Ben (Y2)
1 of 38 The National Strategies Primary Primary Framework for literacy and mathematics, Ben mathematics
Ben
Year 2
Low level 2
Mathematics standards file
About Ben Ben was born in June 2001 and is now seven years old. He is a pupil in a mixed-age class in a small rural school. He transferred to the school during his Reception year, having attended preschool provision and another school for a short period. This standards file represents Ben’s attainment in the summer term of Year 2. Ben's attainment across mathematics Subject level
Ma1
Ma2
Ma3
Ma4
Low level 2
Low level 2
Low level 2
Secure level 2
Low level 2
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Ma1 Using and applying mathematics Make 50
Teacher's notes
Responds to ‘Find different ways to make an answer of 50’.
Works independently choosing to use addition and subtraction.
Uses ‘+’, ‘–’ and ‘=’ signs correctly to record solutions.
Knows the number that is one more/less, ten more/less than 50 and uses this to create 49 + 1 = 50, 60 – 10 = 50 and 40 + 10 = 50.
Uses his understanding of place value to create 10 + 10 + 10 + 10 + 10 = 50.
Knows pairs of numbers that add to ten and uses this with place value to create 44 + 6 = 50 and 43 + 7 = 50.
Is starting to check work but does not spot that 64 – 4 = 50 is incorrect.
Sometimes reverses the number symbol ‘5’.
Transposes some two-digit numbers, e.g. writes 10 as 01 but reads it as 10 when calculating.
Next steps
Ensure that the digits of two-digit numbers are not transposed.
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Find and record all solutions to a number problem, e.g. using number cards 10, 20, 30 and 40, find all totals that can be made by adding numbers on pairs of cards.
Talk about his methods, the strategies he uses and how he knows he has found all possible totals.
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Sharing story Teacher's notes
Sees relevance of mathematics by solving division problems set in context of story.
Shows how to share 12 cakes between two, three, four then six characters.
Interprets solutions to problems by responding to questions, e.g. ‘How many cakes each do they have now?’.
Shows some mental calculation strategies by sharing out 12 cakes among six characters in groups of two rather than one by one.
Knows that 12 cakes divided among 12 characters gives each character one cake.
Next steps
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Without prompting, explain what he finds out after each sharing of cakes.
Record the different ‘sharing’ problems and their solutions.
Start to use the division sign to record results, e.g. 12 ÷ 2 = 6.
Make different arrays with 12 counters and record results.
Explain and compare his results with a partner.
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Fifty pence Teacher's notes
Uses coins and recognises values up to 50p.
Makes amounts totalling 50p using coins of the same value and of mixed values.
Predicts that nine 5p coins will equal 50p and checks.
Counts on in 5p and 10p coins up to 50p.
Checks some amounts by re-counting.
Next steps
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Make a record of some amounts he finds.
Check totals, explaining his mental strategies to a partner.
Investigate whether 50p can made with 1 coin, 2 coins, 3 coins, … 10 coins and record findings.
Find as many ways as possible of making 50p with silver coins only.
Talk about how he knows he has found all possible ways.
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3-D shapes Teacher's notes
Recognises and names common 3-D shapes including square-based pyramid.
Visualises that a hidden 3-D shape with eight edges is a square-based pyramid.
Describes two cylinders using a range of vocabulary, e.g. ‘has a face at the top’, ‘is round at the bottom’ ‘has three faces’.
Describes one cylinder about 3 cm in height as ‘flat’.
Is starting to count faces and edges.
Next steps
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Order 3-D shapes by their number of edges or faces.
Write clue cards about 3-D shapes to which a partner matches the shapes.
Write as many facts as possible about one 3-D shape.
Compare two 3-D shapes to find ways in which they are the same and how they differ.
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Programmable toy Teacher's notes
Programmes toy to reach destination on square grid.
Uses single commands, e.g. ‘forward’ then ‘go’.
Interprets symbols to make robot move towards target.
Uses vocabulary such as ‘forward’, ‘turn’, ‘down’ to explain moves.
With the help of arrow symbols, is starting to distinguish between left and right turns.
Next steps
Programme toy to use multiple commands, e.g. pressing ‘forward, forward, turn left’ then ‘go’.
Programme toy to reach destination using a given number of moves or as few moves as possible.
Record the toy’s journey in words, symbols and pictures.
Instruct another child on how to programme toy to reach a destination.
Start to use ‘clockwise’ and ‘anticlockwise’ to describe direction of turn.
Bee-Bot Floor Robot © Virtual School Consultancy. Used with kind permission.
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Foot lengths Teacher's notes
Applies recent work on measuring in centimetres to collect data on foot length.
Chooses which data to collect.
Designs table to record names of children and length of their feet.
Chooses ruler and uses it correctly to measure feet to nearest centimetre.
Collects data from other children and records data independently.
Records length of feet using ‘cm’ notation, e.g. 23 cm.
Tries to design a block graph independently.
Labels graph ‘graph (on) feet size’.
Responds to questions such as, ‘How many children have feet that are 24 centimetres long?’ by counting blocks.
Next steps
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Check that all of the children in his list are represented on the graph.
Use the convention of leaving a space between columns.
Number the vertical axis accurately in a way that helps to read the number represented rather than counting individual ‘blocks’.
Label the axes to explain what each represents.
Talk or write about what he has found out, e.g. ‘The shortest foot was 17 cm long.’.
Think of questions to ask about his graph then try them out on a partner.
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Shape pattern Teacher's notes
Given the rule that patterns can use only two types of shape, continues the teacher’s pattern.
Describes shapes in pattern as ‘diamonds’ (rhombi) and ‘red things’ (trapezia).
Responds to teacher’s instruction to make his own repeating pattern with two shapes.
Chooses yellow hexagon, green triangle as repeating unit.
Positions 11 shapes that show five repeats of unit and one extra hexagon.
Describes pattern as having ‘six of these roundy yellow things’ (meaning hexagons) then names hexagon correctly after prompt from teacher.
When partner says that hexagon has six sides, implies that it has six corners also.
Names triangles correctly.
Next steps
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Create a shape pattern and describe to a partner how to copy it.
Make a pictorial record of patterns created with dividing lines to show each repeat and details of shapes used.
Make repeating patterns that involve counting sides or corners, e.g. any shape with 3 sides, 4 sides, 5 sides and 6 sides as the repeating unit.
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What the teacher knows about Ben’s attainment in Ma1, Using and applying mathematics Until the start of the summer term, Ben was largely dependent on approaches used by the teacher or classmates to solve problems. He is now starting to show more independence. For example, he chooses to use addition and subtraction to make answers equal to 50 using a range of one-digit and two-digit numbers. He also finds and displays different sets of coins that total 50p. He recognises that counting up to 100 objects in ones ‘will take too long’ and chooses to group and count them in tens. He chooses apparatus such as rulers and weighing scales. He also chooses number lines and 100-squares to help with number work. He is starting to apply knowledge gained in one mathematical context to other contexts. One way he shows this is by transferring knowledge of the sharing aspect of division to solve problems that feature in a story. When given a project on handling data independently, he identifies what he has to do by bringing together several skills previously modelled by the teacher. He starts by choosing to compare foot lengths of classmates, designs a table to record the data, uses a ruler to measure in centimetres, and records measurements. With some support, he then transfers data from the table to a block graph. He is starting to programme a floor ‘robot’ and identifies routes to reach target destinations. When encouraged by his teacher, he checks work, for example by recounting some amounts that total 50p but, as yet, he is not always accurate when checking answers to his written work. Ben responds to questions about mathematics using a range of language but offers descriptions or explanations of his work, especially numbers and calculations, less often. Ben mostly records his work practically and is less likely to use written recording. He contributes to group discussions, for example to give clues about a hidden 3-D shape and to predict that a classmate has hidden a square-based pyramid. Ben discusses work on shape and space with more success than other aspects of mathematics. For example, when describing a cylinder, he says, ‘It’s round at the top; it’s round at the bottom; it has three faces’. He uses a range of vocabulary related to position and movement, for example to describe the movement of a floor ‘robot’. He does not yet pose questions to ask about his work. He answers simple questions, for example, but cannot ask his teacher a question about his graph of foot lengths. Even with support, Ben finds it difficult to explain why an answer is correct. In independent work, he uses the ‘+’, ‘–’ and ‘=’ signs correctly and abbreviations such as ‘cm’. He is starting to create simple tables and graphs to collect and represent data as he shows in his investigations of foot lengths. He shows emerging reasoning skills, for example when considering the best way to count up to 100 objects. He recognises that counting in ones ‘could take too long’ and he ‘will forget’ so he suggests counting in tens. When given the start of a repeating pattern of shapes, he continues the pattern. He also creates simple shape patterns that meet the teacher’s criterion, such as a repeating pattern with two shapes. He chooses his own criterion for sorting, such as choosing to find objects that are longer or shorter than 20 centimetres.
