1. Assessing pupils’
progress in
Mathematics
1

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. 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. THERE ARE TWO MAJOR
AREAS OF ASSESSMENT
IN APP MATHS:
4

5. 1) Using and applying mathematics, shape, space and
measure and handling data
5

6. 2) Number and algebra
6

7. LET’S BREAK
THEM DOWN A
LITTLE
7

8. NO,
NOT LIKE
THAT
8

9. Assessing pupils’ progress in Mathematics -
Using and applying
mathematics, shape, space
and measure and handling
data
9

10. Using and applying
mathematics
10

11. Using and applying mathematics
LEVEL 2
11

12. Using and applying mathematics: LEVEL 2
Teacher's notes
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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. Using and applying mathematics
LEVEL 3
13

14. Using and applying mathematics: LEVEL 3
Teacher's notes
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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. Using and applying mathematics
LEVEL 4
15

16. Using and applying mathematics: LEVEL 4
Teacher's notes
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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. Using and applying mathematics
LEVEL 5
17

18. Using and applying mathematics: LEVEL 5
Teacher's notes
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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. Using and applying mathematics
LEVEL 6
19

20. Using and applying mathematics: LEVEL 6
Teacher's notes
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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. Using and applying mathematics
LEVEL 7
21

22. Using and applying mathematics: LEVEL 7
Teacher's notes
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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. Using and applying mathematics
LEVEL 8
23

24. Using and applying mathematics: LEVEL 8
Teacher's notes
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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. Shape, space and
measure
25

26. Shape, space and measure
LEVEL 2
26

27. Shape, space and measure: LEVEL 2
Teacher's notes
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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. Shape, space and measure
LEVEL 3
28

29. Shape, space and measure: LEVEL 3
Teacher's notes
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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. Shape, space and measure
LEVEL 4
30

31. Shape, space and measure: LEVEL 4
Teacher's notes
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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. Shape, space and measure
LEVEL 5
32

33. Shape, space and measure: LEVEL 5
Teacher's notes
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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. Shape, space and measure
LEVEL 6
34

35. Shape, space and measure: LEVEL 6
Teacher's notes
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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. Shape, space and measure
LEVEL 7
36

37. Shape, space and measure: LEVEL 7
Teacher's notes
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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. Shape, space and measure
LEVEL 8
38

39. Shape, space and measure: LEVEL 8
Teacher's notes
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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. Handling data
40

41. Handling data
LEVEL 2
41

42. Handling data: LEVEL 2
Teacher's notes
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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. Handling data
LEVEL 3
43

44. Handling data: LEVEL 3
Teacher's notes
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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. Handling data
LEVEL 4
45

46. Handling data: LEVEL 4
Teacher's notes
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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. Handling data
LEVEL 5
47

48. Handling data: LEVEL 5
Teacher's notes
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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. Handling data
LEVEL 6
49

50. Handling data: LEVEL 6
Teacher's notes
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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. Handling data
LEVEL 7
51

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. Handling data
LEVEL 8
53

54. Handling data: LEVEL 8
Teacher's notes
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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. Assessing pupils’ progress in Mathematics -
Number and
algebr a
55

56. Algebra
56

57. Algebra
LEVEL 2
57

58. Algebra
LEVEL 3
58

59. Algebra
LEVEL 4
59

60. Algebra
LEVEL 5
60

61. Algebra: LEVEL 5
Teacher's notes
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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. Algebra
LEVEL 6
62

63. Algebra: LEVEL 6
Teacher's notes
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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. Algebra
LEVEL 7
64

65. Algebra: LEVEL 7
Teacher's notes
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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. Algebra
LEVEL 8
66

67. Algebra: LEVEL 8
Teacher's notes
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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. Numbers
and the number system
68

69. Numbers and the number system
LEVEL 2
69

70. Numbers and the number system: LEVEL 2
Teacher's notes
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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. Numbers and the number system
LEVEL 3
71

72. Numbers and the number system: LEVEL 3
Teacher's notes
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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. Numbers and the number system
LEVEL 4
73

74. Numbers and the number system: LEVEL 4
Teacher's notes
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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. Numbers and the number system
LEVEL 5
75

76. Numbers and the number system: LEVEL 5
Teacher's notes
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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. Numbers and the number system
LEVEL 6
77

78. Numbers and the number system: LEVEL 6
Teacher's notes
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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. Numbers and the number system
LEVEL 7
79

80. Numbers and the number system: LEVEL 7
Teacher's notes
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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. Numbers and the number system
LEVEL 8
81

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
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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. Calculating
83

84. Calculating
LEVEL 2
84

85. Calculating
LEVEL 3
85

86. Calculating
LEVEL 4
86

87. Calculating
LEVEL 5
87

88. Calculating: LEVEL 5
Teacher's notes
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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. Calculating
LEVEL 6
89

90. Calculating: LEVEL 6
Teacher's notes
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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. Calculating
LEVEL 7
91

92. Calculating: LEVEL 7
Teacher's notes
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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. Calculating
LEVEL 8
93

94. Calculating: LEVEL 8
Teacher’s notes
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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