whole!numbers! addition!and!subtraction!! multiplication...

Whole Numbers

Multiplication and Division

Patterns and Algebra

Addition and Subtraction

Fractions and Decimals

NUMBER AND ALGEBRA: Whole Numbers

PROMPT LEVELS

LEVEL OF SUPPORT CODE DEFINITION

Full physical assistance

FP Physically assisting a student through every action involved with completing a task.

Partial physical assistance

PP Partial physical guidance to complete a task such as a touch on the hand.

Modelled response M A demonstration to the student of the required action.

Gesture/sign G/S A non-‐verbal action/instruction that cues a student to perform a task or required action. (e.g. signing/pointing)

Verbal V A spoken instruction that informs the student of the desired action.

Independent I Completing a task with no level of support.


NUMERACY LEARNING CONTINUUM

The rate at which each individual student acquires Number and Algebra goals will vary. This will mean that teachers will need to use professional judgement to adjust the teaching ideas suggested on the following pages.

Syllabus Outcomes Early Stage 1 Outcome 2012 NES 1.1: Counts to 30, and orders, reads and represents numbers in the range 0 to 20. WMES1.2 Uses objects, actions, imagery, technology and/or trial and error to explore mathematical problems (Applying Strategies) WMES1.3 Describes mathematical situations using everyday language, actions, materials, and informal recordings (Communicating) WMES1.4 Uses concrete materials and/or pictorial representations to support conclusions (Reasoning) WMES1.5 Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Early Stage 1 content (Reflecting) Early Stage 1 Outcome 2015 MAe-‐1WM Describes mathematical situations using everyday language, actions, materials and informal recordings. Mae-‐2WM Uses objects, actions, technology and/or trial and error to explore mathematical problems. Mae-‐3WM Uses concrete materials and/or pictorial representations to support conclusions. MAe-‐4NA Counts to 30, and orders, reads and represents numbers in the range 0 to 20.

Life Skills 7-‐10 Outcome 2015 MALS-‐4NA: Recognises language to represent number. MALS-‐5NA: Counts in familiar contexts. MALS-‐6NA: Reads and represents numbers. MALS-‐7NA: Compares and orders numbers. MALS-‐12NA: Compares and matches coins and notes.

HSC Life Skills 11-‐12 Outcomes 2007 1.1: Demonstrates understanding of number sense. 1.2: Recognises matches and sorts concrete objects to represent numbers. 1.3: Counts objects in meaningful contexts. 1.4: Understands and uses ordinal terms. 1.5: Reads and writes numbers and demonstrates understanding of place value. 5.1: Understands that money is a medium for purchasing goods and services. 5.2: Identify matches and counts coins and notes.

WHOLE NUMBE

RS

N&A1.1 Students access/interact with the representation of a numeral.

N&A1.2 Students match one numeral with another. (Match to sample)

N&A1.3 Students learn the names of numerals in order to identify them. (Identify the numeral without other numerals present).

N&A1.4 Students identify representations of numerals. (Identify the numeral with other numerals present in random order).

N&A1.5 Students can rote count.

N&A1.6 Students demonstrate an understanding of 1:1 correspondence through matching.

WHOLE NUMBE

RS

N&A1.7a Students demonstrate an understanding of 1:1 correspondence through counting

N&A1.7b Students are able to stop counting objects at the number indicated without continuing to count on.

N&A1.8 Students make groups of objects up to 10.

N&A1.9 Students match numerals to collections of objects.

N&A1.10 Students make comparisons between groups of objects according to number.

N&A1.11 Students sequence numbers to 10.

N&A1.12 Students write numerals 0-‐9 (Students may use different tools in order to write).

N&A1.13 Students will familiarise themselves with money.

Whole Numbers N&A1.1 Students access/interact with the representation of a numeral.

LEARNING EXPERIENCES AND OPPORTUNITIES

N&A1.1

Whole Numbers

Strategies Attributing meaning Contingent responding Modelling Prompting Sensory stimulation Strategic pausing Take up time Touch cues

Levels of Support Full Physical assistance Partial physical assistance Modelled response Gesture/sign Verbal Independent

Activities and Resources Numeral cards Tactile resources Foam / sandpaper Switches Mobiles Song lists

Indicators Teacher Language • Makes eye contact with a numeral.• Reaches for a numeral.• Makes physical contact with a numeral.• Explores a numeral with senses.• WM Explore with senses numeral cards and

tactile resources including foam andsandpaper.

Give an instruction ‘Touch/feel number X’. ‘Look at number X’. Make a statement ‘You have the number X’. ‘You are touching number X’. ‘You are looking at number X’.

When carrying out any of the following teaching activities it will be necessary to use different levels of support as indicated in the guidelines table at the beginning of Number. Fade this support as the student works towards developing independence.

There are a variety of acceptable ways a student can indicate a choice or make a response. These include; head/physical movements (e.g. nodding, pointing and reaching) eye gaze and verbal responses.

Makes eye contact with a numeral Place a representation of a numeral directly in the student’s eyesight and state ‘SN, look at number X’. The student may make eye contact with the item for a brief period of time. Immediately reinforce the student for looking at the numeral even if it’s a fleeting look in order to shape this behaviour into an intentional action. If the student does not make any eye contact, the teacher mirrors student head movement and eye gaze with the numeral so that the numeral is in front of the student’s eyes. ’SN you are looking at number X’. For students who make intentional eye contact with the numeral, activities such as flashing numbers on an interactive whiteboard (IWB) may be appropriate. Some online examples include: Add in links videos etc

• Priory Woods Songs • 10 Little Numbers • The Number Train

• Learn Numbers • Five Little Monkeys • Numberjacks

Reaches for and makes physical contact with a numeral Repeat the above activity with a focus on encouraging the student to reach for and interact with the representation of a numeral and state ‘SN you are touching number X’. Once the student grasps the number reinforce them immediately by saying ‘You have the number X’.

Explores a numeral with senses Touch: Using representations of numbers made from a variety of tactile materials such as felt, sandpaper, satin and fur. Encourage the student to explore and interact with them by tracing the shape of the number. Touch: Draw a number on a surface using shaving cream or sand onto glue and encourage the student to explore and interact with it by running their hand over/through the shape of the number. Teachers are encouraged to use the teacher language above throughout these activities. Sound: Provide the student with opportunities to listen and respond to a variety of songs and rhymes that incorporate number. This may involve the student moving to, clapping, singing/vocalising and expressing their engagement through facial expressions.

Whole Numbers



N&A1.2

Whole Numbers

Strategies Correcting errors Distractors Errorless learning Modelling Match to sample Prompting Questioning Take up time


Activities and Resources Laminated number representations Laminated folder activities Bingo cards Dominos Tactile resources Dice games

Indicators Teacher Language • Matches to sample 1-‐1. • Matches to sample 1-‐3. • Matches to sample 1-‐5. • Matches to sample 1-‐10. • WM Use numeral cards to match a range of

numerals from 1 to 10.

Give an instruction Match number X’. Make a statement ‘This is number X’. ‘You are matching number X’. ‘Say and sign ‘Same’. Correction/prompt ‘Are they the same/ Do they match?’ ‘Try again’.



This goal is purely a matching activity. Identification or recognition of numbers is not the aim. Numbers are used as symbols to be matched and to make students familiar with their form so they are able to progress to the next goals of identifying and recognising numbers.

Matches to sample 1-‐1 This is errorless learning; providing only the correct option so there is no chance of error. To begin this activity, place one card in front of the student with the number X printed on it. Provide the student with an identical card. Model how to match the identical numbers and then provide the student with opportunities to do the same. Teacher states ‘SN this is number X. Match number X. You are matching the number X’. Always say and sign ‘same’ when two numbers are a match to reinforce the concept.

Matches to sample 1-‐3 Once the student has mastered the skill of matching number to number, one distractor would be added. This distractor would be a blank card. Once the student can match number to number with one distractor, display three cards. Cards consist of number X plus two distractors. To begin with, distractors would be blank cards. Provide the student with one card with the number X printed on it. Model how to match the identical numbers and then provide the student with opportunities to do the same. Repeat this activity up to the number 3. Teacher states ‘SN this is number X. Match number X. You are matching number X’. Always say, sign and gesture ‘same’ when two numbers are a match to reinforce the concept. Once the student has mastered the skill of matching number to number, distractors could be changed to include pictures, then other numbers to increase the complexity of the task. Teachers are encouraged to use the teacher language above throughout these activities. The following table provides an example of the sequence you could follow to carry out this activity. Throughout this sequence number X stays the same. Once the sequence has been completed begin again, choosing a different number as number X up to and including number 3.