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Summarising Ben’s attainment in Ma1, Using and applying mathematics Ben meets most of the assessment focuses at level 2 in Ma1. In Problem solving and Communicating, he meets all assessment focuses. In Problem solving he selects the mathematics and apparatus he needs to use. In Communicating, Ben discusses what he does in shape, space and measures in a more knowledgeable way than in number. He is beginning to choose ways to present his work using symbols and diagrams. After reading the complete level description for level 2, his teacher decides that Ben’s attainment in Ma1, Using and applying mathematics, is best described as level 2. To decide whether his attainment is low, secure or high at level 2 in Ma1, his teacher considers four criteria – how much of the level he has covered, how consistently he demonstrates the assessment focuses, how independently he works and the range of contexts where he engages with mathematics. Ben’s teacher judges that, overall, he is not yet working securely at level 2 in Ma1. She makes this judgement for several reasons. First, because much of his progress is recent, he has not yet demonstrated that he can use and apply mathematics consistently. Second, he has not demonstrated his attainment in a wide enough range of contexts, especially in number work. Third, in Reasoning, there are elements of the assessment focus that he has not yet covered, i.e. explaining why an answer is correct, predicting what comes next in simple number patterns and giving reasons for the prediction. After this consideration, Ben’s teacher refines the judgement to low level 2.
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12 of 38 The National Strategies Primary Primary Framework for literacy and mathematics, Ben mathematics To become secure at level 2 in Ma1, Ben should communicate using a wider range of mathematical vocabulary, especially in number work, so that he describes his work and methods in more detail and more accurately. He should develop written methods to show how he works out answers to calculations, especially those involving addition and subtraction that are too difficult to calculate mentally. Similarly, he should write number sentences involving all four operations to represent what he does practically. He should begin to appreciate the need to record. Ben should further develop his reasoning skills. For example, he should visualise familiar 2-D and 3-D shapes. As well as predicting what comes next in simple shape and spatial patterns, he should experience a range of number sequences, explain what comes next and why. He should also have opportunities to explain why answers are correct, for example by testing simple statements.
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Ma2 Number 100 ones Teacher's notes
Recognises that counting cubes in ones up to 100 is not efficient as it will ‘take too long’.
Suggests grouping cubes in tens.
Groups cubes in tens.
Counts on in tens to 100.
Next steps
Record the pattern of numbers he says as he counts on in groups of 10.
Explain how he can recognise numbers that are/are not multiples of 10.
Predict then check how many groups of 2, 5 and 10 can be made from 50 cubes.
Ordering Teacher’s notes
Orders two-digit numbers in ascending order but positions them from right to left.
Recognises that 102 is greater than 98.
Explains that there are nine tens in 98.
Explains that 26 and 27 have the same number of tens.
Next steps
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Say and write missing numbers in sequences such as 68, …, …, …, 72 or 83, 82, …, …, …
Make as many two-digit numbers as possible with three digit cards, e.g. 2, 5 and 8, order them and record findings.
Write the ‘story’ of a number, e.g. all he knows about the number 35.
Reassemble a cut-up 1–100 square.
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Make 50
Teacher's notes
Responds to ‘Find different ways to make an answer of 50.’.
Works independently choosing to use addition and subtraction.
Uses ‘+’, ‘–’ and ‘=’ signs correctly to record solutions.
Knows the number that is one more/less, ten more/less than 50 and uses this to create 49 + 1 = 50, 60 – 10 = 50 and 40 + 10 = 50.
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Uses his understanding of place value to create 10 + 10 + 10 + 10 + 10 = 50.
Knows pairs of numbers that add to ten and uses this with place value to create 44 + 6 = 50 and 43 + 7 = 50.
Is starting to check work but does not spot that 64 – 4 = 50 is incorrect.
Sometimes reverses the number symbol ‘5’.
Transposes some two-digit numbers, e.g. writes 10 as 01 but reads it as 10 when calculating.
Next steps
Ensure that the digits of two-digit numbers are not transposed.
Find and record all solutions to a number problem, e.g. using number cards 10, 20, 30 and 40, find all totals that can be made by adding numbers on pairs of cards.
Talk about his methods, the strategies he uses and how he knows he has found all possible totals.
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Fraction shapes
Teacher's notes
Divides paper circles and rectangles (including squares) into halves then quarters.
Knows that to show halves each shape must be divided into two equal parts.
Knows that to show quarters each shape must be divided into four equal parts.
Next steps
Find different ways to fold rectangles into halves then quarters.
Start to use fraction notation for one-half, one-quarter and three-quarters.
Find halves then quarters of small collections of objects and record findings.
Find ways to calculate halves then quarters of objects that cannot be moved, e.g. are in picture form.
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Marker scores Teacher's notes
In PE game lasting a minute, adds four scores that total 17.
‘Holds’ sub-totals in his head as the game progresses.
Uses fingers to calculate sub-totals.
Calculates final score correctly.
Next steps
Try to score a target number by end of game, e.g. 25; compare results with others.
Try to score a target number in as few moves as possible.
After the game, work out different totals that could be scored by touching, e.g. three markers.
Sharing story Teacher's notes
Sees relevance of mathematics by solving division problems set in context of story.
Shows how to share 12 cakes between two, three, four then six characters.
Interprets solutions to problems by responding to questions, e.g. ‘How many cakes each do they have now?’.
Shows some mental calculation strategies by sharing out 12 cakes among six characters in groups of two rather than one by one.
Knows that 12 cakes divided among 12 characters gives each character one cake.
Next steps
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Record the different ‘sharing’ problems and their solutions.
Start to use the division sign to record results, e.g. 12 ÷ 2 = 6.
Make different arrays with 12 counters and record results.
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Explain and compare his results with a partner.
Fifty pence Teacher's notes
Uses coins and recognises values up to 50p.
Makes amounts totalling 50p using coins of the same value and of mixed values.
Predicts that nine 5p coins will equal 50p and checks.
Counts on in 5p and 10p coins up to 50p.
Checks some amounts by re-counting.
Next steps
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Make a record of some amounts he finds.
Check totals, explaining his mental strategies to a partner.
Investigate whether 50p can made with 1 coin, 2 coins, 3 coins, … 10 coins and record findings.
Find as many ways as possible of making 50p with silver coins only.
Talk about how he knows he has found all possible ways.
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What the teacher knows about Ben’s attainment in Ma2, Number Ben counts sets of up to 100 objects reliably and is starting to count on in tens and ones, having decided that counting on in ones ‘takes too long.’ He reads numbers to 100 and shows the beginnings of understanding place value. For example, he knows that ‘9’ in ‘98’ represents nine tens. He generally writes numbers to 100 correctly but sometimes transposes multiples of 10, e.g. writes ‘02’ for ‘20’ but reads it as twenty. Sometimes he reverses digits, especially 5, but this is becoming less frequent. He orders numbers to 100 and recognises some numbers that are greater than 100. Ben understands addition as finding the total of two or more sets and subtraction as ‘take away’. He uses the ‘+’, ‘–’ and ‘=’ signs correctly, including in independent work as when he ‘makes 50’. He is starting to solve missing number problems. For example, when his teacher covers a number that is part of a calculation he has written, he names the missing number. He finds onehalf and one-quarter of given shapes and knows that the parts in each shape need to be equal. Ben has good mental recall of addition and subtraction facts to 10 and solves missing number problems mentally. For example, when asked what number to add to three to make 10, he answers correctly with little hesitation. He adds several small one-digit numbers during a game that took a minute and gives the correct total. He applies his knowledge of number bonds to 10 to derive answers that use larger numbers, such as 40 + 10. He makes amounts to 50p and counts the amounts mentally using a range of coins. When sharing 12 cakes among six characters, he gives out two cakes at a time, showing that he is working out answers in his head then checking by sharing. He uses mental calculation strategies to count in twos, fives and tens to 50 when counting on using 2p, 5p and 10p coins. Ben has good mental calculation strategies to solve number problems, including those involving money up to £1. Ben solves ‘story’ problems mentally and, with support, is starting to explain how he works out answers. He uses practical materials to solve problems as he does when sharing 12 cakes among characters in a story and finding sets of coins that make 50p. He recognises when he has to add or subtract to solve problems and records using symbols ‘+’, ‘–’ and ‘=’. For example, he uses the symbols correctly when recording different ways to make 50. Ben mostly chooses to solve problems mentally or practically rather than using written methods but, with support, he is starting to record more.
