1 of 33 The National Strategies Primary Primary Framework for literacy and mathematics, Bradley mathematics

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1 1 of 33 The National Strategies Primary Bradley Year 1 Secure level 2 Mathematics standards file About Bradley Bradley was born on 26 September He joined the nursery class of his school before moving into Reception and then Year 1. Bradley is now a six-year-old. This standards file represents his attainment in the summer term of year 1. Bradley s attainment across mathematics Subject level Ma1 Ma2 Ma3 Ma4 Secure level 2 Secure level 2 Secure level 2 Low level 2 High level 2

2 2 of 33 The National Strategies Primary Ma1 Using and applying mathematics Beads problem Is given the problem, There are 20 beads on five strings. How many beads on each string?. Chooses an approach: draws five strings on a white board and counts out twenty plastic beads. Loses sight of the initial problem and counts in twenties to 100 (i.e. finds the total of twenty beads on each of five strings). Reminded of the problem, There are just 20 beads, begins again. Shares 20 beads among the five strings. Concludes there are four beads on each string. Records = 4 next to his arrangement of beads. Solve a range of problems that involve addition, subtraction, multiplication or division. Use resources and his own recording to talk about how he has solved problems.

3 3 of 33 The National Strategies Primary Growing shapes Shown shapes made with linking cubes, understands how the shapes in the sequence grow. Asked to find the number of cubes in the tenth shape, chooses to record on a whiteboard. Writes numbers 1 to 10 and above them records the number of cubes in the first shape, second shape, third etc. Grows the shape and records the number of cubes. Explains his record, I had to find the tenth so I wrote one, two, three, four, five, six, seven, eight, nine, ten. I had three shapes to start with so I wrote one, three, five. I know there are two jumps between so I added on two to each number.. Demonstrates he has recorded the correct number of cubes for the tenth shape by counting the cubes in his model. Knows the number of cubes is always odd. Predicts the number of cubes in shapes up to the twentieth. Pose a similar challenge for other children and check if their solutions are correct.

4 4 of 33 The National Strategies Primary T-shirt patterns Identifies patterns in sequences of T-shirt designs. Predicts the next T-shirt for each sequence. Explains how he knows what comes next. Identify missing terms or what comes next in a number sequence and explain his reasoning.

5 5 of 33 The National Strategies Primary Measuring length Suggests different units and tools to measure the width of the classroom. Talks about how to use felt pens, each 11 centimetres long, and count on in elevens from 22. Decides to use a metre stick. Marks where each metre ends and places the stick accurately for the next metre. Records each metre on paper, up to six metres. On the last move of the stick refers to seven metres and the 65 cm needed to complete the measurement. Check his record of the number of whole metres measured. Compare his measurement of the width of the classroom with another child s and decide how to resolve any difference. Decide how to find out if this classroom is the same size as another and how accurate the measurements need to be for this purpose.

6 6 of 33 The National Strategies Primary Comparing containers Has four containers to find which holds most. With a partner records estimates. Uses a calibrated litre jug to scoop water from a tank but this does not fill the jug to the 1 litre mark. Since the litre jug is not full, decides to record the number (of millilitres) added each time. Records quarter (cworter) for the final small amount added, representing about one-quarter of a litre. Reads the measurements for each container: A, nine hundred and eight hundred and a quarter. B, eight hundred, eight hundred, nine hundred and a nine hundred and a quarter. C, eight hundred, four hundred and eight hundred. D, eight hundred, eight hundred and a seven hundred and a nine hundred. Concludes that container B holds most because it has four (amounts) there and it has a quarter. With the teacher work out how many millilitres in a quarter of the litre jug and use a calculator to find the total number of millilitres poured into each container. Talk about ways to find how many litres each of the containers holds, e.g. fill each container and use the contents to repeatedly fill the litre jug up to the litre mark. Decide how to describe a part of a litre, e.g. using a fraction or millilitres. Compare both sets of results and discuss any differences.