No. given to student Correct Number Distractor 1 Distractor 2 Number X Number X (errorless learning) Number X Number X Blank Number X Number X Blank Blank Number X Number X Picture Blank Number X Number X Picture Picture Number X Number X Number A Picture Number X Number X Number A Number B

Whole Numbers N&A1.2 Students match one numeral with another. (Match to sample) cont.


N&A1.2 cont.

Whole Numbers

Strategies Correcting errors Distractors Errorless learning Modelling Match to sample Prompting Questioning Take up time


Activities and Resources Laminated number representations Laminated folder activities Bingo cards Dominos Tactile resources Dice games Change font, colour or size of numerals

Match to Sample 1-‐5 As the student has already mastered the skill of matching same number with the same number for numbers 1 to 3, errorless learning is not necessary. Display five cards. Cards consist of number X plus four distractors made up of numbers, blank cards and pictures. Provide the student with one card with the number X. Follow teaching procedure as stated above in match to sample 1-‐3.

Number given to student

Correct Number

Distractor 1 Distractor 2 Distractor 3 Distractor 4

Number X Number X Number A Number B Blank Blank Number X Number X Number A Number B Picture Blank Number X Number X Number A Number B Picture Picture Number X Number X Number A Number B Number C Picture Number X Number X Number A Number B Number C Number D

Match to sample 1-‐10 Display ten cards. Cards consist of number X plus nine distractors made up of numbers, blank cards and pictures. Provide the student with one card with the number X. Follow teaching procedure as stated above in match to sample 1-‐3.

No. given to

student

Correct No.

Dis 1 Dis 2 Dis 3 Dis 4 Dis 5 Dis 6 Dis 7 Dis 8 Dis 9

No. X No. X No. A No. B No. C No. D Blank Blank Blank Blank Blank No. X No. X No. A No. B No. C No. D Picture Blank Blank Blank Blank No. X No. X No. A No. B No. C No. D Picture Picture Blank Blank Blank No. X No. X No. A No. B No. C No. D Picture Picture Picture Blank Blank No. X No. X No. A No. B No. C No. D Picture Picture Picture Picture Blank No. X No. X No. A No. B No. C No. D Picture Picture Picture Picture Picture No. X No. X No. A No. B No. C No. D No. E Picture Picture Picture Picture No. X No. X No. A No. B No. C No. D No. E No. F Picture Picture Picture No. X No. X No. A No. B No. C No. D No. E No. F No. G Picture Picture No. X No. X No. A No. B No. C No. D No. E No. F No. G No. H Picture No. X No. X No. A No. B No. C No. D No. E No. F No. G No. H No. I

Whole Numbers N&A1.3 Students learn the names of numerals in order to identify them.

(Identify the numeral without other numerals present). LEARNING EXPERIENCES AND OPPORTUNITIES

N&A1.3

Whole Numbers

Strategies Attributing meaning Correcting errors Errorless learning Incidental teaching Explicit teaching Prompting Questioning Take up time


Activities and Resources Number cards Computers IWB

Indicators Teacher Language • Learns names of numerals to 3. • Learns names of numerals to 5. • Learns names of numerals to 10. • Learns names of numerals to 20. • WM Identifies individual or isolated numerals

presented on cards or computer games.

Give an instruction ‘Look at the number X’. ‘Show me number X’. ‘Point to number X’. ‘Give me number X’. Make a statement ‘This is number X’. Correction/prompt ‘This is number X’. ‘Try again’.



This is instructional teaching so students are given the opportunity to learn the names of individual numerals in order to identify them. Numerals should be presented to students in their written form; that is the number 3 not the word three. At this stage the goal is not to teach counting. During this teaching activity, only the number that is being taught should be visible to the student. Teachers need to be aware that some students may only ever be able to name/identify a limited range of numerals and these may not be sequential.

Learns names of numerals 1-‐20 This activity is taught in the same way for each numeral 1-‐20. Teacher states ‘This is the number X’. ‘Look at the number X’. ‘Show me number X’. ‘Point to number X’. ‘Give me number X’. This may be taught as a one to one or group activity, depending on the ability levels of the students.

Whole Numbers N&A1.4 Students identify representations of numerals.

(Identify the numeral with other numerals present in random order).


N&A1.4

Whole Numbers

Strategies Attributing meaning Correcting errors Errorless learning Incidental teaching Explicit teaching Prompting Questioning Take up time


Activities and Resources Number cards Computers IWB

Indicators Teacher Language • Identifies numerals to 3. • Identifies numerals to 5. • Identifies numerals to 10. • Identifies numerals to 20. • WM Recognise numerals presented on cards

or computer games in random order.

Give an instruction ‘Look at the numbers’. ‘Show me number X’. ‘Point to number X’. ‘Give me the number X’. Correction/prompt ‘This is number X’. ‘Try again’.



In order to teach this goal, students need to have prior knowledge and obtained goals N1.2 and N1.3.Teacher professional judgement needs to be used to determine the length of time and number of opportunities students are given in order to correctly identify a specific numeral. If at any point through the learning process a student is unable to progress to identifying the next sequential number, exposure to that number and following numbers should continue. This is to ensure the students are given the opportunity to identify all numbers irrespective of their order.

Identifies numerals to 20 Teacher places the numbers 1 and 2 in front of the student. Teacher states ‘Show me number X’. Once the student has correctly identified numbers 1 and 2, introduce the number 3. If the student is unable to distinguish between the numbers, reteach using teacher language stated above. Teacher places the number 1, 2 and 3 in front of the student in random order. Teacher states ‘Show me the number X’. Continue this strategy introducing one number at a time, up to the number 20.

Whole Numbers N&A1.5 Students can rote count.


N&A1.5

Whole Numbers

Strategies Independent practise Modelling Strategic pausing Incidental teaching Take up time Levels of Support Full Physical assistance Partial physical assistance Modelled response Gesture/sign Verbal Independent

Activities and Resources Songs Games Visuals Class routines (lining up etc.)

Indicators Teacher Language • Rote counts up to 3. • Rote counts up to 5. • Rote counts up to 10. • Rote counts up to 20. • WM Rote count within the range 3 to 20 in a

variety of contexts or games

Make a statement ‘We are going to count’. Give an instruction ‘It’s your turn to count’. Correction/prompt ‘What number is next?’ ‘Keep counting’.


This activity can be used for students who are verbal, nonverbal but are able to sign, touch or point and students with physical disabilities who can use eye gaze to indicate they are rote counting. Students who rote count may not necessarily have an understanding of one to one correspondence. This is a sequential learning activity. It should become obvious to the teacher when not to progress any further. Opportunities to teach this activity can occur multiple times throughout the day through both structured and incidental teaching. This includes counting students in line, counting items of food, counting the books on the table, IWB activities and structured desk work.

Rote counts up to 3 Teacher discretion is needed to decide whether or not to use a visual aide to assist e.g. counting chart. Teacher states ‘SN, we are going to count’. Teacher demonstrates counting 1 to 3. ‘SN, it’s your turn to count’. Nonverbal students may indicate they are rote counting by touching or pointing at each number as the teacher says it.

Rote counts up to 5, 10 and 20 Follow teaching procedure as stated above.

Whole Numbers N&A1.6 Students demonstrate an understanding of 1:1 correspondence through matching.


N&A1.6

Whole Numbers

Strategies Attributing meaning Contingent responding Correcting errors Errorless learning Incidental teaching Prompting Modelling Take up time


Activities and Resources Setting tables Gives out paint brushes Gives out newspapers Hands out play equipment

Indicators Teacher Language • Distributes 1 object. • Distributes 3 objects. • Distributes 5 objects. • Distributes 10 objects. • WM Give one book to each student in the

class.

Give an instruction ‘Give a ….. to ….….’. ‘Give everyone a …..’. ‘Put one newspaper in each letterbox’. Correction/prompt ‘Only one’. ‘Has he/she got one?’


Teacher provides students with opportunities to distribute objects ensuring there is a corresponding place for each object. For example, ‘Put one newspaper in each letterbox’.

Distributes 1 object. Errorless learning. The teacher provides students the opportunity to distribute one object to one other student. For example, a cup. Teacher says ‘SN, give a ….. to ……..’.

Distributes 3 objects. The teacher provides students the opportunity to distribute: -‐two objects to two students. Teachers says ‘SN, give everyone a cup……..’. -‐three objects to three students. Teachers says ‘SN, give everyone a cup……..’. The teacher must ensure there is the exact amount of objects for each person. For example, when distributing two objects, ‘everyone’ would be two people.