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Summarising Ben’s attainment in Ma2, Number Ben meets the criteria for all six assessment focuses at level 1 for Ma2. At level 2, he meets the majority of the assessment focuses at least in part. In the assessment focus, Operations, relationships between them, Ben has yet to demonstrate attainment at level 2. He does not yet understand that subtraction is the inverse of addition, for example by finding different ways to make four number sentences using trios of numbers such as 15, 8 and 7. He has not made statements such as, ‘Double five is ten. Half of ten is five.’ to help him understand that halving ‘undoes’ doubling. In the assessment focus Fractions, his experience is limited to folding and shading shapes to show halves and quarters so he has yet to find halves and quarters of small numbers of objects or halves of shapes that are divided into, for example, four or eight equal regions. Although he meets the first two assessment criteria in Numbers and the number system, he has yet to recognise sequences of numbers, including odd and even numbers. For the final assessment focus, Written methods, Ben records work in writing but does not yet do so consistently or independently due to his reluctance to show written methods for calculations. Reading the complete level descriptions for level 1 and level 2 confirms Ben’s teacher’s first judgement that his attainment is best described as level 2. Ben’s teacher knows that he has yet to meet some level 2 assessment criteria fully and consistently in different contexts. Consequently, the teacher refines her judgement to describe Ben as working at low level 2 in Ma2. To become more secure at level 2, Ben should partition two-digit numbers into tens and ones, including multiples of 10, so that he uses zero as a place holder in the ‘ones’ position and avoids transposing digits. He should continue sequences of numbers that increase or decrease by a QCA 00022-2009DWO-EN-01
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21 of 38 The National Strategies Primary Primary Framework for literacy and mathematics, Ben mathematics constant amount. He should also recognise odd and even numbers in and out of sequence so that he eventually recognises whether a number is odd or even by its final digit. He should extend his experience of shading shapes to show halves and quarters to finding halves and quarters of small quantities. He should learn about the inverse relationship between addition and subtraction. He should engage in practical then written activities that will lead to him understanding that halving is the inverse of doubling. Ben already has some effective mental strategies for solving number problems and knows when to add or subtract. He should build on these skills by recording how he works out answers to some mental calculations, for example as number sentences or as jumps on a self-drawn number line. He should also solve more addition and subtraction problems using numbers, money or measures that require him to show working. The problems should include adding and subtracting pairs of two-digit numbers that require bridging the tens.
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Ma3 Shape, space and measures 3-D shapes Teacher's notes
Recognises and names common 3-D shapes including square-based pyramid.
Visualises that a hidden 3-D shape with eight edges is a square-based pyramid.
Describes two cylinders using a range of vocabulary, e.g. ‘has a face at the top’, ‘is round at the bottom’ ‘has three faces’.
Describes one cylinder about 3 cm in height as ‘flat’.
Is starting to count faces and edges.
Next steps
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Order 3-D shapes by their number of edges or faces.
Write clue cards about 3-D shapes to which a partner matches the shapes.
Write as many facts as possible about one 3-D shape.
Compare two 3-D shapes to find ways in which they are the same and how they differ.
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Shape pattern Teacher's notes
Responds to teacher’s instruction to make a repeating pattern with two shapes.
Chooses yellow hexagon, green triangle as repeating unit.
Positions 11 shapes that show five repeats of unit and one extra hexagon.
Describes pattern as having ‘six of these yellow roundy things’ (meaning hexagons) then names hexagon correctly after prompt from teacher.
When partner says that the hexagon has six sides, Ben implies that it has six corners also.
Names triangles correctly.
Next steps
Create a shape pattern and describe to a partner how to copy it.
Make a pictorial record of patterns created with dividing lines to show each repeat and details of shapes used.
Make repeating patterns that involve counting sides or corners, e.g. any shape with 3 sides, 4 sides, 5 sides and 6 sides as the repeating unit.
Cylinder Teacher's notes
Visualises a cylinder.
Knows that a cylinder has three faces.
Makes a pictorial record of a shape he is learning about.
Shows understanding that 3-D shapes can be represented in picture form.
Next steps
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Include with drawing all facts known about a cylinder including its name.
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Programmable toy Teacher's notes
Programmes toy to reach destination on square grid.
Uses single commands, e.g. ‘forward’ then ‘go’.
Interprets symbols to make robot move towards target.
Uses vocabulary such as ‘forward’, ‘turn’, ‘down’ to explain moves.
With the help of arrow symbols, is starting to distinguish between left and right turns.
Next steps
Programme toy to use multiple commands, e.g. pressing ‘forward, forward, turn left’ then ‘go’.
Programme toy to reach destination using a given number of moves or as few moves as possible.
Record the toy’s journey in words, symbols and pictures.
Instruct another child on how to programme toy to reach a destination.
Start to use ‘clockwise’ and ‘anticlockwise’ to describe direction of turn.
Bee-Bot Floor Robot © Virtual School Consultancy. Used with kind permission.
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Shapes in place Teacher's notes
Uses ordinal numbers ‘first’ to ‘seventh’.
Responds to questions about name shapes, e.g. ‘Can you name the third shape?’.
Correctly names hexagon, triangle and square.
Uses ordinal numbers to respond to questions about the position of shapes, e.g. ‘What is the position in the row of the gold triangle?’.
Combines knowledge of ordinal numbers and 2-D shapes.
Next steps
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Without prompting, make statements about the position of shapes.
Respond to more complicated questions, e.g. ‘Which shapes come between the second and fifth shapes?’.
Make a row of different 2-D or 3-D shapes, describe to a partner how to copy it, then compare results.
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Turtle Teacher's notes
Begins to use a computer program to move a screen ‘turtle’.
Uses single commands.
Interprets and uses symbols that represent straight-line movements and left and right turns.
Depends on symbols to help him negotiate left and right turns.
Programmes ‘turtle’ to reach a target destination.
Uses language such as ‘forwards’, ‘backwards’ and ‘turn’ to describe movements.
Next steps
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Record route taken by ‘turtle’ so that a partner can recreate it.
Use more than one command for each move.
Extend language of movement to include correct use of vocabulary such as clockwise/anticlockwise, left/right.
Recognise when the ‘turtle’ turns through a right angle.
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Sorting by length
Teacher's notes
After direct teaching, produces related written work independently.
Designs a sorting diagram to categorise objects by length.
Chooses to categorise objects by whether they are shorter or longer than 20 cm.
Designs a two-region sorting diagram using ‘smaller’ or ‘bigger’ as labels.
Finds objects to measure and chooses a ruler as measuring equipment.
Measures lengths of objects to find out if they are longer or shorter than 20 cm.
Records object name and length on his diagram.
Uses abbreviation ‘cm’ for centimetres.
Next steps
Use comparative language related to length more consistently, e.g. ‘longer’ rather than ‘bigger’.
Find objects that are between two lengths, e.g. between 15 cm and 20 cm long.
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Foot lengths Teacher's notes
Applies recent work on measuring in centimetres to collect data on foot length.
Chooses which data to collect.
Designs table to record names of children and length of their feet.
Chooses ruler and uses it correctly to measure feet to nearest centimetre.
Collects data from other children and records data independently.
Records length of feet using ‘cm’ notation, e.g. 23 cm.
Tries to design a block graph independently.
Labels graph ‘graph (on) feet size’.
Responds to questions such as, ‘How many children have feet that are 24 centimetres long?’ by counting blocks.
Next steps
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Check that all of the children in his list are represented on the graph.
Use the convention of leaving a space between columns.
Number the vertical axis accurately in a way that helps to read the number represented rather than counting individual ‘blocks’.
Label the axes to explain what each represents.
Talk or write about what he has found out, e.g. ‘The shortest foot was 17 cm long.’.
Think of questions to ask about his graph then try them out on a partner.
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Weighing Teacher's notes
Chooses mechanical scales when asked to find out how heavy objects are.
After revision, knows the units are kilograms and grams.
With support, interprets divisions that represent 25 gram increments.
After support, reads the scale to the nearest 25 gram division independently.
Records in grams.
Next steps
Record estimates before weighing.
Compare objects and use the language of comparison: heavier, heaviest, lighter, lightest.
Time in order Teacher's notes
Recognises photographs taken at different times during an event at school.
Cuts out six photographs and puts them in time order.
Numbers the photographs then describes what is happening in each.
Answers questions such as, ‘What does the fourth picture show?’.
Next steps
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Record what he is doing at home or school at hourly or half-hourly intervals and show events on a time line.
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30 of 38 The National Strategies Primary Primary Framework for literacy and mathematics, Ben mathematics What the teacher knows about Ben’s attainment in Ma3, Shape, space and measures Ben names triangles, circles, squares, rectangles and hexagons. He identifies edges and vertices and counts them. He uses the terms ‘edges’ and ‘corners’ but not consistently when describing shapes, sometimes resorting to everyday language. For example, he describes a hexagon as a ‘roundy thing’ then corrects to ‘hexagon’ after a prompt and says that ‘it has six of each’, implying six vertices and six edges. Ben recognises and names cubes, cuboids, cylinders, cones and pyramids. When handling shapes, he is starting to count faces, edges and vertices. For example, he explains that a cylinder has three faces, a face at the top, and a face at the bottom and that these two faces are round. During such explanations, he points to the relevant features and properties. He visualises some 3-D shapes, for example he predicts that a hidden shape with eight edges is a square-based pyramid and he draws a cylinder from memory. He often sorts 2-D and 3-D shapes by their mathematical names but, with support, goes on to use criteria such as the number of edges or faces. Ben responds to and uses positional vocabulary such as near, between, next to, across and under in a range of mathematical and cross-curricular activities including PE. He describes two faces of a cylinder as being ‘round at the top’ and ‘round at the bottom’. He also uses ordinal numbers and responds to questions such as, ‘Which is the sixth shape in the row?’ or ‘What is the position in the row of the gold triangle?’ Giving one command at a time, he uses arrow symbols, representing moves forwards and backwards and quarter turns to the left and right, to programme a floor robot to move to a target destination. He uses similar symbols to programme an onscreen ‘turtle’. In both activities, he uses language such as ‘forwards’, ‘backwards’ and ‘turn’ to describe the moves. Ben uses standard units of measurement. He measures lengths using both metres and centimetres. He chooses whether to use a metre stick or ruler depending on the context. For example, when finding objects longer or shorter than 20 centimetres, he chooses a ruler. He describes these objects as ‘bigger’ or ‘smaller’ than 20 cm rather than ‘longer’ or ‘shorter’. He uses a ruler accurately to measure lengths to the nearest centimetre. He knows abbreviations for metre and centimetre and uses them in lists, for example when he records foot lengths. Ben uses a scale labelled every 5 kilograms and with 1 kilogram sub-divisions to weigh himself but needs help to interpret the sub-divisions. When asked to weigh small desktop objects, he chooses a mechanical scale with increments representing 25 grams but labelled at every 100 grams. With support, he weighs objects in grams by reading the scales to the nearest 25 gram division. He records measurements in simple tables and diagrams, some of which he designs independently. After an event at school, he puts six photographs of the event in chronological order. He uses ordinal vocabulary to explain, for example ‘The fourth picture shows some of the houses we built.’. Ben reads an analogue clock face to tell the time on the hour and the half-hour. He is starting to read time on the quarter-hour. To measure capacity, Ben counts how many litre jugs are needed to fill three buckets. He records results and orders the containers by capacity.
