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OUTCOME
A student:
MA1-4NA: applies place value, informally, to count, order, read and represent two- and three-digit numbers
| TEACHING POINT | Students should be made aware that bus, postcode and telephone numbers are said differently from cardinal numbers, ie they are not said using place value language. Ordinal names may be confused with fraction names, eg ‘the third’ relates to order but ‘a third’ is a fraction. The word ’round’ has different meanings in different contexts and some students may confuse it with the word ‘around’. |
| 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, round to, coins, notes, cents, dollars. |
Develop confidence with number sequences to 100 by ones from any starting point (ACMNA012) | count forwards and backwards by ones from a given two-digit number |
| identify the number before and after a given two-digit number | |
| describe the number before as ‘one less than’ and the number after as ‘one more than’ a given number (Communicating) | |
| read and use the ordinal names to at least ‘thirty-first’, eg when reading calendar dates |
Count collections to 100 by partitioning numbers using place value (ACMNA014) | count and represent large sets of objects by systematically grouping in tens |
| use and explain mental grouping to count and to assist with estimating the number of items in large groups | |
| use place value to partition two-digit numbers, eg 32 as 3 groups of ten and 2 ones | |
| state the place value of digits in two-digit numbers, eg ‘In the number 32, the “3” represents 30 or 3 tens’ | |
| partition two-digit numbers in non-standard forms, eg 32 as 32 ones or 2 tens and 12 ones |
Recognise, model, read, write and order numbers to at least 100; locate these numbers on a number line (ACMNA013) | represent two-digit numbers using objects, pictures, words and numerals |
| locate and place two-digit numbers on a number line | |
| apply an understanding of place value and the role of zero to read, write and order two-digit numbers | |
| use number lines and number charts to assist with counting and ordering | |
| give reasons for placing a set of numbers in a particular order (Communicating, Reasoning) | |
| round numbers to the nearest ten | |
| estimate, to the nearest ten, the number of objects in a collection and check by counting, eg estimate the number of children in a room to the nearest ten | |
| solve simple everyday problems with two-digit numbers | |
| choose an appropriate strategy to solve problems, including trial-and-error and drawing a diagram (Communicating, Problem Solving) | |
| ask questions involving two-digit numbers, eg ‘Why are the houses on either side of my house numbered 32 and 36?’ (Communicating) |
Recognise, describe and order Australian coins according to their value (ACMNA017) | identify, sort, order and count money using the appropriate language in everyday contexts, eg coins, notes, cents, dollars |
| recognise that total amounts can be made using different denominations, eg 20 cents can be made using a single coin or two 10-cent coins | |
| recognise the symbols for dollars ($) and cents (c) |
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 | 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. Students need to understand that the requirement to carry out subtraction can be indicated by a variety of language structures. The language used in the ‘comparison’ type of subtraction is quite different from that used in the ‘take away’ type. Students need to understand the different uses for the = sign, eg 4 + 1 = 5, where the = sign indicates that the right side of the number sentence contains ‘the answer’ and should be read to mean ‘equals’, compared to a statement of equality such as 4 + 1 = 3 + 2, where the = sign should be read to mean ‘is the same as’. |
| LANGUAGE | Students should be able to communicate using the following language: counting on, counting back, combine, plus, add, take away, minus, the difference between, total, more than, less than, double, equals, is equal to, is the same as, number sentence, strategy. |
Represent and solve simple addition and subtraction problems using a range of strategies, including counting on, partitioning and rearranging parts | use the terms ‘add’, ‘plus’, ‘equals’, ‘is equal to’, ‘take away’, ‘minus’ and the ‘difference between’ |
| use concrete materials to model addition and subtraction problems involving one- and two-digit numbers | |
| use concrete materials and a number line to model and determine the difference between two numbers, eg | |
| recognise and use the symbols for plus (+), minus (–) and equals (=) | |
| record number sentences in a variety of ways using drawings, words, numerals and mathematical symbols | |
| recognise, recall and record combinations of two numbers that add to 10 | |
| create, record and recognise combinations of two numbers that add to numbers up to and including 9 | |
| model and record patterns for individual numbers by making all possible whole-number combinations, eg 5+0=5 4+1=5 3+2=5 2+3=5 1+4=5 0+5=5 (Communicating, Problem Solving) | |