Distributes 5 and 10 objects. Follow teaching procedures as stated above.

Whole Numbers N&A1.7a Students demonstrate an understanding of 1:1 correspondence through counting.


N&A1.7a

Whole Numbers

Strategies Attributing meaning Contingent responding Correcting errors Errorless learning Explicit teaching Incidental teaching Independent practice Modelling Prompting Questioning Shaping Strategic pausing Take up time


Activities and Resources Morning circle activities (e.g. people at school) Counting dot patterns Laminated folder activities Dominos Bingo Songs Computers / IWB Stories

Indicators Teacher Language • Counts objects to 3. • Counts objects to 5. • Counts objects to 10 • WM Count the number of students present

and correlate with photographs during morning circle.

Make a statement ‘We are going to count to …’. Give an instruction: ‘Count the........’. ‘Count the students at school today’. Correction/Prompt: ‘Try again’.

When carrying out any of the following teaching activities it will be necessary to use different levels of support as indicated in the guidelines table at the beginning of Number. Fade this support as the student works towards developing independence. When this activity is implemented, objects such as counters, teddy bears must be identical to ensure that the student is counting rather than attributing characteristics to numbers e.g. red counters symbolise 1, yellow counters symbolise 2 etc.

Whenever a specific number is being counted, only that number of objects is placed in front of the student.

Counts objects to 3 Only one object is presented to the student. Teachers states ‘We are going to count to 1. Count the ………’. Once the student has independently counted one object, move onto two objects and then three. Encouraged students to touch the objects as they count.

Counts objects to 5 and to 10. Follow teaching procedures as stated above. Do not move onto the next number unless 100% accuracy has been achieved.

Activities that involve counting with one to one correspondence include: Counting students in class, counting chairs for students, pencils for each student etc.

Whole Numbers N&A1.7b Students are able to stop counting objects at the number indicated without

continuing to count on. LEARNING EXPERIENCES AND OPPORTUNITIES

N&A1.7b

Whole Numbers

Strategies Attributing meaning Contingent responding Correcting errors Errorless learning Explicit teaching Incidental teaching Independent practice Modelling Prompting Questioning Shaping Strategic pausing Take up time


Activities and Resources Laminated folder activities Counters Computers / IWB

Indicators Teacher Language

• Counts objects to 3. • Counts objects to 5. • Counts objects to 10. • WM Give the teacher the requested number

of items, ensuring there is more than necessary.

Make a statement ‘We are going to count to …….’. Give an instruction: ‘Give me X ……..’. Correction/Prompt: ‘Try again’.

When carrying out any of the following teaching activities it will be necessary to use different levels of support as indicated in the guidelines table at the beginning of Number. Fade this support as the student works towards developing independence. When this activity is implemented, objects such as counters, teddy bears must be identical to ensure that the student is counting rather than attributing characteristics to numbers e.g. red counters symbolise 1, yellow counters symbolise 2 etc.

Whatever number is being counted, place more objects than is required in front of the student. The student has achieved this goal when they are able to stop counting at the number indicated without continuing to count on. A visual representation of the number to be counted may be shown to the student.

Counts objects to 3 and stops at the appropriate number Teacher states ‘We are going to count to 1. Give me 1 ….’, (ensuring there is a minimum of two objects in front of the student). Once the student has independently counted one object and stopped at the appropriate number, move onto two objects and then three, always ensuring there are more objects than is required. Encouraged students to touch, move or pick up the objects as they count.

Counts objects to 5 and to 10, and stops at the appropriate number Follow teaching procedures as stated above. Do not move onto the next number unless 100% accuracy has been achieved.

Whole Numbers N&A1.8 Students make groups of objects up to 10.


N&A1.8

Whole Numbers Strategies Attributing meaning Contingent responding Correcting errors Explicit teaching Incidental teaching Modelling Prompting Questioning Strategic pausing Take up time


Activities and Resources Laminated folder activities Computers / IWB Number lines Blocks

Indicators Teacher Language • Makes a group of any number of objects. • Makes a group of 2 objects. • Makes groups of 3 to 10 objects. • WM Make a group of teddy bears/cars/dolls

in the range 3 to 10.

Make a statement ‘I have made a group of ….’. ‘Here is a group of ….’. Give an instruction ’It’s your turn to make a group of ….’. Correction/Prompt ‘Try again’. ‘Count the ……………...’. ‘Too many’. ‘Keep counting’. ‘How many have you given me?’


In this activity, students may need to be introduced to the concept of ‘group’. Students are to gather (count) a specified number of objects and place them into a group.

Makes a group of any number of objects At this stage, modelling would be done by the teacher to reinforce the concept of ‘group’. Any objects could be used. For example, teacher would pick up a random number of teddy bears and place them in front of the student and state ‘I have made a group of teddy bear’. Teacher would then say ‘SN, it’s your turn to make a group of teddy bears’.

Makes a group of 2 objects Modelling would be done by the teacher to reinforce the correct number of objects in the group. In this activity, teachers would have many more objects than is required, accessible to the student. Teacher states ‘I am going to make a group of 2 teddy bears’. Teacher takes 2 teddy bears from the larger group and places them on the table and states ‘Here is a group of 2 teddy bears’. Teacher then states ‘SN, it’s your turn to make a group of 2 teddy bears’.

Makes groups of objects from 3 to 10 Implement as above. Do not move onto the next number of objects in a group unless 100% accuracy has been achieved.

Whole Numbers N&A1.9 Students match numerals to collections of objects.


N&A1.9

Whole Numbers

Strategies Attributing meaning Contingent responding Correcting errors Distractors Errorless learning Explicit teaching Match to sample Modelling Prompting Questioning Strategic pausing Take up time


Activities and Resources Numeral cards & physical objects Morning circle activities (e.g. people at school) Matching dot cards Laminated folder activities Dominos Bingo. Computers / IWB Stories Songs

Indicators Teacher Language • Matches numerals to 3 objects. • Matches numerals to 5 objects. • Matches numerals to 10 objects. • WM Count dinosaurs/teddy bears and

match correct numeral cards in the range 3 to 10.

Ask a question ‘How many are there?’ Give an instruction ‘Find the correct number card’. Correction/prompt ‘Is that the same?’ ‘Try again’. ‘Count again’. ‘Keep counting’. ‘Which number have you given me?’


This activity is dependent on students’ ability to identify numerals to 10 and be able to count a group of objects. A set of number cards is required and a collection of objects. eg. Teddy bears, counters.

Matches numerals from 1 to 10 objects Following the sequences outlined in the table below the teacher provides the students with opportunities to match the correct number card to the objects being presented. This activity commences with errorless learning. Teacher states ‘SN, how many are there?’ ‘Find the correct number card’. This is taught sequentially from 1 to 10. Students do not move on until they are able to complete the matching activity independently.

No. of objects

Correct no. card

Dis 1 Dis 2 Dis 3 Dis 4 Dis 5 Dis 6 Dis 7 Dis 8 Dis 9

1 1 No Distractor (Errorless learning)

2 2 No. card 1

3 3 No. card 1

No. card 2

4 4 No. card 1

No. card 2

No. card 3

5 5 No. card 1

No. card 2

No. card 3

No. card 4

6 6 No. card 1

No. card 2

No. card 3

No. card 4

No. card 5

7 7 No. card 1

No. card 2

No. card 3

No. card 4

No. card 5

No. card 6

8 8 No. card 1

No. card 2

No. card 3

No. card 4

No. card 5

No. card 6

No. card 7

9 9 No. card 1

No. card 2

No. card 3

No. card 4

No. card 5

No. card 6

No. card 7

No. card 8

10 10 No. card 1

No. card 2

No. card 3

No. card 4

No. card 5

No. card 6

No. card 7

No. card 8

No. card 9

Whole Numbers N&A1.10 Students make comparisons between groups of objects according to number.


N&A1.10

Whole Numbers

Strategies Attributing meaning Contingent responding Correcting errors Explicit teaching Incidental teaching Modelling Prompting Provide opportunities for choice Questioning Strategic pausing Take up time


Activities and Resources Straws/cotton balls Toy cars and animals Red counters/blue counters Big blocks/little blocks Computers/ IWB Student award charts Number lines

Indicators Teacher Language • Indicates bigger and smaller groups when

displayed in lines. • Indicates bigger and smaller groups when

displayed in bundles. • WM Describe groups that have been made

and compare the sizes of the groups e.g. ten cotton balls and two pegs.

