Statutory assessment at KS1 And KS2 Using the P scales

2008 Guidance and exemplification on attainment in Mathematics at P4 to P8

Lancashire School Effectiveness Service Professional Support Team, Room A39, PO Box 61, County Hall, Preston, PR1 8RJ Tel No: (01772) 531555, Email: pst@ed.lancscc.gov.uk ©/lses/ast/2007

Acknowledgements We would like to thank the following for providing examples for us to use: Brockholes Wood Community Primary School 06008 01772 792302 St Matthew’s Church of England Primary School 06030 01772 794482 St Joseph’s Catholic Primary School 06028 01772 796112 Introduction From 2008 the reporting of P Scales has become statutory for pupils with a Special Educational Need who are working below level 1 of the National Curriculum. The statutory requirements are set out in the ‘Assessment and reporting arrangements’ booklets for KS1 and KS2 in 2008. The materials exemplified here are for pupils who are working at levels P4, P5, P6, P7 and P8 in mathematics. Many schools in Lancashire use PIVATS which break down P scales into smaller sections. PIVATS is a valuable tool to help with tracking and target setting. However for the purposes of reporting a PIVAT score should be converted into a P scale. Further information about PIVATS at www.lancashire.gov.uk/education/pivats/ The exemplification materials in this booklet have been provided by schools in Lancashire. They were collected from pupils working across Key stages 1 / 2. They have been moderated by a working party of schools, the Assessment Team and a Primary Strategy Consultant in mathematics. The booklet has been designed to use alongside the exemplification materials in QCA ‘Using the P scales’ (downloadable from the website). www.qca.org.uk What are P scales? • They are performance descriptors for pupils working towards level 1 of the NC • They are used for pupils aged 5 – 16 working towards level 1 • They provide a summative assessment for end of key stage reporting • They provide a framework for tracking pupil progress • They can be used to support schools with target setting ‘The P scales are not to be used to assess children below year 1 whatever their need or children with English as an additional language (EAL) at any age unless they have additional special educational needs’ ARA booklets 2008 KS1 & 2 It is important to remember that P scales are not applicable for recently arrived children or those new to English unless a SEN is likely to be the only reason for performance below the expected level. Pupils learning English as an additional language and working towards level 1 will be recorded as a ‘W’. Neither are they an appropriate assessment for children in the Reception year unless they have additional special educational needs.

Using the P scales In line with the National Curriculum P scales should be used as ‘best fit’ level indicators’ Evidence • Evidence should be collected over a period of time using a range of contexts. It could

include observational notes or photographs to support your judgements. • Remember one piece of work in itself is not enough evidence to assign a P scale. • There is no requirement to set up specific tasks or tests – assessments should be

manageable and make use of ongoing work. Additional information • pscacles@qca.org.uk • Guidance for using P scales – QCA ref:QCA/05/1538 www.qca.org.uk/303.html • Using the P scale DVD- QCA/051589 (This includes a guidance booklet and video presentations showing examples of pupils’ performance in English, maths and science). Available from the QCA orderline www.qca.org.uk/orderline Breakdown of P scales for statutory reporting

Key stage 1 Assessment and reporting arrangements p. 23 Key stage 2 Assessment and reporting arrangements p. 18

THE P SCALES 4 - 8

Using and Applying P SCALE 4 Pupils are aware of cause and effect in familiar mathematical activities. Pupils show awareness of changes in shape, position or quantity. They anticipate, follow and join in familiar activities when given a contextual clue. P SCALE 5 Pupils sort or match objects or pictures by recognising similarities. They make sets that have the same small number of objects in each. They solve simple problems practically. P SCALE 6 Pupils sort objects and materials according to given criterion .They copy simple patterns or sequences.

. P SCALE 7 Pupils complete a range of classification activities using given criterion They identify when an object is different and does not belong to a given familiar category. They respond appropriately to key vocabulary and questions. P SCALE 8 Pupils talk about, recognise and copy simple repeating patterns and sequences. Pupils use their developing mathematical understanding by counting up to ten to solve simple problems encountered in play, games or other work. Pupils make simple estimates.