7 7 of 33 The National Strategies Primary What the teacher knows about Bradley s attainment in Ma1, Using and applying mathematics Bradley selects the materials and mathematics to use when he solves problems involving shapes, numbers and measuring. For example, he uses fingers and counting to solve problems involving addition and subtraction with numbers beyond the facts he knows. He represents multiplication problems as repeated addition and uses counters and diagrams to represent division problems. He uses a practical approach to begin an investigation such as growing L- shapes made from linking cubes. He recognises this as a number problem and records results in an organised way. As well as recording using symbols and diagrams, Bradley talks about his work using everyday and mathematical language. Bradley demonstrates how he knows an answer is correct, for example he talks through how he performed a calculation to show that he reached the correct answer. He demonstrates how he made a measurement to show that his result is correct. He does not yet talk about why an answer is reasonable. For example, he does not use arguments such as, We both had more than ten pence so altogether we must have more than twenty pence.. Similarly in measurement he does not talk about why a measurement is reasonable. He might explain, for example, I m more than a metre tall and I come more than halfway up the door so I think the height of the door is about two metres.. He is beginning to use pattern in results. For example, he noticed that the number of cubes in sequence of L-shapes increased by two each time and used this to predict how many cubes there would be in shapes up to the twentieth shape. He predicts what comes next in a simple spatial pattern, for example in T-shirt patterns he explains how extra circles are added to the design each time.

8 8 of 33 The National Strategies Primary Summarising Bradley s attainment in Ma1, Using and applying mathematics The teacher has just started to use the level 2/level 3 assessment guidelines, since Bradley has met all of the assessment criteria for level 1 consistently over a period of time. In each assessment focus Bradley s attainment is best described as level 2. Reading the complete level descriptions for these levels confirms her level 2 judgement. Bradley uses and applies mathematics described in levels 1 and 2 in Number, Shape, space and measures and Handling data with increasing independence. His teacher refines her judgement to secure level 2. To be considered as high in level 2, Bradley needs to solve a wider range of problems, investigate a wider range of situations and develop his reasoning.

9 9 of 33 The National Strategies Primary Ma2, Number Growing shapes Shown shapes made with linking cubes, understands how the shapes in the sequence grow. Asked to find the number of cubes in the tenth shape, chooses to record on a whiteboard. Writes numbers 1 to 10 and above them records the number of cubes in the first shape, second shape, third etc. Grows the shape and records the number of cubes. Explains his record, I had to find the tenth so I wrote one, two, three, four, five, six, seven, eight, nine, ten. I had three shapes to start with so I wrote one, three, five. I know there are two jumps between so I added on two to each number.. Demonstrates he has recorded the correct number of cubes for the tenth shape by counting the cubes in his model. Knows the number of cubes is always odd. Predicts the number of cubes in shapes up to the twentieth. Pose a similar challenge for other children and check if their solutions are correct.

10 10 of 33 The National Strategies Primary Number sequences Recognises sequences that increase and decrease in steps of two from an odd or an even number. Recognises when a sequence increases in steps of ten. Calculates other differences, mostly accurately. Talk about patterns in sequences such as 78, 73, 68, 63, 58, 53, 48, 43

11 11 of 33 The National Strategies Primary Halves of shapes and numbers Uses reflection symmetry to colour half of each symmetrical shape. Colours half the number of squares contained by other shapes. Find one-quarter of shapes by folding. Record the fraction he has coloured using fraction notation. Halve quantities and use fraction notation in this context, e.g. 2 1 of 18 = 9

12 12 of 33 The National Strategies Primary Addition and subtraction Knows that addition can be done in any order. Given an addition sentence, generates related addition and subtraction sentences. Talk about a number sentence such as = 23 and the operation that will undo + 18 or get us back to 5 again. Experiment making longer number sentences that begin and end with the same number, e.g = 10, adding several numbers and using subtraction as the inverse for each addition. Doubling and halving

13 13 of 33 The National Strategies Primary Explains how knowing doubles facts can help with halving, You can halve twenty if you know double ten..

14 14 of 33 The National Strategies Primary Using repeated addition Solves word problems such as: Four hens with 2 legs. How many legs altogether? Two teams of 8 children play a game. How many children in the game? Six tables in the classroom and 5 children at each table. How many children altogether? Represents the problems as repeated addition. Counts in twos, fives and tens for some examples. Begin to derive and recall multiplication facts relating to 2, 5 and 10. Money problems

15 15 of 33 The National Strategies Primary Solves money problems involving finding totals and giving change. Uses addition and subtraction sentences to represent the problems. Talks about his results in the context of the problem. Beads problem Is given the problem, There are 20 beads on five strings. How many beads on each string?. Chooses an approach: draws five strings on a white board and counts out twenty plastic beads. Loses sight of the initial problem and counts in twenties to 100 (i.e. finds the total of twenty beads on each of five strings). Reminded of the problem, There are just 20 beads, begins again. Shares 20 beads among the five strings. Concludes there are four beads on each string. Records = 4 next to his arrangement of beads. Solve a range of problems that involve addition, subtraction, multiplication or

16 16 of 33 The National Strategies Primary division. Uses resources and his own recording to talk about how he has solved problems.