Make a statement ‘This line/bundle has ….’. ‘This line/bundle is bigger’. This line/bundle is smaller’. Give an Instruction ‘Let’s count the ..…’. Ask a question ‘Which line is bigger/smaller?’ ‘Which bundle is bigger/smaller?’ Correction/prompt ‘Try again’. ‘Count again’. ‘Have another look’.



In this activity, students may need to be introduced to the concept of ‘big’ and ‘small’ if they have no prior knowledge of these concepts. Modelling would be done by the teacher to reinforce this concept. This activity involves students comparing groups of objects according to the number in those groups, not the size of the objects. It is important when making groups of objects that are bigger and smaller, that the objects in the groups are identical e.g. all counters. The only variant between the 2 groups could be colour, e.g. each group being represented by one colour.

Indicates bigger and smaller groups when displayed in lines (can be taught in no particular order). Bigger -‐ Place the objects in two lines one underneath the other. To begin, one line of objects would be obviously bigger e.g. first line has 2 blue teddy bears and second line has 6 red teddy bears. Teacher models by counting both lines and stating ‘This line has 6. This line has 2. This line is bigger (pointing)’. Using the same lines, teacher would say ‘SN lets count the teddy bears. Which line is bigger?’ Repeat this activity reinforcing the bigger line each time until the student can independently identify it. When repeating this activity, vary:

• The number of objects in each line, as long as one line is obviously bigger.

• The position of the bigger line e.g. on top or beneath the smaller line.

Smaller -‐ Place the objects in two lines one underneath the other. To begin, one line of objects would be obviously smaller e.g. first line has 2 blue teddy bears and second line has 6 red teddy bears. Teacher models by counting both lines and stating ‘This line has 6. This line has 2. This line is smaller (pointing)’. Using the same lines, teacher would say ‘SN lets count the teddy bears. Which line is smaller?’ Repeat this activity reinforcing the smaller line each time until the student can independently identify it. When repeating this activity, vary:

• The number of objects in each line, as long as one line is obviously smaller.

• The position of the smaller line e.g. on top or beneath the bigger line.

Whole Numbers N&A1.10 Students make comparisons between groups of objects according to number. cont.


N&A1.10 cont.

Whole Numbers

Strategies Attributing meaning Contingent responding Correcting errors Explicit teaching Incidental teaching Modelling Prompting Provide opportunities for choice Questioning Strategic pausing Take up time


Activities and Resources Straws/cotton balls Toy cars and animals Red counters/blue counters Big blocks/little blocks Computers/ IWB Student award charts Number lines

Indicates bigger and smaller groups when displayed in bundles. Place the objects into 2 bundles. To begin, one bundle would be obviously bigger/smaller e.g. first bundle has 2 blue teddy bears and second bundle has 6 red teddy bears. Teacher models by counting both bundles and stating ‘This bundle has 6. This bundle has 2. This bundle is bigger/smaller (pointing)’. Using the same bundles, teacher would say ‘SN lets count the teddy bears. Which bundle is bigger/smaller?’ Repeat this activity reinforcing the bigger/smaller bundle each time until the student can independently identify it. When repeating this activity, vary:

• The number of objects in bigger / smaller bundles • Change the position of each bundle – left/right, top/bottom, closer/further.

Whole Numbers N&A1.11 Students sequence numbers to 10.


N&A1.11

Whole Numbers

Strategies Attributing meaning Contingent responding Correcting errors Explicit teaching Modelling Prompting Questioning Strategic pausing Take up time


Activities and Resources Ordering number cards Finding the missing number activities Laminated folder activities Computers / IWB

Indicators Teacher Language • Sequences numbers to 3. • Sequences numbers to 5. • Sequences numbers to 10. • WM Explain or demonstrate how to place

numeral cards in correct order.

Make a statement ‘I am putting the numbers in the correct order…’. Give an instruction ‘It’s your turn now’. ‘Put the numbers in the correct order’. Ask a question ‘Which number is first?’ ‘Which number is next?’ Correction/prompt ‘What number is that?’ ‘Is that in the right order/place?’ ‘Have another look.’


A prerequisite to achieving this goal is students need to be able to identify and name numerals to 10.

Sequences numerals to 3 Students are given number cards 1, 2 and 3 in random order. Teacher would model by placing the number cards 1 to 3 in the correct order and state, ‘I am putting the numbers in the correct order 1, 2 and 3’. Teacher then states ‘SN, it’s your turn. Put the numbers in the correct order. Which one is first?’ Once the student has indicated that number 1 is first, teacher asks ‘Which number is next?’ until the student correctly sequences all numbers 1 to 3. The student cannot progress onto the next number until 100% accuracy has been achieved.

Sequences numerals to 5 Students are given number cards 1, 2, 3, 4 and 5 in random order. Teacher may model by placing the number cards 1 to 5 in the correct order and state, ‘I am putting the numbers in the correct order 1, 2, 3, 4 and 5’. Teacher then states ‘SN, it’s your turn. Put the numbers in the correct order. Which one is first?’ Once the student has indicated that number 1 is first, teacher asks ‘Which number is next?’ until the student correctly sequences all numbers 1 to 5. The student cannot progress onto the next number until 100% accuracy has been achieved.

Sequences numerals to 10 Students are given number cards 1 to 10 in random order. Teacher may model by placing the number cards 1 to 10 in the correct order and state, ‘I am putting the numbers in the correct order 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10’. Teacher then states ‘SN, it’s your turn. Put the numbers in the correct order. Which one is first?’ Once the student has indicated that number 1 is first, teacher asks ‘Which number is next?’ until the student correctly sequences all numbers 1 to 10. The student cannot progress onto the next number until 100% accuracy has been achieved.

Whole Numbers N&A1.12 Students write numerals 0-‐9 (Students may use different tools in order to write).


N&A1.12

Whole Numbers

Strategies Attributing meaning Contingent responding Correcting errors Explicit teaching Independent practice Modelling Prompting


Activities and Resources Computers/IWB Numeral cards 0-‐9 Worksheets Numeral stamps

Indicators Teacher Language • Writes with physical assistance. • Traces numerals. • Copies a model of a numeral. • Independently creates numerals. • WM Trace dotted numerals relating to

illustrations, such as animal booklets.

Make a statement ‘We are going to write the number x’. Give an instruction ‘Trace number X’. ‘Copy number X’. ‘Write number X’. Correction/prompt ‘What number is that?’ ‘What number did you write?’ ‘Try again’. ‘Have a look’.


When beginning to teach this goal the students should be exposed to the correct method of forming numbers. However, how the student eventually writes numbers independently is not a priority. Students need only to be able to consistently represent a number legibly so that others are always able to identify what that number is.

Students would be given a variety of resources to enable them to write the numerals 0-‐9. Depending on student ability, the numbers can be taught in sequential or non-‐sequential order. For students who have difficulty succeeding with this goal, numbers that are easy to write would be focussed on first e.g. 1, 7 and 9. Activities may include number stencils, laminated number sheets and IWB activities.

Writes with physical assistance. Teacher states ‘SN, we are going to write the number X’. Teacher uses hand over hand method to aid the student in writing the number using the correct formation.

Traces numerals. Teacher states ‘SN, trace the number X’. Stencils that have arrows to indicate the correct way of forming the number could be used as a visual prompt when appropriate.

Copies a model of a numeral. A written model of the number is place in front of the student. Teacher states ‘SN, copy the number X’.

Independently creates numerals. Teacher states ‘SN, write the number X’. No visual cues are provided.

Whole Numbers N&A1.13 Students will familiarise themselves with money.


N&A1.13

Whole Numbers

Strategies Attributing meaning Backward chaining Contingent responding Correcting errors Distractors Explicit teaching Incidental teaching Modelling Prompting Questioning Shaping Strategic pausing Take up time Touch cues


Activities and Resources Money Playing shops Community programs Computers/ IWB

Indicators Teacher Language • Makes eye contact with money or

representations of money. • Reaches for money or representations of

money. • Makes physical contact with money or

representations of money. • Identifies what is and what is not money. • Recognises money is used to purchase goods. • WM Indicate that a coin is used to purchase

items (from a selection of a coin or a non-‐money item).

Make a statement ‘This is money’. ‘You have the money’. ‘You are touching the money’. ‘I am touching/picking up the money’. Give an instruction ‘Look at the money’. ‘It’s your turn’. ‘Touch/pick up the money’ (when given a choice between money and a non-‐money item). Ask a question ‘What do you need to buy the …...’. Correction/prompt ‘Try again’. ‘Have a look’.