Number P SCALE 4 Pupils show an awareness of number activities and counting. P SCALE 5 Pupils respond to and join in with familiar rhymes, stories, songs and games. Pupils can indicate ‘one’ or ‘two’. They demonstrate that they are aware of contrasting quantities. P SCALE 6 Pupils demonstrate their understanding of one-to-one correspondence in a range of contexts. Pupils join in rote counting up to five.They count reliably to three, make sets of up to three objects and use numbers to three in familiar activities and games. They demonstrate an understanding of the concept of ‘more’. They join in with new number rhymes, songs, stories and games. P SCALE 7 Pupils join in rote counting to ten. They can count at least five objects reliably. They recognise numerals from 1 to 5 and to understand that each represents a constant number or amount. Pupils demonstrate an understanding of ‘less’. In practical situations, they respond to ‘add one’ when working with a number of objects. P SCALE 8 Pupils join in with rote counting to beyond ten. They continue the rote count onwards from a given small number. Pupils recognise difference in quantity. They recognise numerals from one to nine and relate them to sets of objects. In practical situations they respond to ‘add one’, or ‘take one away’ when working with a number of objects. They use ordinal numbers (first, second or third) when describing the position of objects, people or events. Pupils estimate a small number (up to 10) and check by counting.

Shape, Space and Measures P SCALE 4 Pupils begin to search for objects that have gone out of sight, hearing or touch, demonstrating the beginning of object permanence. Pupils match big objects and small objects. They demonstrate interest in position and the relationship between objects. P SCALE 5 Pupils search intentionally for objects in their usual place. They find big and small objects on request. They compare the overall size of one object with that of another where there is a marked difference. They explore the position of objects. P SCALE 6 Pupils search for objects not found in their usual place demonstrating their understanding of object permanence. They compare the overall size of one object with that of another where the difference is not great. They manipulate three-dimensional shapes. They show understanding of words, signs and symbols that describe positions P SCALE 7 Pupils begin to respond to forwards and backwards. They pick out described shapes from a collection. They use familiar words in practical situations when they compare sizes and quantities. P SCALE 8 Pupils compare objects directly, focusing on one dimension such as length or height where the difference is marked and can indicate the long one or the tall one. They show awareness of time, through some familiarity with names of the days of the week and significant times in their day, such as meal times, bed times. They begin to use mathematical vocabulary such as straight, circle, larger to describe the shape and size of solids and flat shapes. They describe shapes in simple models, pictures and patterns.

Using and Applying CHILD A Mathematics – Using and Applying P Scale: 4

Key Stage 1

Context – resources / support A was involved in a shopping activity with the teacher. Working in a role play situation A was encouraged to exchange a coin for an item in the shop. In a further activity A was able to recall an object which had been placed out of sight Level descriptor P 4 ♦ Pupils are aware of cause and effect in

familiar mathematical activities ♦ Pupils show awareness of changes in

shape, position or quantity ♦ They anticipate, follow and join in familiar

activities when given a contextual clue

Comments A was able to choose coins from tray and exchange for items 3 times. He understood that money is needed to buy things and discussed his own experiences of shopping. 5 objects were placed on a tray. 1 was removed while A looked away. A consistently recognised the missing object very quickly: 3 out of 3 times.

Next steps

• Begin to buy items using correct coins e.g. 3 x 1p coins for an item.

• Increase the number of objects used on the tray.

CHILD B Mathematics – Using and Applying P Scale: 4

Key Stage 1

Context – resources / support B was beginning to enjoy participating in songs and rhymes. He was anticipating what comes next in a range of activities. Level descriptor P 4 ♦ Pupils are aware of cause and effect in

familiar mathematical activities ♦ Pupils show awareness of changes in

shape, position or quantity ♦ They anticipate, follow and join in

familiar activities when given a contextual clue

Comments A group of children were singing ‘head, shoulders, knees and toes’. B joined in with the actions, and when prompted joined in with words. When matching cakes to plates B consistently put 1 cookie on each plate- quickly and confidently.

Next steps

• Explore a variety of action rhymes in small groups. • Continue to develop the range of familiar activities that B can join in with.

