### Specific Life Skills outcomes will be selected on the basis that they meet the particular needs, goals and priorities of each student. Students are not required to complete all outcomes.

### Outcomes may be demonstrated independently or with support. However, in developing programs teachers need to take into consideration relevant system policies regarding mandatory learning experiences.

### In order to provide a relevant and meaningful program of study that reflects the needs, interests and abilities of each student, schools may integrate Mathematics Years 7–10 Life Skills outcomes and content across a variety of school and community contexts.

### A range of curriculum adjustments should be explored before a decision is made to access Years 7–10 Life Skills outcomes and content. Information about curriculum adjustments can be found in *Life Skills Years 7–10 Advice on Planning, Programming and Assessment*.

**8.1 ** **Years 7–10 Life Skills Outcomes **

##

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**Objective **
Students:

### •

understand and connect related mathematical concepts, choosing, applying and communicating approaches in order to investigate and solve problems**Life Skills outcomes **
A student:

LS 1

responds to and uses mathematical language to demonstrate understanding of concepts LS 2

applies a range of mathematical techniques to solve problems LS 3

uses simple reasoning to recognise mathematical relationships

### •

develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation**Life Skills outcomes **
A student:

LS 4

recognises language used to represent number LS 5

counts in familiar contexts LS 6

compares, orders, reads and represents numbers LS 7

recognises and compares fractions in everyday contexts LS 8

represents and operates with fractions, decimals or percentages in everyday contexts LS 9

uses mental strategies and concrete materials to represent addition, subtraction, multiplication and/or division

LS 10

selects and uses a range of strategies for addition, subtraction, multiplication and/or division LS 11

recognises, reads and represents money LS 12

uses money to purchase goods and services LS 13

makes informed decisions about purchasing goods and services LS 14

plans and manages personal finances LS 15

recognises and continues repeating patterns LS 16

calculates missing values by completing simple number sentences

geometric reasoning
**Life Skills outcomes **
A student:

LS 17

recognises and relates time in a range of contexts LS 18

reads and interprets time in a variety of situations LS 19

calculates and measures time and duration in everyday contexts LS 20

organises personal time and manages scheduled activities LS 21

responds to the language of measurement in everyday contexts LS 22

uses informal units for measurement in everyday contexts LS 23

uses and applies formal units for measurement in everyday contexts LS 24

recognises, matches and sorts three-dimensional objects and/or two-dimensional shapes LS 25

identifies the features of three-dimensional objects and/or two-dimensional shapes and applies these in a range of contexts

LS 26

responds to and uses the language of position in everyday contexts LS 27

recognises that maps and plans are a representation of positions in space LS 28

uses maps and plans in a range of contexts

Students:

### •

collect, represent, analyse, interpret and evaluate data, assign and use probabilities, and make sound judgements**Outcomes**
A student:

LS 29

recognises data displayed in a variety of formats LS 30

gathers, organises and displays data LS 31

interprets information and draws conclusions from data displays LS 32

recognises and uses the language of chance in a range of contexts LS 33

recognises the elements of chance and probability in everyday events

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The *Mathematics K-10 Syllabus* is organised into one proficiency strand and three content
strands.

Further information about the organisation of content is provided in Section 7.

**Number and Algebra **
Numeration 1

**Outcomes **
A student:

LS 1 responds to and uses mathematical language to demonstrate understanding of concepts LS 3 uses simple reasoning to recognise mathematical relationships

LS 4 recognises language used to represent number Students:

• recognise language related to number, eg none, few, many, more, less [L]

− respond to questions which involve descriptions of number, eg ‘Are all the books on the shelf?’, ‘Which box has no pencils?’ ‘Which plate has more cakes?’ (Understanding) [L]

[N]

− respond to requests which involve descriptions of number, eg ‘Put all the books on the shelf’, ‘Take some paper from my desk’, ‘Place a few chairs near the table’

(Understanding) [L] [N]

− describe and compare groups of objects using language descriptive of number, eg ‘There are none left on the shelf’, ‘I have more cards than my brother’ (Understanding,

Reasoning) [L] [N]

• recognise ordinal terms, eg first, second, third [L]

− respond to directions involving ordinal terms, eg ‘Give a ball to the first person in each row’, ‘Put a book on every second chair’ (Understanding) [L] [N]

• use ordinal terms in familiar contexts,

eg ‘I go to training on the first and third Wednesday of the month’, ‘The youth group meets on the first Monday of each month’, ‘My birthday is on the fifth of November’, ‘Is the office on the first or second floor?’, ‘Is the post office in the third or fourth street on the left?’

(Understanding) [L] [N]

**Outcomes **
A student:

LS 1 responds to and uses mathematical language to demonstrate understanding of concepts LS 5 counts in familiar contexts

Students:

• count in familiar situations*, *

eg count out books for a group or class, count uniforms for a sports team [N]* *

• count objects by twos, fives, tens [N]

• match groups of objects that have the same number of items [N] [CCT]

− identify groups that have the same number of items as a given group, eg match golf balls with tees, match pieces of cake with people at a party (Understanding, Fluency) [N] [CCT]

• compare and order groups of objects according to the number in the group [N] [CCT]

− identify groups that have more or fewer items than a given group, eg available plates/cups for guests at a party (Understanding, Fluency) [N] [CCT]

− order groups of objects by ascending/descending order according to the number in the group (Fluency) [N] [CCT]

• count with single-digit numbers [N]

• count with two-digit numbers [N]

• count forwards and backwards from a given number in the range 0 to 100 [N]

• solve problems involving counting, eg ‘How many people are in class today?’ (Problem Solving) [CCT] [N]

• count with three digit numbers [N]

• count by twos, fives, tens and hundreds [N]

− tell the time on a watch or clock by counting by fives around the clock or watch face (Fluency, Understanding) [N]

Numeration 3
**Outcomes **
A student:

LS 1 responds to and uses mathematical language to demonstrate understanding of concepts LS 2 applies a range of mathematical techniques to solve problems

