The National Strategies | Primary | Primary Framework for literacy and mathematics
Mathematics standards file – John
Mathematics standards file
John – high level 3
Ma1 Using and applying mathematics
Ma2 Number
Ma3 Shape, space and measures
Ma4 Handling data
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Mathematics standards file – John
Ma1 Using and applying mathematics
Generally odd and even
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Mathematics standards file – John
Teacher’s notes
 understands general statements
 tries several examples and uses the results to complete a general statement
 has support with creating examples and completing the first general statement
 works independently with other statements.
Next steps
 investigate situations from which he can formulate his own ‘rule’ or general
statement.
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Mathematics standards file – John
Wow fact-ors!
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Mathematics standards file – John
Teacher’s notes
 works independently
 knows multiplication facts for 2, 4, 5 and 10 tables
 uses these facts to derive other multiplication and division facts
 factorises given numbers and counts the number of factors
 understands definitions based on the number of factors a number has
 uses definitions to identify which type of number he has factorised.
What the teacher knows about John’s attainment in Ma1
When working on problems that involve finding ‘how many ways…’, John perseveres to
find further solutions. In the ‘Wow fact-ors!’ investigation, he perseveres to find all
factor pairs for each of the numbers. He is beginning to check his work, for example by
making sure that his solution to a problem makes sense in the context of the problem.
John talks about his work using familiar mathematical vocabulary appropriately. He
refers to his written work when providing explanations. John demonstrates his
reasoning, for example by completing generalisations about adding and subtracting
odd and even numbers. When given incomplete generalisations, John works through
appropriate examples, draws conclusions from them and completes the generalisation.
He also uses definitions of prime and square numbers based on their numbers of
factors. By finding the number of factors for given numbers, John is able to identify
those which are prime or square.
Summarising John’s attainment in Ma1
John understands a general statement and finds an example to match it, which is
typical of performance at level 3. He needs more experience of a wider range of
problems, with input on breaking into a problem and developing systematic
approaches, to make further progress within level 3 and into level 4.
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Mathematics standards file – John
Ma2 Number
Improper fractions and mixed numbers
Teacher’s notes
 interprets fractions diagrams
 recognises the unit, for example the circle that represents 1
 records shaded areas as improper fractions and as mixed numbers.
Next steps
 create own diagrams to illustrate improper fractions or mixed numbers
 use own diagrams to support converting improper fractions to mixed numbers
and vice versa.
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Mathematics standards file – John
Chunking
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Mathematics standards file – John
Teacher’s notes
 is secure with multiplication facts for 2, 4, 5 and 10 tables
 uses known multiplication facts to derive others
 uses a vertical method for addition and subtraction efficiently
 in guided work, uses chunking to divide a three-digit by a single-digit number
 checks by using multiplication as the inverse of division
 begins to relate chunking to short division
 does not yet use the chunking method of division independently or recall it when
he has not practised it recently.
Book shelf problem
Teacher’s notes
 solves a word problem involving addition and subtraction
 interprets information in a table
 adds two-digit numbers mentally
 subtracts using complementary addition
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Mathematics standards file – John
 explains how he knows his answer is correct.
Next steps
 solve problems using multiplication or division with addition or subtraction,
including those that involve interpreting a remainder.
What the teacher knows about John’s attainment in Ma2
John recognises number patterns including larger multiples of 5 and 10 and square
numbers up to 10 × 10. He uses his knowledge of multiplication facts to find factor
pairs and to check whether a number is prime, as in ‘Wow fact-ors!’. John understands
place value in two-digit and three-digit numbers and uses it to order numbers, to round
to the nearest 10 or 100 and to multiply whole numbers by 10. John understands
negative numbers in the context of temperature and counting backwards past 0. He
calculates small changes in temperature across 0  Celsius. John understands unit
fractions and those fractions that are several parts of a whole, such as , that he uses
frequently. He knows the percentage equivalents of fractions such as , , and .
He needs further work to understand equivalent fractions more fully and to order
fractions, on a number line, for example. John uses diagrams to help him to convert
mixed numbers to improper fractions and vice versa.
John understands addition and subtraction as inverses, multiplication as repeated
addition and division as the inverse of multiplication. He uses repeated addition to
generate multiplication facts, for example when he multiplies £1.25 by 5 and records ‘1
× £1.25 = £1.25, 2 × £1.25 = £2.50…’
John uses a range of mental strategies to add whole numbers and decimals with one
decimal place. He uses complementary addition when he subtracts mentally. He uses
column methods to add and subtract two-digit and three-digit numbers, including
examples that involve bridging or decomposition of either the tens or hundreds. He has
good recall of multiplication facts for 2, 4, 5 and 10 tables and uses them to derive
associated multiplication and division facts. He multiplies a two-digit or three-digit
number by numbers up to 10 using a grid method. John knows about chunking as a
method of dividing larger numbers, and about short division, but is not yet confident in
dividing a three-digit number by a single-digit or two-digit number independently. John
solves whole number problems that involve using one operation and those that involve
both addition and subtraction.
