# YEAR 4 MATHS FOCUS

## NUMBERS AND ALGEBRA

## WHOLE NUMBERS

OUTCOME

A student:

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

TEACHING POINTS | The convention for writing numbers of more than four digits requires that numerals have a space (and not a comma) to the left of each group of three digits when counting from the units column, eg 16 234. No space is used in a four-digit number, eg 6234. |

Language | Students should be able to communicate using the following language: number before, number after, more than, greater than, less than, largest number, smallest number, ascending order, descending order, digit, zero, ones, groups of ten, tens, groups of one hundred, hundreds, groups of one thousand, thousands, place value, round to. |

The word ‘and’ is used between the hundreds and the tens when reading and writing a number in words, but not in other places, eg 3568 is read as ‘three thousand, five hundred and sixty-eight’. | |

The word ’round’ has different meanings in different contexts, eg ‘The plate is round’, ‘Round 23 to the nearest ten’. |

## Expectations of Attainment

Recognise, represent and order numbers to at least tens of thousands(ACMNA072) | apply an understanding of place value to read and write numbers of up to five digits |

arrange numbers of up to five digits in ascending and descending order | |

state the place value of digits in numbers of up to five digits | |

– pose and answer questions that extend understanding of numbers, eg ‘What happens if I rearrange the digits in the number 12 345?’, ‘How can I rearrange the digits to make the largest number?’ (Communicating, Reasoning) | |

use place value to partition numbers of up to five digits and recognise this as ‘expanded notation’, eg 67 012 is 60 000 + 7000 + 10 + 2 | |

partition numbers of up to five digits in non-standard forms, eg 67 000 as 50 000 + 17 000 | |

round numbers to the nearest ten, hundred, thousand or ten thousand |

## ADDITION & SUBTRACTION

OUTCOME

A student:

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

Teaching Points | Students should be encouraged to estimate answers before attempting to solve problems in concrete or symbolic form. There is still a need to emphasise mental computation, even though students can now use a formal written method. |

In Stage 2, it is important that students apply and extend their repertoire of mental strategies for addition and subtraction. The use of concrete materials to model the addition and subtraction of two or more numbers, with and without trading, is intended to provide a foundation for the introduction of the formal algorithm in Addition and Subtraction 2. | |

When developing a formal written algorithm, it will be necessary to sequence the examples to cover the range of possibilities, which include questions without trading, questions with trading in one or more places, and questions with one or more zeros in the first number. |

LANGUAGE | Students should be able to communicate using the following language: plus, add, addition, minus, the difference between, subtract, subtraction, equals, is equal to, empty number line, strategy, digit, estimate, round to, change (noun, in transactions of money). Word problems requiring subtraction usually fall into two types: Take away – How many remain after some are removed? Comparison – How many more need to be added to a group? What is the difference between two groups? Students need to be able to translate from these different language contexts into a subtraction calculation. |

## Expectations of Attainment

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems(ACMNA073) | select, use and record a variety of mental strategies to solve addition and subtraction problems, including word problems, with numbers of up to and including five digits, eg 159 + 23: ‘I added 20 to 159 to get 179, then I added 3 more to get 182’, or use an empty number line: |

– pose simple addition and subtraction problems and apply appropriate strategies to solve them (Communicating, Problem Solving) | |

use a formal written algorithm to record addition and subtraction calculations involving two-, three-, four- and five-digit numbers, eg |

solve problems involving purchases and the calculation of change to the nearest five cents, with and without the use of digital technologies(ACMNA080) | solve addition and subtraction problems involving money, with and without the use of digital technologies |

– use a variety of strategies to solve unfamiliar problems involving money (Communicating, Problem Solving) | |

– reflect on their chosen method of solution for a money problem, considering whether it can be improved (Communicating, Reasoning) | |

calculate change and round to the nearest five cents | |

use estimation to check the reasonableness of solutions to addition and subtraction problems, including those involving money |

## MULTIPLICATION & DIVISION

OUTCOME

A student:

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

TEACHING POINTS | Students need to understand the different uses for the = sign, eg 4 × 3 = 12, 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 × 3 = 6 × 2, where the = sign should be read to mean ‘is the same as’. |

Linking multiplication and division is an important understanding for students in Stage 2. They should come to realise that division ‘undoes’ multiplication and multiplication ‘undoes’ division. Students should be encouraged to check the answer to a division question by multiplying their answer by the divisor. To divide, students may recall division facts or transform the division into a multiplication and use multiplication facts, eg 35÷7 is the same as □× 7=35. |

LANGUAGE | Students should be able to communicate using the following language: multiply, multiplied by, product, multiplication, multiplication facts, tens, ones, double, multiple, factor, shared between, divide, divided by, division, halve, remainder, equals, is the same as, strategy, digit. |