Makes eye contact with money or representations of money. Place money or a representation of money directly in the student’s eyesight and state ‘This is money. Look at the money’. The student may make eye contact for a brief period of time. Immediately reinforce the student for looking at the money even if it’s a fleeting look in order to shape this behaviour into an intentional action. If the student does not make any eye contact, the teacher mirrors student head movement and eye gaze with the money so that it is in front of the student’s eyes. For students who make intentional eye contact, activities such as flashing pictures of money on an IWB may be appropriate.

Reaches for, explores and makes physical contact with money. Repeat the above activity with a focus on encouraging the student to reach for and interact with the money or representation of money and state ‘You are touching the money’. Once the student grasps it, reinforce them immediately by saying You have the money’. If the student does not reach for it, use the lowest level of support required to assist them to make physical contact.

Identify what is and what is not money. Provide the student with the opportunity to complete this activity using a variety of coins and notes. Teacher places money of any value and any other item, such as a set of keys, in front of the student. Teacher models touching/picking up the money and states ‘I am touching/picking up the money. SN it’s your turn. Touch/pick up the money’. Once the student has independently identified which is the money the teacher needs to modify and repeat this activity by changing the money and/or increasing the amount of non-‐money items.

Whole Numbers N&A1.13 Students will familiarise themselves with money. cont.


N&A1.13 cont.

Whole Numbers

Strategies Attributing meaning Backward chaining Contingent responding Correcting errors Distractors Explicit teaching Incidental teaching Modelling Prompting Questioning Shaping Strategic pausing Take up time Touch cues


Activities and Resources Money Playing shops Community programs Computers/ IWB

Recognise money is used to purchase goods. This skill is taught through providing students with opportunities to exchange money of any value for an item. This can be implemented by having a classroom shop. The value of the money exchanged does not have to match the value of the item purchased. Teacher presents student with a preferred item and states ‘SN, what do you need to buy the …..?’ Student is required to exchange money for the preferred item.

NUMBER & ALGEBRA: Addition & Subtraction



Syllabus Outcomes Early Stage 1 Outcome 2012 NES 1.2 Combines, separates and compares collections of objects, describing using everyday language and records using informal methods. WMES1.3 Describes mathematical situations using everyday language, actions, materials, and informal recordings (Communicating) WMES1.4 Uses concrete materials and/or pictorial representations to support conclusions (Reasoning) WMES1.5 Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Early Stage 1 content (Reflecting) WMES1.1 Asks questions that could be explored using mathematics in relation to Early Stage 1 content WMES1.2 Uses objects, actions, imagery, technology and/or trial and error to explore mathematical problems Early Stage 1 Outcome 2015 MAe-‐1WM Describes mathematical situations using everyday language, actions, materials and informal recordings. Mae-‐2WM Uses objects, actions, technology and/or trial and error to explore mathematical problems. Mae-‐3WM Uses concrete materials and/or pictorial representations to support conclusions. MAe-‐5NA: Combines, separates and compares collections of objects, describing using everyday language and records using informal methods.

Life Skills 7-‐10 Outcome 2015 MALS-‐10NA Selects and uses strategies for addition and subtraction.

HSC Life Skills 11-‐12 Outcomes 2007 2.1 Demonstrates knowledge and understanding of addition, subtraction, multiplication and division processes.

ADDITION &

SUBT

RACT

ION

N&A2.1 Students combine groups of objects in order to make one group.

N&A2.2 Students separate one group of objects in order to make two or more groups.

Addition & Subtraction N&A2.1 Students combine groups of objects in order to make one group.


N&A2.1 Addition


Levels of Support Full physical assistance Partial physical assistance Modelled response Gesture/sign Verbal Independent

Activities and Resources Counters Teddy Bears Pegs Blocks

Indicators Teacher Language • Engages with two or more groups of objects. • Moves two groups of objects towards each

other and combines them. • WM Make one group of blocks from two

piles.

Give an instruction ‘Look at the group’. ‘Look at this group’. ‘Put the two groups together’. Make a Statement ‘This is a group of …’. ‘Here is another group of…’. ‘I am putting two groups of ….together’. ‘I have now made one group of…’. ‘It’s your turn’. ‘We have two groups’. ‘Now you have one group of …..’. Ask a question ‘How many groups are there?’ Correction/prompt ‘Are they all together?’



For this activity, teachers can assist students to understand the concept of grouping by placing one large circle and two smaller circles on the table in front of the student as a guide for where to position objects to form and combine groups. These guides could be cut out cardboard circles or large and small cork placemats. Objects used to form groups need to be identical e.g. groups of counter, teddy bears etc.

Engages with two or more groups of objects. Place two or more groups directly in the student’s eyesight and state ‘This is a group of….. Look at the group. Here is another group of…. Look at this group. We have two groups’. The student may make eye contact for a brief period of time. Immediately reinforce the student for looking at the groups even if it’s a fleeting look in order to shape this behaviour into an intentional action. If the student does not make any eye contact, the teacher mirrors student head movement and eye gaze with the groups so that it is in front of the student’s eyes.

Moves two groups of objects towards each other and combines them. On the two smaller grouping guides, place ‘x’ amount of objects e.g. pegs. These objects must be identical including colour, size and number. Teacher may model how to combine the two groups to make one group. Teacher states ‘I am putting the two groups of pegs together. I have now made one group of pegs’. The teacher states ‘SN it’s your turn. Put the two groups together’. Once student has done this teacher states ‘SN you now have one group of pegs’.

Addition & Subtraction N&A2.2 Students separate one group of objects in order to make two or more groups.

N2.2 Students separate one group of objects in order to make two or more groups.


N&A2.2

Subtraction



Activities and Resources Counters Teddy Bears Pegs Blocks

Indicators Teacher Language • Engages with a group of objects. • Remove items from a group of objects. • WM Make two or more groups of counters /

pencils / blocks from one pile.

Give an instruction ‘Look at the group’. ‘Make two groups of……’. Make a Statement ‘This is a group of …’. ‘I am making two groups of….’. ‘It’s your turn’. ‘I/ You now have two groups of….’. Ask a question ‘How many groups are there?’ Correction/prompt ‘Is there more than one group?’ ‘Have you made more than one group?’



For this activity, teachers can assist students to understand the concept of grouping by placing one large circle and two smaller circles on the table in front of the student as a guide for where to position objects to form and combine groups. These guides could be cut out cardboard circles or large and small cork placemats. Objects used to form groups need to be identical e.g. groups of counter, teddy bears etc.

Engages with a group of objects. Place one group directly in the student’s eyesight and state ‘This is a group of….. Look at the group’. The student may make eye contact for a brief period of time. Immediately reinforce the student for looking at the groups even if it’s a fleeting look in order to shape this behaviour into an intentional action. If the student does not make any eye contact, the teacher mirrors student head movement and eye gaze with the groups so that it is in front of the student’s eyes.

Remove items from a group of objects. On the large grouping guide, place ‘x’ amount of objects e.g. pegs. These objects must be identical including colour, size and number. Teacher may model how to separate the one group of objects to make two groups. Teacher states ‘I am making two groups of pegs. I have now made two groups of pegs’. The teacher states ‘SN it’s your turn. Make two groups of pegs’. Once student has done this teacher states ‘SN you now have two groups of pegs’.

NUMBER & ALGEBRA: Multiplication & Division



Syllabus Outcomes Early Stage 1 Outcome 2012 NES 1.3 Groups, shares and counts collections of objects, describing using everyday language and records using informal methods. WMES1.3 Describes mathematical situations using everyday language, actions, materials, and informal recordings (Communicating) WMES1.5 Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Early Stage 1 content (Reflecting) Early Stage 1 Outcome 2015 MAe-‐1WM Describes mathematical situations using everyday language, actions, materials and informal recordings. Mae-‐2WM Uses objects, actions, technology and/or trial and error to explore mathematical problems. MAe-‐6NA Groups, shares and counts collections of objects, describing using everyday language and records using informal methods.

Life Skills 7-‐10 Outcome 2015 MALS-‐11NSA Selects and uses strategies for multiplication and division

HSC Life Skills 11-‐12 Outcomes (2007) 2.1 Demonstrate knowledge and understanding of addition, subtraction, multiplication and division processes.

Multip

lication &

Division

N&A3 Students participate in activities related to equal distribution of amounts.

Multiplication & Division N&A3 Students participate in activities related to equal distribution of amounts.


N&A3 Multiplication and Division

Strategies Attributing meaning Contingent responding Correcting errors Explicit teaching Incidental teaching Independent practice Modelling Prompting Questioning Shaping Strategic Pausing Take up time Touch Cues


Activities and Resources Food items Plates, cups etc. Paint brushes

Indicators Teacher Language • Engages with activities related to sharing of

an equal number of objects. • Engages with activities related to sharing of

an unequal number of objects. • WM Shares items equally.