Summarising John’s attainment in Ma2
In Ma2 John is best described as working at the top end of level 3, even though he
shows some aspects of level 4. He needs to consolidate his understanding of place
value in whole numbers to multiply by 100 as well as by 10. He also needs to develop
his understanding of place value in decimals, to use decimal notation not just for
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Mathematics standards file – John
money but also for measures, and to add and subtract decimals with two places. John
needs to develop his understanding of equivalent fractions, which will also help him to
order fractions. As well as calculating with decimals, John needs to develop written
methods for division of larger numbers.
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The National Strategies | Primary | Primary Framework for literacy and mathematics
Mathematics standards file – John
Ma3 Shape, space and measures
3-D shape problem
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Teacher’s notes
 interprets an isometric drawing and uses linking cubes to build the 3-D shape
represented
 relates the 3-D shape to a different type of diagram.
Next steps
 build own 3-D shape and design a set of instructions for someone else to build
the same shape without looking at it.
Reflecting 2-D shapes
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Teacher’s notes
 reflects shapes on a square grid
 uses the (perpendicular) distance of vertices from the mirror to reflect accurately
 uses mirror lines that are presented vertically, horizontally or diagonally.
What the teacher knows about John’s attainment in Ma3
John sorts shapes using properties such as number of edges and corners or reflection
symmetry in 2-D shapes. He reflects 2-D shapes on a square grid in a mirror that is
presented vertically or horizontally although is less consistently accurate with a mirror
line presented diagonally. He is beginning to use the perpendicular distance of a vertex
from the mirror line to help him reflect shapes accurately when they are not parallel to
the mirror line. John is less experienced and confident in translating shapes. He makes
3-D shapes, using linking cubes, from a 2-D diagram. He needs more experience of
making nets of cuboids and triangular prisms, for example, to be able to solve
problems such as matching solids to their nets or completing a net where part of it is
given.
John uses non-standard and standard metric units to measure length, capacity and
mass. He measures to the nearest cm and records longer lengths using a mixture of
metres and centimetres: 3 m 45 cm, for example. He knows about area as a measure
of surface and perimeter as a linear measure but needs support to remember which
term refers to which measurement. He finds areas by counting squares. John is not
very accurate in using a protractor to measure angles. He uses standard units of time,
reads the time from an analogue clock and calculates time durations that do not go
over the hour. For example, John calculates how long an event lasts if it begins at
quarter past two in the afternoon and ends at 2:55 pm.
Summarising John’s attainment in Ma3
In Ma3 John is a strong level 3. In working with shapes, he needs more experience of
making 3-D models from nets to progress into level 4. In position and movement he
needs to work more independently with reflecting shapes, recognising rotations and
drawing 2-D shapes in different orientations on grids. In measures John needs to
interpret numbers on a wider range of measuring instruments and scales, to learn to
use a protractor to measure angles with reasonable accuracy, and to distinguish
between perimeter and area independently.
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Mathematics standards file – John
Ma4 Handling data
Dice investigation 1
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Mathematics standards file – John
Teacher’s notes
 works independently to find the frequency of dice scores 1 to 6
 constructs a table of results
 keeps an accurate tally and interprets it
 sketches a bar graph, labelling the vertical axis in ones
 predicts that 4 will be the most common score
 identifies scores 1 and 3 as the modes of his data
 does not yet understand the term frequency (that is, in this investigation, the
frequency of particular scores on the dice).
Next steps
 combine the results of the whole class
 discuss combined results, including the significance of the mode
 draw conclusions from the larger sample about the likelihood of each dice score
 use squared paper to draw graphs more accurately
 use scales where one interval represents 2 or 5 to record combined results.
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Mathematics standards file – John
Sorting numbers
Teacher’s notes
 works independently to sort numbers 1 to 50 using given criteria
 records all numbers below the diagram and begins by crossing off those he has
sorted
 in discussion with the teacher concludes that there are no odd multiples of 6.
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Mathematics standards file – John
What the teacher knows about John’s attainment in Ma4
John uses a Carroll diagram to sort shapes and numbers using two criteria. For shapes
he uses criteria such as ‘has a line of symmetry’ and ‘has four sides’. John uses a tally
to record a count and interprets it accurately. He draws tables of results and interprets
them. He uses information from a table to draw graphs, and numbers the vertical axis
in ones. He is not yet consistent in labelling axes or recording any conclusions from the
information he presents. He uses much of the handling data vocabulary that is
appropriate for the year group but does not yet fully understand the terms frequency,
mode and range. John has been introduced to mode but needs more experience to
understand the types of situation in which knowing the mode of a set of data could be
helpful.
Summarising John’s attainment in Ma4
In Ma4 John’s performance is best described as at secure level 3. He constructs bar
charts, and to consolidate his attainment within level 3 he needs to use a scale for the
vertical axis where one division represents more than one item. He also needs
experience of interpreting and creating pictograms.
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Mathematics standards file – John
Overall assessment summary for John
John’s teacher judges his attainment across mathematics as working at the top of level 3. His attainment in Ma2 and Ma3 is slightly higher than
it is in Ma1 and Ma4.
Assessment guidelines
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The National Strategies | Primary | Primary Framework for literacy and mathematics
Mathematics standards file – John
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The National Strategies | Primary | Primary Framework for literacy and mathematics
Mathematics standards file – John
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The National Strategies | Primary | Primary Framework for literacy and mathematics
Mathematics standards file – John
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The National Strategies | Primary | Primary Framework for literacy and mathematics
Mathematics standards file – John
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