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Summarising Ben’s attainment in Ma3, Shape, space and measures Ben meets the criteria for level 2 in the assessment focus Properties of shape. He names common 2-D and 3-D shapes and describes their properties. He also meets two of the three assessment criteria for Properties of position and movement. He uses positional language and distinguishes between straight and turning movements even though he does not yet give directions using clockwise and anticlockwise or left and right consistently. The gaps in Ben’s attainment in Ma3 relate mainly to work on angles. He does not recognise right angles in turns or understand angle as a measurement of turn. In the assessment focus, Measuring Ben meets the second and third criteria. Ben has progressed from using non-standard units to using standard units of length and mass. He uses metres and centimetres to measure length and is starting to use grams as well as kilograms to measure mass. He measures and compares capacities using a 1 litre measuring jug. He tells the time on analogue clocks at the hour and half-hour and is progressing towards telling time at the quarter-hour. After reading the level descriptions for level 2, Ben’s teacher confirms that level 2 is the ‘best fit’ for Ben’s attainment in Ma3. In view of how much of the level Ben demonstrates compared with what he has yet to achieve, Ben’s teacher recognises that he has achieved most of what is required. Consequently, she refines her judgement to secure level 2 for Ma3. To make further progress within level 2, Ben needs to develop a more in-depth knowledge of turning movements, in particular learning to distinguish between turning left and right and between clockwise and anticlockwise. He should learn to recognise that turning through a right angle is equivalent to making a quarter turn. From there, he should progress to comparing whole, half turns and quarter turns so that he begins to understand angle as a measurement of
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Ma4 Handling data Sorting by length
Teacher's notes
After direct teaching, produces related written work independently.
Designs a sorting diagram to categorise objects by length.
Chooses to categorise objects by whether they are shorter or longer than 20 cm.
Designs a two-region sorting diagram using ‘smaller’ or ‘bigger’ as labels.
Finds objects to measure and chooses a ruler as measuring equipment.
Measures lengths of objects to find out if they are longer or shorter than 20 cm.
Records object name and length on his diagram.
Uses abbreviation ‘cm’ for centimetres.
Next steps
Use comparative language related to length more consistently, e.g. ‘longer’ rather than ‘bigger’.
Find objects that are between two lengths, e.g. between 15 cm and 20 cm long.
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Foot lengths Teacher's notes
Applies recent work on measuring in centimetres to collect data on foot length.
Chooses which data to collect.
Designs table to record names of children and length of their feet.
Chooses ruler and uses it correctly to measure feet to nearest centimetre.
Collects data from other children and records data independently.
Records length of feet using ‘cm’ notation, e.g. 23 cm.
Tries to design a block graph independently.
Labels graph ‘graph (on) feet size’.
Responds to questions such as, ‘How many children have feet that are 24 centimetres long?’ by counting blocks.
Next steps
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Check that all of the children in his list are represented on the graph.
Use the convention of leaving a space between columns.
Number the vertical axis accurately in a way that helps to read the number represented rather than counting individual ‘blocks’.
Label the axes to explain what each represents.
Talk or write about what he has found out, e.g. ‘The shortest foot was 17 cm long.’.
Think of questions to ask about his graph then try them out on a partner.
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What the teacher knows about Ben’s attainment in Ma4, Handling data Ben sorts shapes and other objects using discrete sets, for example sorting 2-D shapes by the number of sides. He sorts using one criterion such as triangles/not triangles using given Carroll and Venn diagrams. Ben is starting to design diagrams, lists, simple tables and block graphs to record data he collects. For example, when sorting objects by length, he designs a two-region sorting diagram to categorise and record object names and their length. Ben also collects data from other children, such the length of their feet. He records the children’s names and foot lengths on a table he designs then uses data on the table to construct a block graph. Ben’s numbering of the frequency axis of his block graphs is not yet secure. For example, in his ‘graph of feet size’ he starts numbering at 1 rather than 0 and consequently colours only four blocks rather than five to represent the number of children with feet 23 cm long. To show the favourite fruits of classmates, he constructs a diagram where one symbol represents one child’s choice. Ben uses his own drawings of each type of fruit. He creates similar diagrams using a computergenerated data-handling program. He has yet to learn the convention for a pictogram of using a single symbol throughout. Ben interprets data by, for example, extracting information from a table and using it to create a block graph. He also interprets data by counting blocks or symbols on graphs and diagrams in response to questions such as ‘How many children like apples best?’ He sorts using one criterion and gives simple explanations about how he sorts objects. For example, when asked how he has sorted 2-D shapes, he points and says, ‘These are triangles. These are not triangles.’ However, Ben typically gives very brief responses to questions. Without prompting, he finds it difficult to explain his data or to make up questions that he can ask others about his work. Ben has made considerable progress in collecting and representing data in the latter part of Year 2.
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Summarising Ben’s attainment in Ma4, Handling data Ben meets all assessment criteria at level 1 in Ma4. He meets most of the criteria across the assessment focuses at level 2, either fully or in part. He has yet to sort objects and classify them using more than one criterion and to collect and sort data to test a simple hypothesis. When interpreting data, he meets part of the assessment criterion for communicating his findings since he does use simple lists and tables. He is also beginning to use block graphs even though he has yet to number the frequency axis accurately and to leave a space between columns. He also uses picture diagrams even though he does not yet use one symbol throughout for the diagram to be a pictogram. After reading across the complete level descriptions for level 1 and level 2, his teacher decides that Ben’s attainment in Ma4 is best described as level 2. To refine her judgement, Ben’s teacher takes into account the progress he has made recently, the gaps in his attainment and his limited talk about his data. Consequently, she refines her judgement to low level 2. To become secure in level 2, Ben needs to progress from sorting using one criterion to using more than one criterion, for example on two-criteria Venn and Carroll diagrams. Ben should continue to construct block graphs, number the frequency axis accurately in ones and then progress to numbering in twos. He should leave a space between columns on his block graphs. He should work independently to test a simple hypothesis that gives him a reason to conduct a survey. Ben should continue to respond to spoken and written questions that require him to interpret data. He should then try to make statements or pose questions about his data for others to answer.
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Taking the test into account Ben’s performance on the 2007 Key Stage 1 test fits the profile of what Ben’s teacher knows about his ongoing work in class. Ben achieved level 2C, using the level 2 paper. He attempted all questions in the test. He scored 11 marks, which is at the top end of the range for level 2C, 7 to 12 marks. He gained marks in questions 2, 3, 5, 6, 7, 9, 11, 13, 15, 23 and 27. From his ongoing classwork, Ben’s teacher describes his attainment in mathematics as a whole as low level 2. She judges that he is secure at level 2 in Ma3, Shape, space and measures and this is reflected in the test. Ben gained 5 of his 11 marks in questions that assess Ma3 and a further mark in a number question that required him to use ordinal numbers to identify a position. In his classwork Ben does not often show working for number problems and this is also evident in his test. Other than jotting down numbers given in the questions, there is no working throughout the booklet, even for calculations such as ‘24 + 68 =’ that Ben does not calculate mentally. In question 17, Ben’s incorrect answer was 10 less than the correct answer and he did not show a complete method to gain one of the two available marks. In the test Ben gained a mark for writing the missing numbers in a sequence that increased in steps of 3. In his ongoing classwork, Ben is not yet consistently accurate with a range of sequences such as those that decrease in steps of a constant size. He has yet to meet the criterion ‘recognise sequences of numbers, including odd and even numbers’. In his classwork, Ben’s reasoning is a weaker aspect of his attainment and, in this assessment focus of using and applying mathematics, is assessed as level 1. Again this was evident in his response to questions such as 12 that involved reasoning. Ben did not identify the two correct statements, ‘28 is less than 32’ and ’50 is more than 15’. Ben’s performance on the test confirms the teacher’s judgement, based on Ben’s ongoing classwork, that his attainment in the subject is best described as low level 2.
