DE - Mathematics, P scales
Mathematics can provide pupils with powerful ways of exploring, investigating and understanding the world. The potential to apply the skills of making comparisons, identifying differences, investigating relationships and establishing connections reflects the importance of the subject across the curriculum during the school years. Mathematics is vital in everyday life as it encourages logical reasoning and the ability to think in abstract ways. At the earliest stages of development, where thinking centres around concrete situations and events, pupils strive to make sense of experiences and sensations that involve changes in pattern, quantity, space and time. Such experiences help them approach problem situations flexibly, to move from random to trial and improvement responses, and on to anticipate and predict. Increasingly, pupils will plan and reflect and come to recognise and evaluate alternative solutions. In this way, mathematical skills and understanding build on the earliest perceptual and cognitive learning.
The Ingot's Mathematics P scales provide learners with the opportunity to:
• build on their awareness of events and actions to recognise changes in pattern, quantity and space in their immediate environment and in the wider world
• use their developing awareness to anticipate and predict changes
• use their awareness and developing understanding of pattern, space, shape and number, to develop problem-solving skills that contribute to making choices, taking decisions and gaining control over their immediate environment
• extend mathematical skills, experiences and understanding which allows them to visualise, compare and estimate
For some pupils this will be achieved in abstract as well as concrete contexts
• begin to think about the strategies they use and explain them to others
• develop a powerful set of thinking tools to help them increase their knowledge and understanding of the world and, during the school years, to learn effectively in different subjects across the curriculum.
In response to these opportunities, pupils can make progress in mathematics by:
• increasing the breadth of their mathematical experience
• moving from an awareness of mathematical properties through using such information to anticipate and predict and then actively solve problems
• developing the ability to form mental representations of increasingly complex and detailed mathematical information
• communicating their understanding to others with increasing clarity
• using mathematical information to make choices and decisions in an increasing range of contexts.
P4 – Mathematics, Number – Learning outcomes and assessment criteria
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Learning Outcome The learner will |
Assessment Criteria The learner can |
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1. Be aware of number activities and counting |
1.1 participate in number activities 1.2 work with single objects 1.3 count objects 1.4 follow a simple counting sequence 1.5 assist with a one-to-one matching activity 1.6 join in the actions to number rhymes |
P4 Pupils show an awareness of number activities and counting, for example, copying some actions during number rhymes, songs and number games; following a sequence of pictures or numbers as indicated by a known person during number rhymes and songs.
P5 – Mathematics, Number – Learning outcomes and assessment criteria
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Learning Outcome The learner will |
Assessment Criteria The learner can |
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1. Participate in familiar number rhymes, stories, songs and games |
1.1 count when playing with numbers in any order 1.2 participate in simple games 1.3 participate in familiar number rhymes 1.4 participate in familiar number stories and songs |
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2. Indicate a knowledge of 1 or 2 |
2.1 indicate 1 object 2.2 indicate 2 objects 2.3 match single objects 2.4 match equal sets of objects |
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3. Show awareness of contrasting quantities |
3.1 make a group of 1 item 3.2 make a group of lots of items 3.3 use the term 'one' appropriately 3.4 use the term 'lots' appropriately 3.5 demonstrate awareness of contrasting quantities |
P5 Pupils respond to and join in with familiar number rhymes, stories, songs and games, for example, using a series of actions during the singing of a familiar song; joining in by saying, signing or indicating at least one of the numbers in a familiar number rhyme. Pupils can indicate one or two, for example, by using eye pointing, blinks, gestures or any other means to indicate one or two, as required. They demonstrate that they are aware of contrasting quantities, for example, ‘one’ and ‘lots’ by making groups of one or lots of food items on plates.