| describe combinations for numbers using words such as ‘more’, ‘less’ and ‘double’, eg describe 5 as ‘one more than four’, ‘three combined with two’, ‘double two and one more’ and ‘one less than six’ (Communicating, Problem Solving) | |
| create, record and recognise combinations of two numbers that add to numbers from 11 up to and including 20 | |
| use combinations for numbers up to 10 to assist with combinations for numbers beyond 10 (Problem Solving) | |
| investigate and generalise the effect of adding zero to a number, eg ‘Adding zero to a number does not change the number’ | |
| use concrete materials to model the commutative property for addition and apply it to aid the recall of addition facts, eg 4 + 5 = 5 + 4 | |
| relate addition and subtraction facts for numbers to at least 20, eg 5 + 3 = 8, so 8 – 3 = 5 and 8 – 5 = 3 | |
| use and record a range of mental strategies to solve addition and subtraction problems involving one- and two-digit numbers, including: | |
| counting on from the larger number to find the total of two numbers | |
| counting back from a number to find the number remaining | |
| counting on or back to find the difference between two numbers | |
| using doubles and near doubles, eg 5 + 7: double 5 and add 2 | |
| combining numbers that add to 10, eg 4 + 7 + 8 + 6 + 3: first combine 4 and 6, and 7 and 3, then add 8 | |
| bridging to 10, eg 17 + 5: 17 and 3 is 20, then add 2 more | |
| using place value to partition numbers, eg 25 + 8: 25 is 20 + 5, so 25 + 8 is 20 + 5 + 8, which is 20 + 13 | |
| choose and apply efficient strategies for addition and subtraction (Problem Solving) | |
| use the equals sign to record equivalent number sentences involving addition, and to mean ‘is the same as’, rather than as an indication to perform an operation, eg 5 + 2 = 3 + 4 | |
| check given number sentences to determine if they are true or false and explain why, eg ‘Is 7 + 5 = 8 + 4 true? Why or why not?’ (Communicating, Reasoning) |
OUTCOME
A student:
MA1-6NA: uses a range of mental strategies and concrete materials for multiplication and division
| Teaching Point | It is preferable that students use ‘groups of’, before progressing to ‘rows of’ and ‘columns of’. The term ‘lots of’ can be confusing to students because of its everyday use and should be avoided, eg ‘lots of fish in the sea’. |
| Language | Students should be able to communicate using the following language: group, number of groups, number in each group, sharing, shared between, left over, total, equal. Sharing – relates to distributing items one at a time into a set number of groups, eg the student has a number of pop sticks and three cups and shares out the pop sticks into the cups one at a time. Grouping – relates to distributing the same number of items into an unknown number of groups, eg the student has 12 pop sticks and wants to make groups of four, so places four pop sticks down, then another four, and so on. |
Skip count by twos, fives and tens starting from zero | count by twos, fives and tens using rhythmic counting and skip counting from zero |
| use patterns on a number chart to assist in counting by twos, fives or tens (Communicating) |
Model and use equal groups of objects as a strategy for multiplication | model and describe collections of objects as ‘groups of’, eg |
| – recognise the importance of having groups of equal size (Reasoning) | |
| – determine and distinguish between the ‘number of groups’ and the ‘number in each group’ when describing collections of objects (Communicating) | |
find the total number of objects using skip counting |
Recognise and represent division as grouping into equal sets | recognise when there are equal numbers of items in groups, eg ‘There are three pencils in each group’ |
| model division by sharing a collection of objects equally into a given number of groups to determine how many in each group, eg determine the number in each group 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 (Communicating, Problem Solving, Reasoning) | |
| model division by sharing a collection of objects into groups of a given size to determine the number of groups, eg determine the number of groups when 20 objects are shared into groups of four | |
| – describe the part left over when a collection cannot be distributed equally using the given group size, eg when 22 objects are shared into groups of four, there are five groups of four and two objects left over (Communicating, Problem Solving, Reasoning) |
OUTCOME
A student:
MA1-7NA: represents and models halves, quarters and eighths
| Teaching Point | Some students may hear ‘whole’ in the phrase ‘part of a whole’ and confuse it with the term ‘hole’. It is not necessary for students to distinguish between the roles of the numerator and the denominator in Stage 1. They may use the symbol 1212 as an entity to mean ‘one-half’ or ‘a half’, and similarly use 1414 to mean ‘one-quarter’ or ‘a quarter’. Three models of fractionsContinuous model, linear – uses one-directional cuts or folds that compare fractional parts based on length; this model should be introduced first. Cuts or folds may be either vertical or horizontal. Continuous model, area – uses multi-directional cuts or folds to compare fractional parts to the whole. This model should be introduced once students have an understanding of the concept of area in Stage 2.