As students become more confident with recalling multiplication facts, they may use less language. For example, ‘five rows (or groups) of three’ becomes ‘five threes’ with the ‘rows of’ or ‘groups of’ implied. This then leads to ‘one three is three’, ‘two threes are six’, ‘three threes are nine’, and so on. | |

The term ‘product’ has a meaning in mathematics that is different from its everyday usage. In mathematics, ‘product’ refers to the result of multiplying two or more numbers together. |

## Expectations of Attainment

Use mental strategies and informal recording methods for division with remainders | model division, including where the answer involves a remainder, using concrete materials |

– explain why a remainder is obtained in answers to some division problems (Communicating, Reasoning)Critical and creative thinking | |

use mental strategies to divide a two-digit number by a one-digit number in problems for which answers include a remainder, eg 27 ÷ 6: if 4 × 6 = 24 and 5 × 6 = 30, the answer is 4 remainder 3 | |

record remainders to division problems in words, eg 17 ÷ 4 = 4 remainder 1. | |

interpret the remainder in the context of a word problem, eg ‘If a car can safely hold 5 people, how many cars are needed to carry 41 people?’; the answer of 8 remainder 1 means that 9 cars will be needed. |

## FRACTIONS & DECIMALS

OUTCOME

A student:

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

TEACHING POINTS | In Stage 2 Fractions and Decimals 2, fractions with denominators of 2, 3, 4, 5, 6, 8, 10 and 100 are studied. Denominators of 2, 3, 4, 5 and 8 were introduced in Stage 2 Fractions and Decimals 1. |

Fractions are used in different ways: to describe equal parts of a whole; to describe equal parts of a collection of objects; to denote numbers (eg 12 is midway between 0 and 1 on the number line); and as operators related to division (eg dividing a number in half). | |

Money is an application of decimals to two decimal places. |

LANGUAGE | Students should be able to communicate using the following language: whole, part, equal parts, half, quarter, eighth, third, sixth, fifth, tenth, hundredth, one-sixth, one-tenth, one-hundredth, fraction, numerator, denominator, whole number, number line, is equal to, equivalent fractions, decimal, decimal point, digit, place value, round to, decimal places, dollars, cents. |

The decimal 1.12 is read as ‘one point one two’ and not ‘one point twelve’. |

## Expectations of Attainment

investigate equivalent fractions used in contexts (ACMNA077) | model, compare and represent fractions with denominators of 2, 4 and 8; 3 and 6; and 5, 10 and 100 |

model, compare and represent the equivalence of fractions with related denominators by redividing the whole, using concrete materials, diagrams and number lines, eg | |

record equivalent fractions using diagrams and numerals, eg 3/5=6/10 |

Recognise that the place value system can be extended to tenths and hundredths, and make connections between fractions and decimal notation (ACMNA079) | recognise and apply decimal notation to express whole numbers, tenths and hundredths as decimals, eg 0.1 is the same as 1/10 |

– investigate equivalences using various methods, e.g. use a number line or a calculator to show that 1/2 is the same as 0.5 and 5/10 (Communicating, Reasoning) | |

– identify and interpret the everyday use of fractions and decimals, such as those in advertisements (Communicating, Problem Solving) | |

state the place value of digits in decimal numbers of up to two decimal places | |

use place value to partition decimals of up to two decimal places, e.g. 5.37=5+3/10+7/100 | |

partition decimals of up to two decimal places in non-standard forms, e.g. 5.37=5+37/100 | |

– apply knowledge of hundredths to represent amounts of money in decimal form, e.g. five dollars and 35 cents is 5 35/100, which is the same as $5.35 (Communicating) | |

model, compare and represent decimals of up to two decimal places | |

– apply knowledge of decimals to record measurements, eg 123 cm = 1.23 m (Communicating) | |

– interpret zero digit(s) at the end of a decimal, eg 0.70 has the same value as 0.7, 3.00 and 3.0 have the same value as 3 (Communicating) | |

– recognise that amounts of money are written with two decimal places, eg $4.30 is not written as $4.3 (Communicating) | |

– use one of the symbols for dollars ($) and cents (c) correctly when expressing amounts of money, ie $5.67 and 567c are correct, but $5.67c is not (Communicating) | |

– use a calculator to create patterns involving decimal numbers, eg 1 ÷ 10, 2 ÷ 10, 3 ÷ 10 (Communicating) | |

place decimals of up to two decimal places on a number line, eg place 0.5, 0.25 and 0.75 on a number line | |

round a number with one or two decimal places to the nearest whole number |

## PATTERNS & ALGEBRA

OUTCOME

A student:

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

TEACHING POINTS | In Stage 2, the investigation of odd and even numbers leads to understanding what happens to numbers when they are added together or multiplied together. For example, ‘An odd number added to an even number always results in an odd number’, ‘An even number multiplied by an even number always results in an even number’. |

LANGUAGE | Students should be able to communicate using the following language: pattern, term, missing number, odd, even, number sentence, is the same as, equals. |

## Expectations of Attainment

Use equivalent number sentences involving addition and subtraction to find unknown quantities (ACMNA083) | complete number sentences involving addition and subtraction by calculating missing numbers, e.g. find the missing numbers: □+55=83, □−15=19 |

– use inverse operations to complete number sentences (Problem Solving)Critical and creative thinking | |

– justify solutions when completing number sentences (Communicating, Reasoning) | |

find the missing number in a number sentence involving operations of addition or subtraction on both sides of the equals sign, eg 8+□=6+7 |

Investigate and use the properties of even and odd numbers (ACMNA071) | investigate and generalise the result of adding, subtracting and multiplying pairs of even numbers, pairs of odd numbers, or one even and one odd number, eg even + odd = odd, odd × odd = odd |

– explain why the result of a calculation is even or odd with reference to the properties of the numbers used in the calculation (Communicating, Reasoning) | |

– predict whether the answer to a calculation will be even or odd by using the properties of the numbers in the calculation (Reasoning) |

Investigate number sequences involving multiples of 3, 4, 6, 7, 8 and 9 (ACMNA074) | generate number patterns using multiples of 3, 4, 6, 7, 8 and 9, eg 3, 6, 9, 12, … |

– investigate visual number patterns on a number chart (Problem Solving) |

Explore and describe number patterns resulting from performing multiplication (ACMNA081) | use the word ‘term’ when referring to numbers in a number pattern |

– describe the position of each term in a given number pattern, eg ‘The first term is 6’ (Communicating) | |

find a higher term in a number pattern resulting from performing multiplication, given the first few terms, eg determine the next term in the pattern 4, 8, 16, 32, 64, … | |

– describe how the next term in a number pattern is calculated, eg ‘Each term in the pattern is double the previous term’ (Communicating) |

## MEASUREMENT AND GEOMETRY

## LENGTH

OUTCOME

A student:

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

TEACHING POINTS | It is important that students have a clear understanding of the distinction between perimeter and area. |

The use of a thermometer to measure temperature is included in the Length substrand of the syllabus, but it is not anticipated that this skill will be taught as part of learning experiences focused on length. It may be helpful to draw students’ attention to the link between negative numbers, which are introduced in Stage 3 Whole Numbers, and a temperature scale. |

LANGUAGE | Students should be able to communicate using the following language: length, distance, metre, centimetre, millimetre, ruler, tape measure, trundle wheel, measure, estimate, perimeter, height, width, temperature, cold, warm, hot, degree (Celsius), thermometer. |

Perimeter’ is derived from the Greek words that mean to measure around the outside: peri, meaning ‘around’, and metron, meaning ‘measure’. | |

The term ‘height’ usually refers to the distance from the ‘base’ to the ‘top’ of an object or shape. The term ‘width’ usually refers to the shorter side of a rectangle; another word for width is ‘breadth’. |

## Expectations of Attainment

Use scaled instruments to measure and compare lengths (ACMMG084) | use a tape measure, ruler and trundle wheel to measure lengths and distances |

– select and use an appropriate device to measure lengths and distances (Problem Solving) | |

– explain why two students may obtain different measures for the same length (Communicating, Reasoning, Critical and creative thinking) | |

select and use an appropriate unit to estimate, measure and compare lengths and distances | |

recognise the features of a three-dimensional object associated with length that can be measured, eg length, height, width, perimeter (Literacy) | |

use the term ‘perimeter’ to describe the total distance around a two-dimensional shape (Literacy) | |

– describe when a perimeter measurement might be used in everyday situations, eg determining the length of fencing required to enclose a playground (Communicating, Literacy, Critical and creative thinking) | |

convert between metres and centimetres, and between centimetres and millimetres | |

– describe one centimetre as one-hundredth of a metre and one millimetre as one-tenth of a centimetre (Communicating, Literacy) | |

– explain the relationship between the size of a unit and the number of units needed, eg more centimetres than metres will be needed to measure the same length (Communicating, Reasoning, Critical and creative thinking) | |

record lengths and distances using decimal notation to two decimal places, eg 1.25 m |

Use scaled instruments to measure and compare temperatures (ACMMG084) | identify temperature as a measure of how hot or cold something is (Literacy) |

use everyday language to describe temperature, eg ‘cold’, ‘warm’, ‘hot’ | |

recognise the need for formal units to measure temperature | |

use a thermometer to measure and compare temperatures to the nearest degree Celsius | |

record temperatures to the nearest degree Celsius using the symbol for degrees (°) | |