P6 – Mathematics, Number – Learning outcomes and assessment criteria
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Learning Outcome The learner will |
Assessment Criteria The learner can |
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1. Understand one-to-one correspondence |
1.1 demonstrate an understanding of one-to-one correspondence 1.2 give an object to a person 1.3 match objects |
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2. Participate in counting up to 5 |
2.1 join in counting to 5 2.2 match numerals to 5 2.3 match objects from a choice of 5 2.4 participate in counting activities to 5 |
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3. Count and work reliably to 3 |
3.1 count reliably to 3 3.2 make sets of up to 3 objects 3.3 participate in familiar activities using numbers to 3 3.4 select an object from a choice of 3 |
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4. Understand the concept 'more' |
4.1 demonstrate an understanding of the concept 'more' |
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5. Participate in new number rhymes, songs, stories and games |
5.1 use counting in play 5.2 join in known number rhymes 5.3 join in new number rhymes |
P6 Pupils demonstrate an understanding of one-to-one correspondence in a range of contexts, for example: matching objects such as cups to saucers, straws to drink cartons. Pupils join in rote counting up to five, for example, saying or signing number names to 5 in counting activities. They count reliably to three, make sets of up to three objects and use numbers to three in familiar activities and games, for example, touching one, two, three items as an adult counts, counting toys or pictures, counting out sets of three, e.g. knife, fork and spoon. They demonstrate an understanding the concept of ‘more’, for example, indicating that more cups, counters, food items are required. They join in with new number rhymes, songs, stories and games.
P7 – Mathematics, Number – Learning outcomes and assessment criteria
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Learning Outcome The learner will |
Assessment Criteria The learner can |
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1. Participate in counting to 10 |
1.1 join in counting to 10 1.2 participate in counting rhymes or games to 10 |
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2. Count at least 5 objects reliably |
2.1 count to 5 independently 2.2 put out objects to 5 2.3 put the correct number of objects (1-5) into containers marked with the numeral |
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3. Recognise numerals from 1 to 5 |
3.1 name numerals from 1 to 5 3.2 sequence numerals from 1 to 5 3.3 match quantities to numerals 1 to 5 |
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4. Understand the concept of less |
4.1 demonstrate an understanding of 'less' 4.2 demonstrate an understanding of 'the least' |
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5. In practical situations, respond appropriately to 'add 1' to a number of objects |
5.1 'add 1' in practical situations 5.2 count how many as a result of adding |
P7 Pupils join in rote counting to 10, for example, saying or signing number names to 10 in counting activities. They can count at least 5 objects reliably, for example, candles on a cake, bricks in a tower. They recognise numerals from 1 to 5 and understand that each represents a constant number or amount, for example, putting correct number of objects (1 to 5) into containers marked with the numeral; collecting the correct number of items up to 5. Pupils demonstrate an understanding of ‘less’, for example, indicating which bottle has less water in it. In practical situations they respond to ‘add one’ to a number of objects, for example, responding to requests such as add one pencil to the pencils in the pot, add one sweet to the dish.
P8 – Mathematics, Number – Learning outcomes and assessment criteria
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Learning Outcome The learner will |
Assessment Criteria The learner can |
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1. Participate in counting to beyond 10 |
1.1 join in counting beyond 10 1.2 count to 10 consistently |
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2. Continue to count onwards from a given small number |
2.1 continue to count from a given small number |
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3. Recognise differences in quantity |
3.1 indicate which contains “more” 3.2 indicate which contains “fewer” 3.3 indicate which is “smaller” 3.4 indicate which is “larger” 3.5 arrange groups of objects from smallest to largest |
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4. Recognise numerals from 1 to 9 |
4.1 match numerals from 1 to 9 4.2 count out quantities 1 to 9 4.3 put the correct number of objects (1-9) into containers marked with the numeral |
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5. In practical situations 'add 1' and 'take away 1' |
5.1 'add 1' and count how many 5.2 'take away 1' and count how many 5.3 find '1 less' 5.4 find '1 more' |
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6. Use ordinal numbers |
6.1 use the term “first” appropriately 6.2 use the term “last” appropriately 6.3 use the term “second” appropriately 6.4 use the term “third” appropriately |
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7. Estimate a small number (up to 10) and check by counting |
7.1 estimate the number of objects with some accuracy 7.2 check my estimates by counting |
P8 Pupils join in with rote counting to beyond 10, for example, they say or sign number names in counting activities. They continue to rote count onwards from a given small number, for example, continuing the rote count onwards in a game using dice and moving counters up to 10; continuing to say, sign or indicate the count aloud when adult begins counting the first two numbers. Pupils recognise differences in quantity, for example, in comparing given sets of objects and saying which has more or less, which is the bigger group or smaller group. They recognise numerals from 1 to 9 and relate them to sets of objects, for example, labelling sets of objects with correct numerals. In practical situations they respond to ‘add one’ to or ‘take one away’ from a number of objects, for example, adding one more to three objects in a box and say, sign or indicate how many are now in the box; at a cake sale saying, signing or indicating how many cakes are left when one is sold. They use ordinal numbers (first, second, third) when describing the position of objects, people or events, for example, indicating who is first in a queue or line; who is first, second and third in a race or competition. Pupils estimate a small number (up to 10) and check by counting, for example, suggesting numbers that can be checked by counting, guessing then counting the number of: pupils in a group; adults in the room; cups needed at break time.