CHILD C Mathematics – Using and Applying P Scale: 5

Key Stage 1

Context – resources / support Working with the teacher over a range of activities and using different equipment C was able to demonstrate her understanding. Level descriptor P 5 ♦ Pupils match objects or pictures by

recognising similarities. ♦ They make sets that have the same

small number of objects in each ♦ They solve simple problems practically

Comments C was given one of each of 4 pairs of wellies. She was able to find the matching pair.

Following a demonstrated task C was encouraged to follow verbal instructions and asked to place 2 bears on each of 6 plates.

C was able to complete a table setting placing a knife and fork by each plate.

Next steps Give opportunities for a greater range of problem solving activities from everyday classroom routines e.g. milk and fruit.

CHILD D Mathematics – Using and Applying P Scale: 6

Key Stage 1

Context – resources / support D was choosing some of the instruments from the percussion box and experimenting with the sounds. The teacher went to join her to see if she could hear and copy a pattern. D also visits the bead table as part of an independent choice activity. Level descriptor P 6 ♦ Pupils sort objects and materials according

to given criteria ♦ They copy simple patterns or

sequences,

Comments She successfully made repeating patterns of beads on string using 2 or 3 colours and was able to talk about and describe her pattern. Working with the teacher and a tambourine. D was at first a little hesitant but after listening and trying several different patterns she was able to reproduce the ‘tap-tap-shake-shake’ pattern modelled by the teacher.

Next steps • Develop a greater awareness of pattern through PE activities and other media. • Try to create more complex patterns.

CHILD E Mathematics – Using and Applying P Scale: 7

Key Stage 1

Context – resources / support E was observed across a range of activities over a short period of time. He was able to respond to questions about why he was doing something and understood the appropriate vocabulary involved. Level descriptor P 7 ♦ Pupils complete a range of

classification activities using given criterion

♦ They identify when an object is different

and does not belong to a given familiar category

♦ They respond appropriately to key

vocabulary and questions,

Comments E was sorting toys into different sets of vehicles, and removed the teddy saying it ‘should be in the teddy box.’ Successfully counted up to ten objects when asked how many buses there were.

E sorted a pile of coins by colour. Completed this task easily and responded to the question ‘how many 1p coins?’ by counting 10 coins back into the tub.

Next steps

• Further coin recognition and counting beyond 10.

CHILD F Mathematics – Using and Applying P Scale: 8

Key Stage 1

Context – resources / support The first activity involves a simple dice game. The second activity was about making an estimate. Both were supported, guided activities. Level descriptor P8 ♦ Pupils talk about, recognise and copy

simple repeating patterns and sequences ♦ Pupils use their developing

mathematical understanding by counting up to ten to solve simple problems encountered in play, games or other work.

♦ They make simple estimates,

Comments Played a simple dice and shape game and matched shapes to the board, describing different positions and turns. F found the task difficult but responded to prompts.

F made a good estimate that 10 vehicles would fit in a plastic cup (correct number was 8).

Next steps • To recognise and describe position e.g. in queues, using the roamer. • To estimate larger quantities and to check his estimate by counting.

Number CHILD G Mathematics – Number P Scale: 6

Key Stage 1

Context – resources / support G has a statement for special needs. He has a global delay and has been on a statement since nursery. G remained reasonably focused for the length of the assessment. This evidence was gathered over a short period of time on several number based activities. Level descriptor P 6 ♦ Pupils demonstrate their understanding of

one-to-one correspondence in a range of contexts

♦ Pupils join in rote counting up to 5. ♦ They count reliably to three, make sets

of up to three objects and use numbers to three in familiar activities and games,

♦ They demonstrate an understanding of

the concept of more, ♦ They join in with new number rhymes,

songs, stories and games.

Comments G could rote count easily to 10. He struggled to count bricks in a tower managed up to 3. He recognized the numerals 1-5 on cards but couldn’t put them in order. He recognized the value of the number card in the bowl but couldn’t consistently put that number of objects into the bowl. He could understand the language of ‘add to’ and ‘take away’. With objects and understood more and less than. When objects placed in a line understood which was first, then second then third. But was less successful if he was asked out of order.

Next steps • Count reliably objects to five. • Collect correct number of objects up to 5.