– use a thermometer to take and record daily temperature readings (Communicating, Sustainability) |

## AREA

OUTCOME

A student:

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

TEACHING POINTS | Area relates to the measurement of two-dimensional space in the same way that volume and capacity relate to the measurement of three-dimensional space. Students should appreciate that measuring area with a square-centimetre grid overlay is more difficult when the shape to be measured is not rectangular (including not square). This leads to an appreciation of the usefulness of the various algebraic formulas for calculating areas that are developed in later stages. |

LANGUAGE | Students should be able to communicate using the following language: area, irregular area, measure, grid, row, column, parts of (units), square centimetre, square metre, estimate. |

The abbreviation m^2 is read as ‘square metre(s)’ and not ‘metre(s) squared’ or ‘metre(s) square’. Similarly, the abbreviation cm^2 is read as ‘square centimetre(s)’ and not ‘centimetre(s) squared’ or ‘centimetre(s) square’. |

## EXPECTATIONS OF ATTAINMENT

Compare the areas of regular and irregular shapes by informal means (ACMMG087) | measure the areas of common two-dimensional shapes using a square-centimetre grid overlay, eg measure the area of a regular hexagon |

– compare how different placements of a grid overlay make measuring area easier or harder, e.g. | |

– develop strategies for counting partial units in the total area of the shape, eg determine two or more partial units that combine to form one whole unit (Communicating, Problem Solving, Critical and creative thinking) | |

measure the areas of irregular shapes using a square-centimetre grid overlay, e.g. | |

compare two or more areas by informal means, eg using tiles or a square-centimetre grid overlay | |

– explain why two students may obtain different measurements of the area of the same irregular shape (Communicating, Reasoning, Critical and creative thinking) |

Compare objects using familiar metric units of area (ACMMG290) | estimate the larger of two or more rectangular areas (including the areas of squares) in square centimetres and then measure in square centimetres to compare the areas |

estimate the larger of two or more rectangular areas (including the areas of squares) in square metres and then measure in square metres to compare the areas |

## VOLUME & CAPACITY

OUTCOME

A student:

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

TEACHING POINTS | The displacement strategy for finding the volume of an object relies on the fact that an object displaces its own volume when it is totally submerged in a liquid. The strategy may be applied in two ways: using a partially filled, calibrated, clear container and noting the change in the level of the liquid when an object is submerged; or submerging an object in a container filled to the brim with liquid and measuring the overflow. See Y3 as well |

LANGUAGE | Students should be able to communicate using the following language: capacity, container, litre, millilitre, volume, measure, estimate. |

Capacity refers to the amount a container can hold, whereas volume refers to the amount of space an object or substance (including liquids) occupies. |

## EXPECTATIONS OF ATTAINMENT

Use scaled instruments to measure and compare capacities (ACMMG084) | recognise the need for a formal unit smaller than the litre to measure volume and capacity |

recognise that there are 1000 millilitres in one litre, i.e. 1000 millilitres = 1 litre | |

– relate the millilitre to familiar everyday containers and familiar informal units, eg 250 mL fruit juice containers, 1 teaspoon is approximately 5 mL (Reasoning) | |

make a measuring device calibrated in multiples of 100 mL to measure volume and capacity to the nearest 100 mL | |

use the millilitre as a unit to measure volume and capacity, using a device calibrated in millilitres, eg place a measuring cylinder under a dripping tap to measure the volume of water lost over a particular period of time (Sustainability) | |

record volumes and capacities using the abbreviation for millilitres (mL) {Literacy} | |

convert between millilitres and litres, e.g. 1250 mL = 1 litre 250 millilitres | |

compare and order the capacities of two or more containers measured in millilitres | |

– interpret information about volume and capacity on commercial packaging {Communicating, Literacy} | |

estimate the capacity of a container in millilitres and check by measuring | |

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

– estimate the change in water level when an object is submerged {Reasoning, Critical and creative thinking} | |

measure the overflow in millilitres when different objects are submerged in a container filled to the brim with water | |

estimate the volume of a substance in a partially filled container from the information on the label detailing the contents of the container |

## MASS

OUTCOME

A student:

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

TEACHING POINTS | In Stage 2, students should appreciate that formal units allow for easier and more accurate communication of measures. Students are introduced to the kilogram and gram. They should develop an understanding of the size of these units, and use them to measure and estimate. |

LANGUAGE | Students should be able to communicate using the following language: mass, measure, scales, kilogram, gram. The term ‘scales’, as in a set of scales, may be confusing for some students who associate it with other uses of the word ‘scales’, eg fish scales, scales on a map, or musical scales. These other meanings should be discussed with students. |

