Justin s mathematics (overall level 2A)

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1 Ma KEY STAGE 1 Mathematics exemplification SEPTEMBER 2006 This is one of a series of six leaflets intended to exemplify children s performance in mathematics at levels 2A and 3. They illustrate how judgements can be made by taking into account strengths and weaknesses in performance across a range of contexts and over a period of time, rather than focusing on a single piece of work. They also show how a child s test result can be taken into account when making a judgement. The examples show work typical of the child s performance across mathematics. They are followed by details of how the teacher uses the work to make a judgement about the child s level. Justin s mathematics (overall level 2A) Ma1 Using and applying mathematics Corners problem uses practical resources provided by the teacher: squares, hexagons, triangles and a bag baseboard selects shapes until he has 24 corners records results as a list succeeds in finding four of the nine possibilities compare results with other children identify results that are the same compile a group list of different possibilities Justin uses the approaches modelled by the teacher to solve problems and investigate situations. For example he found how many different towers can be built with three cubes that could be red or yellow by building them. He displayed the towers of cubes as his record. When he ran out of cubes, Justin recorded those he had made by colouring on squared paper. He found the eight possibilities. When solving the corners problem, Justin placed shapes on a bag baseboard until he had the required 24 corners and then recorded the number of different shapes. When prompted, Justin checked that he did not have any repeats. In both activities, Justin finished when he could not think of other possibilities. He needs further modelling of collecting and ordering class results to develop his own strategies for checking. QCA/06/2870 Qualifications and Curriculum Authority

2 Ma2 Number Multiplication as arrays and repeated addition represents multiplication as arrays beginning to represent multiplication as repeated addition finds answers to calculations by drawing dots and counting in ones consolidate multiplication as repeated addition use known addition and multiplication facts when calculating 2 and 2 understands doubling as 2 and halving as 2 knows halves and doubles up to double 10 doubles and halves some two-digit and larger numbers Justin finds missing numbers in sequences that go up or down in steps of 2 or 10 and sequences of multiples of 5. He has a developing understanding of place value, representing two-digit numbers with base 10 rods and cubes. Although he reversed digits when recording numbers earlier in the year, he now uses his understanding of place value to record two- and three-digit numbers correctly. He rounds a two-digit number to the nearest 10. Justin is beginning to use p notation to record amounts of money such as 1.56 where there are 10 or more pence. He finds one half and one quarter of shapes and numbers up to 20 where the answer is a whole number. Justin knows addition and subtraction facts to 10. He is beginning to use these facts and his understanding of place value when he adds and subtracts multiples of 10. He understands subtraction as taking away and as the inverse of addition. Using base 10 rods and cubes and a number line, Justin compare numbers and is working towards understanding subtraction as difference. Justin represents multiplication as an array of dots and understands it as repeated addition. He understands division as sharing and is beginning to understand it as repeated subtraction or, for example, how many fives in 30. When calculating, Justin often draws dots or uses a 100-square and counts. However, he can work mentally to add two two-digit numbers where he does not need to bridge 10. As a written method, Justin partitions two-digit numbers, adds the tens and the units digits and then uses these results to reach the total. Using this written method he is successful with examples that involve bridging tens. Justin knows multiplication and division facts relating to the 10 and 2 tables. He counts on from 0 and back in steps of 5 or 3. He solves money problems such as finding the total cost of an item at 24p and one at 13p. With support he finds change from 1. QCA/06/2870 Qualifications and Curriculum Authority

3 Ma2 Number: Processing, representing and interpreting data (level descriptions in Ma4 Handling data) Favourite fruit interprets table of class votes to draw a block graph independently changes the labelling of the vertical axis to help read the heights of columns accurately checks heights of columns and corrects by crossing out one block uses the graph to answer questions about most popular, how many more children liked apple than pear and how many voted altogether consolidate labelling of vertical axis to help read the height of columns record graph on smaller grid using one block to represent two votes Justin records data as tallies. He draws block graphs and pictograms where one square or symbol represents one item or event. Where the recording grid was not long enough to record all of the votes for one flavour of icecream, Justin did not consider using one symbol to represent two votes or using a larger grid. He overcame the difficulty by ignoring one vote. Justin counts squares or symbols to answer questions such as: How many more children voted for strawberry than vanilla ice-cream? How many children voted altogether? Which was the most popular flavour? Which was least popular? He does not yet number the vertical axis of his block graph to be able to read the height of columns. QCA/06/2870 Qualifications and Curriculum Authority