CHILD H Mathematics – Number P Scale: 6

Key Stage 1

Context – resources / support H constantly talked the whole way through the activity, both regarding the activities and other things that interested her. This evidence was gathered over a short period of time on several number based activities. Level descriptor P 6 ♦ Pupils demonstrate their understanding of

one-to-one correspondence in a range of contexts

♦ Pupils join in rote counting up to 5. ♦ They count reliably to three, make sets

of up to three objects and use numbers to three in familiar activities and games,

♦ They demonstrate an understanding of

the concept of more, ♦ They join in with new number rhymes,

songs, stories and games.

Comments H could rote count confidently up to 20 but though she recognized the number cards to 5, she could not put them in order without support. Was able to recognize the number in the dish and was fine at put matching objects into the bowl if a small enough number but struggled to count larger numbers of objects. Understood with objects to add one more and take away one. In a line of objects could not recognize ordinal numbers to differentiate between first and second.

Next steps

• Put the numbers 1 to 5 in order. • Collect correct number of objects up to 5.

CHILD I Mathematics – Number P Scale: 7

Key Stage 1

Context – resources / support I concentrated for short periods of time. This evidence was gathered over a short period of time on several number based activities. Level descriptor P 7 ♦ Pupils join in rote counting to ten ♦ They can count at least five objects

reliably ♦ They recognise numerals from 1 to 5

and to understand that each represents a constant number or amount

♦ Pupils demonstrate an understanding of

less ♦ In practical situations, they respond to add

one to a number of objects,

Comments I was able to count by rote to 10. She can count a given number of cubes in a tower. And could order number cards to 5. I understood ‘one more’ and ‘one less’ when referring taking amounts from groups of objects but couldn’t when it was presented to her as a number story such as how many cakes would be left if one was sold. Still developing the ability to count accurately in an array. When given a number in a plate couldn’t put that number of objects into the plate. Understood what objects came last and first in a line. Could estimate reasonably accurately the number of objects in a group and then received support to count them accurately.

Next steps • To consistently recognise numerals from 6 to 9 and match to the correct number of

objects. • To understand questions related to one more and one less when in the context of

number stories.

CHILD J Mathematics – Number P Scale: 8

Key Stage 1

Context – resources / support J was very well focused throughout the activities. Level descriptor P8 ♦ Pupils join in with rote counting to

beyond ten, ♦ They continue the rote count onwards

from a given small number ♦ Pupils recognise difference in quantity, ♦ They recognise numerals from one to

nine and relate them to sets of objects,

♦ In practical situations they respond to add one more to, or take one away from a number of objects,

♦ They use ordinal numbers (first, second

or third) when describing the position of objects, people or events

♦ Pupils estimate a small number (up to

10) and check by counting

Comments J could count bricks in a tower could count by rote numbers to ten and beyond. Could order number cards 1-5 and place the correct number of objects in a plate to match the number card. Understood concept of ‘one more’ and ‘one less’ could compare numbers of objects. Could work out how many cakes or sausages would be left if one was sold. Recognized all ordinal numbers 1-5 of objects in a line. Developing ability to physically add groups of numbers together and understand that as addition.

Next steps • To move to adding one more and taking one away using objects. • Physically grouping objects for addition.

Shape, space and measures CHILD K Mathematics – shape, space and measures P Scale: 5

Key Stage 1

Context – resources / support Following a range of activities over a period of time this assessment was made on K. K was working with the TA using compare bears – he was asked to make some large ones grouped together and some small ones. He was then given a group of different sizes of compare bears to choose which is biggest/smallest. When the compare bears were placed side by side he was asked to indicate the tall one, small one. Level descriptor P 5 ♦ Pupils search intentionally for objects in

their usual place,

♦ They find big and small objects on request,

♦ They compare the overall size of one

object with that of another where there is a marked difference

♦ They explore the position of objects

Comments Two groups of bears were on the table – a group of large bears and a group of small bears. K was asked to match the bear with the correct group. This was successfully completed.

K was then asked to sort a group of different sized bears – he sorted the bears successfully. When given two bears of different sizes stood side by side K was able to indicate which one is small, then which one is tall.