Discrete model – uses separate items in collections to represent parts of the whole group.
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| Language | Students should be able to communicate using the following language: whole, part, equal parts, half, halves, about a half, more than a half, less than a half. |
Recognise and describe one-half as one of two equal parts of a whole | use concrete materials to model half of a whole object, eg
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| describe two equal parts of a whole object, eg ‘I folded my paper into two equal parts and now I have halves’ (Communicating) | |
| recognise that halves refer to two equal parts of a whole | |
| describe parts of a whole object as ‘about a half’, ‘more than a half’ or ‘less than a half’ | |
record two 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), eg
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use concrete materials to model half of a collection, eg
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| – describe two equal parts of a collection, eg ‘I have halves because the two parts have the same number of seedlings’ (Communicating) | |
record two equal parts of a collection, and the relationship of the parts to the whole, using pictures and fraction notation for half (12), eg
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OUTCOME
A student:
MA1-8NA: creates, represents and continues a variety of patterns with numbers and objects
Teaching Point | In Stage 1, students further explore additive number patterns that increase or decrease. Patterns could now include any patterns observed on a number chart and these might go beyond patterns created by counting in ones, twos, fives or tens. This links closely with the development of Whole Numbers and Multiplication and Division. |
Repeating patterns of objects or symbols are described using numbers that indicate the number of elements that repeat, eg A, B, C, A, B, C, … has three elements that repeat and is referred to as a ‘three’ pattern. |
| Language | Students should be able to communicate using the following language: pattern, number line, number chart, odd, even. |
Investigate and describe number patterns formed by skip counting and patterns with objects | identify and describe patterns when skip counting forwards or backwards by ones, twos, fives and tens from any starting point |
| – use objects to represent counting patterns (Communicating) | |
| – investigate and solve problems based on number patterns (Problem Solving) | |
| represent number patterns on number lines and number charts | |
| recognise, copy and continue given number patterns that increase or decrease, eg 1, 2, 3, 4, … 20, 18, 16, 14, … | |
| – describe how number patterns are made and how they can be continued (Communicating, Problem Solving) | |
| create, record and describe number patterns that increase or decrease | |
| recognise, copy and continue patterns with objects or symbols | |
| – recognise when an error occurs in a pattern and explain what is wrong (Communicating, Problem Solving) | |
| create, record and describe patterns with objects or symbols | |
describe a repeating pattern of objects or symbols in terms of a ‘number’ pattern, eg | |
| – make connections between repeating patterns and counting, eg a ‘three’ pattern and skip counting by threes (Communicating, Reasoning) | |
| model and describe ‘odd’ and ‘even’ numbers using counters paired in two rows | |
| – describe the pattern created by modelling odd and even numbers (Communicating) |
OUTCOME
A student:
MA1-9MG: measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres
| Teaching Points | Using the terms ‘make’, ‘mark’ and ‘move’ assists students in understanding the concept of repeated units. By placing a unit on a flat surface, marking where it ends, moving it along and continuing the process, students see that the unit of measurement is the space between the marks on a measuring device and not the marks themselves. Recognising that a length may be divided and recombined to form the same length is an important component of conserving length. It is important that students have had some measurement experiences before being asked to estimate lengths and distances, and that a variety of estimation strategies is taught. |
| Language | Students should be able to communicate using the following language: length, distance, end, end-to-end, side-by-side, gap, overlap, measure, estimate, handspan. |
Measure and compare the lengths of pairs of objects using uniform informal units | use uniform informal units to measure lengths and distances by placing the units end-to-end without gaps or overlaps |
| – select appropriate uniform informal units to measure lengths and distances, eg paper clips instead of pop sticks to measure a pencil, paces instead of pop sticks to measure the length of the playground (Problem Solving) | |
| – measure the lengths of a variety of everyday objects, eg use handspans to measure the length of a table (Problem Solving) | |