LS 3 uses simple reasoning to recognise mathematical relationships LS 6 compares, orders, reads and represents numbers

Students:

• read, order and record numbers 0 to 9 [N]* *

− identify some of the ways numbers are used in our lives, eg telephone numbers, bus numbers, Personal Identification Number (PIN) (Understanding, Reasoning) [N]

• read, order and record two-digit numbers [N]

• recognise, read and interpret numerical information in a range of formats, eg recipes, medication dosages [L] [N]

− identify and locate numbers in a range of situations, eg table of contents in a book, seat numbers in a theatre, odd and even house numbers (Understanding) [N]

• recognise, read and convert Roman numerals used in everyday contexts [N] [CCT]

• read, order and record three-digit numbers [N]

• recognise odd and even numbers [N]

• recognise and read numbers with more than three digits [N]

**Outcomes **
A student:

LS 1 responds to and uses mathematical language to demonstrate understanding of concepts LS 2 applies a range of mathematical techniques to solve problems

LS 7 recognises and compares fractions in everyday contexts Students:

• recognise the need for two equal parts when dividing a whole in half [N]

− allocate portions or divide materials, eg cut a length of ribbon into equal pieces (Fluency, Problem Solving, Understanding) [N] [PSC]

• recognise halves [N]

− identify items that are a half, eg half of an apple, half of a pizza (Understanding) [N]

− identify items that are less than a half or more than a half, eg ‘The glass is more than half full’ (Understanding) [N]

− determine if parts of a whole object, or collection of objects, are equal, eg ‘Has the cake been cut into two equal parts?’ (Reasoning, Understanding) [N]

− share an object into two equal parts, eg giving half a sandwich (Fluency, Understanding) [N] [PSC]

• recognise and use the terms ‘half’ and ‘halves’ [L]

− describe situations using the terms ‘half’ and ‘halves’, eg ‘The television program is half an hour long’ (Understanding) [N] [L]

− follow an instruction involving fraction language in everyday contexts, eg ‘Move to the other half of the soccer field’ (Understanding) [N] [L]

• recognise the need for four equal parts when dividing a whole into quarters [N]

− allocate portions or divide materials, eg cut a cake into equal pieces (Fluency, Problem Solving, Understanding) [N] [PSC]

• recognise quarters [N]

− identify items that are a quarter of a whole, eg quarter of an apple, quarter of a sandwich (Understanding) [N]

− identify items that are less than a quarter or more than a quarter (Understanding) [N]

− determine if parts of a whole object, or collection of objects, are equal, eg ‘Has the cake been cut into four equal parts?’ (Understanding, Problem Solving) [N]

− put two quarters together to make a half (Understanding) [N]

− share an object into four equal parts, eg giving a quarter of an apple (Fluency, Understanding) [N] [PSC]

• recognise and use the term ‘quarter’ [L]

− describe situations using the term ‘quarter’, eg ‘Lunch is three-quarters of an hour’

(Understanding) [L] [N]

Numeration 4

− follow an instruction involving fraction language in everyday contexts, eg ‘Give a quarter of the orange to your friend’ (Fluency, Understanding) [L] [N]

• compare fractions,

eg half of the pizza is more than a quarter [N] [CCT]

**Outcomes **
A student:

LS 1 responds to and uses mathematical language to demonstrate understanding of concepts LS 2 applies a range of mathematical techniques to solve problems

LS 3 uses simple reasoning to recognise mathematical relationships

LS 8 represents and operates with fractions, decimals or percentages in everyday contexts Students:

*Fractions *

• use fraction notation to represent parts of a whole,

eg [N]

− interpret the denominator as the number of equal parts a whole has been divided into (Understanding) [N]

− interpret the numerator as the number of equal fractional parts, eg means 3 equal parts of 4 (Understanding) [N]

• add a fraction to a whole number using concrete materials and record the result as a mixed numeral,

eg [N]

• add a fraction to another fraction so the total is no more than one whole using concrete materials [N]

• add a fraction to another fraction so the total is more than one whole using concrete materials and represent this as a mixed numeral,

eg five quarter slices of pizza is pizzas [N]

• subtract a fraction from one whole using concrete materials,

eg subtract three quarters of a pizza and find the fraction remaining [N]

• find a unit fraction of a quantity, eg etc [N]

− recognise that finding a unit fraction of a quantity is related to division, eg half of $60 is the same as $60 divided by 2 (Understanding, Fluency) [N] [CCT]

• find any fraction of a quantity, eg etc [N]

− recognise the relationship between finding a unit fraction of a quantity and any fraction of a quantity, eg to find three-quarters of one hour, first find one quarter of an hour and then multiply by 3 (Understanding, Fluency) [N] [CCT]

*Decimals *

• read numbers as decimals,

eg is read as ‘three point five’ [N]

− recognise the use of decimals in the community, eg advertisements for interest rates (Understanding, Reasoning) [N] [PSC]

Operations 1

− recognise the use of decimals for recording measurements, eg 3.5 metres means three and a half metres, timing swimming races to tenths and hundredths of a second

(Understanding, Reasoning) [N] [PSC]

• recognise commonly used fractions in decimal notation,

eg , [N]

• add and subtract numbers correct to two decimal places in the context of money,

eg [N]

• relate fractions to decimals in the context of parts of one dollar,

eg , [N]

• interpret decimal notation for tenths and hundredths, eg is the same as , is the same as [N]

− interpret calculator displays involving decimals (Understanding, Reasoning) [L]

• compare decimals with the same number of decimal places, eg is less than [N]

− use a number line to position decimals between 0 and 1 (Understanding, Fluency) [N]

• round decimals in the context of money, eg rounding to [N]

− explain the result of rounding when purchasing goods where the total number of cents involved cannot be made up using 5 and 10 cent pieces, eg round to , round

to (Understanding, Fluency, Reasoning) [N] [CCT] [PSC]

*Percentages *

• read the symbol % as ‘percent’ [L]