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Acknowledgements
Bee-Bot Floor Robot © Virtual School Consultancy. Used with kind permission.
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Ben
Year 2
Low level 2
Mathematics standards file
About Ben Ben was born in June 2001 and is now seven years old. He is a pupil in a mixed-age class in a small rural school. He transferred to the school during his Reception year, having attended preschool provision and another school for a short period. This standards file represents Ben’s attainment in the summer term of Year 2. Ben's attainment across mathematics Subject level
Ma1
Ma2
Ma3
Ma4
Low level 2
Low level 2
Low level 2
Secure level 2
Low level 2
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Ma1 Using and applying mathematics Make 50
Teacher's notes
Responds to ‘Find different ways to make an answer of 50’.
Works independently choosing to use addition and subtraction.
Uses ‘+’, ‘–’ and ‘=’ signs correctly to record solutions.
Knows the number that is one more/less, ten more/less than 50 and uses this to create 49 + 1 = 50, 60 – 10 = 50 and 40 + 10 = 50.
Uses his understanding of place value to create 10 + 10 + 10 + 10 + 10 = 50.
Knows pairs of numbers that add to ten and uses this with place value to create 44 + 6 = 50 and 43 + 7 = 50.
Is starting to check work but does not spot that 64 – 4 = 50 is incorrect.
Sometimes reverses the number symbol ‘5’.
Transposes some two-digit numbers, e.g. writes 10 as 01 but reads it as 10 when calculating.
Next steps
Ensure that the digits of two-digit numbers are not transposed.
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Find and record all solutions to a number problem, e.g. using number cards 10, 20, 30 and 40, find all totals that can be made by adding numbers on pairs of cards.
Talk about his methods, the strategies he uses and how he knows he has found all possible totals.
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Sharing story Teacher's notes
Sees relevance of mathematics by solving division problems set in context of story.
Shows how to share 12 cakes between two, three, four then six characters.
Interprets solutions to problems by responding to questions, e.g. ‘How many cakes each do they have now?’.
Shows some mental calculation strategies by sharing out 12 cakes among six characters in groups of two rather than one by one.
Knows that 12 cakes divided among 12 characters gives each character one cake.
Next steps
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Without prompting, explain what he finds out after each sharing of cakes.
Record the different ‘sharing’ problems and their solutions.
Start to use the division sign to record results, e.g. 12 ÷ 2 = 6.
Make different arrays with 12 counters and record results.
Explain and compare his results with a partner.
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Fifty pence Teacher's notes
Uses coins and recognises values up to 50p.
Makes amounts totalling 50p using coins of the same value and of mixed values.
Predicts that nine 5p coins will equal 50p and checks.
Counts on in 5p and 10p coins up to 50p.
Checks some amounts by re-counting.
Next steps
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Make a record of some amounts he finds.
Check totals, explaining his mental strategies to a partner.
Investigate whether 50p can made with 1 coin, 2 coins, 3 coins, … 10 coins and record findings.
Find as many ways as possible of making 50p with silver coins only.
Talk about how he knows he has found all possible ways.
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3-D shapes Teacher's notes
Recognises and names common 3-D shapes including square-based pyramid.
Visualises that a hidden 3-D shape with eight edges is a square-based pyramid.
Describes two cylinders using a range of vocabulary, e.g. ‘has a face at the top’, ‘is round at the bottom’ ‘has three faces’.
Describes one cylinder about 3 cm in height as ‘flat’.
Is starting to count faces and edges.
Next steps
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Order 3-D shapes by their number of edges or faces.
Write clue cards about 3-D shapes to which a partner matches the shapes.
Write as many facts as possible about one 3-D shape.
Compare two 3-D shapes to find ways in which they are the same and how they differ.
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Programmable toy Teacher's notes
Programmes toy to reach destination on square grid.
Uses single commands, e.g. ‘forward’ then ‘go’.
Interprets symbols to make robot move towards target.
Uses vocabulary such as ‘forward’, ‘turn’, ‘down’ to explain moves.
With the help of arrow symbols, is starting to distinguish between left and right turns.
Next steps
Programme toy to use multiple commands, e.g. pressing ‘forward, forward, turn left’ then ‘go’.
Programme toy to reach destination using a given number of moves or as few moves as possible.
Record the toy’s journey in words, symbols and pictures.
Instruct another child on how to programme toy to reach a destination.
Start to use ‘clockwise’ and ‘anticlockwise’ to describe direction of turn.
Bee-Bot Floor Robot © Virtual School Consultancy. Used with kind permission.
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Foot lengths Teacher's notes
Applies recent work on measuring in centimetres to collect data on foot length.
Chooses which data to collect.
Designs table to record names of children and length of their feet.
Chooses ruler and uses it correctly to measure feet to nearest centimetre.
Collects data from other children and records data independently.
Records length of feet using ‘cm’ notation, e.g. 23 cm.
Tries to design a block graph independently.
Labels graph ‘graph (on) feet size’.
Responds to questions such as, ‘How many children have feet that are 24 centimetres long?’ by counting blocks.
Next steps
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Check that all of the children in his list are represented on the graph.
Use the convention of leaving a space between columns.
Number the vertical axis accurately in a way that helps to read the number represented rather than counting individual ‘blocks’.
Label the axes to explain what each represents.
Talk or write about what he has found out, e.g. ‘The shortest foot was 17 cm long.’.
Think of questions to ask about his graph then try them out on a partner.
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Shape pattern Teacher's notes
Given the rule that patterns can use only two types of shape, continues the teacher’s pattern.
Describes shapes in pattern as ‘diamonds’ (rhombi) and ‘red things’ (trapezia).
Responds to teacher’s instruction to make his own repeating pattern with two shapes.
Chooses yellow hexagon, green triangle as repeating unit.
Positions 11 shapes that show five repeats of unit and one extra hexagon.
Describes pattern as having ‘six of these roundy yellow things’ (meaning hexagons) then names hexagon correctly after prompt from teacher.
When partner says that hexagon has six sides, implies that it has six corners also.
Names triangles correctly.
Next steps
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Create a shape pattern and describe to a partner how to copy it.
Make a pictorial record of patterns created with dividing lines to show each repeat and details of shapes used.
Make repeating patterns that involve counting sides or corners, e.g. any shape with 3 sides, 4 sides, 5 sides and 6 sides as the repeating unit.
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What the teacher knows about Ben’s attainment in Ma1, Using and applying mathematics Until the start of the summer term, Ben was largely dependent on approaches used by the teacher or classmates to solve problems. He is now starting to show more independence. For example, he chooses to use addition and subtraction to make answers equal to 50 using a range of one-digit and two-digit numbers. He also finds and displays different sets of coins that total 50p. He recognises that counting up to 100 objects in ones ‘will take too long’ and chooses to group and count them in tens. He chooses apparatus such as rulers and weighing scales. He also chooses number lines and 100-squares to help with number work. He is starting to apply knowledge gained in one mathematical context to other contexts. One way he shows this is by transferring knowledge of the sharing aspect of division to solve problems that feature in a story. When given a project on handling data independently, he identifies what he has to do by bringing together several skills previously modelled by the teacher. He starts by choosing to compare foot lengths of classmates, designs a table to record the data, uses a ruler to measure in centimetres, and records measurements. With some support, he then transfers data from the table to a block graph. He is starting to programme a floor ‘robot’ and identifies routes to reach target destinations. When encouraged by his teacher, he checks work, for example by recounting some amounts that total 50p but, as yet, he is not always accurate when checking answers to his written work. Ben responds to questions about mathematics using a range of language but offers descriptions or explanations of his work, especially numbers and calculations, less often. Ben mostly records his work practically and is less likely to use written recording. He contributes to group discussions, for example to give clues about a hidden 3-D shape and to predict that a classmate has hidden a square-based pyramid. Ben discusses work on shape and space with more success than other aspects of mathematics. For example, when describing a cylinder, he says, ‘It’s round at the top; it’s round at the bottom; it has three faces’. He uses a range of vocabulary related to position and movement, for example to describe the movement of a floor ‘robot’. He does not yet pose questions to ask about his work. He answers simple questions, for example, but cannot ask his teacher a question about his graph of foot lengths. Even with support, Ben finds it difficult to explain why an answer is correct. In independent work, he uses the ‘+’, ‘–’ and ‘=’ signs correctly and abbreviations such as ‘cm’. He is starting to create simple tables and graphs to collect and represent data as he shows in his investigations of foot lengths. He shows emerging reasoning skills, for example when considering the best way to count up to 100 objects. He recognises that counting in ones ‘could take too long’ and he ‘will forget’ so he suggests counting in tens. When given the start of a repeating pattern of shapes, he continues the pattern. He also creates simple shape patterns that meet the teacher’s criterion, such as a repeating pattern with two shapes. He chooses his own criterion for sorting, such as choosing to find objects that are longer or shorter than 20 centimetres.