## EXPECTATIONS OF ATTAINMENT

Use scaled instruments to measure and compare masses (ACMMG084) | recognise the need for a formal unit smaller than the kilogram |

recognise that there are 1000 grams in one kilogram, i.e. 1000 grams = 1 kilogram | |

use the gram as a unit to measure mass, using a scaled instrument | |

– associate gram measures with familiar objects, eg a standard egg has a mass of about 60 grams {Reasoning} | |

record masses using the abbreviation for grams (g) {Literacy} | |

compare two or more objects by mass measured in kilograms and grams, using a set of scales | |

interpret statements, and discuss the use of kilograms and grams, on commercial packaging {Communicating, Problem Solving, Literacy Critical and creative thinking} | |

interpret commonly used fractions of a kilogram, including 1/2, 1/4, 3/4, and relate these to the number of grams | |

– solve problems, including those involving commonly used fractions of a kilogram {Problem Solving, Critical and creative thinking} | |

record masses using kilograms and grams, eg 1 kg 200 g |

## TIME

OUTCOME

A student:

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

TEACHING POINTS | Midday and midnight need not be expressed in am or pm form. ’12 noon’ or ’12 midday’ and ’12 midnight’ should be used, even though 12:00 pm and 12:00 am are sometimes seen. |

The terms ‘am’ and ‘pm’ are used only for the digital form of time recording and not with the ‘o’clock’ terminology. | |

It is important to note that there are many different forms used in recording dates, including abbreviated forms. | |

Different notations for dates are used in different countries, eg 8 December 2014 is usually recorded as 8/12/14 in Australia, but as 12/8/14 in the United States of America. | |

Refer also to background information in Time 1. |

LANGUAGE | Students should be able to communicate using the following language: calendar, date, timetable, timeline, time, hour, minute, second, midday, noon, midnight, am (notation), pm (notation). |

The term ‘am’ is derived from the Latin ante meridiem, meaning ‘before midday’, while ‘pm’ is derived from the Latin post meridiem, meaning ‘after midday’. |

## EXPECTATIONS OF ATTAINMENT

Convert between units of time (ACMMG085) | convert between units of time and recall time facts, e.g. 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day |

explain the relationship between the size of a unit and the number of units needed, eg fewer hours than minutes will be needed to measure the same duration of time {Communicating, Reasoning, Critical and creative thinking} |

Use am and pm notation and solve simple time problems (ACMMG086) | record digital time using the correct notation, including am and pm, e.g. 9:15 am {Literacy} |

– describe times given using am and pm notation in relation to ‘midday’ (or ‘noon’) and ‘midnight’, eg ‘3:15 pm is three and a quarter hours after midday’ {Communicating, Literacy} | |

relate analog notation to digital notation for time, eg ten to nine in the morning is the same time as 8:50 am {Literacy} | |

solve simple time problems using appropriate strategies, eg calculate the time spent on particular activities during the school day {Critical and creative thinking} |

Read and interpret simple timetables, timelines and calendars | read and interpret timetables and timelines {Literacy, Critical and creative thinking Personal and social capability} |

read and interpret calendars {Literacy, Critical and creative thinking Personal and social capability} | |

– explore and use different notations to record the date {Communicating, Literacy, Critical and creative thinking Personal and social capability} | |

– explore and use the various date input and output options of digital technologies {Communicating, Information and communication technology capability, Personal and social capability} |

## THREE-DIMENSIONAL SPACE

OUTCOME

A student:

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

TEACHING POINTS | The formal names for particular prisms and pyramids are not introduced in Stage 2. Prisms and pyramids are to be treated as classes for the grouping of all prisms and all pyramids. Names for particular prisms and pyramids are introduced in Stage 3. |

LANGUAGE | Students should be able to communicate using the following language: object, two-dimensional shape (2D shape), three-dimensional object (3D object), cone, cube, cylinder, prism, pyramid, sphere, top view, front view, side view, isometric grid paper, isometric drawing, depth. Refer also to language in Three-Dimensional Space 1. |

## EXPECTATIONS OF ATTAINMENT

Investigate and represent three-dimensional objects using drawings | identify prisms (including cubes), pyramids, cylinders, cones and spheres in the environment and from drawings, photographs and descriptions {Literacy} |

– investigate types of three-dimensional objects used in commercial packaging and give reasons for some being more commonly used {Communicating, Reasoning, Critical and creative thinking Personal and social capability} | |

sketch prisms (including cubes), pyramids, cylinders and cones, attempting to show depth | |

– compare their own drawings of three-dimensional objects with other drawings and photographs of three-dimensional objects {Reasoning} | |

– draw three-dimensional objects using a computer drawing tool, attempting to show depth {Communicating, Information and communication technology capability} | |

sketch three-dimensional objects from different views, including top, front and side views | |

