, it is the same but upside-down’ (Communicating) | |

record the result of performing full-, half- and quarter-turns of a shape, with and without the use of digital technologies | |

– copy and manipulate a shape using the computer function for turn (Communicating)Information and communication technology capability | |

determine the number of half-turns required for a full-turn and the number of quarter-turns required for a full-turn | |

– connect the use of quarter- and half-turns to the turn of the minute hand on a clock for the passing of quarter- and half-hours (Communicating, Reasoning) |

Position

OUTCOME

A student:

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

TEACHING POINTS | Making models and drawing simple sketches of their models is the focus for students in Stage 1. Students usually concentrate on the relative positions of objects in their sketches. Representing the relative size of objects is difficult and will be refined over time, leading to the development of scale drawings in later stages. Accepting students’ representations in models and sketches is important. |

LANGUAGE | Students should be able to communicate using the following language: position, location, map, path. |

Interpret simple maps of familiar locations and identify the relative positions of key features(ACMMG044) | interpret simple maps by identifying objects in different locations, eg find a classroom on a school plan mapLiteracy |

describe the positions of objects in models, photographs and drawings | |

– give reasons when answering questions about the positions of objects (Communicating, Reasoning) | |

make simple models from memory, photographs, drawings or descriptions, eg students make a model of their classroom | |

– use knowledge of positions in real-world contexts to re-create models (Communicating) | |

draw a sketch of a simple model | |

use drawings to represent the positions of objects along a path |

Data

Chance

Data

OUTCOME

A student:

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

TEACHING POINTS | Making models and drawing simple sketches of their models is the focus for students in Stage 1. Students usually concentrate on the relative positions of objects in their sketches. Representing the relative size of objects is difficult and will be refined over time, leading to the development of scale drawings in later stages. Accepting students’ representations in models and sketches is important. |

LANGUAGE | Students should be able to communicate using the following language: position, location, map, path. |

Interpret simple maps of familiar locations and identify the relative positions of key features(ACMMG044) | interpret simple maps by identifying objects in different locations, eg find a classroom on a school plan mapLiteracy |

describe the positions of objects in models, photographs and drawings | |

– give reasons when answering questions about the positions of objects (Communicating, Reasoning) | |

make simple models from memory, photographs, drawings or descriptions, eg students make a model of their classroom | |

– use knowledge of positions in real-world contexts to re-create models (Communicating) | |

draw a sketch of a simple model | |

use drawings to represent the positions of objects along a path |

Chance

OUTCOME

A student:

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

TEACHING POINTS | Students should be encouraged to recognise that, because of the element of chance, their predictions will not always be proven true. |

When discussing certainty, there are two extremes: events that are certain to happen and those that are certain not to happen. Words such as ‘might’, ‘may’ and ‘possible’ are used to describe events between these two extremes. |

LANGUAGE | Students should be able to communicate using the following language: chance, certain, uncertain, possible, impossible, likely, unlikely. The meaning of ‘uncertain’ is ‘not certain’ – it does not mean ‘impossible’. |

Identify practical activities and everyday events that involve chance (ACMSP047) | recognise and describe the element of chance in familiar activities and events, eg ‘I might play with my friend after school’ |

– predict what might occur during the next lesson or in the near future, eg ‘How many people might come to your party?’, ‘How likely is it to rain if there are no clouds in the sky?’ (Communicating, Reasoning) |

Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (ACMSP047) | describe possible outcomes in everyday activities and events as being ‘likely’ or ‘unlikely’ to happen |

compare familiar activities and events and describe them as being ‘likely’ or ‘unlikely’ to happen | |

identify and distinguish between ‘possible’ and ‘impossible’ events | |

– describe familiar events as being ‘possible’ or ‘impossible’, eg ‘It is possible that it will rain today’, ‘It is impossible to roll a standard six-sided die and get a 7’ (Communicating) | |

identify and distinguish between ‘certain’ and ‘uncertain’ events | |

– describe familiar situations as being certain or uncertain, eg ‘It is uncertain what the weather will be like tomorrow’, ‘It is certain that tomorrow is Saturday’ (Communicating) |