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Summarising Ben’s attainment in Ma1, Using and applying mathematics Ben meets most of the assessment focuses at level 2 in Ma1. In Problem solving and Communicating, he meets all assessment focuses. In Problem solving he selects the mathematics and apparatus he needs to use. In Communicating, Ben discusses what he does in shape, space and measures in a more knowledgeable way than in number. He is beginning to choose ways to present his work using symbols and diagrams. After reading the complete level description for level 2, his teacher decides that Ben’s attainment in Ma1, Using and applying mathematics, is best described as level 2. To decide whether his attainment is low, secure or high at level 2 in Ma1, his teacher considers four criteria – how much of the level he has covered, how consistently he demonstrates the assessment focuses, how independently he works and the range of contexts where he engages with mathematics. Ben’s teacher judges that, overall, he is not yet working securely at level 2 in Ma1. She makes this judgement for several reasons. First, because much of his progress is recent, he has not yet demonstrated that he can use and apply mathematics consistently. Second, he has not demonstrated his attainment in a wide enough range of contexts, especially in number work. Third, in Reasoning, there are elements of the assessment focus that he has not yet covered, i.e. explaining why an answer is correct, predicting what comes next in simple number patterns and giving reasons for the prediction. After this consideration, Ben’s teacher refines the judgement to low level 2.
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12 of 38 The National Strategies Primary Primary Framework for literacy and mathematics, Ben mathematics To become secure at level 2 in Ma1, Ben should communicate using a wider range of mathematical vocabulary, especially in number work, so that he describes his work and methods in more detail and more accurately. He should develop written methods to show how he works out answers to calculations, especially those involving addition and subtraction that are too difficult to calculate mentally. Similarly, he should write number sentences involving all four operations to represent what he does practically. He should begin to appreciate the need to record. Ben should further develop his reasoning skills. For example, he should visualise familiar 2-D and 3-D shapes. As well as predicting what comes next in simple shape and spatial patterns, he should experience a range of number sequences, explain what comes next and why. He should also have opportunities to explain why answers are correct, for example by testing simple statements.
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Ma2 Number 100 ones Teacher's notes
Recognises that counting cubes in ones up to 100 is not efficient as it will ‘take too long’.
Suggests grouping cubes in tens.
Groups cubes in tens.
Counts on in tens to 100.
Next steps
Record the pattern of numbers he says as he counts on in groups of 10.
Explain how he can recognise numbers that are/are not multiples of 10.
Predict then check how many groups of 2, 5 and 10 can be made from 50 cubes.
Ordering Teacher’s notes
Orders two-digit numbers in ascending order but positions them from right to left.
Recognises that 102 is greater than 98.
Explains that there are nine tens in 98.
Explains that 26 and 27 have the same number of tens.
Next steps
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Say and write missing numbers in sequences such as 68, …, …, …, 72 or 83, 82, …, …, …
Make as many two-digit numbers as possible with three digit cards, e.g. 2, 5 and 8, order them and record findings.
Write the ‘story’ of a number, e.g. all he knows about the number 35.
Reassemble a cut-up 1–100 square.
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Make 50
Teacher's notes
Responds to ‘Find different ways to make an answer of 50.’.
Works independently choosing to use addition and subtraction.
Uses ‘+’, ‘–’ and ‘=’ signs correctly to record solutions.
Knows the number that is one more/less, ten more/less than 50 and uses this to create 49 + 1 = 50, 60 – 10 = 50 and 40 + 10 = 50.
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Uses his understanding of place value to create 10 + 10 + 10 + 10 + 10 = 50.
Knows pairs of numbers that add to ten and uses this with place value to create 44 + 6 = 50 and 43 + 7 = 50.
Is starting to check work but does not spot that 64 – 4 = 50 is incorrect.
Sometimes reverses the number symbol ‘5’.
Transposes some two-digit numbers, e.g. writes 10 as 01 but reads it as 10 when calculating.
Next steps
Ensure that the digits of two-digit numbers are not transposed.
Find and record all solutions to a number problem, e.g. using number cards 10, 20, 30 and 40, find all totals that can be made by adding numbers on pairs of cards.
Talk about his methods, the strategies he uses and how he knows he has found all possible totals.
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Fraction shapes
Teacher's notes
Divides paper circles and rectangles (including squares) into halves then quarters.
Knows that to show halves each shape must be divided into two equal parts.
Knows that to show quarters each shape must be divided into four equal parts.
Next steps
Find different ways to fold rectangles into halves then quarters.
Start to use fraction notation for one-half, one-quarter and three-quarters.
Find halves then quarters of small collections of objects and record findings.
Find ways to calculate halves then quarters of objects that cannot be moved, e.g. are in picture form.
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Marker scores Teacher's notes
In PE game lasting a minute, adds four scores that total 17.
‘Holds’ sub-totals in his head as the game progresses.
Uses fingers to calculate sub-totals.
Calculates final score correctly.
Next steps
Try to score a target number by end of game, e.g. 25; compare results with others.
Try to score a target number in as few moves as possible.
After the game, work out different totals that could be scored by touching, e.g. three markers.
Sharing story Teacher's notes
Sees relevance of mathematics by solving division problems set in context of story.
Shows how to share 12 cakes between two, three, four then six characters.
Interprets solutions to problems by responding to questions, e.g. ‘How many cakes each do they have now?’.
Shows some mental calculation strategies by sharing out 12 cakes among six characters in groups of two rather than one by one.
Knows that 12 cakes divided among 12 characters gives each character one cake.
Next steps
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Record the different ‘sharing’ problems and their solutions.
Start to use the division sign to record results, e.g. 12 ÷ 2 = 6.
Make different arrays with 12 counters and record results.
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Explain and compare his results with a partner.
Fifty pence Teacher's notes
Uses coins and recognises values up to 50p.
Makes amounts totalling 50p using coins of the same value and of mixed values.
Predicts that nine 5p coins will equal 50p and checks.
Counts on in 5p and 10p coins up to 50p.
Checks some amounts by re-counting.
Next steps
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Make a record of some amounts he finds.
Check totals, explaining his mental strategies to a partner.
Investigate whether 50p can made with 1 coin, 2 coins, 3 coins, … 10 coins and record findings.
Find as many ways as possible of making 50p with silver coins only.
Talk about how he knows he has found all possible ways.
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What the teacher knows about Ben’s attainment in Ma2, Number Ben counts sets of up to 100 objects reliably and is starting to count on in tens and ones, having decided that counting on in ones ‘takes too long.’ He reads numbers to 100 and shows the beginnings of understanding place value. For example, he knows that ‘9’ in ‘98’ represents nine tens. He generally writes numbers to 100 correctly but sometimes transposes multiples of 10, e.g. writes ‘02’ for ‘20’ but reads it as twenty. Sometimes he reverses digits, especially 5, but this is becoming less frequent. He orders numbers to 100 and recognises some numbers that are greater than 100. Ben understands addition as finding the total of two or more sets and subtraction as ‘take away’. He uses the ‘+’, ‘–’ and ‘=’ signs correctly, including in independent work as when he ‘makes 50’. He is starting to solve missing number problems. For example, when his teacher covers a number that is part of a calculation he has written, he names the missing number. He finds onehalf and one-quarter of given shapes and knows that the parts in each shape need to be equal. Ben has good mental recall of addition and subtraction facts to 10 and solves missing number problems mentally. For example, when asked what number to add to three to make 10, he answers correctly with little hesitation. He adds several small one-digit numbers during a game that took a minute and gives the correct total. He applies his knowledge of number bonds to 10 to derive answers that use larger numbers, such as 40 + 10. He makes amounts to 50p and counts the amounts mentally using a range of coins. When sharing 12 cakes among six characters, he gives out two cakes at a time, showing that he is working out answers in his head then checking by sharing. He uses mental calculation strategies to count in twos, fives and tens to 50 when counting on using 2p, 5p and 10p coins. Ben has good mental calculation strategies to solve number problems, including those involving money up to £1. Ben solves ‘story’ problems mentally and, with support, is starting to explain how he works out answers. He uses practical materials to solve problems as he does when sharing 12 cakes among characters in a story and finding sets of coins that make 50p. He recognises when he has to add or subtract to solve problems and records using symbols ‘+’, ‘–’ and ‘=’. For example, he uses the symbols correctly when recording different ways to make 50. Ben mostly chooses to solve problems mentally or practically rather than using written methods but, with support, he is starting to record more.