| – explain the relationship between the size of a unit and the number of units needed, eg more paper clips than pop sticks will be needed to measure the length of the desk (Communicating, Reasoning) | |
| record lengths and distances by referring to the number and type of uniform informal unit used | |
| – investigate different informal units of length used in various cultures, including those used in Aboriginal communities (Communicating) | |
| compare the lengths of two or more objects using appropriate uniform informal units and check by placing the objects side-by-side and aligning the ends | |
| – explain why the length of an object remains constant when units are rearranged, eg ‘The book was seven paper clips long. When I moved the paper clips around and measured again, the book was still seven paper clips long’ (Communicating, Reasoning) | |
| estimate linear dimensions and the lengths of curves by referring to the number and type of uniform informal unit used and check by measuring | |
| – discuss strategies used to estimate lengths, eg visualising the repeated unit, using the process ‘make, mark and move’ (Communicating, Problem Solving) |
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, row, column, gap, overlap, parts of (units), estimate. |
Measure and compare areas using uniform informal units | compare, indirectly, the areas of two surfaces that cannot be moved or superimposed, eg by cutting paper to cover one surface and superimposing the paper over the second surface |
| predict the larger of the areas of two surfaces of the same general shape and compare these areas by cutting and covering | |
| use uniform informal units to measure area by covering the surface in rows or columns without gaps or overlaps | |
| – select and use appropriate uniform informal units to measure area (Reasoning) | |
| – explain the relationship between the size of a unit and the number of units needed to measure an area, eg ‘I need more tiles than workbooks to measure the area of my desktop’ (Communicating, Reasoning) | |
| – describe why the area remains constant when units are rearranged (Communicating, Reasoning) | |
| – describe any parts of units left over when counting uniform informal units to measure area (Communicating) | |
| – use computer software to create a shape and use a simple graphic as a uniform informal unit to measure its area (Communicating) | |
| record areas by referring to the number and type of uniform informal unit used, eg ‘The area of this surface is 20 tiles’ | |
| estimate areas by referring to the number and type of uniform informal unit used and check by measuring | |
| – discuss strategies used to estimate area, eg visualising the repeated unit (Communicating, Problem Solving) |
OUTCOME
A student:
MAe-11MG: describes and compares the capacities of containers and the volumes of objects or substances using everyday language
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. |
Volume and capacity relate to the measurement of three-dimensional space, in the same way that area relates to the measurement of two-dimensional space. | |
The attribute of volume is the amount of space occupied by an object or substance and can be measured in cubic units, eg cubic centimetres (cm3) and cubic metres (m3). | |
Capacity refers to the amount a container can hold, and can be measured in millilitres (mL) and/or litres (L). Capacity is only used in relation to containers and generally refers to liquid measurement. The capacity of a closed container will be slightly less than its volume – capacity is based on the inside dimensions, while volume is determined by the outside dimensions of the container. It is not necessary to refer to these definitions with students (capacity is not taught as a concept separate from volume until Stage 4). | |
Students need experience in filling containers both with continuous material (eg water) and with discrete objects (eg marbles). The use of continuous material leads to measurement using the units litre and millilitre in later stages. The use of blocks leads to measurement using the units cubic metre and cubic centimetre. |
| Language | Students should be able to communicate using the following language: capacity, container, liquid, full, empty, volume, gap, measure, estimate. |
Measure and compare the capacities of pairs of objects using uniform informal units (ACMMG019) | use uniform informal units to measure the capacities of containers by counting the number of times a smaller container can be filled and emptied into the container being measured |
| – select appropriate uniform informal units to measure the capacities of containers, eg using cups rather than teaspoons to fill a bucket (Problem Solving) | |
| – explain the relationship between the size of a unit and the number of units needed, eg more cups than ice cream containers will be needed to fill a bucket (Communicating, Reasoning) | |
| record capacities by referring to the number and type of uniform informal unit used | |
| compare the capacities of two or more containers using appropriate uniform informal units | |
