Maths app annotated_-_copy

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Maths app annotated_-_copy

  1. 1. Assessing pupils’ progress in Mathematics 1
  2. 2. KEY All text in black is quoted from the Big Sheets. The entire text of the Mathematics Assessment Criteria appear in this PowerPoint. 2
  3. 3. KEY All Teacher’s notes in white are taken from the guidance on the DCSF website for primary and secondary school’s. The links (in blue as below) are to the web-pages or documents from which each example is taken, which go into more detail. (Please note that some slides are used twice if they apply to two Assessment Focuses) Primary Maths APP guidance Secondary Maths APP guidance 3
  4. 4. THERE ARE TWO MAJOR AREAS OF ASSESSMENT IN APP MATHS: 4
  5. 5. 1) Using and applying mathematics, shape, space and measure and handling data 5
  6. 6. 2) Number and algebra 6
  7. 7. LET’S BREAK THEM DOWN A LITTLE 7
  8. 8. NO, NOT LIKE THAT 8
  9. 9. Assessing pupils’ progress in Mathematics - Using and applying mathematics, shape, space and measure and handling data 9
  10. 10. Using and applying mathematics 10
  11. 11. Using and applying mathematics LEVEL 2 11
  12. 12. Using and applying mathematics: LEVEL 2 Teacher's notes        Identifies what she has to do. Models the problem with paper circles and counters. Starts by placing three counters on each paper circle. Moves one counter at a time and checks results. Writes numbers in the given diagram to record her arrangement of counters. Finds arrangements where lines total 8 but forgets there must be a different number on each plate. Places a different number on each plate and creates lines that add to 9. APP mathematics standards file: Hannah (Year 2 secure level 2
  13. 13. Using and applying mathematics LEVEL 3 13
  14. 14. Using and applying mathematics: LEVEL 3 Teacher's notes       understands the criteria: quilts have six squares and at least one square of each of three available patterns decides to use a trial approach identifies lines of symmetry within the time limit, compares diagrams with others in the group to draw her own conclusion in discussion with the teacher, convinces herself that it is not possible to make a quilt with two lines of symmetry explains the problem to others. APP mathematics standards file: Saleema (Year 4, secure level 3)
  15. 15. Using and applying mathematics LEVEL 4 15
  16. 16. Using and applying mathematics: LEVEL 4 Teacher's notes    recognises the least number that can be made is 2 and the greatest is 18 works systematically to list all possible addition pairs for each total describes patterns in the columns of numbers she has recorded APP in mathematics at Key Stage 3: Standards file – Pupil B p.6
  17. 17. Using and applying mathematics LEVEL 5 17
  18. 18. Using and applying mathematics: LEVEL 5 Teacher's notes      works methodically, drawing and labelling rectangles of increasing length presents her work in a clear and organised way identifies a pattern in results and expresses a generalisation using function machines predicts the number of border tiles needed for much longer rectangles poses her own questions to extend the work and investigates borders for rectangles that are 2 units wide, then 3 units wide APP in mathematics at Key Stage 3: Standards file – Pupil C p.18
  19. 19. Using and applying mathematics LEVEL 6 19
  20. 20. Using and applying mathematics: LEVEL 6 Teacher's notes      uses trial and improvement to create parallelograms with the same base and area• looks for relationships between the parallelograms and the rectangle other than base and area concludes that they all have the same (perpendicular) height even though the sloping sides are different lengths asserts a formula is possible ‘but you must use height because the sloping side changes so you can’t use it’ gives the formula as A = b × h APP in mathematics at Key Stage 3: Standards file – Pupil R p.12
  21. 21. Using and applying mathematics LEVEL 7 21