− recognise the use of the % symbol in a variety of contexts, eg advertising, discounts (Understanding) [L]

• recognise commonly used percentages as fractions,

eg , , [N]

• recognise that percentages are parts of 100,

eg [N]

• interpret the use of percentages in everyday contexts [N]

− interpret advertising and media reports involving percentages, eg success rate for goal kicking, more chocolate (Understanding, Reasoning) [N] [CCT] [PSC]

− decide which is the best interest rate offered for a loan using online calculators (Fluency, Reasoning) [N] [CCT] [WE]

• calculate simple percentages,

eg off a item, adding GST to a bill [N]

• recognise calculations as the same,

eg finding of a quantity is the same as dividing a quantity by 2 [N] [CCT]

Operations 2
**Outcomes **
A student:

LS 3 uses simple reasoning to recognise mathematical relationships

LS 9 uses mental strategies and concrete materials to represent addition, subtraction, multiplication and/or division

Students:

• model addition using concrete materials [N]

− combine two or more groups of objects (Understanding, Fluency) [N]

− compare two groups of objects to determine how many more in the larger group (Understanding, Reasoning) [N]

• model subtraction using concrete materials [N]

− separate and take part of a group of objects away to model subtraction (Fluency, Understanding) [N]

• respond to and use the language of addition and subtraction in everyday contexts,

eg ‘add’, ‘plus’, ‘equals’, ‘is equal to’, ‘take away’, ‘minus’, and ‘the difference between’ [L]

− recognise terms in a range of situations, eg difference between scores in a computer game (Understanding) [L]

− use terms in a range of situations, eg ‘My allowance plus birthday money equals ’ (Understanding) [L]

• add two numbers using concrete materials and/or mental strategies

− count on from the larger number to find the total of two numbers (Fluency) [N]

• subtract a number from a given number using concrete materials and/or mental strategies [N]

− count back from a number to find the number remaining (Fluency) [N]

• model multiplication using concrete materials [N]

− combine equal groups of objects, eg three boxes each containing four pencils (Understanding, Fluency) [N]

• model division using concrete materials [N]

− share a group of objects equally amongst people, eg 12 balls among 3 students (Understanding, Fluency) [N] [PSC]

− use repeated subtraction with concrete materials, eg determine how many bags of golf balls can be created by placing 5 golf balls into each bag (Understanding, Fluency) [N]

• multiply two numbers using concrete materials and/or mental strategies

− collect groups of items from two or more people and determine how many items there are altogether (Fluency, Understanding) [N]

− share a number of items between two or more people using concrete materials (Understanding, Fluency) [N] [PSC]

Operations 3
**Outcomes **
A student:

LS 2 applies a range of mathematical techniques to solve problems LS 3 uses simple reasoning to recognise mathematical relationships

LS 10 selects and uses a range of strategies for addition, subtraction, multiplication and/or division Students:

• recognise and apply the symbols +, – and =

• add two numbers using mental strategies, written processes and/or calculator strategies [N]

− create combinations for numbers to at least 10, eg ‘How many more to make ten?’

(Understanding, Fluency) [N]

− estimate the sum of two numbers and check by performing the calculation or using a calculator (Fluency, Problem Solving) [N] [CCT]

• subtract a number from a given number using mental strategies, written processes and/or calculator strategies [N]

− estimate how much will be left over when one number is subtracted from another and check by performing the calculation or using a calculator (Fluency, Problem Solving) [CCT] [N]

• add more than two numbers using mental, written and/or calculator strategies,

eg [N]

• subtract more than two numbers using mental, written and/or calculator strategies,

eg [N]

• select and apply appropriate mental, written and/or calculator strategies for addition and subtraction to solve problems in a range of contexts (Problem Solving) [N] [CCT]

− calculate the total cost when purchasing more than one item, eg total cost of a juice and a $4.50 sandwich (Fluency, Problem Solving) [N] [PSC]

− calculate the change when purchasing an item, eg change from $10 when purchases total

$3.50 (Fluency, Problem Solving) [N] [PSC]

• recognise and apply the symbols , and =

• multiply two numbers using mental strategies, written processes and/or calculator strategies [N]

− multiply numbers using an array of equal rows

(Fluency) [N] [L]

− determine quantities needed when preparing a meal for several people using a recipe based on ingredients for one person (Problem Solving) [N] [CCT] [PSC]

− estimate the product of two numbers and check by performing the calculation or using a calculator (Fluency, Problem Solving) [CCT] [N]

• • • •

••••

••••

3 groups of 4 is 12 eg

− divide numbers using an array of equal rows

(Fluency) [N] [L]

− determine quantities needed when preparing a meal for one person using a recipe based on ingredients for four people (Problem Solving) [CCT] [N] [PSC]

− calculate the cost of a single item when given the price of a pack containing several items (Fluency, Problem Solving) [CCT] [N] [PSC]

− estimate the result when dividing two numbers and check by performing the calculation or
using a calculator (Fluency, Problem Solving) [N] [CCT]* *

• multiply more than two numbers using mental, written and/or calculator strategies,

eg [N]

• divide more than two numbers using mental, written and/or calculator strategies,

eg [N]

• select and apply appropriate mental, written and/or calculator strategies for multiplication and division to solve problems in a range of contexts (Problem Solving) [N] [CCT]

− determine the total cost of a number of items given the price of one, eg calculate the combined cost of train travel over two or more days for two or more people (Fluency, Problem Solving) [N] [CCT] [PSC]

− determine the unit cost of an item or service when sold as a group, eg calculate the daily cost of shared accommodation over a set period of time for two or more people (Fluency, Problem Solving) [N] [CCT] [PSC]

••••

••••

• • • •

12 shared among 3 is 4 eg

Money 1
**Outcomes **
A student:

LS 11 recognises, reads and represents money Students:

• recognise a range of coins and notes [N] [WE]

• match and sort coins and notes into groups on the basis of face value [N]

• recognise that coins and notes have different values [WE]

− order coins and notes on the basis of face value (Understanding, Fluency) [N]

