Year 4 Curriculum for Depth 2014-15 – May DRAFT
Welcome to the Mathematics Mastery Curriculum for Depth for Year 4.
Problem solving is at the heart of the mastery approach, so we make sure we dedicate sufficient time to each new concept or skill for every pupil to gain
the fluency and reasoning they need to solve new problems in unfamiliar contexts. Our Curriculum for Depth is a cumulative curriculum. This means that
each school year begins with a focus on the concepts and skills (such as place value) that have the most connections, and the most opportunities for
consolidation, throughout the year. Once a new concept has been introduced, it is applied and connected to many other areas of mathematics. For more
information about the underlying principles of the mastery approach, please visit www.mathematicsmastery.org
We make sure that the requirements of the 2014 National Curriculum for England are fully met. Each year group’s Curriculum for Depth includes all of the
National Curriculum objectives for that year, plus a small number from the year above – usually from number – where we feel these wil help pupils make
connections with their learning (in measures, for example). References to the statutory requirements of the National Curriculum are in bold [e.g. ‘They will
“solve number and practical problems that involve all of the above and with increasingly large positive numbers” (NC Y4: p24)’]. This Year 4 Curriculum
for Depth includes every single statutory requirement of the 2014 National Curriculum for Year 4. References to the non-statutory ‘notes and guidance’ in
the 2014 National Curriculum are in italics. [e.g. ‘As per the notes and guidance, “pupils solve two-step problems in contexts, choosing the appropriate
operation, working with increasingly harder numbers.” (NC Y4: p26)’]. There are approximately 5 planned weeks for each half term. Any additional time for
mathematics should be planned around the specific needs of the pupils, including clarifying any misconceptions, opportunities for consolidation, and
further application and problem solving.
This document is a starting point for continuous improvement and development. During 2014-15, we will be working closely with our National Practitioner
Panels, and consulting with all teachers in our partnership, with a view to making improvements in the sequencing and timing of the curriculum for 201516. If you have any suggestions, we’d love to hear from you. Please contact us at [email protected].
Dr Helen Drury
Director, Mathematics Mastery
May 2014
The Mathematics Mastery programme of study for Year 4 is copyright © 2013-14 Mathematics Mastery. It is designed for use by school leaders and teachers in schools in the Mathematics Mastery partnership.
We are happy to share this programme of study with schools beyond this community, in order to support preparation for and implementation of the new National Curriculum.
Autumn 1 – May DRAFT
Week
Autumn 1
Mathematics lesson foci
We begin Year 4 by strengthening the essential foundations of place value, addition and subtraction, word problems and money (with pounds and pence
calculated separately until Units 8 and 9, when decimal notation is formally introduced). Place value and number sense with numbers to 10,000 were introduced
in the Mastery Curriculum in Year 3, and Unit 1 of Year 4 is an opportunity to build on this and develop pupils’ mathematical reasoning. In this fortnight, pupils will
“find 1000 more or less than a given number; recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones); and order
and compare numbers beyond 1000” (NC Y4: p24). Throughout this unit, and continuously across the school year, they will “solve number and practical problems
that involve all of the above and with increasingly large positive numbers” (NC Y4: p24).
Unit 1
2
weeks
Reasoning with 4
digit numbers
Representations are vital to deepening understanding of the number system. “Using a variety of representations, including measures, pupils become fluent in the
order and place value of numbers beyond 1000, including counting in tens and hundreds, and maintaining fluency in other multiples through varied and frequent
practice.” (NC Y4: p24). Pupils will “identify, represent and estimate numbers using different representations; and round any number to the nearest 10, 100 or
1000” (NC Y4: p24). It is important that pupils “connect estimation and rounding numbers to the use of measuring instruments” (NC Y4: p24).