  22. 22. Using and applying mathematics: LEVEL 7 Teacher's notes   Solves multi-step problems requiring Pythagoras’ theorem Calculates accurately using mental and calculator methods Standards file – Pupil V p.11  APP in mathematics at Key Stage 3: Selects appropriate methods and communicates clearly
  23. 23. Using and applying mathematics LEVEL 8 23
  24. 24. Using and applying mathematics: LEVEL 8 Teacher's notes    sketches graphs to represent height of water against volume of water in the container (denoted by time as it was assumed that the volume was increasing at a constant rate) justifies shape of the graph uses mathematical language to discuss results APP in mathematics at Key Stage 3: Standards file – Pupil N p.10
  25. 25. Shape, space and measure 25
  26. 26. Shape, space and measure LEVEL 2 26
  27. 27. Shape, space and measure: LEVEL 2 Teacher's notes     Initially sorts 2-D shapes by colour only. When asked to sort in a different way, classifies them by number of sides and colour. When asked to sort in yet another way, classifies them by number of corners and colour. Goes on to make labels such as 'red and has 3 sides' for each discrete set. APP mathematics standards file: Hannah (Year 2 secure level 2)
  28. 28. Shape, space and measure LEVEL 3 28
  29. 29. Shape, space and measure: LEVEL 3 Teacher's notes    sorts 2–D shapes according to properties: quadrilateral/not quadrilateral and regular/not regular knows that in a regular shape the sides are the same length and angles are equal uses the number of sides and other properties to name 2–D shapes. APP mathematics standards file: Saleema (Year 4, secure level 3)
  30. 30. Shape, space and measure LEVEL 4 30
  31. 31. Shape, space and measure: LEVEL 4 Teacher's notes      creates squares in different orientations on grids uses coordinates in the first quadrant finds families of squares, for example, those with a vertex at (0, 0) searches for pattern in the coordinates of vertices in a row of overlapping, congruent squares identifies a pattern in the coordinates of one of the pairs of opposite vertices APP in mathematics at Key Stage 3: Standards file – Pupil B p.11
  32. 32. Shape, space and measure LEVEL 5 32
  33. 33. Shape, space and measure: LEVEL 5 Teacher's notes     interprets the diagrams and calculates edge lengths that are not given converts metres to centimetres and centimetres to millimetres, even though units are mixed in the labels for each diagram calculates mentally the areas of rectangles and adds or subtracts areas appropriately in self-evaluation, reminds herself that ‘All units must be the same’ APP in mathematics at Key Stage 3: Standards file – Pupil C p.11
  34. 34. Shape, space and measure LEVEL 6 34
  35. 35. Shape, space and measure: LEVEL 6 Teacher's notes      uses trial and improvement to create parallelograms with the same base and area• looks for relationships between the parallelograms and the rectangle other than base and area concludes that they all have the same (perpendicular) height even though the sloping sides are different lengths asserts a formula is possible ‘but you must use height because the sloping side changes so you can’t use it’ gives the formula as A = b × h APP in mathematics at Key Stage 3: Standards file – Pupil R p.12
  36. 36. Shape, space and measure LEVEL 7 36
  37. 37. Shape, space and measure: LEVEL 7 Teacher's notes    Uses 2-D representations of 3-D shapes Uses the formula for circumference and area of a circle Calculates surface areas of compound APP in mathematics at Key Stage 3: Standards file – Pupil V p.12
  38. 38. Shape, space and measure LEVEL 8 38
  39. 39. Shape, space and measure: LEVEL 8 Teacher's notes   uses standard formulae for mensuration calculates volumes and surface areas of cylinders and right prisms APP in mathematics at Key Stage 3: Standards file – Pupil N p.12
  40. 40. Handling data 40
  41. 41. Handling data LEVEL 2 41
  42. 42. Handling data: LEVEL 2 Teacher's notes     After teacher introduction, sorts given numbers using criterion odd/not odd. Organises work by crossing out each number as it is entered on to sorting diagrams. Goes on to choose and enter additional numbers. Reasons that 'not odd' numbers are 'even' and are the ‘answers’ when she recalls multiplication facts for 2. APP mathematics standards file: Hannah (Year 2 secure level 2)