− indicate the appropriate coin to purchase a specific item in the school canteen, eg 50 cent coin, $2 coin (Understanding) [N] [PSC]

− indicate the most appropriate note to purchase an item in a shop, eg five dollar note, twenty dollar note (Understanding) [N] [PSC]

• recognise the cost of goods or services,

eg read price tags attached to clothing, identify the cost of items in a supermarket as indicated on the shelf, read a notice board at a theatre to determine the price of entry [N] [L] [PSC]

− identify the cost of items up to $10 in value by locating prices, eg a drink at the school canteen is $2, a magazine at the supermarket is (Understanding, Problem Solving) [N] [PSC]

− identify the cost of items up to $100 in value by locating prices, eg a meal at a restaurant is

$22, a jacket is $80, a pair of sunglasses is (Understanding, Problem Solving) [N]

[PSC]

• write amounts in cents,

eg 35 cents is written as 35 c [N]

• write amounts in dollars, eg 5 dollars is written as $5 [N]

• write amounts of money using decimal notation [N]

− write amounts of money involving cents, dollars, and combinations of dollars and cents,

eg , , , (Fluency) [N]

• write amounts of money in words [L]

− complete a deposit form using words and decimal notation (Understanding, Fluency) [L]

[N] [PSC]

**Outcomes **
A student:

LS 12 uses money to purchase goods and services Students:

• use the language of money in a range of contexts, eg ‘dollars’, ‘cents’, ‘purchases’, ‘cost’, ‘change’ [L]

• add coins of the same denomination [N]

• add coins of different denominations [N]

• add notes of the same denomination [N]

• add notes of different denominations [N]

• combine a range of coins to demonstrate equivalence of value,

eg cent coins and cent coin is equivalent to a 50 cent coin, cent coins is equivalent to cent coins [N]

• combine a range of notes to demonstrate equivalence of value, eg notes and note is equivalent to a $20 note [N]

• calculate the amounts of money using mental, written and/or calculator strategies to tender for goods or services [N] [PSC]

• estimate amounts of money to tender for goods or services [N] [CCT] [PSC]

− estimate the cost of a range of items and select the appropriate coin or note to pay for the items, eg select a $2 coin to pay for a drink or snack, select a $20 note to pay for a t-shirt, estimate that a $50 note will be needed to pay for a number of items at a supermarket (Understanding, Fluency) [N] [CCT] [PSC]

• calculate the amount of change due in relation to a transaction for goods or services, using mental, written and/or calculator strategies [N]

• estimate the amount of change due in relation to a transaction for goods or service [N] [CCT]

− estimate the amount of change due for a purchase and check using a calculator, eg the change due for a purchase of if a $5 note is tendered (Fluency, Problem Solving) [N] [CCT] [PSC]

Money 3
**Outcomes **
A student:

LS 3 uses simple reasoning to recognise mathematical relationships LS 13 makes informed decisions about purchasing goods and services Students:

• recognise the relationship between value and price of a range of goods and services [WE]

• compare costs of goods and services [CCT]

− calculate discounts and compare this to full price (Fluency, Reasoning) [N] [CCT]

− compare the cost of goods using price comparison websites (Reasoning, Fluency) [CCT]

[ICT] [PSC]

− compare, using the internet, the interest rates and other costs for loans and investments (Reasoning, Fluency) [ICT] [PSC]

• determine the value of a range of goods and services [N] [PSC]

− investigate ‘unit pricing’ used by retailers and use this to determine the best buy (Understanding, Fluency) [N] [CCT] [PSC]

− determine the value of ‘deals’ when purchasing goods or services, eg buy-one-get-one free, buy-one-get-another-half-price (Problem Solving, Fluency) [N] [CCT]

− determine the costs involved when purchasing via different mediums, eg cash, lay-by, credit card, loans, online (Problem Solving, Reasoning) [N] [CCT]

• identify the implications of terms and conditions,

eg fees, penalties, interest, warranties [L] [CCT] [PSC] [EU]

• investigate the process of refunding and exchanging goods [L] [PSC] [EU]

− recognise the difference between refunding and exchanging goods (Understanding) [PSC]

− recognise how refund and exchange policies vary between businesses, eg time limits, condition of the product, sale items (Understanding, Reasoning) [PSC] [L] [EU]

− understand the process involved when refunding or exchanging an item, such as producing a receipt as proof of purchase (Understanding) [PSC] [EU]

• recognise the relationship between warranties and value [L] [PSC]

− recognise the purpose of a warranty, eg for refund, exchange, repair of faulty goods or services (Understanding, Reasoning) [PSC] [EU]

− identify types of goods and services that offer warranties (Understanding)

− recognise how warranty policies vary between businesses, eg length of warranty, what is covered, cost, receipt as proof of purchase, registering online, extended warranties (Understanding, Reasoning) [PSC] [L] [EU]

**Outcomes **
A student:

LS 14 plans and manages personal finances Students:

• identify financial matters which influence daily life, eg spending, earning, saving [PSC]

− allocate amounts of money from an allowance for specific purposes, eg ‘From my $10 allowance I need to keep $4 for pool entry, so I have $6 to spend or save’(Fluency, Problem Solving) [N] [PSC]

• calculate earnings from a range of sources, eg allowance, casual or part-time work [N] [WE]

− use a pay slip to determine amount of pay (Understanding) [L] [WE]

− calculate a week’s wage given the hourly rate of pay and number of hours worked (Fluency) [N] [WE]

− read and interpret a timesheet to calculate weekly earning (Fluency) [L] [WE] [N]

• interpret information from a variety of bills [L] [ N]

− recognise common terms used on bills, such as ‘amount due’, ‘interest charged’,

‘discount’, ‘due date’ (Understanding) [L] [PSC]

− interpret the variety of payment options, eg BPay, direct debit, phone payments using credit card (Understanding) [PSC] [L]

− interpret information presented graphically, eg electricity usage (Understanding) [L] [PSC]

• manage income and expenditure [N] [PSC]

