Statistics and Probability 13th November - Every …everystudent-sws.nsw.edu.au/assets/files/Numeracy Documents/Modu… · Statistics&’Probability:’Data ... situationsusing!everyday!language,!actions,!

Data

Statistics & Probability: Data

NUMERACY LEARNING CONTINUUM

The rate at which each individual student acquires Statistics and Probability 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 DES1.1 Students recognise there is a difference between the characteristics of two objects. 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) WMS1.5 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-‐3WM Uses concrete materials and/or pictorial representations to support conclusions and informal recordings. MAe-‐17SP Represents data and interprets data displays made from objects.

Life Skills 7-‐10 Outcome 2015 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-‐35SP Recognises data displayed in a range of formats. MALS-‐36SP Gathers, organises and displays data. MALS-‐37SP Interprets information and draws conclusions from data displays.

HSC Life Skills 11-‐12 Outcomes 2007 6.3 Reads and interprets a variety of graphs and tables.

DAT

A

S&P1a Students access/interact with objects that are the same and different.

S&P1b Students recognise there is a difference between the characteristics of two objects.

S&P2 Students sort objects into 2 or more groups.

S&P3 Students sort objects into two or more groups when there is a difference of one or more characteristic.


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.

Statistics & Probability: Data S&P1a Students access/interact with objects that are the same and different.

LEARNING EXPERIENCES AND OPPORTUNITIES

S&P1a

Data

Strategies Attributing meaning Contingent responding Correcting errors Explicit teaching Guided practice Prompting Provide opportunities for choice Scaffolding 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 Objects that are identical e.g. two identical bottles of water. Object that are obviously different e.g. keys and a bottle of water, a toy and a book.

Indicators Teacher Language Makes eye contact with objects that are the same and different. Reaches for and makes physical contact with objects that are the same and different. WM Uses eye gaze and explores with senses objects that are the same and different.

Give an Instruction ‘Look at the …..…’. Make a Statement ‘They are the same’. ‘They are different’. ‘You are touching the …..….’. ‘You have the ……… ’.

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 objects that are the same and different Place two identical objects e.g. two water bottles directly in the student’s eyesight and state ‘Look at the …… (name objects). They are the same’. The student may make eye contact with the item for a brief period of time. Immediately reinforce the student for looking at the identical object even if it’s a fleeting look. If the student does not make any eye contact, the teacher mirrors student head movement and eye gaze with the identical objects so that the objects are in front of the student’s eyes. The teacher would reinforce the language of ‘They are the same’.

Place two different objects e.g. keys and a bottle of water, directly in the student’s eyesight and state ‘Look at the …….. (name object 1). Look at the …… (name object 2) They are different’. The student may make eye contact with the item for a brief period of time. Immediately reinforce the student for looking at the objects even if it’s a fleeting look. If the student does not make any eye contact, the teacher mirrors student head movement and eye gaze with the different objects so that the objects are in front of the student’s eyes. The teacher would reinforce the language of ‘They are different’.

Reaches for and makes physical contact with objects that are the same and different Repeat the above activity with a focus on encouraging the student to reach for and interact with both objects that are the same and both objects that are different and state ‘You are touching the ……. (name objects)’. Once the student grasps the objects reinforce them immediately by saying ‘You have the …… (name objects.) They are the same’. ‘You have the ……. (name objects). They are different’.

Statistics & Probability: Data S&P1b Students recognise there is a difference between the characteristics of two objects.


S&P1b

Data



Activities and Resources Items that are identical except for 1 characteristic: e.g. blue car/red car

Indicators Teacher Language • Makes a distinction between two objects

using eye gaze. • Makes a distinction between two objects

by reaching/ pointing. • Makes a distinction between two objects

by using augmentative communication. • WM Uses eye gaze and touch to select

between two offered paint colours or food choices.

Give an instruction ‘Look at the red….’. ‘Look at the blue…’. ‘Touch the red…...’. ‘Touch the blue….’. Make a Statement ‘You are looking at/touching the red/blue….’. ‘The cars are different. ‘This one is red’. ‘This one is blue’. Correction/prompt ‘Is that the red/blue…?’

Prior to beginning this activity, students need to have been exposed to the concepts of same and different (as taught above).



Makes a distinction between two objects using eye gaze For this activity, it is necessary to have two objects that are identical except for one characteristic e.g. colour. This could include toy cars, pegs, teddy bears etc.

Teacher would place the two objects in front of the student and instructs ‘SN, look at the red car’. Teacher would touch the red car whilst stating this. Teacher instructs ‘SN, look at the blue car’. Teacher would touch the blue car whilst stating this. Teacher states ‘The cars are different. This one is red (touching) this one is blue (touching). SN look at the red car. Look at the blue car’. This activity could be done using a variety of characteristics including colour, size, and shape. There should only be one characteristic different for the objects used in each teaching activity.