  43. 43. Handling data LEVEL 3 43
  44. 44. Handling data: LEVEL 3 Teacher's notes    uses tallies to record data in a given table uses some conventions for a bar chart, such as bars of equal width and spaces between bars representing discrete data responds to questions such as 'How many…?', 'How many more…?', 'Which is the most common…?' APP mathematics standards file: Saleema (Year 4, secure level 3)
  45. 45. Handling data LEVEL 4 45
  46. 46. Handling data: LEVEL 4 Teacher's notes      decides on the choice of colours to offer in her survey designs a table to record other pupils’ choices of favourite colour keeps a tally of choices describes the most common and least common choices identifies the mode of the set of data APP in mathematics at Key Stage 3: Standards file – Pupil B p.15
  47. 47. Handling data LEVEL 5 47
  48. 48. Handling data: LEVEL 5 Teacher's notes    decides both outcomes, right hand and left hand, are equally likely and the probability of a correct guess is one half records the results of experiments clearly explains ‘you can’t expect to get exactly ten out of 20 each time’ and ‘if you did a 100 you should get about 50’ APP in mathematics at Key Stage 3: Standards file – Pupil C p.14
  49. 49. Handling data LEVEL 6 49
  50. 50. Handling data: LEVEL 6 Teacher's notes   identifies the mode and calculates the mean of sets of data explains and justifies choice of average in discussion APP in mathematics at Key Stage 3: Standards file – Pupil R p.14
  51. 51. Handling data LEVEL 7 51
  52. 52. Handling data: LEVEL 7 Teacher's notes  Generates data using ICT  Processes the data to calculate relative frequencies of the outcome ‘six’  Uses relative frequency to compare outcomes  Comments on results and relates them to the original problem APP in mathematics at Key Stage 3: Standards file – Pupil V p.15
  53. 53. Handling data LEVEL 8 53
  54. 54. Handling data: LEVEL 8 Teacher's notes  constructs cumulative frequency curves  constructs box plots from cumulative frequency curves APP in mathematics at Key Stage 3: Standards file – Pupil N p.15
  55. 55. Assessing pupils’ progress in Mathematics - Number and algebr a 55
  56. 56. Algebra 56
  57. 57. Algebra LEVEL 2 57
  58. 58. Algebra LEVEL 3 58
  59. 59. Algebra LEVEL 4 59
  60. 60. Algebra LEVEL 5 60
  61. 61. Algebra: LEVEL 5 Teacher's notes    understands multiplication is distributive over addition and subtraction multiplies by fractions and decimals such as 3/4 and 0.6 substitutes values to check her result has the same value as the original expression APP in mathematics at Key Stage 3: Standards file – Pupil C p.9
  62. 62. Algebra LEVEL 6 62
  63. 63. Algebra: LEVEL 6 Teacher's notes     solves linear equations with the unknown on one side only generally transforms both sides in the same way also uses two-step inverse operations calculates with decimals mentally APP in mathematics at Key Stage 3: Standards file – Pupil R p.8
  64. 64. Algebra LEVEL 7 64
  65. 65. Algebra: LEVEL 7 Teacher's notes    finds the product of two linear expressions simplifies the resulting quadratic expressions identifies the difference of two squares as a special case APP in mathematics at Key Stage 3: Standards file – Pupil V p.7
  66. 66. Algebra LEVEL 8 66
  67. 67. Algebra: LEVEL 8 Teacher's notes    factorises quadratic expressions with a positive coefficient of x-squared partitions the x-term to obtain common factors uses a grid method to find factors APP in mathematics at Key Stage 3: Standards file – Pupil N p.8
  68. 68. Numbers and the number system 68
  69. 69. Numbers and the number system LEVEL 2 69
  70. 70. Numbers and the number system: LEVEL 2 Teacher's notes         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. APP mathematics standards file: Bradley (Year 1 secure level 2)
  71. 71. Numbers and the number system LEVEL 3 71