− check bank statements online (Understanding, Fluency) [N] [ICT] [PSC]

− investigate different methods for making payments, eg direct debit (Understanding) [PSC]

− use ICT to manage accounts, eg alerts and reminders via SMS and email (Understanding, Fluency) [L] [ICT] [PSC]

• balance expenses with available funds [N] [PSC]

− identify personal funds available for specific purposes, eg ‘From my weekly wages I have saved $30 this month which I can spend at the movies on Saturday’ (Fluency, Problem Solving) [N] [PSC]

− calculate the amount of time it will take to save for items at a specific amount per week or month (Fluency, Problem Solving) [N] [PSC]

− develop a budget, with or without ICT, to meet personal financial needs (Understanding, Fluency, Problem Solving) [N] [PSC] [ICT]

Money 4

• identify and describe financial terms,

eg income, expenditure, saving, borrowing, interest [L]

− use a variety of banking services, eg over the counter, ATM, EFTPOS, cheque book, telephone banking, internet banking, credit cards (Understanding, Fluency) [PSC] [ICT]

− keep and check records of financial transactions, eg keep card/PIN confidential and in a safe place, retain card and receipt after using ATM, retain and check receipts after purchasing goods and services, record receipt number when using telephone or internet services to make payments (Understanding, Problem Solving) [PSC] [L] [N] [ICT]

− retain and review bank statements (Understanding, Problem Solving) [L] [N] [PSC]

**Outcomes **
A student:

LS 1 responds to and uses mathematical language to demonstrate understanding of concepts LS 3 uses simple reasoning to recognise mathematical relationships

LS 15 recognises and continues repeating patterns Students:

• recognise what comes next in a repeating pattern of familiar objects, eg blue button, red button, blue button, red button, _____ [N]

− copy a pattern involving familiar objects (Understanding, Fluency)

− sequence a pattern of beads to make a necklace, place knives and forks in the correct places on a dinner table (Understanding, Fluency)

− complete a pattern involving familiar objects, eg a place setting at a dinner table, put a program on every second chair (Understanding, Fluency)

• recognise what comes next in a simple pattern of shapes [N]

− recognise repeating patterns in a range of contexts, eg paving patterns, wallpaper (Understanding)

• recognise what comes next in a simple sound or action pattern, eg two claps, one clap, two claps, _____ [N]

− recognise repeating patterns in a range of contexts, eg dance, music (Understanding)

• recognise when an error occurs in a pattern and describe what is wrong,

eg when making a bracelet, recognise a red bead has been used instead of a blue and correct the error [N] [CCT]

• create number patterns using concrete materials [N]

• continue simple number patterns that increase [N], eg 2, 4, 6, 8, __

• continue simple number patterns that decrease [N], eg 9, 7, 5, 3, __

• describe number patterns when counting forwards or backwards [N] [L], eg 3, 6, 9, 12 where three is added each time

eg , , , , , …

Patterns and Algebra 2
**Outcomes **

A student:

LS 16 calculates missing values by completing simple number sentences Students:

• complete number sentences involving one operation by calculating missing values, eg find if +5=8; find if ×3=12 [N]

− describe strategies for calculating missing values (Understanding) [CCT]

• use a number sentence to solve a given problem,

eg ‘I have $25 and the CD costs $31. How much more money do I need to purchase the CD?’

This can be solved by $31−$25= (Problem Solving) [N] [PSC]

**Outcomes **
A student:

LS 1 responds to and uses mathematical language to demonstrate understanding of concepts LS 17 recognises and relates time in a range of contexts

Students:

• associate familiar activities with times of the day [PSC]

− recognise an association between a time of the day and a range of familiar activities, eg daily routines at school and home (Understanding) [PSC]

− identify activities that occur on weekdays, eg school and class timetables, after-school activities (Understanding) [PSC]

− identify activities that occur on the weekend, eg sport, outings (Understanding) [PSC]

− identify activities that occur on specific days and at specific times, eg gym group is on Wednesday evenings during school terms, the dance is held every second Saturday in the afternoon (Understanding) [PSC]

• relate time to a personal context [PSC]

− respond to questions related to time, eg ‘What time does your bus leave?’ (Understanding) [N]

− identify time related to personal activities, eg ‘I need to catch the bus at 13 minutes past 5’

(Understanding) [N] [PSC]

• recognise the language of time in relation to personal activities and events,

eg ‘It is now 12 o’clock and it’s time for lunch’, ‘It is time to pack up because the bus will be here in 10 minutes’ [L] [N] [PSC]

• recognise the language of time in a range of everyday contexts [L]

− respond to questions involving the language of time, eg ‘Did you have your shower before
or after breakfast?’, ‘Will you be going to training this afternoon?’* *(Understanding) [PSC]

• describe activities using the language of time in a range of everyday situations [L] [PSC]

− describe personal activities and events, eg ‘I did my homework after dinner last night’, ‘I will be going to the football tomorrow afternoon’, ‘There was a delay of half an hour this morning on the school bus’, ‘I will be going to a barbecue next weekend’, ‘The holidays are only three weeks away’ (Understanding) [L] [PSC]

• recognise language related to representations of time on a calendar,

eg a week is seven days, a weekend is two days, a fortnight is two weeks or 14 days, a month is four weeks or a certain number of days [L] [N]

Time 2
**Outcomes **
A student:

LS 18 reads and interprets time in a variety of situations Students:

*Clocks and Watches *

• read and relate ‘hour’, ‘half hour,’ ‘quarter hour’ and ‘minutes’ in analog and digital format in a range of contexts [L] [N]

− interpret digital formats of time to determine which numbers represent hours and which numbers represent minutes (Understanding) [L] [N]

− identify minutes and hours on a clock face (Understanding) [L] [N]

− count around a clock face by fives to determine minutes past the hour (Fluency) [N]

• understand the relationship between analog and digital time, eg ‘12:30 is the same as half past 12’ [N] [CCT]

• identify and relate am and pm on digital clocks or watches, eg set an alarm clock for 7 am [N]