P4 – Mathematics, Shape, Space and Measures – Learning outcomes and assessment criteria
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Learning outcome The learner will |
Assessment criteria The learner can |
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1. Search for objects that have gone out of sight, hearing or touch |
1.1 search for hidden objects 1.2 know when something has been removed |
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2. Match big objects and small objects |
2.1 match objects by their size 2.2 make a group of large objects 2.3 make a group of small objects |
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3. Demonstrate an interest in position and the relationship between objects |
3.1 use shapes 3.2 use construction materials 3.3 dismantle an object 3.4 demonstrate an interest in position 3.5 demonstrate an interest in the relationship between objects |
P4 Pupils search for objects that have gone out of sight, hearing or touch, demonstrating the beginning of object permanence, for example, searching for an object or sound when it is removed. Pupils match big objects and small objects, for example, finding a big football to place in a net with other big footballs, matching a small model car with a similar sized model car. They demonstrate interest in position and the relationship between objects, for example, stacking or joining objects or using construction materials.
P5 – Mathematics, Shape, Space and Measures – Learning outcomes and assessment criteria
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Learning outcome The learner will |
Assessment criteria The learner can |
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1. Search intentionally for objects in their usual place |
1.1 locate personal items when in their usual place 1.2 locate class equipment when in its usual place 1.3 search for specific objects |
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2. Find big and small items on request |
2.1 locate big items on request 2.2 locate small items on request |
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3. Compare the overall size of objects |
3.1 identify the larger shape, where there is a marked difference 3.2 identify the smaller shape, where there is a marked difference |
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4. Explore the position of objects |
4.1 put the equipment away in the correct place 4.2 explore the position of objects |
P5 Pupils search intentionally for objects in their usual place, for example, going to the mathematics shelf for the box of shapes. They find big and small objects on request, for example, from a choice of two objects, identifying the ‘big’ and ‘small’. They compare the overall size of one object with that of another where there is a marked difference, for example, they indicate which of two shoes is the bigger, compare objects – big boxes and small boxes. They explore the position of objects, for example, placing objects in and out of containers, placing objects inside and outside a hoop, fitting as many objects as possible into a box.
P6 – Mathematics, Shape, Space and Measures – Learning outcomes and assessment criteria
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Learning outcome The learner will |
Assessment criteria The learner can |
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1. Search for objects not found in their usual place |
1.1 search for hidden objects 1.2 search for an item not in its usual place |
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2. Compare objects by size |
2.1 order objects by size 2.2 compare the size of an object with that of another where the difference is not great 2.3 order objects according to length |
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3. Manipulate three-dimensional shapes |
3.1 have experienced various 3D shapes 3.2 use 3D shapes in different contexts |
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4. Understand words, signs and symbols that describe positions |
4.1 use words that describe position 4.2 use signs that describe positions 4.3 use symbols that describe positions |
P6 Pupils search for objects not found in their usual place demonstrating their understanding of object permanence, for example, looking for cups when they are not in their usual cupboard. They compare the overall size of one object with that of another where the difference is not great, for example, identifying the bigger of two Russian dolls or nesting cubes. They manipulate three-dimensional shapes, for example, putting shapes into a shape sorter, using 3D objects to build and manipulate in role-play, rolling a tube in a race with a partner. They show understanding of words, signs and symbols that describe positions, for example, responding to a request to put an object in, on, under or inside another object.