| – recognise that containers of different shapes may have the same capacity (Reasoning) | |
| estimate capacities by referring to the number and type of uniform informal unit used and check by measuring | |
| pack cubic units (eg blocks) into rectangular containers so that there are no gaps | |
| – recognise that cubes pack better than other objects in rectangular containers (Reasoning) | |
| measure the volume of a container by filling the container with uniform informal units and counting the number of units used, eg the number of blocks a box can hold | |
| – devise and explain strategies for packing and counting units to fill a box, eg packing in layers and ensuring that there are no gaps between units (Communicating, Problem Solving) | |
| – explain that if there are gaps when packing and stacking, this will affect the accuracy of measuring the volume (Communicating, Reasoning) | |
| record volumes by referring to the number and type of uniform informal unit used | |
| estimate volumes of containers by referring to the number and type of uniform informal unit used and check by measuring | |
| – explain a strategy used for estimating a volume (Communicating, Problem Solving) | |
| – predict the larger volume of two or more containers and check by measuring using uniform informal units (Reasoning) | |
| estimate the volume of a pile of material and check by measuring, eg estimate how many buckets would be used to form a pile of sand |
OUTCOME
A student:
MA1-12MG: measures, records, compares and estimates the masses of objects using uniform informal units
Teaching Points | Mass is an intrinsic property of an object, but its most common measure is in terms of weight. Weight is a force that changes with gravity, while mass remains constant. |
| As the terms ‘weigh’ and ‘weight’ are common in everyday usage, they can be accepted in student language should they arise. |
| Language | Students should be able to communicate using the following language: mass, heavy, heavier, light, lighter, about the same as, pan balance, (level) balance. |
Investigate mass using a pan balance | identify materials that are light or heavy |
| place objects on either side of a pan balance to obtain a level balance | |
| use a pan balance to compare the masses of two objects | |
| – discuss the action of a pan balance when a heavy object is placed in one pan and a lighter object in the other pan (Communicating) | |
| – predict the action of a pan balance before placing particular objects in each pan (Reasoning) | |
| sort objects on the basis of their mass | |
| use a pan balance to find two collections of objects that have the same mass, eg a collection of blocks and a collection of counters | |
| use drawings to record findings from using a pan balance |
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. |
Duration It 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. | |
Time Telling
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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, days, date, month, year, seasons, time, clock, analog, digital, hour hand, minute hand, o’clock, half past. The terms ‘hour hand’ and ‘minute hand’, rather than ‘big hand’ and ‘little hand’, should be used to promote understanding of their respective functions. |
Name and order months and seasons (ACMMG040) | name and order the months of the year |
| recall the number of days that there are in each month | |
| name and order the seasons, and name the months for each season | |
| – describe the environmental characteristics of each season, eg ‘Winter is cool and some trees lose their leaves’ (Communicating) | |
| – recognise that in some cultures seasonal changes mark the passing of time, eg the flowering of plants and the migration patterns of animals are used by many peoples, including Aboriginal people (Reasoning) | |
| – recognise that in countries in the northern hemisphere, the season is the opposite to that being experienced in Australia at that time (Reasoning) |
Use a calendar to identify the date and determine the number of days in each month (ACMMG041) | identify a day and date using a conventional calendar |
| – identify personally or culturally significant days (Communicating) | |
| – identify the different uses of calendars in various communities (Communicating) |
Tell time to the half-hour (ACMMG020) | read analog and digital clocks to the half-hour using the terms ‘o’clock’ and ‘half past’ |
| describe the position of the hands on a clock for the half-hour | |
| – explain why the hour hand on a clock is halfway between the two hour-markers when the minute hand shows the half-hour (Communicating, Reasoning) | |
| – describe everyday events with particular hour and half-hour times, eg ‘We start school at 9 o’clock’ (Communicating) | |
| record hour and half-hour time on analog and digital clocks |
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, cone, cube, cylinder, sphere, prism, surface, flat surface, curved surface, face. |