By the end of Year 4, the NC states that all pupils must be able to, “read Roman numerals to 100 (I to C) and know that over time, the numeral system changed
to include the concept of zero and place value”. (NC Y4: p24) We recommend that the school curriculum is designed in such a way that work on Roman numerals
takes place outside of dedicated mathematics lessons. In history, or topic-based work, in line with the notes and guidance, “Roman numerals should be put in their
historical context so pupils understand that there have been different ways to write whole numbers and that the important concepts of zero and place value were
introduced over a period of time.” (NC Y4: p24)
Transition chanting should include opportunities to “count in multiples of 6, 7, 9, 25 and 1000” (NC Y4: p24). ‘Skip-counting’ in 6s, 7s, 8s and 9s will have formed a
regular part of Maths Meetings and transitions in Year 3.
Place value is further explored in Unit 2, where pupils “add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and
subtraction where appropriate” (NC Y4: p25).
Unit 2
3
weeks
Problem solving
with integer
addition and
subtraction
Recording of the calculation using a formal written method should not be seen as an alternative to the use of Dienes blocks or other concrete manipulatives, but
rather as a more abstract representation to be used alongside. Even pupils who do not ‘need’ the concrete apparatus will benefit from manipulating them to both
demonstrate and deepen their understanding of place value. Modelling their addition and subtraction methods using concrete manipulatives and diagrams is an
essential component of mastering these concepts, for every child. As part of developing their number sense, pupils should be continually expected to “estimate
and use inverse operations to check answers to a calculation” (NC Y4: p25).
Before pupils “solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why” (NC Y4: p25), we
dedicate time to exploring alternative ways of representing such two-step contextual problems, in particular through the use of bar models. This representation of
contextual problems – a separate processes from selecting operations to use, or from actually calculating a solution – is key to pupils succeeding with word
problems. In solving problems involving addition and subtraction, pupils should be supported to independently select an appropriate mental or written calculation
method.
The Mathematics Mastery programme of study for Year 4 is copyright © 2013-14 Mathematics Mastery. It is designed for use by school leaders and teachers in schools in the Mathematics Mastery partnership.
We are happy to share this programme of study with schools beyond this community, in order to support preparation for and implementation of the new National Curriculum.
Autumn 2 – May DRAFT
Week
Autumn 2
Unit 3
2
weeks
1
week
2
weeks
Multiplication
and division
Unit 4
Time
Unit 5
Area and
perimeter
Mathematics lesson foci
This unit is about much more than pupils merely being able to “recall multiplication and division facts for multiplication tables up to 12 × 12” (NC Y4: p25). It is
important that all pupils develop conceptual understanding of both multiplication and division. As per the notes and guidance, “pupils solve two-step problems in
contexts, choosing the appropriate operation, working with increasingly harder numbers. This should include correspondence questions such as the numbers of
choices of a meal on a menu, or three cakes shared equally between 10 children.” (NC Y4: p26). All pupils must “solve problems involving multiplying and adding,
including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects
are connected to m objects.” (NC Y4: p25)
Through experience and exploration of multiplication, pupils will “recognise and use factor pairs and commutativity in mental calculations” (NC Y4: p25), and will
begin to “write statements about the equality of expressions (for example, use the distributive law 39 × 7 = 30 × 7 + 9 × 7 and associative law (2 × 3) × 4 = 2 × (3 ×
4)). They combine their knowledge of number facts and rules of arithmetic to solve mental and written calculations for example, 2 x 6 x 5 = 10 x 6 = 60.” (NC Y4: p26)
Building on place value work from Y4 Unit 1, pupils “use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1;
dividing by 1; and multiplying together three numbers” (NC Y4: p25) “Pupils practise mental methods and extend this to three-digit numbers to derive facts, (for
example 600 ÷ 3 = 200 can be derived from 2 x 3 = 6).” (NC Y4: p25). This leads to them being able to “multiply two-digit and three-digit numbers by a one-digit
number using formal written layout” (NC Y4: p25). In the context of problem solving and investigation, “pupils practise to become fluent in the formal written
method of short multiplication and short division with exact answers” (NC Y4: p26).
Pupils have been counting in multiples of 2, 5 and 10 since Year 1, they connect multiples of 3 to finding a third of a quantity in Year 2, and our Curriculum for Depth
includes counting in multiples from 2 to 10 in Year 3. Year 4 pupils should therefore be secure with use of the term ‘multiple’, and this term should be used
frequently throughout the year. Year 4 is the first time pupils are formally introduced to the term ‘factor’. Ensuring pupils are secure with the term ‘multiple’
before introducing ‘factor’ will help those pupils who might otherwise have difficulty distinguishing between the two terms.