Next steps

• to compare the overall size of one object with that of another where the difference is not great,

CHILD L Mathematics – shape, space and measures P Scale: 6

Key Stage 1

Context – resources / support L was playing in the construction area with a variety of 3D blocks. He was very proud of his stable. Level descriptor P 6 ♦ Pupils search for objects not found in their

usual place demonstrating their understanding of object permanence,

♦ They compare the overall size of one

object with that of another where the difference is not great,

♦ They manipulate three-dimensional

shapes, ♦ They show understanding of words, signs

and symbols that describe positions

Comments Using a range of different 3D blocks L made a stable for the toy horse he had brought from the continuous provision.

Next steps

• To use his models to increase his understanding of words that describe position.

CHILD M Mathematics – shape, space and measures P Scale: 6

Key Stage 1

Context – resources / support A group of children were playing with a box of objects – observations of their play were made by the TA. Later using the same box direct instructions were given to place objects in, on, under, or inside and to move objects forwards and backwards Level descriptor P 6 ♦ Pupils search for objects not found in their

usual place demonstrating their understanding of object permanence,

♦ They compare the overall size of one

object with that of another where the difference is not great,

♦ They manipulate three-dimensional

shapes, ♦ They show understanding of words,

signs and symbols that describe positions

Comments M made boxes for the animals, she put chickens together inside a box and placed the calves with a cow and a horse. She was able to follow instructions to place the dinosaurs in, on and under when different buildings etc. She was able to moves objects up and down.

Next steps • begin to respond to forwards and backwards

CHILD N Mathematics – shape, space and measures P Scale: 7

Key Stage 1

Context – resources / support After looking at and talking about some shapes the pupils went then go on a shape hunt in the classroom.. Level descriptor P 7 ♦ Pupils begin to respond to forwards and

backwards, ♦ They pick out described shapes from a

collection ♦ They use familiar words in practical situations when they compare sizes and quantities,

Comments N could identify shapes (circle, triangle, rectangle) around the classroom and made a collection.

Next steps

• To begin to use mathematical vocabulary such as straight, circle, larger to describe the shape and size of solids and flat shapes,

CHILD O Mathematics – shape, space and measures P Scale: 8

Key Stage 1

Context – resources / support Working with the TA pupils were being questioned about the days of the week. What day is it today? What day was it yesterday/is it tomorrow? Can they know the days of the week? Can they sequence them? Pupils were shown pictures of some daily events and asked them to sequence up to four that they were familiar with. Level descriptor P8 ♦ Pupils compare objects directly, focusing

on one dimension such as length or height where the difference is marked and can indicate the long one or the tall one,

♦ They show awareness of time, through

some familiarity with names of the days of the week and significant times in their day, such as meal times, bed times,

♦ They begin to use mathematical vocabulary such as straight, circle, larger to describe the shape and size of solids and flat shapes,

♦ They describe shapes in simple models,

pictures and patterns.

Comments When asked what day it was the O replied Monday (it was Tuesday) When asked ‘What is the first day of the week?” Thursday was the answer given. The pupil could name all the days of the week but not in any sequence.

When presented with pictures from a visual timetable the pupil could sequence successfully the events of the day in the correct sequence.

Next steps

• To begin to sequence days of the week and build up appropriate time vocabulary.