P7 – Mathematics, Shape, Space and Measures – Learning outcomes and assessment criteria
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Learning outcome The learner will |
Assessment criteria The learner can |
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1. Respond appropriately to forwards and backwards |
1.1 demonstrate an understanding of a forward movement 1.2 demonstrate an understanding of a backward movement 1.3 describe the directional movement of an object |
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2. Pick out described shapes from a collection |
2.1 pick out a specific shape from a collection 2.2 locate a shape from its description 2.3 group shapes according to their description 2.4 match geometric shapes with pictures of shape |
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3. Use familiar words in practical situations when comparing size and quantities |
3.1 use correct vocabulary when comparing size 3.2 use correct vocabulary when comparing quantities 3.3 use appropriate terms in practical situations |
P7 Pupils respond to ‘forwards’ and ‘backwards’, for example, moving forwards and backwards on request, recognising when a vehicle is moving forwards or backwards, moving a counter forwards or backwards on a board game. They pick out described shapes from a collection, for example, picking out all the round shapes in the classroom, finding shapes with straight edges, fitting shapes into matching holes. They use familiar words in practical situations when they compare sizes and quantities, for example, using the words ‘heavy’ and ‘light’, ’more’ and ‘ less’, ’enough’ or ‘not enough’ to compare objects or quantities.
P8 – Mathematics, Shape, Space and Measures – Learning outcomes and assessment criteria
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Learning outcome The learner will |
Assessment criteria The learner can |
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1. Compare objects directly, focusing on one dimension |
1.1 compare objects or items using their lengths
1.2 compare objects or items using their widths
1.3 compare objects or items using their heights |
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2. Show awareness of time |
2.1 name the days of the week 2.2 correctly sequence the days of the week 2.3 order events in my day on a daily timetable 2.4 know what time specific events occur during the day |
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3. Respond to mathematical vocabulary |
3.1 locate objects based on different attributes 3.2 locate an object with 2 given attributes 3.3 sort 3D objects according to shape |
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4. Describe shapes in simple models, pictures and patterns |
4.1 name various shapes 4.2 describe simple shapes 4.3 use shapes to create a picture or pattern 4.4 identify shapes |
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’, for example, comparing two plants, placed side by side and indicating the tall one or comparing two zips and indicating the long 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, for example, ordering events in their day on a visual daily timetable, understanding and using names of days of the week, ‘no school on Saturday or Sunday, swimming on Wednesday’. They respond to mathematical vocabulary such as ‘straight’, ‘circle’, ‘larger’ to describe the shape and size of solids and flat shapes, for example, when shopping, pupils find boxes with straight edges to pack into the carrier bag; identify the larger circle when stacking two cans. They describe shapes in simple models, pictures and patterns, for example, stamping shapes in sand and describing them, using a set of flat shapes to make pictures or patterns, naming some of the shapes used, identifying specific shapes from pictures, simple models or patterns.
P4 – Mathematics, Using and Applying – Learning outcomes and assessment criteria
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Learning outcome The learner will |
Assessment criteria The learner can |
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1. Be aware of cause and effect in familiar mathematical activities |
1.1 demonstrate awareness of cause and effect in familiar mathematical activities 1.2 repeat an action to cause an effect |
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2. Be aware of changes in shape, position or quantity |
2.1 group objects according to shape 2.2 use materials to create different shapes 2.3 locate objects and familiar items that have been moved or hidden from view 2.4 identify which contains the most 2.5 identify which contains the least |
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3. Anticipate, follow and join in familiar activities when given a contextual clue |
3.1 anticipate the next action or chorus in a familiar song or rhyme 3.2 relate familiar items with other items 3.3 recognise simple patterns |
P4 Pupils are aware of cause and effects in familiar mathematical activities, for example, knowing that in a role-play shop a coin can be exchanged for an item; hitting a mathematical shape on a concept keyboard to make it appear on the screen. Pupils show awareness of changes in shape, position or quantity, for example, grouping objects that have similar key features such as shape; creating very simple sequences of light or sound using switched equipment; recalling an object which has been placed out of sight. They anticipate, follow and join in familiar activities when given a contextual clue, for example, anticipating the next chorus or action in songs and rhymes; matching cakes to plates.