Pupils build strong foundations for this in Year 3, through telling and writing the time on analogue clocks (including with Roman numerals), as well as through use
of digital 12-hour clocks. In Year 4 Unit 4, word problems include opportunities for pupils to practice and apply their skill in “convert[ing] between different units
of measure [for example, hour to minute]” (NC Y4: p27), and pupils will “solve problems involving converting from hours to minutes; minutes to seconds; years
to months; weeks to days” (NC Y4: p28). In this unit, pupils also “read, write and convert time between analogue and digital 12- and 24-hour clocks” (NC Y4: p28).
The expectation for Year 5 time is that pupils will ‘solve problems involving converting between units of time’ – Year 4 is the opportunity to learn the essential
concepts and methods for this future problem solving.
In Year 3, pupils measured the perimeter of simple 2D shapes. In Year 4 Unit 5, they build on this to “measure and calculate the perimeter of a rectilinear figure
(including squares) in centimetres and metres” (NC Y4: p27). “Perimeter can be expressed algebraically as 2(a + b) where a and b are the dimensions in the same
unit.” (NC Y4: p28). Work on perimeter provides an opportunity for pupils to practice and apply their skill in “convert[ing] between different units of measure [for
example, kilometre to metre]” (NC Y4: p27). “They use multiplication to convert from larger to smaller units.” (NC Y4: p28)
This Year 4 unit also sees the introduction of area, as pupils “find the area of rectilinear shapes by counting squares” (NC Y4: p27) and “relate area to arrays and
multiplication.” (NC Y4: p28). This is therefore a great opportunity for pupils to explore the perimeters and areas of different rectilinear figures, and to begin to
understand how an increase in one of these does not necessitate an increase in the other.
The Mathematics Mastery programme of study for Year 4 is copyright © 2013-14 Mathematics Mastery. It is designed for use by school leaders and teachers in schools in the Mathematics Mastery partnership.
We are happy to share this programme of study with schools beyond this community, in order to support preparation for and implementation of the new National Curriculum.
Spring 1 – May DRAFT
Week
3
weeks
Spring 1
Unit 6
1
2
4
8
9
3
or = )” (NC Y4: p27).
Fractions
Unit 7
2
weeks
Mathematics lesson foci
Year 4 is the third year that pupils have been formally working with fractions. In Year 2, pupils began to learn about how fractions can be numbers in their own
right (and positioned, say, on a number line), and how they can also be operators (so you can find a fraction of something). This distinction is further emphasised in
Year 3, and now Year 4. When working with fractions as numbers, pupils, “extend the use of the number line to connect fractions, numbers and measures.” (NC Y4:
p27). “Pupils continue to practise adding and subtracting fractions with the same denominator, to become fluent through a variety of increasingly complex
problems beyond one whole.” (NC Y4: p27). In Year 4 pupils “add and subtract fractions with the same denominator” (NC Y4: p26). In Year 3, pupils began to
recognise and show, using diagrams, equivalent fractions with small denominators. They build on this in Year 4 to “recognise and show, using diagrams, families of
6
2
common equivalent fractions”(NC Y4: p26). “Pupils use factors and multiples to recognise equivalent fractions and simplify where appropriate (for example, =
Discrete and
continuous data
This unit also provides an opportunity to look in more depth at tenths and hundredths, already introduced in Maths Meetings, so that pupils, “count up and down
in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.” (NC Y4: p26). At this stage in Year 4, tenths
and hundredths are recorded in fraction notation; decimal notation is introduced in Unit 8.
Pupils also work with fractions as operators. They “understand the relation between non-unit fractions and multiplication and division of quantities, with particular
emphasis on tenths and hundredths.” (NC Y4: p27). “Pupils make connections between fractions of a length, of a shape and as a representation of one whole or set
of quantities.” (NC Y4: p27). All pupils “solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including
non-unit fractions where the answer is a whole number” (NC Y4: p26).