In geometry, the term ‘face’ refers to a flat surface with only straight edges, as in prisms and pyramids, eg a cube has six faces. Curved surfaces, such as those found in cones, cylinders and spheres, are not classified as faces. Similarly, flat surfaces with curved boundaries, such as the circular surfaces of cones and cylinders, are not faces. |
Recognise and classify familiar three-dimensional objects using obvious features (ACMMG022) | manipulate and describe familiar three-dimensional objects, including cones, cubes, cylinders, spheres and prisms |
| identify and name familiar three-dimensional objects, including cones, cubes, cylinders, spheres and prisms, from a collection of everyday objects | |
| – select an object from a description of its features, eg find an object with six square faces (Reasoning) | |
| use the terms ‘surface’, ‘flat surface’ and ‘curved surface’ in describing familiar three-dimensional objects | |
| – identify the type and number of flat and curved surfaces of three-dimensional objects, eg ‘This prism has eight flat surfaces’, ‘A cone has two surfaces: one is a flat surface and the other is a curved surface’ (Reasoning) | |
| use the term ‘face’ to describe the flat surfaces of three-dimensional objects with straight edges, including squares, rectangles and triangles | |
| – distinguish between ‘flat surfaces’ and ‘curved surfaces’ and between ‘flat surfaces’ and ‘faces’ when describing three-dimensional objects (Communicating) | |
| sort familiar three-dimensional objects according to obvious features, eg ‘All these objects have curved surfaces’ | |
| select and name a familiar three-dimensional object from a description of its features, eg find an object with six square faces | |
| recognise that three-dimensional objects look different from different vantage points | |
identify cones, cubes, cylinders and prisms when drawn in different orientations, eg
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| recognise familiar three-dimensional objects from pictures and photographs, and in the environment |
OUTCOME
A student:
MA1-15MG: manipulates, sorts, represents, describes and explores two-dimensional shapes, including quadrilaterals, pentagons, hexagons and octagons
Teaching Points | Students need to be able to recognise shapes presented in different orientations. They need to develop an understanding that changing the orientation of a shape does not change its features or its name. |
| Students should have experiences identifying both regular and irregular shapes, although it is not expected that students understand or distinguish between regular and irregular shapes in Stage 1. Regular shapes have all sides and all angles equal. | |
| Many shapes used in Aboriginal art are used with specific meanings. Local Aboriginal communities and many education consultants can provide examples. Further exploration of such meanings could be incorporated in students’ studies within the Creative Arts Key Learning Area. |
Language | Students should be able to communicate using the following language: shape, circle, triangle, quadrilateral, square, rectangle, pentagon, hexagon, octagon, orientation, features, side, vertex (vertices), vertical, horizontal, portrait (orientation), landscape (orientation), parallel. |
| The term ‘vertex’ (plural: vertices) refers to the point where two straight sides of a two-dimensional shape meet (or where three or more faces of a three-dimensional object meet). | |
The term ‘shape’ refers to a two-dimensional figure. The term ‘object’ refers to a three-dimensional figure. |
Recognise and classify familiar two-dimensional shapes using obvious features (ACMMG022) | identify vertical and horizontal lines in pictures and the environment and use the terms ‘vertical’ and ‘horizontal’ to describe such lines |
| – relate the terms ‘vertical’ and ‘horizontal’ to ‘portrait’ and ‘landscape’ page orientation, respectively, when using digital technologies (Communicating) | |
| identify parallel lines in pictures and the environment and use the term ‘parallel’ to describe such lines | |
| – recognise that parallel lines can occur in orientations other than vertical and horizontal (Reasoning) | |
| – give everyday examples of parallel lines, eg railway tracks (Reasoning) | |
| manipulate, compare and describe features of two-dimensional shapes, including triangles, quadrilaterals, pentagons, hexagons and octagons | |
| – describe features of two-dimensional shapes using the terms ‘side’ and ‘vertex’ (Communicating) | |
| sort two-dimensional shapes by a given attribute, eg by the number of sides or vertices | |
| – explain the attribute used when sorting two-dimensional shapes (Communicating, Reasoning) | |
identify and name two-dimensional shapes presented in different orientations according to their number of sides, including using the terms ‘triangle’, ‘quadrilateral’, ‘pentagon’, ‘hexagon’ and ‘octagon’, eg | |
– recognise that the name of a shape does not change when the shape changes its orientation in space, eg a square turned on its vertex is still a square (Communicating, Reasoning)
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| – select a shape from a description of its features (Reasoning) | |
