4 Maths framework
4.1 Maths framework overview
Domains Main concept Code
Number (whole number and 4 Understand Naming, Conserving, and Counting C
operations)
Understand the number system N
Understand Subitising / Estimating SE
Understanding Place Value PV
Understanding Adding and Subtracting AS
Understanding Multiplication and Division MD
Fractions, Decimals & Percentages Understanding Decimal System, Equivalences, and DEP
(and 4 operations) Place Value
Understanding Adding and Subtracting (Decimal) ASD
Understanding Fractions as Parts and Equivalences FPE
Comparing Fractions CoF
Understanding Adding and Subtracting (fractions) ASF
Understanding Percentage and Equivalences PE
Understanding Multiplication and Division MDD
(Decimal)
Understanding Multiplication and Division MDF
(fractions)
Geometry Shape Shp
Position-Space P-S
Symmetry and Isometric transformations SIT
Constructions Con
Congruent and similar shapes C&S
Pythagoras Pyt
Measure Length Len
Area Are
Volume/Capacity Vol
Angle Ang
Weight Wei
Time Tm
Algebra working and thinking Equivalence EQ
Inequalities INQ
Relationships + Functions RF
Patterns + Functions PF
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Change + Functions CF
Data handling Understanding and working with data. UWD
Considering data distribution variability measure DVM
and representations.
Working with time series and bivariate data TSB
Risk Using probability to understand issues of risk. P&R
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DOMAIN MAIN CONCEPT CODE 4 5 6
Number Understand Naming, C
(whole Conserving, and
number and 4 Counting
operations)
Understand the N Write natural numbers as a product of Recognise square numbers and cube
number system two or more factors. Develop numbers in terms of their multiplicative
awareness of the significance of prime structure, as well as their geometrical
numbers as the 'building blocks' of the representations (area and volume).
natural numbers, recognising that all
natural numbers have factors that are
prime, and can be expressed as a
product of prime factors.
Understand Subitising SE Round values and measurements to
/ Estimating suitable levels of accuracy.
Understanding Place PV Recognise the similarities between the Recognise the relationships between
Value structure of the whole numbers and large numbers such as billions, millions
decimals. and trillions. Have a sense of their size
with respect to real life objects.
Understanding AS Using informal written and mental Develop a sense of how the 'column
Adding and strategies of addition and subtraction. method' or 'vertical algorithm' may be
Subtracting used as a formal written method for
addition and subtraction. Compare and
contrast this method with other,
informal, written and mental strategies.
Understanding MD Recall multiplicative products and Explore the commutative, associative, Use multiplicative reasoning, the
Multiplication and work flexibly with them. summative and distributive properties distributive property of multiplication,
Division of multiplication. and known multiplication facts, to
solve problems involving multiplication
of numbers with one and two digits.
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DOMAIN MAIN CONCEPT CODE 4 5 6
Fractions, Understanding DEP Position decimals on a number line. Measure/round to a given number of
Decimals & Decimal System, decimal places.
Percentages Equivalences, and
(and 4 Place Value
operations)
Understanding ASD Using a sense of place value, to
Adding and recognise the similarities in the
Subtracting behaviour of counting numbers and
(Decimal) decimal numbers. Develop a sense of
how the 'column method' or 'vertical
algorithm' may be used as a formal
written method for addition and
subtraction.
Compare and contrast this method
with other, informal, written and
mental strategies.
Understanding FPE Recognise that a fraction has multiple
Fractions as Parts meanings and may be interpreted and
and Equivalences represented in a variety of ways,
including division and proportion.
Comparing Fractions CoF Position fractions between 0 and 1 on Compare fractions with different Recognise simple examples of
an empty number line. denominators using a variety of equivalent fractions, understanding
strategies, such as using benchmark that equivalent fractions are equal in
values, the size of denominator, area size (for example, they are located at
and linear models the same position on a number line,
represent the same area in a bar
diagram, and so on).
Understanding ASF Add and subtract fractions with
Adding and related denominators (one a multiple
Subtracting of the other).
(fractions)
Understanding PE Connecting the notion of percentage Relate percentage knowledge for Working with benchmark values such
Percentage and to experiences with fractions, "special" values such as: 50%; 25%; as 10%, 25%, 50%, and recognise
Equivalences particularly those with denominators 100%; 75%; and 10% to their how to compose other proportions
of 100. Explore a range of contexts, from these, reinforcing the
problems, and representations that
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involve a notion of 'parts-per- fractional equivalents. Find these connections to fractional
hundred'. proportions of amounts. representations of proportion.
Understanding MDD
Multiplication and
Division (Decimal)
Understanding MDF
Multiplication and
Division (fractions)
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DOMAIN MAIN CODE 4 5 6
CONCEPT
Geometry Shape Shp Describe properties of 3D shapes in Analyse properties of 2D shape, consider
terms of faces, equality of faces/edges, the hierarchy and family links between
and cross-sections. Recognise and shapes.
identify 3D shapes using the above
properties.
Position-Space P-S Work with Cartesian co-ordinates Connect various symbolic Identify and draw plans and elevations of
representations to a position and line of 3D objects. Identify 3D objects from
sight on a map or plan. their plans and elevations.
Symmetry and SIT Reflect simple patterns and shapes on Identify repeating patterns in culturally Identify tessellating patterns or tilings,
Isometric paper. Rotate simple patterns and shapes appropriate contexts. Identify the tessellating/tiling unit/s, including a
transformations on paper, with no centre or with a centre reflections, glide reflections, rotations, lattice structure and its geometrical
on one vertex of the pattern or shape, in and translations in these patterns using properties. Identify, describe, carry out
multiples of quarter turns. informal explanations. and analyse translations (including
identifying the non-existence of invariant
points) expressed in words.