4 Ma3 Shape, space and measures Irregular shapes sorts irregular shapes using the number of edges identifies pentagons, hexagons and octagons Reflection reflects half-letter shapes to find words draws some lines of symmetry on 2-D shapes Capacity investigation estimates how many small cups of water will fill five different containers records pictorially by drawing estimated number of cups overturned above each container, 1 5 measures accurately using small cups of water and records the number when measuring the capacity of larger containers, stop at about half-way and decide if the estimate need to be adjusted In practical activities, Justin names 2-D shapes and 3-D shapes such as cube, sphere and cone. He talks about the properties of shapes, describing a cone as having one corner, one curved edge and one flat face, for example. He recognises right angles in a range of regular and irregular 2-D shapes and points out the right angles on the faces of a cube. He reflects simple patterns and shapes in a mirror line and draws some lines of symmetry on 2-D shapes. Justin follows instructions using left and right. He rotates shapes and drawings through quarter- and half-turns, clockwise and anticlockwise. He knows that a full turn brings a shape back to its starting position. Justin measures to the nearest centimetre using a ruler, or to the nearest metre when using a metre stick for longer distances. He tells the time on an analogue clock on the hour, half-hour and at quarter to and quarter past. He is reasonably confident about units of time: 60 seconds in a minute; 60 minutes in an hour; 24 hours in a day; and 7 days in a week. He makes a sensible choice of unit to measure the time it takes for different activities, for example to write his name, walk to school, go swimming or for a holiday. He uses units of 100 grams for weighing. QCA/06/2870 Qualifications and Curriculum Authority

5 Reaching an overall judgement for mathematics from ongoing work Overall, in Ma1 Using and applying mathematics, Justin s teacher considers he is best described as a secure level 2. He follows the approaches that are modelled and sometimes selects the mathematics to use. He uses mathematical language to talk about his work and records it using simple diagrams and symbols. For Ma2 Number including handling data, Justin s teacher considers him to be a strong level 2. To move into level 3, Justin needs to develop his use of decimal notation for money including the use of zero as a place holder in amounts such as 2.05 and the convention of always showing two decimal places in amounts such as He should be introduced to negative numbers in a context. He needs a firmer grasp of addition and subtraction facts to 20 and to become more fluent with multiplication facts for 5 as well as 2 and 10 tables. This should increase his confidence when calculating and reduce his need to count in ones. To move into level 3 for handling data, Justin should learn to draw graphs and pictograms where one square or symbol represents more than one item. His teacher judges that Justin is working at the top of level 2 in Ma3 Shape, space and measures. To move into level 3, Justin needs to consolidate his knowledge of common 3-D shapes and recognise them from drawings. He needs more experience of measuring for a purpose, such as comparing two distances jumped to see who has jumped furthest. In contexts like this he should develop a sense of appropriate accuracy. He should begin to use mixed metres and centimetres to measure lengths between whole metres more accurately, for example 1 m 15 cm. He should also begin to measure small lengths to the nearest half-centimetre. Across mathematics, Justin s performance is best described as level 2A. Taking the test into account Justin achieved level 2A in the 2006 key stage 1 test, using the 2005 level 2 paper. Justin attempted all of the questions in the test. He made errors in questions 4, 8, 14, 16, 18b and 25. He scored 22, which is 3 marks above the 2A threshold. His performance on the test is typical of his work in class. He finds ways to get started on problems. For example, in question 23, he had to draw a square, on a grid, so that there were 16 small squares inside. He started by drawing a 6 6 square and numbering the small squares inside. He recognised his square was too big and drew dots in rows of five as a next trial. Finally he drew dots in rows of four and drew around them to make the correct 4 4 square. Justin solves word problems where he can calculate mentally, as in questions 6 and 9, but does not always manage those involving larger numbers. In question 25, for example, Justin recorded 4 15 as the correct operation for the problem but was not able to calculate correctly. He showed good understanding of place value in his response to question 19. He identified the largest number from the set of 201, 211, 102, 120 and 210. He uses a number line confidently for addition and, in question 24, identified the sum that Fred s number line record represents. In question 10, Justin used the nearest multiple of ten when he adds 7 to 13 to achieve 20 and then added the additional 3 to reach 23. He understands that subtraction is the inverse of addition and used the numbers in the addition sentence, in question 20, to make the two subtraction sentences correct. He identified multiples of 5, in question 21. In question 12, Justin counted the number of shells and shared the 12 shells between four children. He drew four faces and recorded the division by showing equal groups of three dots alongside each face. However, he did not use a pictorial or other written approach to answer question 14, How many 2p coins make 20p? and was not successful in working mentally. For the first part of question 4, Justin drew a ring around two different numbers and crossed each of them out. He did not circle 34 and his teacher assumes that he misheard. In the second part of the question, Justin did not notice that the grid had rows of eight squares and treated it as a 100-square. He wrote 56 as the number that should appear below 46. Although Justin is beginning to use addition facts to 20 and place value to add and subtract multiples of 10, he did not give the correct answer to question 16, which was =. When interpreting the graph in question 18, Justin compared the bar for green car with the bar for the blue car to answer, How much further did the green car roll than the red? He did, however, interpret the numbering of the axis and gave the answer 10. Justin did not interpret the 2-D drawing of the 3-D shape, in question 8, and selected the triangle as the shape that Fred drew around the base of the cone. The test result confirms the teacher s judgement that Justin s mathematics is best described at level 2A. QCA/06/2870 Qualifications and Curriculum Authority