17 17 of 33 The National Strategies Primary What the teacher knows about Bradley s attainment in Ma2, Number Bradley groups larger numbers of objects and counts reliably in twos, fives and tens. Bradley uses base 10 materials to represent numbers to 100. He puts sets of numbers up to 100 into order. Bradley recognises ascending and descending sequences of odd and even numbers. When growing an L-shape with linking cubes, for example, he recognised that he added two cubes each time and predicted the number of cubes in shapes up to the twentieth in the sequence. With sequences such as 26, 36, 46 he often counts on to find the difference between terms. Bradley is beginning to use place value and pattern in the digits to recognise that a sequence such as this increases in steps of ten. He recognises multiples of 5 and multiples of 10 although he does not yet use the term multiples. Bradley folds a range of paper shapes into halves and quarters: He finds different ways to fold the square into halves and quarters and different ways to fold the long rectangle into quarters. He identifies the region that represents one-half or one-quarter of each shape. When colouring halves of shapes drawn on squared paper, as well as using reflection symmetry Bradley also counts squares and colours half of them. In giving and following instructions, Bradley uses whole, half and quarter turns. Bradley knows the names of these fractions but does not yet use fraction notation. Working with money, Bradley has been introduced to decimal notation for pounds and pence. Bradley understands that addition can be done in any order. He knows that subtraction can be used to undo addition. He uses this to generate sets of related number sentences involving addition and subtraction. Bradley explains how knowing doubles facts can help to halve a number. He knows doubles facts up to double ten and uses them to halve an even number up to 20. He doubles and halves some numbers beyond this range. Bradley recalls addition and subtraction facts to 10. Bradley uses mental calculation and counting to solve word problems. He solves problems involving addition and subtraction including finding total costs and giving change. He records his calculations as number sentences. Bradley uses objects and drawings to model and solve multiplication and division problems. He uses repeated addition to represent some multiplication problems and counts in twos, fives and tens or uses doubling to solve them.

18 18 of 33 The National Strategies Primary Summarising Bradley s attainment in Ma2, Number Bradley s attainment in Number is best described as level 2 in each assessment focus for number. Reading the complete level descriptions for levels 2 and 3 confirms the teacher s level 2 judgement. Considering how much of the level Bradley demonstrates, his teacher recognises that Bradley has some more learning to do within level 2. He needs to consolidate and extend his understanding of place value and operations, for example using a number line as well as base 10 materials to represent numbers and calculations. He needs to develop his use of addition facts to help him calculate rather than count. For example, he might find pairs of numbers that add to 10 when he adds several single-digit numbers or solves problems involving larger numbers. Apart from these aspects, Bradley demonstrates the mathematics independently and in a range of contexts. His teacher refines her judgement to secure level 2.

19 19 of 33 The National Strategies Primary Ma3 Shape, space and measures Sorting 3-D shapes Chooses his own criteria to sort 3-D shapes into a Venn diagram. Uses flat faces and curved faces. Overlaps the sorting circles to create a region for shapes that meet both criteria. Use discussion to refine understanding of terms such as, face, edge, vertex, surface. Choose other criteria for sorting the same shapes so that some shapes do not belong in either circle. Set problems for others to solve, e.g. sort shapes and ask a partner to work out the criteria used.

20 20 of 33 The National Strategies Primary Moves The Infant Video Toolkit 2Simple Software Used with kind permission. Uses arrow keys and numbers to move a car around the computer screen. Distinguishes straight and turning movements. Describes the direction of straight-line moves and turns in relation to his own position, e.g. go right three times and go backward as the car moves forward. Instruct a programmable toy to move along a desired pathway on the floor. Record individual instructions/moves. Use the record to plan a set of instructions for the complete journey. Test by entering the set of instructions and checking that the toy completes the journey.

21 21 of 33 The National Strategies Primary Measuring length Suggests different units and tools to measure the width of the classroom. Talks about how to use felt pens, each 11 centimetres long, and count on in elevens from 22. Decides to use a metre stick. Marks where each metre ends and places the stick accurately for the next metre. Records each metre on paper, up to six metres. On the last move of the stick refers to seven metres and the 65 cm needed to complete the measurement. Check his record of the number of whole metres measured. Compare his measurement of the width of the classroom with another child s and decide how to resolve any difference. Decide how to find out if this classroom is the same size as another and how accurate the measurements need to be for this purpose.