– investigate different two-dimensional representations of three-dimensional objects in the environment, e.g. in Aboriginal art {Communicating, Information and communication technology capability, Aboriginal and Torres Strait Islander histories and cultures} | |

draw different views of an object constructed from connecting cubes on isometric grid paper | |

interpret given isometric drawings to make models of three-dimensional objects using connecting cubes |

## TWO-DIMENSIONAL SPACE

OUTCOME

A student:

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

TEACHING POINTS | Students should be given the opportunity to attempt to create tessellating designs with a selection of different shapes, including shapes that do not tessellate. |

LANGUAGE | Students should be able to communicate using the following language: shape, two-dimensional shape (2D shape), triangle, quadrilateral, parallelogram, rectangle, rhombus, square, trapezium, kite, pentagon, hexagon, octagon, line (axis) of symmetry, reflect (flip), translate (slide), rotate (turn), tessellate, clockwise, anti-clockwise, half-turn, quarter-turn, three-quarter-turn. |

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

## EXPECTATIONS OF ATTAINMENT

Compare and describe two-dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088) | combine common two-dimensional shapes, including special quadrilaterals, to form other common shapes or designs, eg combine a rhombus and a triangle to form a trapezium |

– describe and/or name the shape formed from a combination of common shapes {Communicating, Literacy} | |

– follow written or verbal instructions to create a common shape using a specified set of two or more common shapes, eg create an octagon from five squares and four triangles {Communicating, Problem Solving, Literacy Critical and creative thinking} | |

– use digital technologies to construct a design or logo by combining common shapes {Communicating, Information and communication technology capability Critical and creative thinking} | |

split a given shape into two or more common shapes and describe the result, e.g. ‘I split the parallelogram into a rectangle and two equal-sized triangles’ | |

compare the area of the given shape with the area of each of the shapes it is split into, eg if a pentagon is split into five equal triangles, describe the area of the pentagon as five times the area of one triangle, or the area of one triangle as 1/5 of the area of the pentagon {Communicating, Reasoning, Critical and creative thinking} | |

record the arrangements of common shapes used to create other shapes, and the arrangement of shapes formed after splitting a shape, in diagrammatic form, with and without the use of digital technologies {Information and communication technology capability} | |

– record different combinations of common shapes that can be used to form a particular regular polygon, eg a hexagon can be created from, or split into, many different arrangements, such as {Communicating, Problem Solving, Critical and creative thinking} |

Create symmetrical patterns, pictures and shapes, with and without the use of digital technologies (ACMMG091) | create symmetrical patterns, designs, pictures and shapes by translating (sliding), reflecting (flipping) and rotating (turning) one or more common shapes |

– use different types of graph paper to assist in creating symmetrical designs {Communicating} | |

– use digital technologies to create designs by copying, pasting, reflecting, translating and rotating common shapes {Communicating, Problem Solving, Information and communication technology capability} | |

– apply and describe amounts of rotation, in both ‘clockwise’ and ‘anti-clockwise’ directions, including half-turns, quarter-turns and three-quarter-turns, when creating designs {Communicating, Problem Solving, Literacy} | |

– describe the creation of symmetrical designs using the terms ‘reflect’, ‘translate’ and ‘rotate’ {Communicating, Reasoning, Literacy Critical and creative thinking} | |

create and record tessellating designs by reflecting, translating and rotating common shapes | |

– use digital technologies to create tessellating designs (Communicating)Information and communication technology capability | |

– determine which of the special quadrilaterals can be used to create tessellating designs {Reasoning, Critical and creative thinking} | |

– explain why tessellating shapes are best for measuring area {Communicating, Reasoning, Critical and creative thinking} | |

identify shapes that do and do not tessellate {Critical and creative thinking} | |

– explain why a shape does or does not tessellate {Communicating, Reasoning)Critical and creative thinking} | |

draw the reflection (mirror image) to complete symmetrical pictures and shapes, given a line of symmetry, with and without the use of digital technologies {Information and communication technology capability Critical and creative thinking} |

## ANGLES

OUTCOME

A student:

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

TEACHING POINTS | A simple ‘angle tester’ can be made by placing a pipe-cleaner inside a straw and bending the straw to form two arms. Another angle tester can be made by joining two narrow straight pieces of card with a split-pin to form the rotatable arms of an angle. |

LANGUAGE | Students should be able to communicate using the following language: angle, arm, vertex, right angle, acute angle, obtuse angle, straight angle, reflex angle, angle of revolution. |

The use of the terms ‘sharp’ and ‘blunt’ to describe acute and obtuse angles, respectively, is counterproductive in identifying the nature of angles. Such terms should not be used with students as they focus attention on the external points of an angle, rather than on the amount of turning between the arms of the angle. |

