NSW Syllabuses

# Mathematics K–10 - Life Skills - Number and Algebra Numeration

## Numeration: Language of Numbers

### Outcomes

#### A student:

• MALS-1WM

responds to and uses mathematical language to demonstrate understanding

• MALS-3WM

uses reasoning to recognise mathematical relationships

• MALS-4NA

recognises language used to represent number

Related Stage 4/5 outcome: MA4-4NA

### Content

• Students:
• recognise language related to number, eg none, few, many, more, less
• respond to questions that involve descriptions of number, eg 'Are all the books on the shelf?', 'Which box has no pens?', 'Which plate has more cakes?' (Communicating, Understanding)
• respond to requests that 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' (Communicating, Understanding)
• 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' (Communicating, Reasoning, Understanding)
• recognise that some languages other than English, such as Aboriginal and Torres Strait Islander languages, may have interchangeable terms with the same meaning
• recognise ordinal terms, eg first, second, third
• respond to directions involving ordinal terms, eg 'Give a ball to the first person in each row', 'Put a book on every second chair' (Communicating, Understanding)
• 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?' (Communicating, Understanding)

## Numeration: Counting

### Outcomes

#### A student:

• MALS-1WM

responds to and uses mathematical language to demonstrate understanding

• MALS-5NA

counts in familiar contexts

Related Stage 4/5 outcome: MA4-4NA

### Content

• Students:
• count in familiar contexts, eg count out books for a group or class, count uniforms for a sports team, count seedlings when re-planting
• count objects by twos, fives and tens
• match groups of objects that have the same number of items
• 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)
• count with single-digit numbers, eg count the number of coins needed to purchase a bus ticket
• count with two-digit numbers
• count with coins and notes of the same denomination (Fluency)
• count with coins and notes of different denominations (Fluency)
• count forwards and backwards from a given number in the range 0 to 100
• solve problems involving counting, eg 'How many people are in class today?', 'How many coins do I have in my wallet?'
• count with three-digit numbers
• count by twos, fives, tens and hundreds
• tell the time on a watch or clock by counting by fives around the watch or clock face (Communicating, Understanding, Fluency)
• count out coins and notes when giving change to a customer (Reasoning, Fluency)
• recognise alternative means of counting, eg the abacus in Asian cultures

## Numeration: Representing Numbers

### Outcomes

#### A student:

• MALS-1WM

responds to and uses mathematical language to demonstrate understanding

• MALS-2WM

applies mathematical strategies to solve problems

• MALS-3WM

uses reasoning to recognise mathematical relationships

• MALS-6NA

Related Stage 4/5 outcome: MA4-4NA

### Content

• Students:
• read and record the numbers 0 to 9
• identify some of the ways numbers are used in everyday life, eg telephone numbers, bus numbers, personal identification numbers (PINs) (Reasoning, Understanding)
• read and record two-digit numbers
• recognise, read and interpret numerical information in a range of formats, eg recipes, medication dosages
• identify and locate numbers in a range of situations, eg the table of contents in a book, seat numbers in a theatre, odd and even house numbers (Understanding)
• recognise, read and convert Roman numerals used in everyday contexts
• read and record three-digit numbers
• recognise odd and even numbers
• recognise and read numbers with more than three digits

## Numeration: Comparing and Ordering Numbers

### Outcomes

#### A student:

• MALS-2WM

applies mathematical strategies to solve problems

• MALS-3WM

uses reasoning to recognise mathematical relationships

• MALS-7NA

compares and orders numbers

Related Stage 4/5 outcome: MA4-4NA

### Content

• Students:
• compare and order groups of objects according to the number in the group
• identify groups that have more or fewer items than a given group, eg available plates/cups for guests at a party (Understanding, Fluency)
• order groups of objects in ascending/descending order according to the number in the group (Fluency)
• compare and order the numbers from 0 to 9
• compare and order two-digit numbers
• order teams in a competition based on points scored (Reasoning)
• locate a given seat in a theatre according to the seat number on the ticket (Reasoning, Understanding)
• identify the value of a given number in relation to other numbers
• recognise whether a given number comes before or after other numbers, eg arrange students in a class in order of age, identify how many people finished a race before or after a given person (Reasoning, Problem Solving)
• use ordinal terms to describe the value of a given number in relation to other numbers, eg identify the position of a sporting team on the competition ladder (Reasoning)
• compare and order three-digit numbers
• order schools according to the size of the student population (Reasoning)

## Numeration: Fractions

### Outcomes

#### A student:

• MALS-1WM

responds to and uses mathematical language to demonstrate understanding

• MALS-2WM

applies mathematical strategies to solve problems

• MALS-8NA

recognises and compares fractions in everyday contexts

Related Stage 4/5 outcome: MA4-5NA

### Content

• Students:
• recognise the need for two equal parts when dividing a whole in half
• allocate portions or divide materials, eg cut a length of tape/rope into equal pieces (Problem Solving, Understanding, Fluency)
• recognise halves
• identify items that are a half, eg half an apple, half a pizza (Understanding)
• identify items that are less than a half or more than a half (Understanding)
• 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)
• share an object into two equal parts, eg give half a sandwich (Understanding, Fluency)
• recognise and use the terms 'half' and 'halves'
• describe situations using the terms 'half' and 'halves', eg 'The television program is half an hour long' (Communicating, Understanding)
• follow an instruction involving fraction language in everyday contexts, eg 'Move to the other half of the soccer field' (Understanding)
• recognise the need for four equal parts when dividing a whole into quarters
• allocate portions or divide materials, eg cut a cake into equal pieces (Problem Solving, Understanding, Fluency)
• recognise quarters
• identify items that are a quarter of a whole, eg quarter of an apple, quarter of a sandwich (Understanding)
• identify items that are less than a quarter or more than a quarter (Understanding)
• determine if parts of a whole object, or collection of objects, are equal, eg 'Has the cake been cut into four equal parts?' (Reasoning, Understanding)
• put two quarters together to make a half (Communicating, Understanding)
• share an object into four equal parts, eg give a quarter of an apple (Understanding, Fluency)
• recognise and use the term 'quarter'
• describe situations using the term 'quarter', eg 'Lunch is three-quarters of an hour' (Communicating, Understanding)
• follow an instruction involving fraction language in everyday contexts, eg 'Give a quarter of the orange to your friend' (Understanding, Fluency)
• recognise fractions in everyday contexts, eg three-quarters of Australia is dry desert, more than half of the Earth is covered by water, one-quarter of the class have migrated to Australia
• compare fractions, eg half of the pizza is more than a quarter of the pizza