P5 – Mathematics, Using and Applying – Learning outcomes and assessment criteria
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Learning outcome The learner will |
Assessment criteria The learner can |
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1. Recognise similarities |
1.1 collect objects from a given criterion 1.2 find matching pairs from a collection of pictures 1.3 match a picture to an object 1.4 match colours 1.5 sort small items from big items |
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2. Group a small number of objects |
2.1 make a small set of objects 2.2 sort similar objects into small groups |
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3. Solve simple problems practically |
3.1 select an appropriate container for items of different sizes 3.2 select an appropriate tool for a task 3.2 indicate a knowledge of relationships between familiar objects 3.4 solve simple problems practically |
P5 Pupils sort or match objects or pictures by recognising similarities, for example, matching shoes or socks by placing next to one placed by an adult; find matching pairs from a collection of pictures; collecting objects given one criterion, e.g. blue or big. They make sets that have the same small number of objects in each, for example, distributing sweets into containers so that there are one or two in each. They solve simple problems practically, for example, selecting appropriate containers for items of different sizes; checking there is a knife for every fork.
P6 – Mathematics, Using and Applying – Learning outcomes and assessment criteria
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Learning outcome The learner will |
Assessment criteria The learner can |
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1. Sort objects and materials |
1.1 identify a requested colour 1.2 identify a requested object 1.3 match pairs of objects 1.4 sort objects by my own criteria 1.5 sort objects by given criteria |
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2. Copy simple patterns and sequences |
2.1 copy simple patterns 2.2 copy simple sequences |
P6 Pupils sort objects and materials according to a given criteria, for example, sorting footballs into a net and table tennis balls into a box. They copy simple patterns or sequences, for example, copying a drumbeat; copying a simple pattern of repeated movements; copying a pattern of large and small cups.
P7 – Mathematics, Using and Applying – Learning outcomes and assessment criteria
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Learning outcome The learner will |
Assessment criteria The learner can |
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1. Complete a range of classification activities |
1.1 match and group objects according to shape 1.2 match and group objects according to colour 1.3 match and group objects according to size 1.4 match and group objects according to length 1.5 match and group objects according to weight |
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2. Identify when an object is different and not belong to a given familiar category |
2.1 identify the odd one out 2.2 identify odd items from sets and remove them into the correct set |
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3. Respond appropriately to key vocabulary and questions |
3.1 respond appropriately to key vocabulary 3.2 respond appropriately to key questions |
P7 Pupils complete a range of classification activities using a given criterion, for example, sorting a pile of coins by size, colour or shape; sorting all the blue Wellington boots; sorting all the size 6 shoes. They identify when an object is different and does not belong to a given familiar category, for example, removing odd items from sets; collecting items into sorting boxes or drawers. They respond appropriately to key vocabulary and questions, for example, ‘How many?’
P8 – Mathematics, Using and Applying – Learning outcomes and assessment criteria
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Learning outcome The learner will |
Assessment criteria The learner can |
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1. Use simple repeating patterns and sequences |
1.1 copy simple patterns and sequences 1.2 identify the next shape from a choice 1.3 describe simple repeating patterns |
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2. Use developing mathematical understanding of counting up to 10 |
2.1 use ordinal words to describe positions and turns 2.2 use tokens or marks to tally events or scoring in a game 2.3 play counting games using different equipment 2.4 complete a 10 piece puzzle 2.5 solve simple mathematical problems |
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3. Make simple estimates |
3.1 guess up to 3 objects without counting 3.2 make simple estimates 3.3 count the objects to see if I am correct |
P8 Pupils talk about, recognise and copy simple repeating patterns and sequences, for example, recognising and describing simple repeating patterns on textiles or necklaces from different cultures; recognising and describing a pattern of socks on a line; joining in a pattern of hand claps; talking about and copying patterns such as beats in familiar music; shapes made by hand and feet in damp sand; sponge prints. Pupils use their developing mathematical understanding of counting up to ten to solve simple problems encountered in play, games or other work, for example, using tokens or marks to tally events or scoring in games; counting in the school environment; using ordinal words to describe positions and turns. Pupils make simple estimates, for example, estimating the number of cubes that will fit into a box or the number of strides across a room.