## EXPECTATIONS OF ATTAINMENT

Compare angles and classify them as equal to, greater than or less than a right angle (ACMMG089) | compare angles using informal means, such as by using an ‘angle tester’ |

recognise and describe angles as ‘less than’, ‘equal to’, ‘about the same as’ or ‘greater than’ a right angle {Literacy} | |

classify angles as acute, right, obtuse, straight, reflex or a revolution {Literacy} | |

– describe the size of different types of angles in relation to a right angle, eg acute angles are less than a right angle {Communicating} | |

– relate the turn of the hour hand on a clock through a right angle or straight angle to the number of hours elapsed, eg a turn through a right angle represents the passing of three hours {Reasoning, Critical and creative thinking} | |

identify the arms and vertex of the angle in an opening, a slope and/or a turn where one arm is visible and the other arm is invisible, eg the bottom of an open door is the visible arm and the imaginary line on the floor across the doorway is the other arm | |

create, draw and classify angles of various sizes, eg by tracing along the adjacent sides of shapes | |

– draw and classify the angle through which the minute hand of a clock turns from various starting points {Communicating, Reasoning} |

## POSITION

OUTCOME

A student:

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

TEACHING POINT | Students need to have experiences identifying north from a compass in their own environment and then determining the other three key directions: east, south and west. This could be done in the playground before introducing students to using these directions on maps to describe the positions of various places. The four directions NE, SE, SW and NW could then be introduced to assist with descriptions of places that lie between N, E, S and W. |

LANGUAGE | Students should be able to communicate using the following language: position, location, map, plan, legend, key, scale, directions, compass, compass rose, north, east, south, west, north-east, south-east, south-west, north-west. |

The word ‘scale’ has different meanings in different contexts. Scale could mean the enlargement or reduction factor for a drawing, the scale marked on a measuring device, a fish scale or a musical scale. |

## EXPECTATIONS OF ATTAINMENT

Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090) | use a legend (or key) to locate specific objects on a map {Literacy} |

use a compass to find north and then east, south and west | |

use N, E, S and W to indicate north, east, south and west, respectively, on a compass rose | |

use an arrow to represent north on a map | |

determine the directions north, east, south and west when given one of the directions | |

use north, east, south and west to describe the location of a particular object in relation to another object on a simple map, given an arrow that represents north, eg ‘The treasure is east of the cave’ {Literacy} | |

use NE, SE, SW and NW to indicate north-east, south-east, south-west and north-west, respectively, on a compass rose, e.g. | |

determine the directions NE, SE, SW and NW when given one of the directions | |

use north-east, south-east, south-west and north-west to describe the location of an object on simple maps, given a compass rose, e.g. ‘The tree is south-west of the sign’ {Literacy} | |

calculate the distance between two points on a map using a simple given scale | |

use scales involving multiples of 10 to calculate the distance between two points on maps and plans | |

– interpret simple scales on maps and plans, eg ‘One centimetre on the map represents one metre in real life’ {Reasoning, Literacy} | |

– give reasons for using a particular scale on a map or plan {Communicating, Reasoning, Critical and creative thinking} | |

recognise that the same location can be represented by maps or plans using different scales {Critical and creative thinking} |

## STATISTICS AND PROBABILITY

## DATA

OUTCOME

A student:

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

TEACHING TIPS | A scale of many-to-one correspondence in a picture graph or column graph uses one symbol or one unit to represent more than one item or response, eg = 10 people, or 1 centimetre represents 5 items/responses. |

LANGUAGE | Students should be able to communicate using the following language: data, collect, survey, recording sheet, rating scale, category, display, symbol, tally mark, table, column graph, picture graph, vertical columns, horizontal bars, scale, equal spacing, title, key, vertical axis, horizontal axis, axes, spreadsheet, misleading. Refer also to language in Data 1. |

## Expectations of Attainment

Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095) | create a survey and related recording sheet, considering the appropriate organisation of categories for data collection {Difference and diversity} |

– choose effective ways to collect and record data for an investigation, eg creating a survey with a scale of 1 to 5 to indicate preferences (1 = don’t like, 2 = like a little, 3 = don’t know, 4 = like, 5 = like a lot) {Communicating, Problem Solving, Literacy} | |

refine survey questions as necessary after a small trial {Critical and creative thinking} | |

– discuss and decide the most suitable question to investigate a particular matter of interest, eg by narrowing the focus of a question from ‘What is the most popular playground game?’ to ‘What is the most popular playground game among Year 3 students at our school?’ {Communicating, Reasoning, Literacy Critical and creative thinking} | |

conduct a survey to collect categorical data {Difference and diversity} | |

– after conducting a survey, discuss and determine possible improvements to the questions or recording sheet {Communicating, Reasoning, Critical and creative thinking} | |

compare the effectiveness of different methods of collecting and recording data, eg creating categories of playground games and using tally marks, compared to asking open-ended questions such as ‘What playground game do you like to play?’ {Critical and creative thinking} | |