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Summarising Ben’s attainment in Ma2, Number Ben meets the criteria for all six assessment focuses at level 1 for Ma2. At level 2, he meets the majority of the assessment focuses at least in part. In the assessment focus, Operations, relationships between them, Ben has yet to demonstrate attainment at level 2. He does not yet understand that subtraction is the inverse of addition, for example by finding different ways to make four number sentences using trios of numbers such as 15, 8 and 7. He has not made statements such as, ‘Double five is ten. Half of ten is five.’ to help him understand that halving ‘undoes’ doubling. In the assessment focus Fractions, his experience is limited to folding and shading shapes to show halves and quarters so he has yet to find halves and quarters of small numbers of objects or halves of shapes that are divided into, for example, four or eight equal regions. Although he meets the first two assessment criteria in Numbers and the number system, he has yet to recognise sequences of numbers, including odd and even numbers. For the final assessment focus, Written methods, Ben records work in writing but does not yet do so consistently or independently due to his reluctance to show written methods for calculations. Reading the complete level descriptions for level 1 and level 2 confirms Ben’s teacher’s first judgement that his attainment is best described as level 2. Ben’s teacher knows that he has yet to meet some level 2 assessment criteria fully and consistently in different contexts. Consequently, the teacher refines her judgement to describe Ben as working at low level 2 in Ma2. To become more secure at level 2, Ben should partition two-digit numbers into tens and ones, including multiples of 10, so that he uses zero as a place holder in the ‘ones’ position and avoids transposing digits. He should continue sequences of numbers that increase or decrease by a QCA 00022-2009DWO-EN-01
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21 of 38 The National Strategies Primary Primary Framework for literacy and mathematics, Ben mathematics constant amount. He should also recognise odd and even numbers in and out of sequence so that he eventually recognises whether a number is odd or even by its final digit. He should extend his experience of shading shapes to show halves and quarters to finding halves and quarters of small quantities. He should learn about the inverse relationship between addition and subtraction. He should engage in practical then written activities that will lead to him understanding that halving is the inverse of doubling. Ben already has some effective mental strategies for solving number problems and knows when to add or subtract. He should build on these skills by recording how he works out answers to some mental calculations, for example as number sentences or as jumps on a self-drawn number line. He should also solve more addition and subtraction problems using numbers, money or measures that require him to show working. The problems should include adding and subtracting pairs of two-digit numbers that require bridging the tens.
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Ma3 Shape, space and measures 3-D shapes Teacher's notes
Recognises and names common 3-D shapes including square-based pyramid.
Visualises that a hidden 3-D shape with eight edges is a square-based pyramid.
Describes two cylinders using a range of vocabulary, e.g. ‘has a face at the top’, ‘is round at the bottom’ ‘has three faces’.
Describes one cylinder about 3 cm in height as ‘flat’.
Is starting to count faces and edges.
Next steps
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Order 3-D shapes by their number of edges or faces.
Write clue cards about 3-D shapes to which a partner matches the shapes.
Write as many facts as possible about one 3-D shape.
Compare two 3-D shapes to find ways in which they are the same and how they differ.
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Shape pattern Teacher's notes
Responds to teacher’s instruction to make a repeating pattern with two shapes.
Chooses yellow hexagon, green triangle as repeating unit.
Positions 11 shapes that show five repeats of unit and one extra hexagon.
Describes pattern as having ‘six of these yellow roundy things’ (meaning hexagons) then names hexagon correctly after prompt from teacher.
When partner says that the hexagon has six sides, Ben implies that it has six corners also.
Names triangles correctly.
Next steps
Create a shape pattern and describe to a partner how to copy it.
Make a pictorial record of patterns created with dividing lines to show each repeat and details of shapes used.
Make repeating patterns that involve counting sides or corners, e.g. any shape with 3 sides, 4 sides, 5 sides and 6 sides as the repeating unit.
Cylinder Teacher's notes
Visualises a cylinder.
Knows that a cylinder has three faces.
Makes a pictorial record of a shape he is learning about.
Shows understanding that 3-D shapes can be represented in picture form.
Next steps
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Include with drawing all facts known about a cylinder including its name.
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Programmable toy Teacher's notes
Programmes toy to reach destination on square grid.
Uses single commands, e.g. ‘forward’ then ‘go’.
Interprets symbols to make robot move towards target.
Uses vocabulary such as ‘forward’, ‘turn’, ‘down’ to explain moves.
With the help of arrow symbols, is starting to distinguish between left and right turns.
Next steps
Programme toy to use multiple commands, e.g. pressing ‘forward, forward, turn left’ then ‘go’.
Programme toy to reach destination using a given number of moves or as few moves as possible.
Record the toy’s journey in words, symbols and pictures.
Instruct another child on how to programme toy to reach a destination.
Start to use ‘clockwise’ and ‘anticlockwise’ to describe direction of turn.
Bee-Bot Floor Robot © Virtual School Consultancy. Used with kind permission.
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Shapes in place Teacher's notes
Uses ordinal numbers ‘first’ to ‘seventh’.
Responds to questions about name shapes, e.g. ‘Can you name the third shape?’.
Correctly names hexagon, triangle and square.
Uses ordinal numbers to respond to questions about the position of shapes, e.g. ‘What is the position in the row of the gold triangle?’.
Combines knowledge of ordinal numbers and 2-D shapes.
Next steps
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Without prompting, make statements about the position of shapes.
Respond to more complicated questions, e.g. ‘Which shapes come between the second and fifth shapes?’.
Make a row of different 2-D or 3-D shapes, describe to a partner how to copy it, then compare results.
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Turtle Teacher's notes
Begins to use a computer program to move a screen ‘turtle’.
Uses single commands.
Interprets and uses symbols that represent straight-line movements and left and right turns.
Depends on symbols to help him negotiate left and right turns.
Programmes ‘turtle’ to reach a target destination.
Uses language such as ‘forwards’, ‘backwards’ and ‘turn’ to describe movements.
Next steps
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Record route taken by ‘turtle’ so that a partner can recreate it.
Use more than one command for each move.
Extend language of movement to include correct use of vocabulary such as clockwise/anticlockwise, left/right.
Recognise when the ‘turtle’ turns through a right angle.
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Sorting by length
Teacher's notes
After direct teaching, produces related written work independently.
Designs a sorting diagram to categorise objects by length.
Chooses to categorise objects by whether they are shorter or longer than 20 cm.
Designs a two-region sorting diagram using ‘smaller’ or ‘bigger’ as labels.
Finds objects to measure and chooses a ruler as measuring equipment.
Measures lengths of objects to find out if they are longer or shorter than 20 cm.
Records object name and length on his diagram.
Uses abbreviation ‘cm’ for centimetres.
Next steps
Use comparative language related to length more consistently, e.g. ‘longer’ rather than ‘bigger’.
Find objects that are between two lengths, e.g. between 15 cm and 20 cm long.
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Foot lengths Teacher's notes
Applies recent work on measuring in centimetres to collect data on foot length.
Chooses which data to collect.
Designs table to record names of children and length of their feet.
Chooses ruler and uses it correctly to measure feet to nearest centimetre.
Collects data from other children and records data independently.
Records length of feet using ‘cm’ notation, e.g. 23 cm.
Tries to design a block graph independently.
Labels graph ‘graph (on) feet size’.
Responds to questions such as, ‘How many children have feet that are 24 centimetres long?’ by counting blocks.
Next steps
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Check that all of the children in his list are represented on the graph.
Use the convention of leaving a space between columns.
Number the vertical axis accurately in a way that helps to read the number represented rather than counting individual ‘blocks’.
Label the axes to explain what each represents.
Talk or write about what he has found out, e.g. ‘The shortest foot was 17 cm long.’.
Think of questions to ask about his graph then try them out on a partner.
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Weighing Teacher's notes
Chooses mechanical scales when asked to find out how heavy objects are.
After revision, knows the units are kilograms and grams.
With support, interprets divisions that represent 25 gram increments.
After support, reads the scale to the nearest 25 gram division independently.
Records in grams.
Next steps
Record estimates before weighing.
Compare objects and use the language of comparison: heavier, heaviest, lighter, lightest.
Time in order Teacher's notes
Recognises photographs taken at different times during an event at school.
Cuts out six photographs and puts them in time order.
Numbers the photographs then describes what is happening in each.
Answers questions such as, ‘What does the fourth picture show?’.
Next steps
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Record what he is doing at home or school at hourly or half-hourly intervals and show events on a time line.
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30 of 38 The National Strategies Primary Primary Framework for literacy and mathematics, Ben mathematics What the teacher knows about Ben’s attainment in Ma3, Shape, space and measures Ben names triangles, circles, squares, rectangles and hexagons. He identifies edges and vertices and counts them. He uses the terms ‘edges’ and ‘corners’ but not consistently when describing shapes, sometimes resorting to everyday language. For example, he describes a hexagon as a ‘roundy thing’ then corrects to ‘hexagon’ after a prompt and says that ‘it has six of each’, implying six vertices and six edges. Ben recognises and names cubes, cuboids, cylinders, cones and pyramids. When handling shapes, he is starting to count faces, edges and vertices. For example, he explains that a cylinder has three faces, a face at the top, and a face at the bottom and that these two faces are round. During such explanations, he points to the relevant features and properties. He visualises some 3-D shapes, for example he predicts that a hidden shape with eight edges is a square-based pyramid and he draws a cylinder from memory. He often sorts 2-D and 3-D shapes by their mathematical names but, with support, goes on to use criteria such as the number of edges or faces. Ben responds to and uses positional vocabulary such as near, between, next to, across and under in a range of mathematical and cross-curricular activities including PE. He describes two faces of a cylinder as being ‘round at the top’ and ‘round at the bottom’. He also uses ordinal numbers and responds to questions such as, ‘Which is the sixth shape in the row?’ or ‘What is the position in the row of the gold triangle?’ Giving one command at a time, he uses arrow symbols, representing moves forwards and backwards and quarter turns to the left and right, to programme a floor robot to move to a target destination. He uses similar symbols to programme an onscreen ‘turtle’. In both activities, he uses language such as ‘forwards’, ‘backwards’ and ‘turn’ to describe the moves. Ben uses standard units of measurement. He measures lengths using both metres and centimetres. He chooses whether to use a metre stick or ruler depending on the context. For example, when finding objects longer or shorter than 20 centimetres, he chooses a ruler. He describes these objects as ‘bigger’ or ‘smaller’ than 20 cm rather than ‘longer’ or ‘shorter’. He uses a ruler accurately to measure lengths to the nearest centimetre. He knows abbreviations for metre and centimetre and uses them in lists, for example when he records foot lengths. Ben uses a scale labelled every 5 kilograms and with 1 kilogram sub-divisions to weigh himself but needs help to interpret the sub-divisions. When asked to weigh small desktop objects, he chooses a mechanical scale with increments representing 25 grams but labelled at every 100 grams. With support, he weighs objects in grams by reading the scales to the nearest 25 gram division. He records measurements in simple tables and diagrams, some of which he designs independently. After an event at school, he puts six photographs of the event in chronological order. He uses ordinal vocabulary to explain, for example ‘The fourth picture shows some of the houses we built.’. Ben reads an analogue clock face to tell the time on the hour and the half-hour. He is starting to read time on the quarter-hour. To measure capacity, Ben counts how many litre jugs are needed to fill three buckets. He records results and orders the containers by capacity.