| – recognise that shapes with the same name may have sides of equal or different lengths (Reasoning) | |
| recognise that rectangles and squares are quadrilaterals | |
| identify and name shapes embedded in pictures, designs and the environment, eg in Aboriginal art | |
| – use computer drawing tools to outline shapes embedded in a digital picture or design (Communicating) |
OUTCOME
A student:
MA1-16MG: represents and describes the positions of objects in everyday situations and on maps
| Teaching Points | Being able to describe the relative positions of objects in a picture or diagram requires interpretation of a two-dimensional representation. |
Language | Students should be able to communicate using the following language: position, left, right, directions, turn. |
In Stage 1, students use the terms ‘left’ and ‘right’ to describe position from the perspective of a person facing in the opposite direction, whereas in Early Stage 1, students used the terms ‘left’ and ‘right’ to describe position in relation to themselves. |
Give and follow directions to familiar locations (ACMMG023) | use the terms ‘left’ and ‘right’ to describe the positions of objects in relation to themselves and from the perspective of a person facing in the opposite direction, eg ‘The ball is on her left’ |
| give and follow directions, including directions involving turns to the left and right, to move between familiar locations, eg within the classroom or school | |
| – use amounts of turn (full and half) to describe direction (Communicating) | |
| give and follow instructions to position objects in models and drawings, eg ‘Draw the bird between the two trees’ | |
| – give and follow simple directions using a diagram or description (Communicating) | |
| describe the path from one location to another on drawings | |
| – use a diagram to give simple directions (Communicating) | |
| – create a path from one location to another using computer software (Communicating) |
OUTCOME
A student:
MA1-17SP: gathers and organises data, displays data in lists, tables and picture graphs, and interprets the results
Teaching Points | In Stage 1, students are introduced to the abstract notion of representing an object with a different object, picture or drawing. |
| It is important that each object in a three-dimensional graph represents one object, except in the case where items are used in pairs, eg shoes. One object can also represent an idea, such as a person’s preference. | |
| When collecting information to investigate a question, students can develop simple ways of recording. Some methods include placing blocks or counters in a line, colouring squares on grid paper, and using tally marks. | |
A single mark in a tally represents one observation. Tally marks are usually drawn in groups of five. The first four marks are vertical, with the fifth mark drawn diagonally through the first four to make counting more efficient, eg  represents 3,  represents 5,  represents 9. |
| Language | Students should be able to communicate using the following language: information, data, collect, gather, display, objects, symbol, tally mark, picture, row. |
Choose simple questions and gather responses (ACMSP262) | investigate a matter of interest by choosing suitable questions to obtain appropriate data |
| gather data and track what has been counted by using concrete materials, tally marks, words or symbols |
Represent data with objects and drawings where one object or drawing represents one data value and describe the displays(ACMSP263) | use concrete materials or pictures of objects as symbols to create data displays where one object or picture represents one data value (one-to-one correspondence), eg use different-coloured blocks to represent different-coloured cars |
| – record a data display created from concrete materials or pictures of objects (Communicating) | |
| interpret information presented in data displays where one object, picture or drawing represents one data value, eg weather charts | |
| – describe information presented in simple data displays using comparative language such as ‘more than’ and ‘less than’, eg ‘There were more black cars than red cars’ (Communicating, Reasoning) | |
| – explain interpretations of information presented in data displays, eg ‘More children like dogs because there are more dog pictures than cat pictures’ (Communicating, Reasoning) | |
| – write a simple sentence to describe data in a display, eg ‘The most popular fruit snack is an apple’ (Communicating) |
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: will happen, might happen, won’t happen, probably. |
Identify outcomes of familiar events involving chance and describe them using everyday language, such as ‘will happen’, ‘won’t happen’ or ‘might happen’ (ACMSP024) | identify possible outcomes of familiar activities and events, eg the activities that might happen if the class is asked to sit on the floor in a circle |
| use everyday language to describe the possible outcomes of familiar activities and events, eg ‘will happen’, ‘might happen’, ‘won’t happen’, ‘probably’ |