Give an instruction ‘Lets share the….’. ‘It is now your turn to share.’ Make a Statement. ‘This is your …..’. ‘This is my ……’. ‘ We have shared the …..’. ‘We have the same amount’. ‘We have shared the ….. equally but we have some left over’. Ask a question ‘Whose ……..is that?’


Engages with activities related to sharing of an equal number of objects The teacher will model how to distribute an equal number of items between two people e.g. lollies. Teacher states ‘SN lets share the lollies. That is your lolly, this is my lolly.’ Continue until all lollies are distributed equally. Teacher states ‘We have shared the lollies. We have the same amount’. Teacher then states ‘SN it is now your turn to share.’ Guide the student as necessary, using questioning when needed. e.g. ‘Whose lolly is that?’

Once student is able to distribute in equal amounts between 2 people, move onto three or more people.

Engages with activities related to sharing of an unequal number of objects It is a prerequisite that students have achieved the above goal before progressing onto the distribution of unequal numbers.

The teacher will model how to distribute an unequal number of items between two people resulting in items being left over e.g. lollies. The aim is for students to identify there are left over items and to stop when the distribution can no longer be equal. Teacher states ‘SN lets share the lollies. That is your lolly, this is my lolly.’ Continue until lollies can no longer be distributed equally. Teacher states ‘We have shared the lollies equally but we have some left over’. Teacher then states ‘SN it is now your turn to share.’ Guide the student as necessary, using questioning when needed. e.g. ‘Whose lolly is that?’

Once student is able to distribute in equal amounts between 2 people, with left overs, move onto three or more people.

NUMBER: Fractions & Decimals



Syllabus Outcomes Early Stage 1 Outcome 2012 NES 1.4 Describes halves, encountered in everyday contexts, as two equal parts of an object. WMES1.1 Asks questions that could be explored using mathematics in relation to Early Stage 1 content (Questioning) WMES1.2 Uses objects, actions, imagery, technology and/or trial and error to explore mathematical problems (Applying Strategies) WMES1.3 Describes mathematical situations using everyday language, actions, materials, and informal recordings (Communicating) WMES1.4 Uses concrete materials and/or pictorial representations to support conclusions (Reasoning) Early Stage 1 Outcome 2015 MAe-‐1WM Describes mathematical situations using everyday language, actions, materials and informal recordings. Mae-‐3WM Uses concrete materials and/or pictorial representations to support conclusions. MAe-‐7NA: Describes two equal parts as halves.

Life Skills 7-‐10 Outcome 2015 MALS-‐8NA Recognises and compares fractions in everyday contexts.

HSC Life Skills 11-‐12 Outcomes 2007 1.6 demonstrates knowledge, understanding and application of basic fractions and decimals.

Fractio

ns &

Decim

als N&A4.1 Students access / interact with the representation of parts of objects.

N&A4.2 Students manipulate two parts of a given object, activity/puzzle.

N&A4.3 Students make parts from a whole object or activity.

Fractions & Decimals N&A4.1 Students access/interact with the representation of parts of objects.


N&A4.1 Fractions & Decimals



Activities and Resources Food items Toys with parts /pieces

Indicators Teacher Language • Makes eye contact with the parts of objects. • Reaches for the parts of objects. • Makes physical contact with the parts of

objects. • Explores the parts of objects with senses. • WM Explore with senses the servings of a cut

cake or muffin.

Give an instruction ‘Look at the parts of the puzzle’. ‘Touch/feel the parts of the puzzle’. Make a Statement ‘You are looking at the parts of the puzzle’. ‘You are touching/feeling the parts of the puzzle’.



Makes eye contact with the parts of objects Place parts of an object e.g. a two piece puzzle directly in the student’s eyesight and state ‘SN look at the parts of the puzzle’. The student may make eye contact with the item for a brief period of time. Immediately reinforce the student for looking at the parts of the object even if it’s a fleeting look in order to shape this behaviour into an intentional action. If the student does not make any eye contact, the teacher mirrors student head movement and eye gaze with the parts so they are in front of the student’s eyes. ’SN you are looking at the parts of the puzzle’.

Reaches for, explores and makes physical contact with parts of an object Repeat the above activity with a focus on encouraging the student to reach for and interact with the parts of an object e.g. a two piece puzzle and state ‘SN touch the parts of the puzzle’. Once the student grasps the parts, reinforce them immediately by saying ‘SN you are touching the parts of the puzzle’.

Fractions & Decimals N&A4.2 Students manipulate two parts of a given object, activity/puzzle.



Strategies Attributing meaning Correcting errors Independent practice Modelling Prompting Questioning Role play Shaping Strategic pausing Take up time Touch cues


Activities and Resources Puzzles Photographs Lego/Duplo Train tracks File folder

Indicators Teacher Language • Moves two parts of an object or puzzle

towards each other and combines them. • WM Complete a two piece puzzle.

Give an instruction ‘Move the parts of the puzzle’. ‘SN, put the parts of the puzzle together.’ Make a Statement ‘These are parts of the puzzle.’ ‘These parts make a whole.’ Correction/prompt ‘Are the parts together?’ ‘Is that a whole?’


Moves two pieces of an object or puzzle towards each other and combines them. Place parts of an object e.g. a two piece puzzle directly in front of the student and state ‘SN these are parts of the puzzle. Move the parts of the puzzle’. Once the student has moved the parts in any direction, instruct the student to put the parts together. ‘SN, put the parts of the puzzle together’. When the student has successfully put the two pieces of the puzzle together teacher states ‘These parts make a whole’.

Fractions & Decimals N&A4.3 Students make parts from a whole object or activity.



Strategies Attributing meaning Correcting errors Independent practice Modelling Prompting Questioning Role play Shaping Strategic pausing Take up time Touch cues


Activities and Resources Train tracks Opening containers / lunchboxes Cutting/ripping paper. Lego / Duplo Puzzles Play dough Food File folders

Indicators Teacher Language • Interacts with a whole object, activity or

puzzle and separates into parts. • WM Cut a play dough snake into pieces and

report on the number of pieces.

Give an instruction ‘SN now you take the pizza apart’. Make a Statement ‘This is a picture of a …..’. ‘I am taking this ….. apart and making X pieces’. ‘These X pieces make a whole ……’. ‘You have made x pieces’. Ask a question ‘How many pieces do you have?’ ‘Can you make a whole…..’. Correction/prompt ‘Is it in parts?’ ‘Are there more parts?’


Teachers are to give a student the opportunity to interact with puzzles/items that have more than two parts. Teacher states, ‘This is a picture of a …..e.g. pizza’. (Picture has 6 pieces / parts). Teacher is to ensure the picture is complete and all parts are in their correct place. The teacher models first, taking the picture/puzzle apart into more than two pieces. Teacher states, ‘I am taking this pizza apart and making 6 pieces. These 6 pieces make a whole pizza’. Once this is done, the teacher puts the pizza back together and states ‘SN, now you take the pizza apart. You have made 6 pieces’.

NUMBER: Patterns & Algebra



Syllabus Outcomes Early Stage 1 Outcome 2012 NES 1.3 Groups, shares and counts collections of objects, describing using everyday language and records using informal methods WMES1.2 Uses objects, actions, imagery, technology and/or trial and error to explore mathematical problems (Applying Strategies) WMES1.3 Describes mathematical situations using everyday language, actions, materials, and informal recordings (Communicating) WMES1.4 Uses concrete materials and/or pictorial representations to support conclusions (Reasoning) WMES1.5 Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Early Stage 1 content (Reflecting) Early Stage 1 Outcome 2015 MAe-‐1WM Describes mathematical situations using everyday language, actions, materials and informal recordings. Mae-‐2WM Uses objects, actions, technology and/or trial and error to explore mathematical problems. Mae-‐3WM Uses concrete materials and/or pictorial representations to support conclusions MAe-‐8NA: Recognises, describes and continues repeating patterns.


HSC Life Skills 11-‐12 Outcomes (2007) 2.1 demonstrate knowledge and understanding of addition, subtraction, multiplication and division processes.

Paterns &

Algeb

ra

N&A5.1a Respond to repeated patterns of sound and actions.

N&A5.1b Respond to repeated visual patterns.

N&A5.2a Initiates own response to patterns of sound and action.

N&A5.2b Initiates own response to visual patterns.

Patterns & Algebra N&A5.1a Students respond to repeated patterns of sound and actions.

N&A5.1b Students respond to repeated visual patterns.