Wherever possible, this unit should involve familiar or otherwise relevant contexts for pupils to engage with. Pupils have worked with bar charts, pictograms and
tables in previous years, but Year 4 sees a shift from more straightforward questions such as ‘How many fewer?’, to being able to “solve comparison, sum and
difference problems using information presented in bar charts, pictograms, tables and other graphs.” (NC Y4: p29). Pupils also broaden their repertoire of graphs
to include time graphs, and so are able to “interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and
time graphs.” (NC Y4: p29). “Pupils begin to relate the graphical representation of data to recording change over time“, (NC Y4: p29).
A further development from KS1 and Year 3 is that, “pupils understand and use a greater range of scales in their representations.” (NC Y4: p29). This unit may offer
a good opportunity to look forward to Unit 10, when pupils will use coordinates to describe position.
The Mathematics Mastery programme of study for Year 4 is copyright © 2013-14 Mathematics Mastery. It is designed for use by school leaders and teachers in schools in the Mathematics Mastery partnership.
We are happy to share this programme of study with schools beyond this community, in order to support preparation for and implementation of the new National Curriculum.
Spring 2 – May DRAFT
Week
2
weeks
Spring 2
Unit 8
Decimals
Mathematics lesson foci
This half term is significant in being pupils’ first formal introduction to decimal notation. In Year 3, as part of their work on fractions, pupils counted up and down in
tenths, recognised that tenths arise from dividing an object into 10 equal parts, and divided one-digit numbers or quantities by 10. In Unit 6 of Year 4, pupils extend
this to include work with hundredths. Prior to Unit 8 of Year 4, tenths and hundredths were recorded as fractions. Year 4 is a key year for pupils to understand the
connections between fraction and decimal representation, including realising that a given number or proportion may be represented using either decimal or
fraction notation. “Pupils are taught throughout that decimals and fractions are different ways of expressing numbers and proportions.” (NC Y4: p27). In this unit,
pupils “find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths”
(NC Y4: p26) and “recognise and write decimal equivalents of any number of tenths or hundredths” (NC Y4: p26). As per the notes and guidance, “Pupils’
understanding of the number system and decimal place value is extended at this stage to tenths and then hundredths. This includes relating the decimal notation to
division of whole number by 10 and later 100.” (NC Y4: p27)
“Pupils learn decimal notation and the language associated with it, including in the context of measurements. They make comparisons and order decimal amounts
and quantities that are expressed to the same number of decimal places. They should be able to represent numbers with one or two decimal places in several ways,
such as on number lines.” (NC Y4: p27).
Through working with concrete manipulatives and pictorial representations of tenths and hundredths, pupils come to “recognise and write decimal equivalents to
𝟏 𝟏 𝟑
, , ” (NC Y4: p26). Throughout this, the language and concepts of Unit 6 fractions must be used wherever appropriate.
𝟒 𝟐 𝟒
Unit 9
2
weeks
Solving problems
with addition
and subtraction
of decimals
Pupils “round decimals with one decimal place to the nearest whole number” and “compare numbers with the same number of decimal places up to two
decimal places” (NC Y4: p26).
It is always essential that connections are clearly made between number and measures. “Pupils should connect hundredths to tenths and place value and decimal
measure.” (NC Y4: p27). “Pupils build on their understanding of place value and decimal notation to record metric measures, including money” (NC Y4: p28). In Unit
9, pupils apply the concepts of skills of Unit 8 in the context of measures. They “solve simple measure and money problems involving fractions and decimals to
two decimal places.” (NC Y4: p26) and “estimate, compare and calculate different measures, including money in pounds and pence” (NC Y4: p27).
The Mathematics Mastery programme of study for Year 4 is copyright © 2013-14 Mathematics Mastery. It is designed for use by school leaders and teachers in schools in the Mathematics Mastery partnership.
We are happy to share this programme of study with schools beyond this community, in order to support preparation for and implementation of the new National Curriculum.