22 22 of 33 The National Strategies Primary Comparing containers Has four containers to find which holds most. With a partner records estimates. Uses a calibrated litre jug to scoop water from a tank but this does not fill the jug to the 1 litre mark. Since the litre jug is not full, decides to record the number (of millilitres) added each time. Records quarter (cworter) for the final small amount added, representing about one-quarter of a litre. Reads the measurements for each container: A, nine hundred and eight hundred and a quarter. B, eight hundred, eight hundred, nine hundred and a nine hundred and a quarter. C, eight hundred, four hundred and eight hundred. D, eight hundred, eight hundred and a seven hundred and a nine hundred. Concludes that container B holds most because it has four (amounts) there and it has a quarter. With the teacher work out how many millilitres in a quarter of the litre jug and use a calculator to find the total number of millilitres poured into each container. Talk about ways to find how many litres each of the containers holds, e.g. fill each container and use the contents to repeatedly fill the litre jug up to the litre mark. Decide how to describe a part of a litre, e.g. using a fraction or millilitres. Compare both sets of results and discuss any differences.

23 23 of 33 The National Strategies Primary Parcels problem Solves the problem of ordering parcels for dad to carry the heaviest, Biff the middle parcel and Kipper the lightest. Describes ordering the parcels by feeling how heavy they are. Demonstrates by balancing pairs of parcels. Prompted by the teacher, uses weights. Balances each parcels with a number of uniform masses. Records the numbers: 22, 14, 32. Counts on from 22 to 32 to find how many more balanced with Dad s parcel than Biff s.

24 24 of 33 The National Strategies Primary What the teacher knows about Bradley s attainment in Ma3, Shape, space and measures Bradley names shapes, such as circle, square, triangle, pentagon, hexagon, cube, cuboid and cylinder. He uses everyday language to talk about the features of shapes, for example faces, edges and corners. Bradley describes the properties of shapes that he sorts, for example he explains the pentagon has five sides and five corners. Bradley responds to positional language, for example he locates the tenth rung of the ladder. He distinguishes between straight and turning movements when he instructs a car to move around a map onscreen, commenting Turn right and stay on that spot.. Bradley uses whole, half and quarter turns, left and right in instructions. He knows left and right in relation to his own position. He does not yet recognise right and left for a partner who is facing him. He understands how to use uniform non-standard and standard units to measure length. Bradley knows that centimetres and metres are widely used and chooses a ruler to measure straight lengths. He positions a ruler with reasonable accuracy and measures short lengths to the nearest centimetre. Bradley uses a metre stick with centimetres labelled to measure longer lengths such as the width of the classroom. He describes the measurement using a number of whole metres and centimetres but does not yet record using mixed units. To solve a weighing problem, Bradley handles three objects and estimates which is the heaviest and the lightest. When using the balance he understands that the bar should be level to start. He balances pairs of objects to confirm which is heavier and uses logic to order three items. He also balances objects with a number of uniform masses but does not yet use grams or kilograms. To compare how much different containers hold he starts with them empty and counts how many cupfuls of water he pours in to fill them. He aims to fill each almost to the top. Bradley knows the litre as a unit for measuring liquids. He uses a litre jug and is aware of a scale on the jug. He reads numbers from the scale to the nearest hundred. He does not yet know that the scale shows millilitres or how these relate to the litre. When he found which of four containers held most, he recorded several amounts in hundreds to represent the water he poured into them. He also recorded smaller amounts as a quarter. For two containers he recorded four amounts in hundreds. Comparing his recorded information about them, he reasoned that one held more because it has four (amounts) there and it has a quarter. He treated the listed amounts as roughly comparable and used the extra quarter of a jug to decide which was the larger. Bradley knows the order of everyday events and reads the time from an analogue clock on the hour.

25 25 of 33 The National Strategies Primary Summarising Bradley s attainment in Ma3, Shape, space and measures In each assessment focus his teacher judges that Bradley s attainment is best described as level 2. Bradley does not meet all of the assessment criteria for level 2 and his attainment in Shape, space and measures is not as strong as in the other attainment targets. Consequently his teacher reads the complete level descriptions for levels 2 and 3 and checks back to level 1, to confirm her level 2 judgement. Reviewing how much of the level, how consistently Bradley demonstrates the mathematics and the range of contexts in which he applies it, his teacher refines the overall judgement for Shape, space and measures to low in level 2. To make further progress within level 2 and towards level 3 Bradley needs to refine his understanding of the features and properties of shapes. He should apply his understanding to shapes that do not have equal sides and equal angles. He might recognise, for example, that all of the examples below have five edges and are pentagons and refine his understanding of corner. He should use the term right angle to describe a quarter turn and recognise right angles in shapes. He should begin to sort shapes using two criteria, for example to identify pentagons that have a right angle.