Constructions Con Investigate the variety of configurations Copy and construct shapes/patterns
possible using lines and circles on a accurately on dotted or lattice paper.
plane. Identify these configurations in Reproduce circle diagrams from drawn
more complicated diagrams. (Investigate examples or written instructions. Label
the variety of configurations possible vertices, edges and angles accurately.
using three lines in 3D)
Congruent and C&S Draw and investigate the properties of
similar shapes enlargements of pictures on sheared
grids, stretched grids, and enlarged grids.
Pythagoras Pyt
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DOMAIN MAIN CODE 4 5 6
CONCEPT
Measure Length Len Identify and use the correct measuring Use the meaning of kilo, hect, dec, deci,
tool, and therefore unit, to measure centi and mili to convert between metric
angle, length or volume. Be familiar and units of length. Recognise suitable
have a sense of (benchmarks) the units of situations for the variety of units and
cm and m, use these to judge the validity establish benchmarks for each unit.
of a measured value. Estimate and Combining a variety of length
measure the length of a path, including measurements in a variety of units.
perimeters of polygons and the (shortest)
distance between two points. Investigate
the effect of zooming in on a ruler on the
structure of the measuring tool; including
scales of none-unit steps. Identify the
dimensions of a rectangle. Identify the
dimensions of a cuboid from a model or
2D representation.
Area Are Use a logical enumeration of an array to Calculate, with explanation, how many
develop an efficient strategy to find the square centimetres in a square metre.
total number of unit squares. Develop Convert between units before and after
and work with the formula (ab=c) to calculating areas.
solve problems involving the area of a
rectangle in multiple situations.
Volume/ Vol Develop and use a volume measuring
Capacity tool to compare volumes and recognise
the effect the shape of the container has
on any scale. Estimate and measure
volumes in litres.
Angle Ang Identify, label accurately, estimate and Deduce missing angles using the axioms Measure, demonstrate and justify the
measure angles including those caused of angles meeting at a point and angles triangle angle rules.
by rotation/turn, turn in a path or a meeting along a straight line. Use the
slope, using a 360˚ moving arm axioms of angles meeting at a point and
protractor. angles meeting along a straight line, to
deduce whether a set of angles form such
structures. Investigate the relationship of
vertically opposite angles. Give an
argument to explain the equality of
vertically opposite angles.
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Weight Wei Construct and use a measuring scale
using a spring and non-standard unit.
Develop and use the standard unit of
kilogram (discussion of weight vs mass
to follow in science).
Time Tm Work with cyclical number and nature of Read and write time in a digital and Move between three representations of
days of the week, and days in a month, analogue representation. recorded time; in words, digital and
to calculate time intervals in days. analogue representations.
Estimate and measure the time of events
or activities. Give sensible estimates for
longer activities.
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DOMAIN MAIN CONCEPT CODE 4 5 6
Algebra Equivalence EQ Recognise that adding or subtracting Recognise that multiplying or dividing
working and the same quantity to both sides of an both sides of an equivalence
thinking equivalence relationship (= and ≠) relationship (= and ≠) by the same
preserves the equivalence. nonzero quantity preserves the
equivalence.
Recognise the effect of multiplying or
dividing both sides of an equivalence
relationship (= and ≠) by zero has on
the equivalence.
Inequalities INQ Recognise the effect of multiplying or
dividing both sides of an inequality
(>, ≤, ≥ and ≠) relationship by the
same negative quantity.
Relationships + RF Explore the different ways to operate Identify (examples and non- Use multiple representations to solve
Functions on a number to get from one to examples), describe, represent and direct proportion problems and 1-step
another. work with directly proportional multiplicative equations and
Develop recognition of additive, relationships using tables, cartesian inequalities, including symbolic
multiplicative and multi-step co-ordinates and algebraic manipulation.
processes. representations, in a variety of
contexts (explicit and implicit
functions). Recognise contexts when it
is appropriate to join co-ordinates to
produce a graph.
Patterns + Functions PF Continue number patterns, such as
two, four, six, eight and begin to
generalise the term to term rule (in
words)
Change + Functions CF Sketch and investigate graphs that
describe movement over time.
Describe movement represented in a
sketched graph.
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DOMAIN MAIN CONCEPT CODE 4 5 6
Data Understanding and UWD Consider a range of possible measures Select appropriate measures based on Organise and represent quantitative
handling working with data. to capture important aspects of an consideration of reliability, data both formally and informally in
object or phenomena replicability, and accuracy to answer order to gain insight into contextual
questions in a motivating context. questions that arise.
Considering data DVM Describe data using mode and Describe data using median, range, Describe data using mean and
distribution subjective description of variation, and interquartile range, and know subjective description of variation,
variability measure and know when it is appropriate to when it is appropriate to use these and know when it is appropriate to
and representations. use these measures. measures. use these measures.
Working with time TSB Plan to capture and record time-series Plan to capture and record bivariate Select appropriate scales in order to
series and bivariate data systematically and carefully. data systematically and carefully. emphasis relationships and trends in
data Represent, describe and interpret Represent, describe and interpret time-series and bivariate data
time-series data, communicating bivariate data, communicating trends
trends and relationships and relationships
Risk Using probability to P&R Calculate probabilities based on Calculate theoretical probabilities
understand issues of experimental results as the proportion based on the structure of a sample
risk. of the result for a specific outcome space as the proportion of the sample
given a sufficiently large number of space for a specific outcome
trials
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