Appendix C –PIVATS Conversion Table

PIVATS PIVATS PIVATS PIVATS P Scale / National curriculum Level

level PSD level Equivalent point score

Suggested National Curriculum point score

Benchmark Cohort

N/A P1(i)e 0.15 0 1 N/A P1(i)d 0.3 0 1 N/A P1(i)c 0.45 0 1 N/A P1(i)b 0.6 0 1 P1(i) P1(i)a 0.75 0 1 P1(i) P1(ii)e PSD1e 0.9 0 1 P1(i) P1(ii)d PSD1d 1.05 0 1 P1(i) P1(ii)c PSD1c 1.2 0 1 P1(i) P1(ii)b PSD1b 1.35 0 1 P1(ii) P1(ii)a PSD1a 1.5 0 1 P1(ii) P2(i)e 1.65 0 1 P1(ii) P2(i)d 1.8 0 1 P1(ii) P2(i)c 1.95 0 1 P1(ii) P2(i)b 2.1 0 1 P2(i) P2(i)a 2.25 0 1 P2(i) P2(ii)e PSD2e 2.4 0 1 P2(i) P2(ii)d PSD2d 2.55 0 1 P2(i) P2(ii)c PSD2c 2.7 0 1 P2(i) P2(ii)b PSD2b 2.85 0 1 P2(ii) P2(ii)a PSD2a 3 0 1 P2(ii) P3(i)e 3.2 0 1 P2(ii) P3(i)d 3.4 0 1 P2(ii) P3(i)c 3.6 0 1 P2(ii) P3(i)b 3.8 0 1 P3(i) P3(i)a 4 0 1 P3(i) P3(ii)e PSD3e 4.2 0 1 P3(i) P3(ii)d PSD3d 4.4 0 1 P3(i) P3(ii)c PSD3c 4.6 0 1 P3(i) P3(ii)b PSD3b 4.8 0 1 P3(ii) P3(ii)a PSD3a 5 1 1 P3(ii) P4e 5.2 1.1 1 P3(ii) P4d 5.4 1.2 1 P3(ii) P4c 5.6 1.3 1 P3(ii) P4b 5.8 1.4 1

P4 P4a 6 1.5 1 P4 P5e PSD5e 6.4 1.6 2 P4 P5d PSD5d 6.8 1.7 2 P4 P5c PSD5c 7.2 1.8 2 P4 P5b PSD5b 7.6 1.9 2 P5 P5a PSD5a 8 2 2 P5 P6e PSD6e 8.4 2.1 2 P5 P6d PSD6d 8.8 2.2 2 P5 P6c PSD6c 9.2 2.3 2 P5 P6b PSD6b 9.6 2.4 2 P6 P6a PSD6a 10 2.5 2

P6 P7e PSD7e 11 2.6 2 P6 P7d PSD7d 12 2.7 2 P6 P7c PSD7c 13 2.8 2 P6 P7b PSD7b 14 2.9 2 P7 P7a PSD7a 15 3 2 P7 P8e PSD8e 16 3.4 3 P7 P8d PSD8d 17 3.8 3 P7 P8c PSD8c 18 4.2 3 P7 P8b PSD8b 19 4.5 3 P8 P8a PSD8a 20 5 3 P8 1Ce PSD9e 21 5.4 3 P8 1Cd PSD9d 22 5.8 3 P8 1Cc PSD9c 23 6.2 3 P8 1Cb PSD9b 24 6.6 3 1C 1Ca PSD9a 25 7 3 1C 1Ba PSD10e 26 7.4 3 1C 1Bd PSD10d 27 7.8 3 1C 1Bb PSD10c 28 8.2 3 1C 1Bc PSD10b 29 8.6 3 1B 1Ba PSD10a 30 9 3 1B 1Ae PSD11e 31 9.4 4 1B 1Ad PSD11d 32 9.8 4 1B 1Ac PSD11c 33 10.2 4 1B 1Ab PSD11b 34 10.6 4 1A 1Aa PSD11a 35 11 4 1A 2Ce PSD12e 36.5 11.4 4 1A 2Cd PSD12d 38 11.8 4 1A 2Cc PSD12c 39.5 12.2 4 1A 2Cb PSD12b 41 12.6 4 2C 2Ca PSD12a 42.5 13 4 2C 2Be PSD13e 44 13.4 5 2C 2Bd PSD13d 45.5 13.8 5 2C 2Bc PSD13c 47 14.2 5 2C 2Bb PSD13b 48.5 14.6 5 2B 2Ba PSD13a 50 15 5 2B 2Ae PSD14e 52 15.4 5 2B 2Ad PSD14d 54 15.8 5 2B 2Ac PSD14c 56 16.2 5 2B 2Ab PSD14b 58 16.6 5 2A 2Aa PSD14a 60 17 5 2A 3e PSD15e 62 19 6 2A 3d PSD15d 64 20 6 2A 3c PSD15c 66 21 6 2A 3b PSD15b 68 22 6 3 3a PSD15a 70 23 6 3 4e PSD16e 72 25 6 3 4d PSD16d 74 26 6 3 4c PSD16c 76 27 6 3 4b PSD16b 78 28 6 4 4a PSD16a 80 29 6