• apply understanding of the passage of time to plan or participate in a range of activities or events [PSC]

*Timetables *

• read and interpret a written timetable in a range of formats and variety of contexts, eg coordinating travel arrangements [L] [N]

− read and follow an individual sequence chart, or timetable, for a range of activities (Understanding) [L] [N] [PSC]

− read and follow a school timetable for group or class activities (Understanding) [L] [PSC]

− investigate and use the internet to determine travel arrangements by using searchable transport timetables (Problem Solving, Fluency) [L] [N] [ICT] [PSC]

*Calendars and Planners *

• identify the names or symbols for days of the week on a calendar [L] [PSC]

• identify the months of the year on a calendar [L] [PSC]

• locate special days and events on a calendar, eg ‘Anzac Day is on the 25th of April’ [L] [PSC]

− locate birthdays of significant people on a calendar, eg family, friends (Understanding) [L]

[PSC]

• identify representations of time on a calendar, eg week, weekend, fortnight, month [L] [N]

− identify number of days, weeks, months, between one event and another, eg ‘It’s three days until the weekend’, ‘There are four more weeks until the end of term’

(Understanding, Fluency) [N] [PSC]

• recognise that calendars are used to plan events and activities,

eg school term plan in the newsletter, coming events in the newspaper [PSC]

Time 3
**Outcomes **
A student:

LS 3 uses simple reasoning to recognise mathematical relationships LS 19 calculates and measures time and duration in everyday contexts Students:

• identify the duration of a range of activities and events for a variety of purposes [N] [CCT]

− select a track of music to fit a time frame, eg for a dance piece, a multimedia presentation (Problem Solving) [N] [PSC]

− identify length of time of a movie to determine if the activity fits into a personal schedule (Problem Solving) [N] [PSC]

• measure and calculate the time taken for a variety of activities or events, eg use a stopwatch to time a race [N]

− record starting and finishing times to calculate the duration of an activity or event (Understanding, Fluency) [N]

− use addition/subtraction strategies to calculate the length of time of an activity or event (Fluency) [N]

• recognise that there are differences in time zones around the world [PSC]

• compare and calculate the local time in a range of places nationally and internationally [L] [N]

[CCT]

− identify time differences of various locations, eg London is ten hours behind Sydney (Understanding) [L]

− use appropriate addition/subtraction strategies to calculate the local time in a particular location, eg given that London is 10 hours behind Sydney, find the time in London when it is 6 pm in Sydney (Fluency) [N]

− solve problems about international time in everyday contexts, eg determine whether a soccer game in another country can be watched live on television during the day (Problem Solving) [N] [CCT]

− recognise the influence of daylight saving on local time (Reasoning, Understanding) [N]

**Outcomes **
A student:

LS 3 uses simple reasoning to recognise mathematical relationships LS 20 organises personal time and manages scheduled activities Students:

• identify the amount of time needed for a range of activities [N]

− recognise that specific activities require a particular amount of time, eg ‘I need half an hour to have a shower and get dressed’, ‘It takes me 10 minutes to walk from home to the railway station’ (Understanding) [N] [PSC]

• make choices and decisions about activities on the basis of time available, eg ‘I can’t make that movie because I have training at that time’ [N] [PSC]

• schedule events over a day or week taking into account a range of activities and personal responsibilities [PSC]

− identify priorities in relation to personal time, and discriminate between essential and non- essential activities (Understanding, Reasoning) [PSC]

− plan personal time over a day or a week so that activities do not clash (Problem Solving) [PSC] [N]

• prepare and follow a personal timetable/schedule [L] [N] [CCT] [PSC]

− use electronic formats of calendars and planners (Fluency) [L] [PSC]

− use a calendar/diary to plan for regular activities, eg swimming every second Friday, PE each Tuesday (Understanding, Fluency) [N] [PSC]

− use a calendar to plan events and activities, eg camp, birthday party (Understanding, Fluency) [N] [PSC]

− use a calendar or planner to calculate time for particular activities, eg block out three weeks for completion of a school project (Understanding, Fluency) [N] [PSC]

Measurement 1
**Outcomes **
A student:

LS 1 responds to and uses mathematical language to demonstrate understanding of concepts LS 21 responds to the language of measurement in everyday contexts

Students:

• respond to language related to length, height and distance,

eg long, short, tall, higher than, lower than, the same as, near, far, closer [L]

• respond to language related to temperature,

eg hot, cold, warm, lukewarm, freezing, boiling, hotter, colder [L]

• respond to language related to the mass of objects, eg light, heavy, harder to push/pull, heavier, lightest [L]

• respond to language related to perimeter, eg distance around [L]

• respond to language related to area,

eg bigger/smaller than, the same as, surface [L]

• respond to language related to capacity and volume,

eg full, empty, half-full, has more/less, will hold more/less [L]

• make comparisons based on attributes that can be measured,

eg ‘I am taller than my brother’, ‘John is the tallest in the class’ [N] [CCT]

• respond to instructions that involve language of comparison,

eg ‘Please bring me the empty container’, ‘Put the heavy book on the bottom shelf’ [N] [L]

**Outcomes **
A student:

LS 1 responds to and uses mathematical language to demonstrate understanding of concepts LS 3 uses simple reasoning to recognise mathematical relationships

LS 22 uses informal units for measurement in everyday contexts Students:

• recognise features of an object associated with length that can be measured, eg length, breadth, height [L] [N]

• use informal units to measure length,

eg measure the length of a table in equal hand spans, without gaps or overlaps [N]

− compare and order two or more lengths or distances using informal units (Understanding, Problem Solving) [N] [CCT]

• use informal units to measure capacity,

eg count the number of times a glass can be filled and emptied into a jug [N]

• use informal units to measure volume,

eg count the number of same sized marbles required to fill a box, ensuring there are no large spaces [N]

− compare and order the volume of two or more models by counting the number of blocks used in each model (Understanding, Problem Solving) [N] [CCT]