26 26 of 33 The National Strategies Primary Bradley needs to measure in a broader range of contexts. He should measure for a purpose, such as comparing two lengths that cannot be placed side by side. He should also measure in contexts that require some consideration of appropriate accuracy.

27 27 of 33 The National Strategies Primary Ma4 Handling data Sorting 3-D shapes Chooses his own criteria to sort 3-D shapes into a Venn diagram. Uses flat faces and curved faces. Overlaps the sorting circles to create a region for shapes that meet both criteria. Use discussion to refine understanding of terms such as, face, edge, vertex, surface. Choose other criteria for sorting the same shapes so that some shapes do not belong in either circle. Set problems for others to solve, e.g. sort shapes and ask a partner to work out the criteria used.

28 28 of 33 The National Strategies Primary Favourite 2-D shapes Ginn and Co. (1999) Abacus Evolve Activity Book PCM29. Used with permission from Pearson Education Ltd. Asks children to choose their favourite shape from the class set. Lists shapes and records children s names as they choose. Represents the information on a prepared block graph. Answers questions that involve comparing two columns, e.g. How many more children like squares than circles?. Poses his own question, How much people like hexagons than rectangles?. Goes on to count the blocks he has coloured to find out how many children took part in the survey. Recognises the first column represents four children and counts on in ones. Pose his own questions that begin, How many more. Begin to interpret graphs and diagrams where one symbol represents two items or events. Ginn and Co. (1999) Abacus Evolve Activity Book PCM29. Used with permission from Pearson Education Ltd.

29 29 of 33 The National Strategies Primary Letters Chooses his own subject for a survey and asks children to choose a letter group. Uses a tally to records children s choices. Represents the information in a block graph. Knows the convention of leaving a space between columns. Writes a question to ask about his graph: How much children like A D and V Z?. Talk about what his graph shows. Refine questions about his graph. Talk about the types of information from surveys that could be useful, e.g. children s favourite stories could be used to help the teacher decide which to read.

30 30 of 33 The National Strategies Primary Cars Given a set of information about the colours of cars enters it in a database. Selects a format for the graph and chooses symbols, each to represent one car and its colour. Gives the graph a title. Answers questions about the most popular colour, least popular colour, the number of people choosing a particular colour and how many more preferred one colour to another.

31 31 of 33 The National Strategies Primary What the teacher knows about Bradley s attainment in Ma4, Handling data Bradley sorts objects using one or two criteria into Venn diagrams. In science, for example, he sorts musical instruments according to how the sound is produced. He uses criteria such as tapping and rubbing. He knows that sound is produced on some instruments by tapping and by rubbing and recognises that overlapping the circles provides a region for them. He places instruments such as the panpipes outside the circles as they do not meet either criterion. Bradley suggests how to find the favourite book of the class by writing all of the titles and asking everyone which one they choose. He explains that to be fair everyone should be asked only once. Bradley chooses his own subject for a survey. For example, he asks other children to choose their favourite from his list of 2-D shapes. For his surveys, he keeps a tally or lists children s names against choices. He uses a block graph or bar chart to represent data, with one block or one increment on the vertical scale representing one item. He interprets a pictogram where one symbol represents one person. Interpreting his own and other children s graphs and diagrams, Bradley identifies the most and least common or popular categories. He counts the number represented in one category and is beginning to use the scale to read values. He counts symbols to find out how many children took part in the survey. He compares data to answer questions such as How many more children chose red than chose blue?. Bradley poses clear questions about some aspects of his data although his comparative language is confused. For example, he asks, How much people like hexagons than rectangles?.

32 32 of 33 The National Strategies Primary Summarising Bradley s attainment in Ma4, Handling data In both assessment focuses Bradley s attainment is best described as level 2. Reading the complete level descriptions for levels 2 and 3 confirms the level 2 judgement. Bradley meets most of the assessment criteria in level 2 consistently and is beginning to meet some in level 3. His teacher refines the judgement to high level 2. To consolidate his progress in level 2 and move into level 3, Bradley should begin to sort numbers as well as shapes and other objects. He should collect and sort data to test a simple hypothesis such as more children read fiction than non-fiction when we choose books. Bradley should begin to group tallies in fives, for example, to make counting them easier. As he represents larger numbers, he should use one symbol to represent 2 items and interpret the scale on graphs where one division represents 2.

33 33 of 33 The National Strategies Primary Acknowledgements The Infant Video Toolkit 2Simple Software Used with kind permission. Ginn and Co. (1999) Abacus Evolve Activity Book PCM29. Used with permission from Pearson Education Ltd.