N&A5.1a &

N&A5.1b Patterns & Algebra

Strategies Attributing meaning Independent practice Modelling Sensory stimulation Shaping Strategic pausing Take up time Touch cues Levels of Support Full Physical assistance Partial physical assistance Modelled response Gesture/sign Verbal Independent

Activities and Resources Body parts

Instruments

Computers / IWB

Indicators Teacher Language • Turns head in the direction of a sound and

action pattern or a visual pattern. • Moves in response to a sound and action

pattern or a visual pattern. • Makes vocalisations in response to a sound

and action pattern or a visual pattern. • WM Responds to a pattern on the computer

screen or IWB.

Give an instruction ‘Listen to the pattern in the sound’. ‘Look at the pattern’. Make a Statement ‘You are listening to the pattern in the sound’. ‘You are looking at the pattern’.



In this activity, we are looking for a response from the student to a pattern. Therefore, when beginning this goal, teachers would need to give the student time to respond independently to the pattern before any instructions are given. If no response is given after a period of time, teacher states ‘SN, listen to the pattern in the sound’. ‘SN, look at the pattern’.

Please note that the sounds the teacher creates in this activity need to be simple repeated patterns.

Turns head, moves and vocalises in the direction of a sound and action pattern. Teachers are to give a student the opportunity to respond to repeated patterns of sounds and actions. This could involve clapping hands, using a musical instrument such as a drum or using technology to make repeated patterns of sound and action. Teacher would observe if the student has responded to the pattern by observing if the student has turned towards the sound, made eye contact, body movement or vocalisation. Once the student has made a response, teacher states ‘SN, you are listening to the pattern in the sound.’

Turns head, moves and vocalises in the direction of a visual pattern. Teachers are to give a student the opportunity to respond to visual patterns. This can be in the form of repeated visual patterns in a file folder or on the IWB or iPad. Teacher would observe if the student has responded to the pattern by observing if they have turned towards the visual pattern, made eye contact, body movement or vocalisation. Once the student has made a response, teacher states ‘SN, you are looking at the pattern.’

Patterns & Algebra N&A5.2a Students initiate own response to patterns of sound or action.

N&A5.2b Students initiate own response to visual patterns.


N&A5.2a

N&A5.2b Patterns & Algebra

Strategies Attributing meaning Independent practice Modelling Sensory stimulation Shaping Strategic pausing Take up time Touch cues Levels of Support Full Physical assistance Partial physical assistance Modelled response Gesture/sign Verbal Independent

Activities and Resources Body parts Instruments Music Action Songs Rhymes Computers / IWB Photographs Laminated folder activities.

Indicators Teacher Language • Selects appropriate object / implement to

create sound or action pattern. • Selects appropriate object / implement to

create a visual pattern. • WM Creates own pattern in response to

music. e.g. Heads, shoulders, knees and toes. • WM Creates own pattern using computer

software in response to a visual pattern.

Give an instruction ‘Copy the action /sound’. ‘Repeat the action/sound’. Make a Statement ‘You have made a pattern’. Ask a question ‘Does that sound /look the same?’ ‘What would you use to make that pattern?’ ‘What sound/ picture is first?’ Correction / Prompt ‘Is it the same?’ ‘Listen / look again’.



Whilst the instruction ‘copy’ is used, the student is only required to initiate their own response to visual patterns and patterns of sound.

Selects appropriate object / implement to create sound or action pattern. Teacher selects an object or implement to create a simple sound pattern e.g. drum and hits it 3 times. Teacher instructs ‘SN, copy the sound’. ‘SN, you have made a pattern’.

Selects appropriate object / implement to create a visual pattern. Teacher selects objects or implements to create a simple visual pattern e.g. teddy bears of two colours or file folder activities. Teacher instructs ‘SN, What would you use to finish that pattern?’ ‘SN, you have made a pattern.’

Assessing Whole Numbers

Assessing Multiplication and Division

Assessing Patterns and Algebra

Assessing Addition and Subtraction

Assessing Fractions and Decimals



The rate at which each individual student acquires Number and Algebra goals will vary. This will mean that teachers will use professional judgement to adjust the teaching ideas suggested on the following pages.

Syllabus Outcomes Early Stage 1 Outcome 2012 NES 1.1: Counts to 30, and orders, reads and represents numbers in the range 0 to 20. WMES1.2 Uses objects, actions, imagery, technology and/or trial and error to explore mathematical problems (Applying Strategies) WMES1.3 Describes mathematical situations using everyday language, actions, materials, and informal recordings (Communicating) WMES1.4 Uses concrete materials and/or pictorial representations to support conclusions (Reasoning) WMES1.5 Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Early Stage 1 content (Reflecting) Early Stage 1 Outcome 2015 MAe-‐1WM Describes mathematical situations using everyday language, actions, materials and informal recordings. Mae-‐2WM Uses objects, actions, technology and/or trial and error to explore mathematical problems. Mae-‐3WM Uses concrete materials and/or pictorial representations to support conclusions. MAe-‐4NA Counts to 30, and orders, reads and represents numbers in the range 0 to 20.

Life Skills 7-‐10 Outcome 2015 MALS-‐4NA: Recognises language to represent number. MALS-‐5NA: Counts in familiar contexts. MALS-‐6NA: Reads and represents numbers. MALS-‐7NA: Compares and orders numbers. MALS-‐12NA: Compares and matches coins and notes.

HSC Life Skills 11-‐12 Outcomes 2007 1.1: Demonstrates understanding of number sense. 1.2: Recognises matches and sorts concrete objects to represent numbers. 1.3: Counts objects in meaningful contexts. 1.4: Understands and uses ordinal terms. 1.5: Reads and writes numbers and demonstrates understanding of place value. 5.1: Understands that money is a medium for purchasing goods and services. 5.2: Identify matches and counts coins and notes.

WHOLE NUMBE

RS

N&A1.1 Students access/interact with the representation of a numeral.


N&A1.3 Students learn the names of numerals in order to identify them. (Identify the numeral without other numerals present).

N&A1.4 Students identify representations of numerals. (Identify the numeral with other numerals present in random order).

N&A1.5 Students can rote count.

N&A1.6 Students demonstrate an understanding of 1:1 correspondence through matching.

N&A1.7a Students demonstrate an understanding of 1:1 correspondence through counting.

N&A1.7b Students are able to stop counting objects at the number indicated without continuing to count on.

N&A1.8 Students make groups of objects up to 10.

N&A1.9 Students match numerals to collections of objects.

N&A1.10 Students make comparisons between groups of objects according to number.

N&A1.11 Students sequence numbers to 10.

N&A1.12 Students write numerals 0-‐9. (Students may use different tools in order to write)

N&A1.13 Students will familiarise themselves with money.

WHOLE NUMBE

RS

Whole Numbers N&A1.1 Students access/interact with the representation of a numeral.

ASSESSMENT RECORD

Code Level of Support Code Level of Support Code Level of Support

FP Full physical assistance M Model V Verbal

PP Partial physical assistance G/S Gesture/Sign I Independent

Indicator FP PP M G/S V I

Makes eye contact with a numeral

Reaches for a numeral

Makes physical contact with a numeral

Explores a numeral with senses

Comments

Whole Numbers N&A1.2 Students match one numeral with another. (Match to sample)

ASSESSMENT RECORD





Matches to sample 1-‐1




Comments

Whole Numbers Goal: N&A1.3 Students learn the names of numerals in order to identify them. (Identify the

numeral without other numerals present). ASSESSMENT RECORD





Learns names of numerals to 3




Comments

Whole Numbers Goal: N&A1.4 Students identify representations of numerals. (Identify the numeral with

other numerals present in random order) ASSESSMENT RECORD





Identify numerals to 3




Comments Note: Begin with one distractor and then increase the number with success. Record the number of distractors used.

Whole Numbers Goal: N&A1.5 Students can rote count.

ASSESSMENT RECORD





Rote counts up to 3

Rote counts up to 5

Rote counts up to 10

Rote counts up to 20

Comments

Whole Numbers Goal: N&A1.6 Students demonstrate an understanding of 1:1 correspondence through matching.

ASSESSMENT RECORD





Distributes 1 object

Distributes 3 objects



Comments

Whole Numbers Goal: N&A1.7a Students demonstrate an understanding of 1:1 correspondence through

counting. ASSESSMENT RECORD





Counts objects to 3

Counts objects to 5

Counts objects to 10

Comments

Whole Numbers Goal: N&A1.7b Students are able to stop counting objects at the number indicated without

continuing to count on. ASSESSMENT RECORD





Counts objects to 3

Counts objects to 5

Counts objects to 10

Comments

Whole Numbers Goal: N&A1.8 Students make groups of objects up to 10.