• use informal units to measure mass,

eg use balance scales to find how many same sized blocks are equivalent to a pencil case [N]

− compare and order the masses of two or more objects by lifting them and then check using an equal arm balance (Understanding, Problem Solving) [N] [CCT]

• use informal units to measure area,

eg count the number of equal sized pieces of paper required to cover a table, without gaps or overlaps [N]

− compare the area of two similar shapes by cutting the shapes out and placing one over the other (Understanding, Problem Solving) [N] [CCT]

Measurement 3
**Outcomes **
A student:

LS 23 uses and applies formal units for measurement in everyday contexts Students:

• recognise the appropriate device for measuring an attribute: [CCT]

− temperature, eg thermometer, oven dial

− length, eg ruler, measuring tape, trundle wheel, odometer

− capacity, eg measuring cup, measuring spoon

− mass, eg scales, weigh station

− investigate how the odometer of a car can measure distance (Understanding)

• recognise the appropriate unit of measurement and its abbreviation for measuring an attribute [CCT] [L]

− temperature, eg degrees Celsius ( °C)

− length, eg centimetres (cm), metres (m), kilometres (km)

− capacity, eg millilitres (mL), litres (L)

− volume, eg cubic centimetres ( ), cubic metres ( )

− mass, eg grams (g), kilograms (kg)

− area, eg square centimetres ( ), square metres ( )

• select and use the appropriate unit and device for measuring an attribute,

eg measure the height of students in their class using a metre ruler and record the results in a table [N] [CCT]

• recognise the relationship between commonly used units of measurement [N] [CCT]

− length, eg 100 cm = 1 metre

− capacity, eg 1000 mL = 1L

− mass, eg 1000 g = 1 kg

• convert larger units to smaller units, eg 3 m = 300 cm [N]

• estimate measurements of everyday objects and check using a measuring device, eg estimate the length of a room and check using a measuring tape [N] [CCT]

− identify the concept of measurement in a problem (Understanding) [N]

− select and use appropriate strategies, including calculations, to solve the problem (Fluency) [N]

**Outcomes **
A student:

LS 3 uses simple reasoning to recognise mathematical relationships

LS 24 recognises, matches and sorts three-dimensional objects and/or two-dimensional shapes Students:

• recognise three-dimensional objects in the environment [N]

− identify and name three-dimensional objects that are used in everyday situations, eg cones, cubes and cylinders (Understanding) [L]

− identify three-dimensional objects in pictures, computer displays and within the environment (Understanding) [CCT]

• match three-dimensional objects based on an attribute, eg shape, size, function [N]

• sort three-dimensional objects based on an attribute, eg shape, colour, size, function [N] [CCT]

− sort items on the basis of their shape, size, function, eg crockery, cutlery, sports equipment, clothes for washing (Understanding) [N] [CCT]

− indicate the reasons for sorting items in a particular way (Reasoning) [CCT]

− predict and describe the ways in which particular items can be stacked and test the prediction by stacking them (Reasoning, Problem Solving) [CCT]

• recognise three-dimensional objects from different orientations using dynamic geometry software [N] [ICT]

• identify two-dimensional shapes found in the environment [N]

• match two-dimensional shapes based on an attribute, eg size, shape [N]

− match circles, squares, triangles and rectangles (Understanding) [N]

• sort two-dimensional shapes based on an attribute, eg number of corners or sides [N] [CCT]

− circle all the three-sided shapes in a group of mixed shapes (Understanding) [N]

− construct a table classifying shapes according to the number of angles they have (Understanding, Reasoning) [N] [CCT]

• match and sort two-dimensional shapes when presented in different orientations using dynamic geometry software [N] [ICT]

Two-dimensional and Three-dimensional Space 2
**Outcomes **

A student:

LS 25 identifies the features of three-dimensional objects and/or two-dimensional shapes and applies these in a range of contexts

Students:

• describe the features of common three-dimensional objects using everyday language, eg flat, round, curved [L]

• describe the features of common two-dimensional shapes using everyday language, eg sides, corners [L]

• recognise similarities and differences of a variety of three-dimensional objects in a range of contexts [CCT]

• recognise and describe the attributes of two-dimensional shapes [N] [L]

− identify circles, squares, triangles and rectangles in the built environment (Understanding) [CCT]

− draw two-dimensional shapes using computer software (Understanding, Fluency) [ICT]

• identify the result of putting together (or separating) two-dimensional shapes, eg ‘This house shape is made up of a triangle and a square’ [CCT]

• apply knowledge of the features of three-dimensional objects in a range of contexts [CCT]

− pack a lunch box, organise pantry, stack shelves (Problem Solving) [CCT]

− complete a technology project involving materials of different shapes and sizes, eg quilt for textiles, wood inlay (Problem Solving) [CCT]

− construct and describe models using a variety of three-dimensional objects (Understanding, Problem Solving) [CCT]

• apply knowledge of the features of two-dimensional shapes in a range of contexts [CCT]

− make representations of two-dimensional shapes using a variety of materials (Understanding) [CCT]

− put a ticket/card into the correct slot in a machine (Understanding, Reasoning) [CCT]

**Outcomes **
A student:

LS 1 responds to and uses mathematical language to demonstrate understanding of concepts LS 26 responds to and uses the language of position in everyday contexts

Students:

• recognise and respond to the language of position in a range of contexts [L]

− identify preference for a position in response to a question, eg ‘Would you rather lie on your side or sit in the chair?’, ‘Would you rather sit next to John or Sam?’ (Understanding)

− follow spoken instructions relating to the language of position, eg ‘Put your bag on the top hook’, ‘Take the books from the cupboard behind the desks’, ‘Please move inside the carriage’ (Understanding) [PSC]

− follow symbols and written instructions relating to the language of position, eg follow arrows to locate an office on an upper floor, follow symbols to carry a container right side up, follow written instructions to stack items in a storeroom (Understanding, Fluency) [PSC]

• use the language of position [L]