Makes a distinction between 2 objects by reaching / pointing Teacher would place the two objects in front of the student and instructs ‘SN, look at the red car’. Teacher would touch the red car whilst stating this. Teacher instructs ‘SN, look at the blue car’. Teacher would touch the blue car whilst stating this. Teacher states ‘The cars are different. This one is red (touching) this one is blue (touching). SN, touch the red car. Touch the blue car’. This activity could be done using a variety of characteristics including colour, size, and shape. There should only be one characteristic different for the objects used in each teaching activity.

Makes a distinction between two objects by using augmentative communication Following the teaching sequence above, this teaching activity should be implemented using a progressive sequence of real objects to photographs and pictorials representations.

Statistics & Probability: Data S&P2 Students sort objects into 2 or more groups.


S&P2

Data



Activities and Resources Tactile resources Straws and cotton balls Toys, cars and animals Red counters / blue counters Big blocks / little blocks Computers / IWB

Indicators Teacher Language • Sorts objects into two groups (e.g.

pegs and feathers).

• Sort objects into three groups.

• Sort objects into four or more groups.

• WM Sorts a pile of materials into groups of cotton balls, straws and blocks.

Give an instruction ‘Put the pegs in one group’. ‘Put the feathers in one group’. ‘Put the straws in one group, the cotton balls in another group and the blocks in another group’. ‘Put the straws in one group, the cotton balls in another group and the blocks in a different group’. Make a Statement ‘This is a peg’. “This is a feather’. ‘They are different’. ‘This is a group of pegs’. ‘This is a group of feathers’. ‘This is a straw’. ‘This is a cotton ball’. ‘This is a block’. ‘They are different’. ‘This is a group of straws, they are the same’. ‘This is a group of cotton balls, they are the same’. ‘This is a group of blocks, they are the same’. Correction / Prompt ‘How many groups do you have?’ Questioning ‘Are the objects in each group the same?’



Sorts objects into two groups For this activity, it is necessary to have a collection of objects e.g. feathers and pegs, that can be divided into two groups. This is done to assist students to easily sort objects into the correct group using the following sequence. Teachers are encouraged to use the teacher language above throughout these activities.

Teacher states ‘We are going to make two groups. This is a feather and this is a peg (showing the student each object). They are different. Put the pegs in one group and the feathers in a different group’. A visual prompt of two placemats etc. may be needed to encourage students to sort the objects into two groups. Once the groups have been completed teacher states ‘This is a group of feathers. They are all the same. This is a group of pegs. They are all the same’.

It is essential that the objects in each group are the same. For example all the feathers would be exactly the same including colour, size and shape, as would the pegs. The colour characteristic would be the same across both groups. This would mean that the students are sorting pegs and feathers i.e. not colours.

Statistics & Probability: Data D2 Students sort objects into two groups. cont.


Data S&P2 cont.




Sort objects into 3 groups For this activity it is necessary to have objects such as straws, cotton balls and blocks that can be divided into three groups. The object of the activity is to have the students sorts the objects into groups where the characteristics are the same. Repeat activity as above using three sets of objects. Teacher states. ‘We are going to make three groups. This is a straw, this is a cotton ball and this is a block (showing the student each object). They are different. Put the straws in one group, the cotton balls in another group and the blocks in a different group’. A visual prompt of three placemats may be needed to encourage students to sort the objects into three groups. Once the groups have been completed teacher states ‘This is a group of straws, they are the same. This is a group of cotton balls, they are the same. This is a group of blocks, they are the same’.

Sort objects into 4 or more groups. For this activity, it is necessary to have objects that can be divided into four groups. The object of the activity is to have the students sort the objects into groups where the characteristics are the same. Repeat activity as above using four sets of objects.

Statistics & Probability: Data S&P3 Students sort objects into two or more groups when there is a difference of one or

more characteristic. LEARNING EXPERIENCES AND OPPORTUNITIES

S&P3

Data

Strategies Attributing meaning Contingent responding Correcting errors Explicit teaching Guided practice Prompting Provide opportunities for choice Scaffolding Sensory stimulation Strategic pausing Take up time Touch cues Levels of Support Full physical assistance Partial physical assistance Modelled response Gesture/sign Verbal Independent


Indicators Teacher Language • Sorts objects with a difference of one

characteristic (e.g. red counters/blue counters, big blocks /little blocks).

• Sorts objects with a difference of more than one characteristic into two categories (e.g. various toy cars and various toy animals).

• WM Sorts a pile of materials into groups of cotton balls, straws and pegs.