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Summarising Ben’s attainment in Ma3, Shape, space and measures Ben meets the criteria for level 2 in the assessment focus Properties of shape. He names common 2-D and 3-D shapes and describes their properties. He also meets two of the three assessment criteria for Properties of position and movement. He uses positional language and distinguishes between straight and turning movements even though he does not yet give directions using clockwise and anticlockwise or left and right consistently. The gaps in Ben’s attainment in Ma3 relate mainly to work on angles. He does not recognise right angles in turns or understand angle as a measurement of turn. In the assessment focus, Measuring Ben meets the second and third criteria. Ben has progressed from using non-standard units to using standard units of length and mass. He uses metres and centimetres to measure length and is starting to use grams as well as kilograms to measure mass. He measures and compares capacities using a 1 litre measuring jug. He tells the time on analogue clocks at the hour and half-hour and is progressing towards telling time at the quarter-hour. After reading the level descriptions for level 2, Ben’s teacher confirms that level 2 is the ‘best fit’ for Ben’s attainment in Ma3. In view of how much of the level Ben demonstrates compared with what he has yet to achieve, Ben’s teacher recognises that he has achieved most of what is required. Consequently, she refines her judgement to secure level 2 for Ma3. To make further progress within level 2, Ben needs to develop a more in-depth knowledge of turning movements, in particular learning to distinguish between turning left and right and between clockwise and anticlockwise. He should learn to recognise that turning through a right angle is equivalent to making a quarter turn. From there, he should progress to comparing whole, half turns and quarter turns so that he begins to understand angle as a measurement of
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Ma4 Handling data Sorting by length
Teacher's notes
After direct teaching, produces related written work independently.
Designs a sorting diagram to categorise objects by length.
Chooses to categorise objects by whether they are shorter or longer than 20 cm.
Designs a two-region sorting diagram using ‘smaller’ or ‘bigger’ as labels.
Finds objects to measure and chooses a ruler as measuring equipment.
Measures lengths of objects to find out if they are longer or shorter than 20 cm.
Records object name and length on his diagram.
Uses abbreviation ‘cm’ for centimetres.
Next steps
Use comparative language related to length more consistently, e.g. ‘longer’ rather than ‘bigger’.
Find objects that are between two lengths, e.g. between 15 cm and 20 cm long.
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Foot lengths Teacher's notes
Applies recent work on measuring in centimetres to collect data on foot length.
Chooses which data to collect.
Designs table to record names of children and length of their feet.
Chooses ruler and uses it correctly to measure feet to nearest centimetre.
Collects data from other children and records data independently.
Records length of feet using ‘cm’ notation, e.g. 23 cm.
Tries to design a block graph independently.
Labels graph ‘graph (on) feet size’.
Responds to questions such as, ‘How many children have feet that are 24 centimetres long?’ by counting blocks.
Next steps
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Check that all of the children in his list are represented on the graph.
Use the convention of leaving a space between columns.
Number the vertical axis accurately in a way that helps to read the number represented rather than counting individual ‘blocks’.
Label the axes to explain what each represents.
Talk or write about what he has found out, e.g. ‘The shortest foot was 17 cm long.’.
Think of questions to ask about his graph then try them out on a partner.
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What the teacher knows about Ben’s attainment in Ma4, Handling data Ben sorts shapes and other objects using discrete sets, for example sorting 2-D shapes by the number of sides. He sorts using one criterion such as triangles/not triangles using given Carroll and Venn diagrams. Ben is starting to design diagrams, lists, simple tables and block graphs to record data he collects. For example, when sorting objects by length, he designs a two-region sorting diagram to categorise and record object names and their length. Ben also collects data from other children, such the length of their feet. He records the children’s names and foot lengths on a table he designs then uses data on the table to construct a block graph. Ben’s numbering of the frequency axis of his block graphs is not yet secure. For example, in his ‘graph of feet size’ he starts numbering at 1 rather than 0 and consequently colours only four blocks rather than five to represent the number of children with feet 23 cm long. To show the favourite fruits of classmates, he constructs a diagram where one symbol represents one child’s choice. Ben uses his own drawings of each type of fruit. He creates similar diagrams using a computergenerated data-handling program. He has yet to learn the convention for a pictogram of using a single symbol throughout. Ben interprets data by, for example, extracting information from a table and using it to create a block graph. He also interprets data by counting blocks or symbols on graphs and diagrams in response to questions such as ‘How many children like apples best?’ He sorts using one criterion and gives simple explanations about how he sorts objects. For example, when asked how he has sorted 2-D shapes, he points and says, ‘These are triangles. These are not triangles.’ However, Ben typically gives very brief responses to questions. Without prompting, he finds it difficult to explain his data or to make up questions that he can ask others about his work. Ben has made considerable progress in collecting and representing data in the latter part of Year 2.
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Summarising Ben’s attainment in Ma4, Handling data Ben meets all assessment criteria at level 1 in Ma4. He meets most of the criteria across the assessment focuses at level 2, either fully or in part. He has yet to sort objects and classify them using more than one criterion and to collect and sort data to test a simple hypothesis. When interpreting data, he meets part of the assessment criterion for communicating his findings since he does use simple lists and tables. He is also beginning to use block graphs even though he has yet to number the frequency axis accurately and to leave a space between columns. He also uses picture diagrams even though he does not yet use one symbol throughout for the diagram to be a pictogram. After reading across the complete level descriptions for level 1 and level 2, his teacher decides that Ben’s attainment in Ma4 is best described as level 2. To refine her judgement, Ben’s teacher takes into account the progress he has made recently, the gaps in his attainment and his limited talk about his data. Consequently, she refines her judgement to low level 2. To become secure in level 2, Ben needs to progress from sorting using one criterion to using more than one criterion, for example on two-criteria Venn and Carroll diagrams. Ben should continue to construct block graphs, number the frequency axis accurately in ones and then progress to numbering in twos. He should leave a space between columns on his block graphs. He should work independently to test a simple hypothesis that gives him a reason to conduct a survey. Ben should continue to respond to spoken and written questions that require him to interpret data. He should then try to make statements or pose questions about his data for others to answer.
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Taking the test into account Ben’s performance on the 2007 Key Stage 1 test fits the profile of what Ben’s teacher knows about his ongoing work in class. Ben achieved level 2C, using the level 2 paper. He attempted all questions in the test. He scored 11 marks, which is at the top end of the range for level 2C, 7 to 12 marks. He gained marks in questions 2, 3, 5, 6, 7, 9, 11, 13, 15, 23 and 27. From his ongoing classwork, Ben’s teacher describes his attainment in mathematics as a whole as low level 2. She judges that he is secure at level 2 in Ma3, Shape, space and measures and this is reflected in the test. Ben gained 5 of his 11 marks in questions that assess Ma3 and a further mark in a number question that required him to use ordinal numbers to identify a position. In his classwork Ben does not often show working for number problems and this is also evident in his test. Other than jotting down numbers given in the questions, there is no working throughout the booklet, even for calculations such as ‘24 + 68 =’ that Ben does not calculate mentally. In question 17, Ben’s incorrect answer was 10 less than the correct answer and he did not show a complete method to gain one of the two available marks. In the test Ben gained a mark for writing the missing numbers in a sequence that increased in steps of 3. In his ongoing classwork, Ben is not yet consistently accurate with a range of sequences such as those that decrease in steps of a constant size. He has yet to meet the criterion ‘recognise sequences of numbers, including odd and even numbers’. In his classwork, Ben’s reasoning is a weaker aspect of his attainment and, in this assessment focus of using and applying mathematics, is assessed as level 1. Again this was evident in his response to questions such as 12 that involved reasoning. Ben did not identify the two correct statements, ‘28 is less than 32’ and ’50 is more than 15’. Ben’s performance on the test confirms the teacher’s judgement, based on Ben’s ongoing classwork, that his attainment in the subject is best described as low level 2.
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Acknowledgements
Bee-Bot Floor Robot © Virtual School Consultancy. Used with kind permission.
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