− indicate the position of objects or buildings in response to a question, eg ‘The books are on the shelf in the classroom’, ‘The seats are under the trees in the playground’, ‘The

supermarket is next to the garage in the main street’, ‘The yellow tulips are in the middle of the row in the garden’ (Understanding) [PSC]

− describe the position of objects or buildings in a range of contexts, eg ‘I went to the ticket office inside the railway station’, ‘The bus stop is opposite the main gate’, ‘Appliances are located on the ground floor’, ‘This lift goes to the upper level’, ‘Tickets are purchased at the office beside the turnstiles’ (Understanding) [PSC]

− give directions in a range of contexts, eg ‘Stand behind the line to throw the ball’, ‘Walk towards the doorway’, ‘Turn left at the top of the stairs’(Understanding) [PSC]

Position 2
**Outcomes **
A student:

LS 27 recognises that maps and plans are a representation of positions in space Students:

• recognise the purpose and functions of maps and plans, eg to provide directions, location of object/features

• recognise that buildings can be represented as a plan, eg classroom

• identify how key features such as doors, windows, tables, chairs, cupboards are represented on a plan [CCT]

− construct or draw a plan showing key features of specific environments, eg classroom, school, community (Problem Solving) [CCT] [N]

− locate floor plans of properties for sale on the internet and interpret them (Fluency, Understanding) [ICT] [L]

**Outcomes **
A student:

LS 28 uses maps and plans in a range of contexts Students:

• use maps and plans to locate position and follow routes [N]

− locate seat on a plan of a movie theatre (Understanding) [N]

− locate classroom on a plan of the school (Understanding) [N]

− locate house or street using a print or online map, eg Google Earth (Understanding) [ICT]

− use a map to show direction from classroom to the library (Understanding, Problem Solving) [N]

− identify direction on a map, eg north/south, left/right (Understanding) [N]

• use maps for a variety of purposes,

eg use a street directory, web-based maps, GPS technology [N] [ICT]

− use a map to find a location (Understanding, Problem Solving) [N]

− locate specific sites using grid references in street directories and road maps (Understanding, Problem Solving) [N] [CCT]

− identify and describe features of an environment using map keys/legends (Understanding) [CCT] [L] [N]

Data 1
**Outcomes **
A student:

LS 1 responds to and uses mathematical language to demonstrate understanding of concepts LS 29 recognises data displayed in a variety of formats

Students:

• recognise that information can be presented in tables and graphs,

eg picture graph to show favourite foods, column graph to show classroom gender, sector graph to represent sports students play, table to record daily rainfall [CCT]

• identify information on graphs using features such as heading/title of graph, labels on axes, scale, key [L]

• recognise data displayed in different ways, eg table and graph to show climate

**Outcomes **
A student:

LS 3 uses simple reasoning to recognise mathematical relationships LS 30 gathers, organises and displays data

Students:

• collect data about themselves and their environment [N] [L]

− pose a question to be answered using a survey, eg ‘What is the most popular sport among students in our class?’ (Understanding) [CCT]

− record collected data using a variety of processes, eg concrete materials, symbols, words, tally marks (Understanding) [N]

• sort collected data into groups [CCT]

• display data using tables, column graphs, line graphs and/or pie charts [N] [CCT]

− use appropriate strategies, including ICT, to display data (Understanding, Fluency) [ICT]

[N]

− follow conventions for displaying data including equal spacing, same-sized symbols, key for symbols, headings, labels for axes (Understanding, Fluency) [L] [N]

• gather and display data for a specific purpose,

eg to determine the range of eye colour represented in a class of students [N] [CCT]

− select an appropriate method and use this to collect data, eg survey, questionnaire (Fluency, Problem Solving) [N]

− sort collected data appropriately (Understanding, Fluency) [N] [CCT]

− decide on the most appropriate way to display the data collected, eg line graph, pie chart, table (Understanding, Fluency) [N] [CCT]

− construct data display (Understanding, Fluency) [CCT] [N]

− communicate and interpret findings from collected data (Reasoning) [L] [N] [CCT]

Data 3
**Outcomes **
A student:

LS 3 uses simple reasoning to recognise mathematical relationships LS 31 interprets information and draws conclusions from data displays Students:

• interpret information presented in tables and graphs to answer questions,

eg ‘The columns show that there are more boys than girls’, ‘Swimming is the most popular sport among students in our class’ (Problem Solving) [L] [CCT]

• interpret graphs and tables from a variety of sources, eg newspapers, television, internet [L] [CCT]

• compare tables and graphs constructed from the same data to determine which is the most appropriate method of display [CCT]

• draw conclusions on the basis of the information displayed in tables and graphs [CCT]

**Outcomes **
A student:

LS 32 recognises and uses the language of chance in a range of contexts Students:

• distinguish between events that are certain and uncertain, eg having a birthday, winning a lottery [CCT]

• describe the likelihood of familiar events using informal terms, eg might, certain, probable, likely, unlikely, possible, impossible [L]

− predict possible outcomes in everyday situations, eg decide what might occur in a movie before the ending of the story (Reasoning) [CCT]

− ask questions related to the likelihood of events, eg ‘Do I need to take my umbrella if the sky is grey?’ (Reasoning) [CCT]

− use the language of chance in everyday situations (Understanding) [L]

• order events from least likely to most likely [CCT]

Chance 2
**Outcomes **
A student:

LS 3 uses simple reasoning to recognise mathematical relationships LS 33 recognises the elements of chance and probability in everyday events Students:

• recognise the element of chance in familiar events, eg tossing a coin, rolling a dice [N]

• interpret numerical values assigned to the probability of events occurring in real life contexts, eg , 1 in 2, 1 in 100, 1 in a million [N]

− use the internet to determine the likelihood of winning prizes in various lottery divisions (Fluency, Problem Solving) [ICT] [N]

− evaluate the probability of winning prizes in lotteries and other competitions (Reasoning) [CCT] [N]

• conduct simple experiments to determine probability of an outcome,

eg spin a spinner twenty times and predict, record and communicate the results [N] [CCT]