Give an instruction ‘Put the red counters in one group’. Put the blue counters in one group’. ‘Put all the cars in a group’. Put all the pegs in a group’. ‘Put red counters in one group and white counters in another group’. ‘Look at the pegs’. ‘Sort them into two groups of cars and pegs’. Make a statement ‘We have some counters’. ‘This is a white counter’. ‘This is a red counter’. ‘They are different colours’. ‘We are going to sort them into two groups. A red group and a white group’. ‘Look at the cars’. ‘Some are red/blue’. ‘Some are different shapes’. ‘They are different but they are all cars’. ‘Some are wood/plastic’. ‘Some are different colours’. ‘They are different but they are all pegs’.



Students need to have independently achieved goal S&P2 before attempting this goal.

Sorts objects with a difference of one characteristic For this activity, use objects that are the same except for one characteristic e.g. colour. Teachers are encouraged to use the teacher language above throughout these activities. Teacher states ‘We have some counters. This is a white counter’. Teacher places a white counter on the table. Teacher states ‘This is a red counter’. Teacher places a red counter on the table. ‘They are different colours. We are going to sort them into two groups. A red group and a white group’. ‘Put red counters in one group and white counters in another group’.

Statistics & Probability: Data cont. S&P3 Students sort objects into two or more groups when there is a difference of one or

more characteristic. LEARNING EXPERIENCES AND OPPORTUNITIES

S&P3

Data cont.

Strategies Attributing meaning Contingent responding Correcting errors Explicit teaching Guided practice Prompting Provide opportunities for choice Scaffolding Sensory stimulation Strategic pausing Take up time Touch cues Levels of Support Full physical assistance Partial physical assistance Modelled response Gesture/sign Verbal Independent


Sorts objects with a difference of more than one characteristic into two categories (various toy cars and various toy animals) The aim of this activity is to develop students’ ability to recognise that while objects can have different characteristics they can still be the same. For example; cars that have a different colour and shape are still all cars.

For this activity, it is necessary to have objects that can be divided into two groups. The objects could be cars and pegs. The cars would have two characteristics that are different. For example; each car would be a different colour and shape. Likewise the pegs would have two different characteristics. For example; colour and size. The object of the activity is to have the student sort the objects into groups where the characteristics are the same, that is all cars and all pegs.

Teacher places a number of cars with more than one difference on the desk in front of the student. Teacher states ‘Look at the cars. Some are red/blue and some are different shapes. They are different but they are all cars’. Teacher states ‘Look at the pegs. Some are wood/plastic and some are different colours. They are different but they are all pegs. Sort them into groups of cars and pegs’.

Assessing Data


NUMERACY LEARNING CONTINUUM

The rate at which each individual student acquires Statistics and Probability 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 DES1.1 Students recognise there is a difference between the characteristics of two objects. 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) WMS1.5 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-‐3WM Uses concrete materials and/or pictorial representations to support conclusions and informal recordings. MAe-‐17SP Represents data and interprets data displays made from objects.

Life Skills 7-‐10 Outcome 2015 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-‐35SP Recognises data displayed in a range of formats. MALS-‐36SP Gathers, organises and displays data. MALS-‐37SP Interprets information and draws conclusions from data displays.

HSC Life Skills 11-‐12 Outcomes 2007 6.3 Reads and interprets a variety of graphs and tables.

DAT

A

S&P1a Students access/interact with objects that are the same and different.

S&P1b Students recognise there is a difference between the characteristics of two objects.

S&P2 Students sort objects into 2 or more groups.

S&P3 Students sort objects into two or more groups when there is a difference of one or more characteristic.

Statistics & Probability: Data S&P1a Students access/interact with objects that are the same and different.


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 objects that are the same and different

Reaches for and makes physical contact with objects that are the same and different

Comments

Statistics & Probability: Data Goal: S&P1b Students recognise there is a difference between the characteristics of two

objects. LEARNING EXPERIENCES AND OPPORTUNITIES





Makes a distinction between two objects using eye gaze

Makes a distinction between two objects by reaching/pointing

Makes a distinction between two objects by using augmentative communication

Comments

Statistics & Probability: Data Goal: S&P2 Students sort objects into 2 or more groups.






Sorts objects into two groups (e.g. pegs and feathers)

Sorts objects into three groups

Sorts objects into four or more groups

Comments

Statistics & Probability: Data Goal: S&P3 Students sort objects into two or more groups when there is a difference of one

or more characteristic. LEARNING EXPERIENCES AND OPPORTUNITIES





Sorts objects with a difference of one characteristic (e.g. red counters / blue counters, big blocks/little blocks)

Sorts objects with a difference of more than one characteristic into two categories (e.g. various toy cars and various toy animals)

Comments