Summer 1 – May DRAFT
Week
Summer 1
Unit 10
5
weeks
Coordinates,
shape and
symmetry
Mathematics lesson foci
All bullet points are taken from the National Curriculum (2014) programme of study – Y3 if not otherwise stated
Pupils have worked with graphs in mathematics since Year 2, including in Unit 7 of Year 4. However, this half-term is the first formal introduction of coordinates. As
pupils are not yet familiar with negative numbers, the focus is on the first quadrant (where x-axis and y-axis values are positive). As per the notes and guidance,
“pupils draw a pair of axes in one quadrant, with equal scales and integer labels. They read, write and use pairs of coordinates, for example (2, 5), including using
coordinate-plotting ICT tools.” (NC Y4: p29)
On the coordinate grid, pupils will:

“describe positions on a 2-D grid as coordinates in the first quadrant” (NC Y4: p29)

“describe movements between positions as translations of a given unit to the left/right and up/down” (NC Y4: p29)

“plot specified points and draw sides to complete a given polygon” (NC Y4: p29)
Not all work with geometric shapes in Year 4 is restricted to the coordinate grid. Pupils will “compare and classify geometric shapes, including quadrilaterals and
triangles, based on their properties and sizes” in a variety of contexts (NC Y4: p28). “Pupils continue to classify shapes using geometrical properties, extending to
classifying different triangles (for example, isosceles, equilateral, scalene) and quadrilaterals (for example, parallelogram, rhombus, trapezium)” (NC Y4: p28).
Angles have been a feature of Maths Meetings throughout the year. In Year 3, pupils worked with right angles, horizontal, vertical, perpendicular and parallel lines. In
Year 4, they begin to use the language ‘acute’ and ‘obtuse’ as they “compare and order angles in preparation for using a protractor and compare lengths and angles
to decide if a polygon is regular or irregular.” (NC Y4: p28). All pupils will “identify acute and obtuse angles and compare and order angles up to two right angles by
size” (NC Y4: p28).
From the start of Year 4, Maths Meetings, Do Nows and other opportunities are used to introduce symmetry. Art and other opportunities in the wider school
curriculum should be used to demonstrate to pupils the wide variety of situations in which symmetry can be observed. In Unit 10, pupils “draw symmetric patterns
using a variety of media to become familiar with different orientations of lines of symmetry; and recognise line symmetry in a variety of diagrams, including where the
line of symmetry does not dissect the original shape.” (NC Y4: p28). They will “identify lines of symmetry in 2-D shapes presented in different orientations” and
“complete a simple symmetric figure with respect to a specific line of symmetry” (NC Y4: p28).
The Mathematics Mastery programme of study for Year 4 is copyright © 2013-14 Mathematics Mastery. It is designed for use by school leaders and teachers in schools in the Mathematics Mastery partnership.
We are happy to share this programme of study with schools beyond this community, in order to support preparation for and implementation of the new National Curriculum.
Summer 2 – May DRAFT
Week
Summer 2
Unit 11
5
weeks
Calculating
with whole
numbers and
decimals
Mathematics lesson foci
Our Curriculum for Depth limits new concepts and methods to the first five half-terms of Year 4, leaving this half term for deeper exploration of the number system.
There are therefore no new statements from the National Curriculum for this half-term, instead the time is dedicated to exploration, clarification, practice and
application of all content previously met in Year 4. Independent application of mathematical ideas in a problem solving context is a particular priority.
In addition to learning activity planned significantly in advance that incorporates key ideas from the mathematics curriculum so far, during this time teachers will use
pupil assessment formatively to inform their teaching priorities during this half-term.
This unit is an important consolidation opportunity for all pupils. Contexts can be drawn from across (and beyond) the maths curriculum. There is a focus on devising
and explaining efficient methods for different calculations. With all multiplication tables from 2x to 12x now learnt, this is an opportunity for pupils to realise how
powerful known facts can be in deriving unknown facts.
The Mathematics Mastery programme of study for Year 4 is copyright © 2013-14 Mathematics Mastery. It is designed for use by school leaders and teachers in schools in the Mathematics Mastery partnership.
We are happy to share this programme of study with schools beyond this community, in order to support preparation for and implementation of the new National Curriculum.