The National Curriculum for
mathematics aims to ensure that all pupils:
become fluent in the fundmentals of mathematics, so that
pupils have conceptual understanding and can recall and
apply their knowledge rapidly and accurately to
problems.
reason mathematically by following a line of enquiry,
conjecturing relationships and generalisations, and
developing an argument or proof using mathematical
language.
can solve problems by applying their mathematics to a
variety of routine and non-routine problems with
increasing sophistication, including breaking down
problems into a series of simpler steps and persevering
in seeking solution.
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Learning Objectives |
Additional Information |
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Number and Place Value |
Read, write, order and compare numbers to at least 1000000 and
determine the value of each digit.
Interpret negative numbers in context.
Count forwards and backwards with positive and negative
whole numbers including through zero. |
Large numbers of six digits are named in a pattern of three:
hundreds of
thousands, tens of thousands, ones of thousands, mirroring hundreds, tens and
ones. It is helpful to relate large numbers to real-world contexts, for example
the number of people that a local sports arena can hold.
Calculation policy page:
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Addition and Subtraction |
Add and subtract whole numbers with more than four digits, including using
formal written methods (columnar addition and subtraction).
Add and subtract
numbers mentally with increasingly large numbers (e.g. 12462 – 2300 = 10162).
Solve problems involving numbers up to three decimal
places. |
Before starting any calculation is it helpful to think about whether or not you
are confident that you can do it mentally. For example, 3689 + 4998 may be done
mentally, but 3689 + 4756 may require paper and pencil. Carrying out an
equivalent calculation might be easier than carrying out the given calculation.
For example 3682 – 2996 is equivalent to 3686 – 3000 (constant difference).
Calculation policy page: 14
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Multiplication and Division |
Identify multiples and factors, including finding all factor pairs of a number,
and common factors of two numbers.
Multiply numbers up to four digits by a 1 or
2-digit number using a formal written method, including long multiplication for
2-digit numbers.
Multiply and divide numbers mentally drawing upon known
facts.
Divide numbers up to four digits by a 1-digit number using the formal
written method of short division and interpret remainders appropriately for the
context.
Multiply and divide whole numbers and those involving decimals by 10,
100 and 1000.
Recognise and use square numbers and cube numbers, and the notation for squared
(2 ) and cubed (3 ).
Solve problems involving multiplication and division.
Use knowledge of factors and multiples, squares and cubes.
Solve problems involving addition, subtraction,
multiplication and division and a combination of these,
including understanding the meaning of the equals sign.
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Pupils have a firm understanding of what multiplication and division mean and
have a range of strategies for dealing with large numbers, including both mental
and standard written methods.
They see the idea of factors, multiples and prime
numbers as connected and not separate ideas to learn. They recognise how to use
their skills of multiplying and dividing in new problem solving
situations.
Fractions and division are connected ideas:
36 ÷ 18= 36/18
36/18 =
2
Factors and multiples are connected ideas: 48 is a multiple of 6 and 6 is a factor of 48.
Calculation policy page:
15-16 |
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Fractions |
Compare and order fractions whose denominators are
multiples of the same number.
Identify, name and write equivalent fractions of a given
fraction, represented visually, including tenths and
hundredths.
Recognise mixed numbers and improper fractions and
convert from one form to the other and write
mathematical statements > 1 as a mixed number (for
example, 2/5 + 4/5 = 6/5 = 1 1/5).
Add and subtract fractions with the same denominator and
denominators that are multiples of the same number.
Multiply proper fractions and mixed numbers by whole
numbers, supported by materials and diagrams.
Recognise
the per cent symbol (%) and understand that per cent
relates to ‘number of parts per hundred’.
Write
percentages as a fraction with denominator 100, and as a
decimal.
Read and write decimal numbers as fractions [e.g 0.71 =
71/100].
Solve problems which require knowing percentage and
decimal equivalents of 1/ 2 , 1/ 4 , 1 /5 , 2/ 5 , 4/ 5
and those fractions with a denominator of a multiple of
10 or 25.
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Representations that may appear different sometimes have similar underlying
ideas. For example 1/4 , 0·25 and 25% are used in different contexts but are all
connected to the same idea.
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Decimals |
Read, write, order and compare numbers with up to three decimal places.
Recognise
and use thousandths and relate them to tenths, hundredths and decimal
equivalents.
Round decimals with two decimal places to the nearest whole number
and to one decimal place.
Solve problems involving number up to three decimal
places.
Multiply and divide whole numbers and those involving
decimals by 10, 100 and 1000.
Use all four operations to solve problems involving
measure [for example, length, mass, volume, money] using
decimal notation, including scaling.
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Percentages |
Recognise the per cent symbol (%) and understand that
per cent relates to ‘number of parts per hundred’.
Write percentages as a fraction with denominator 100,
and as a decimal.
Solve problems which require knowing percentage and
decimal equivalents of ½, ¼, 1/5, 2/5, 4/5, and those
fractions with a denominator of a multiple of 10 or 25.
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Measurement |
Convert between different units of metric measure (for example, kilometre and
metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre
and millilitre).
Measure and calculate the perimeter of composite rectilinear
shapes in centimetres and metres.
Calculate and compare the area of rectangles
(including squares), and including using standard units, square centimetres (cm2)
and square metres (m2 ).
Estimate the area of irregular shapes.
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The relationship between area and perimeter is not a simple one.
Increasing or decreasing area does not necessarily mean the
perimeter increases or decreases respectively, or vice versa.
Area is measured in square units. For rectangles, measuring the
length and breadth is a shortcut to finding out how many squares
would fit into
each of these dimensions. |
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Geometry |
Identify 3-D shapes, including cubes and other cuboids, from 2-D representations
know angles are measured in degrees.
Estimate and compare acute, obtuse and
reflex angles draw given angles, and measure them in degrees (o
)
Identify:
- angles at a point and one whole turn (total 360o)
- angles at a point on a straight line and 1/2 a turn (total 180o)
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other multiples of 90o
Use the properties of rectangles to deduce related facts and find missing
lengths and angles.
Distinguish between regular and irregular polygons based on
reasoning about equal sides and angles. |
During this year, pupils increase the range of 2-D and
3-D shapes that they are familiar with.
With 3-D shapes they think about the faces as well as
the number of vertices and through considering nets
think about the 2-D shapes that define the 3-D shapes.
Pupils learn about a range of angle facts and use them
to describe certain shapes and derive facts about them.
Regular shapes have to have all sides and all angles the
same. Although non-square rectangles have four equal
angles, the fact that they do not have four equal sides
means that they are not regular.
Some properties of shapes are dependent upon other
properties. For example, a rectangle has opposite sides
equal because it has four right angles.
A rectangle is
defined as a quadrilateral with four right angles. It
does not have to be defined as a quadrilateral with four
right angles and two pairs of equal sides.
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Statistics |
Solve comparison, sum and difference problems using
information presented in a line graph.
Complete, read and interpret information in tables,
including timetables.
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Different representations highlight different aspects of data.
It is important to be able to answer questions
about data using inference and deduction, not just
direct retrieval. |