– discuss the advantages and/or disadvantages of open-ended questions in a survey, compared to questions with predetermined categories {Communicating, Reasoning, Literacy Critical and creative thinking} |

Construct suitable data displays, with and without the use of digital technologies, from given or collected data; include tables, column graphs and picture graphs where one picture can represent many data values (ACMSP096) | represent given or collected categorical data in tables, column graphs and picture graphs, using a scale of many-to-one correspondence, with and without the use of digital technologies |

– discuss and determine a suitable scale of many-to-one correspondence to draw graphs for large data sets and state the key used, e.g. 🙂 = 10 people, if there are 200 data values {Communicating, Reasoning} | |

– use grid paper to assist in drawing graphs that represent data using a scale of many-to-one correspondence {Communicating} | |

– use data in a spreadsheet to create column graphs with appropriately labelled axes {Communicating, Problem Solving, Information and communication technology capability} | |

– mark equal spaces on axes, name and label axes, and choose appropriate titles for graphs {Communicating, Literacy} |

Evaluate the effectiveness of different displays in illustrating data features, including variability (ACMSP097) | interpret and evaluate the effectiveness of various data displays found in media and in factual texts, where displays represent data using a scale of many-to-one correspondence {Literacy, Information and communication technology capability, Critical and creative thinking, Personal and social capability, Ethical understanding, Civics and citizenship} |

– identify and discuss misleading representations of data {Communicating, Reasoning, Literacy, Critical and creative thinking, Personal and social capability, Ethical understanding, Civics and citizenship} | |

– discuss and compare features of data displays, including considering the number and appropriateness of the categories used, eg a display with only three categories (blue, red, other) for car colour is not likely to be useful {Communicating, Literacy, Critical and creative thinking, Ethical understanding} | |

– discuss the advantages and disadvantages of different representations of the same categorical data, eg column graphs compared to picture graphs that represent data using scales of many-to-one correspondence {Communicating, Critical and creative thinking, Ethical understanding} |

## CHANCE

OUTCOME

A student:

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

TEACHING POINT | Theoretically, when a fair coin is tossed, there is an equal chance of obtaining a head or a tail. If the coin is tossed and five heads in a row are obtained, there is still an equal chance of a head or a tail on the next toss, since each toss is an independent event. |

LANGUAGE | Students should be able to communicate using the following language: chance, event, possible, impossible, likely, unlikely, less likely, more likely, most likely, least likely, equally likely, experiment, outcome. |

## EXPECTATIONS OF ATTAINMENT

Describe possible everyday events and order their chances of occurring (ACMSP092) | use the terms ‘equally likely’, ‘likely’ and ‘unlikely’ to describe the chance of everyday events occurring, eg ‘It is equally likely that you will get an odd or an even number when you roll a die’ {Literacy} |

compare the chance of familiar events occurring and describe the events as being ‘more likely’ or ‘less likely’ to occur than each other {Literacy} | |

order events from least likely to most likely to occur, eg ‘Having 10 children away sick on the same day is less likely than having one or two away’ | |

compare the likelihood of obtaining particular outcomes in a simple chance experiment, eg for a collection of 7 red, 13 blue and 10 yellow marbles, name blue as being the colour most likely to be drawn out and recognise that it is impossible to draw out a green marble. |

Identify everyday events where one occurring cannot happen if the other happens (ACMSP093) | identify and discuss everyday events occurring that cannot occur at the same time, eg the sun rising and the sun setting {Critical and creative thinking} |

Identify events where the chance of one occurring will not be affected by the occurrence of the other (ACMSP094) | identify and discuss events where the chance of one event occurring will not be affected by the occurrence of the other, eg obtaining a ‘head’ when tossing a coin does not affect the chance of obtaining a ‘head’ on the next toss |

– explain why the chance of each of the outcomes of a second toss of a coin occurring does not depend on the result of the first toss, whereas drawing a card from a pack of playing cards and not returning it to the pack changes the chance of obtaining a particular card or cards in future draws {Communicating, Literacy, Critical and creative thinking} | |

compare events where the chance of one event occurring is not affected by the occurrence of the other, with events where the chance of one event occurring is affected by the occurrence of the other, eg decide whether taking five red lollies out of a packet containing 10 red and 10 green lollies affects the chance of the next lolly taken out being red, and compare this to what happens if the first five lollies taken out are put back in the jar before the sixth lolly is selected {Critical and creative thinking} |