  72. 72. Numbers and the number system: LEVEL 3 Teacher's notes    recognises the rule in sequences that go up in steps of a regular size, including those that begin with negative numbers relates these sequences to recent work on temperature finds missing numbers and continues the sequence. APP mathematics standards file: Saleema (Year 4, secure level 3)
  73. 73. Numbers and the number system LEVEL 4 73
  74. 74. Numbers and the number system: LEVEL 4 Teacher's notes    recognises the least number that can be made is 2 and the greatest is 18 works systematically to list all possible addition pairs for each total describes patterns in the columns of numbers she has recorded APP in mathematics at Key Stage 3: Standards file – Pupil B p.6
  75. 75. Numbers and the number system LEVEL 5 75
  76. 76. Numbers and the number system: LEVEL 5 Teacher's notes     uses equivalence between fractions, decimals and percentages expresses an improper fraction as a mixed number reduces some of the fractions to their simplest form understands place value in decimals as well as whole numbers APP in mathematics at Key Stage 3: Standards file – Pupil C p.7
  77. 77. Numbers and the number system LEVEL 6 77
  78. 78. Numbers and the number system: LEVEL 6 Teacher's notes      knows and uses procedures for the conversion of fractions, decimals and percentages expresses decimals with two or three decimal places as fractions with a denominator of 100 or 1000 appropriately reduces fractions to their simplest form by cancelling common factors expresses 3.335 as a mixed number and 2 5/6 as a percentage greater than 100 divides the numerator by the denominator to convert a fraction to a decimal, using a written method of division, and then multiplies by 100 to convert the decimal to a percentage APP in mathematics at Key Stage 3: Standards file – Pupil R p.6
  79. 79. Numbers and the number system LEVEL 7 79
  80. 80. Numbers and the number system: LEVEL 7 Teacher's notes    converts between mixed numbers and improper fractions finds common denominators adds, subtracts, multiplies and divides fractions APP in mathematics at Key Stage 3: Standards file – Pupil V p.6
  81. 81. Numbers and the number system LEVEL 8 81
  82. 82. Numbers and the number system: LEVEL 8 Teacher's notes  uses an algebraic method to convert a recurring decimal to a fraction Next steps    explore patterns arising from converting rational numbers to decimal form, for example, by division reason about the results demonstrate and justify a noncalculator method for converting a recurring decimal to a fraction APP in mathematics at Key Stage 3: Standards file – Pupil N p.6
  83. 83. Calculating 83
  84. 84. Calculating LEVEL 2 84
  85. 85. Calculating LEVEL 3 85
  86. 86. Calculating LEVEL 4 86
  87. 87. Calculating LEVEL 5 87
  88. 88. Calculating: LEVEL 5 Teacher's notes      solves a word problem without a calculator identifies the appropriate operation to use uses a non-calculator method to divide a three-digit by a two-digit number rounds up after the division explains why rounding up is appropriate APP in mathematics at Key Stage 3: Standards file – Pupil C p.6
  89. 89. Calculating LEVEL 6 89
  90. 90. Calculating: LEVEL 6 Teacher's notes     adds and subtracts mixed numbers by expressing the fractional parts with a common denominator solves subtraction problems that involve breaking down a unit, e.g. 3 1/9 – 5/7 uses addition and subtraction as inverse operations to find missing values usually reduces fractions to their simplest form APP in mathematics at Key Stage 3: Standards file – Pupil R p.7
  91. 91. Calculating LEVEL 7 91
  92. 92. Calculating: LEVEL 7 Teacher's notes    converts between mixed numbers and improper fractions finds common denominators adds, subtracts, multiplies and divides fractions APP in mathematics at Key Stage 3: Standards file – Pupil V p.6
  93. 93. Calculating LEVEL 8 93
  94. 94. Calculating: LEVEL 8 Teacher’s notes    identifies square numbers and factor pairs manipulates surds competently and simplifies sums and products uses accurate notation APP in mathematics at Key Stage 3: Standards file – Pupil N p.7

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