ASSESSMENT RECORD





Makes a group of any number of objects

Makes a group of 2 objects

Makes groups of 3 to 10 objects

Comments

Whole Numbers Goal: N&A1.9 Students match numerals to collections of objects.

ASSESSMENT RECORD





Matches numerals to 3 objects



Comments

Whole Numbers Goal: N&A1.10 Students make comparisons between groups of objects according to

number. ASSESSMENT RECORD





Indicates bigger and smaller groups when displayed in lines

Indicates bigger and smaller groups when displayed in bundles

Comments

Whole Numbers Goal: N&A1.11 Students sequence numbers to 10.

ASSESSMENT RECORD





Sequences numbers to 3



Comments

Whole Numbers Goal: N&A1.12 Students write numerals 0-‐9. (Students may use different tools in order to

write) ASSESSMENT RECORD





Writes with physical assistance

Traces numerals

Copies a model of a numeral

Independently creates numerals

Comments

Whole Numbers Goal: N&A1.13 Students will familiarise themselves with money.

ASSESSMENT RECORD





Makes eye contact with money or representations of money

Reaches for money or representations of money

Makes physical contact with money or representations of money

Identifies what is and what is not money

Recognises money is used to purchase goods

Comments

NUMBER & ALGEBRA: Addition & Subtraction



Syllabus Outcomes Early Stage 1 Outcome 2012 NES 1.2 Combines, separates and compares collections of objects, describing using everyday language and records using informal methods. WMES1.1 Asks questions that could be explored using mathematics in relation to Early Stage 1 content (Questioning) WMES1.2 Uses objects, actions, imagery, technology and/or trial and error to explore mathematical problems (Applying Strategies) WMES1.3 Describes mathematical situations using everyday language, actions, materials, and informal recordings (Communicating) WMES1.4 Uses concrete materials and/or pictorial representations to support conclusions (Reasoning) WMES1.5 Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Early Stage 1 content (Reflecting) Early Stage 1 Outcome 2015 MAe-‐1WM Describes mathematical situations using everyday language, actions, materials and informal recordings. Mae-‐2WM Uses objects, actions, technology and/or trial and error to explore mathematical problems. Mae-‐3WM Uses concrete materials and/or pictorial representations to support conclusions. MAe-‐5NA: Combines, separates and compares collections of objects, describing using everyday language and records using informal methods.

Life Skills 7-‐10 Outcome 2015 MALS-‐10NA Selects and uses strategies for addition and subtraction.

HSC Life Skills 11-‐12 Outcomes 2007 2.1 Demonstrates knowledge and understanding of addition, subtraction, multiplication and division processes.

ADDITION &

SUBT

RACT

ION

N&A2.1 Students combine groups of objects in order to make one group.

N&A2.2 Students separate one group of objects in order to make two or more groups.

Addition & Subtraction Goal: N&A2.1 Addition: Students combine groups of objects in order to make one group.

ASSESSMENT RECORD





Engages with two or more groups of objects

Moves two groups of objects towards each other and combines them

Comments

Addition & Subtraction Goal: N&A2.2 Subtraction: Students separate one group of objects in order to make two or

more groups. ASSESSMENT RECORD





Engages with two or more groups of objects

Moves two groups of objects towards each other and combines them

Comments

NUMBER & ALGEBRA: Multiplication & Division



Syllabus Outcomes Early Stage 1 Outcome 2012 NES 1.3 Groups, shares and counts collections of objects, describing using everyday language and records using informal methods. WMES1.3 Describes mathematical situations using everyday language, actions, materials, and informal recordings (Communicating) WMES1.5 Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Early Stage 1 content (Reflecting) Early Stage 1 Outcome 2015 MAe-‐1WM Describes mathematical situations using everyday language, actions, materials and informal recordings. Mae-‐2WM Uses objects, actions, technology and/or trial and error to explore mathematical problems. MAe-‐6NA Groups, shares and counts collections of objects, describing using everyday language and records using informal methods.


HSC Life Skills 11-‐12 Outcomes (2007) 2.1 Demonstrate knowledge and understanding of addition, subtraction, multiplication and division processes.

Multip

lication &

Division

N&A3 Students participate in activities related to equal distribution of amounts.

Multiplication & Division N&A3 Students participate in activities related to equal distribution of amounts.

ASSESSMENT RECORD





Engages with activities related to sharing of an equal number of objects

Engages with activities related to sharing of an unequal number of objects

Comments

NUMBER: Fractions & Decimals



Syllabus Outcomes Early Stage 1 Outcome 2012 NES 1.4 Describes halves, encountered in everyday contexts, as two equal parts of an object. WMES1.1 Asks questions that could be explored using mathematics in relation to Early Stage 1 content (Questioning) WMES1.2 Uses objects, actions, imagery, technology and/or trial and error to explore mathematical problems (Applying Strategies) WMES1.3 Describes mathematical situations using everyday language, actions, materials, and informal recordings (Communicating) WMES1.4 Uses concrete materials and/or pictorial representations to support conclusions (Reasoning) Early Stage 1 Outcome 2015 MAe-‐1WM Describes mathematical situations using everyday language, actions, materials and informal recordings. Mae-‐3WM Uses concrete materials and/or pictorial representations to support conclusions. MAe-‐7NA: Describes two equal parts as halves.

Life Skills 7-‐10 Outcome 2015 MALS-‐8NA Recognises and compares fractions in everyday contexts.

HSC Life Skills 11-‐12 Outcomes 2007 1.6 demonstrates knowledge, understanding and application of basic fractions and decimals.

Fractio

ns &

Decim

als N&A4.1 Students access / interact with the representation of parts of objects.

N&A4.2 Students manipulate two parts of a given object, activity/puzzle.

N&A4.3 Students make parts from a whole object or activity.

Fractions & Decimals N&A4.1 Students access/interact with the representation of parts of objects.

ASSESSMENT RECORD





Makes eye contact with the parts of objects

Reaches for the parts of objects

Makes physical contact with the parts of objects

Explores the parts of objects with senses

Comments

Fractions & Decimals Goal: N&A4.2 Students manipulate two parts of a given object, activity or puzzle.

ASSESSMENT RECORD





Moves two pieces of an object or puzzle towards each other and combines them

Comments

Fractions & Decimals Goal: N&A4.3 Students make parts from a whole object or activity.

ASSESSMENT RECORD





Interacts with a whole object, activity or puzzle and separates into parts

Comments

NUMBER: Patterns & Algebra



Syllabus Outcomes Early Stage 1 Outcome 2012 NES 1.3 Groups, shares and counts collections of objects, describing using everyday language and records using informal methods WMES1.2 Uses objects, actions, imagery, technology and/or trial and error to explore mathematical problems (Applying Strategies) WMES1.3 Describes mathematical situations using everyday language, actions, materials, and informal recordings (Communicating) WMES1.4 Uses concrete materials and/or pictorial representations to support conclusions (Reasoning) WMES1.5 Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Early Stage 1 content (Reflecting) Early Stage 1 Outcome 2015 MAe-‐1WM Describes mathematical situations using everyday language, actions, materials and informal recordings. Mae-‐2WM Uses objects, actions, technology and/or trial and error to explore mathematical problems. Mae-‐3WM Uses concrete materials and/or pictorial representations to support conclusions MAe-‐8NA: Recognises, describes and continues repeating patterns.


HSC Life Skills 11-‐12 Outcomes (2007) 2.1 demonstrate knowledge and understanding of addition, subtraction, multiplication and division processes.

Paterns &

Algeb

ra

N&A5.1a Respond to repeated patterns of sound and actions.

N&A5.1b Respond to repeated visual patterns.

N&A5.2a Initiates own response to patterns of sound and action.

N&A5.2b Initiates own response to visual patterns.

Patterns & Algebra N&A5.1a Students respond to repeated patterns of sound and actions.

N&A5.1b Students respond to repeated visual patterns.

ASSESSMENT RECORD





Turns head in the direction of sound and action pattern or a visual pattern

Moves in response to a sound and action pattern or a visual pattern

Makes vocalisations in response to a sound and action pattern or a visual pattern

Comments

Patterns & Algebra Goals: N&A5.2a Students initiate own response to patterns of sound or action.

N&A5.2b Students initiate own response to visual patterns.

ASSESSMENT RECORD





Selects appropriate object/ implement to create sound or action pattern

Selects appropriate object/ implement to create a visual pattern

Comments

whole!numbers! addition!and!subtraction!! multiplication...

Documents