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Outlined below is the Year 5 Maths Curriculum which includes details of both the National Curriculum and the KPS Curriculum. The first column indicates what we have to teach with guidance for this given in the second column. The third column enhances the first by outlining our expectations based on our knowledge of the children of KPS and what we want them to learn and our expectations for their achievement and attainment.
Programmes of Study
STATUTORYNotes and Guidance
NON STATUTORYKexborough Primary School
OUR EXPECTATIONS AND NON NEGOTIABLESNUMBER PLACE VALUEPupils should be taught to:
read, write, order and compare numbers to at least 1000000 and determine the value of each digit
count forwards or backwards in steps of powers of 10 for any given number up to 1000000
interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero
round any number up to 1000000 to the nearest 10, 100, 1000, 10000 and 100000
solve number problems and practical problems that involve all of the above
read Roman numerals to 1000 (M) and recognise years written in Roman numerals.Pupils identify the place value in large whole numbers.
They continue to use number in context, including measurement. Pupils extend and apply their understanding of the number system to the decimal numbers and fractions that they have met so far.
They should recognise and describe linear number sequences, including those involving fractions and decimals, and find the term-to-term rule.
They should recognise and describe linear number sequences (for example, 3, 3EMBED Equation.3, 4, 4EMBED Equation.3...), including those involving fractions and decimals, and find the term-to-term rule in words (for example, add EMBED Equation.3).Number continues to be revisited continually during the Year 5 curriculum, during mental and oral starters and through direct teaching.
It is vital to equip chn with an understanding of negative numbers, most often taught in the context of temperature, including its raising and lowering. This will enable chn to order a given set of positive and negative integers when given in context.
Chn need to be able to recognise & extend number sequences formed by counting from any number in steps of a constant size (Eg 25, 0.1), extending beyond 0 when counting back.
When rounding, chn should be able to round a number with one or two decimal places to the nearest integer.NUMBER ADDITION AND SUBTRACTIONPupils should be taught to:
add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
add and subtract numbers mentally with increasingly large numbers
use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.Pupils practise using the formal written methods of columnar addition and subtraction with increasingly large numbers to aid fluency (see HYPERLINK \l "MathematicsAppendix1Examples" HYPERLINK \l "MathematicsAppendix1Examples" Mathematics Appendix 1).
They practise mental calculations with increasingly large numbers to aid fluency (forexample, 12462 2300 = 10162).The Calculation Policy is a non-negotiable and MUST be followed to ensure consistency of approach and progression throughout school.
To maintain childrens interest in calculations, it is vital to give them real contexts and purposes for their calculating. They should be able to confidently use and apply formal written methods to solving problems involving all four number operations. All working must be shown in sequenced steps and more formal methods must be encouraged.
NUMBER MULT AND DIVPupils should be taught to:
identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers
know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
establish whether a number up to 100 is prime and recall prime numbers up to 19
multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
multiply and divide numbers mentally drawing upon known facts
divide numbers up to 4 digits by a one-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 including using their 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
solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.Pupils practise and extend their use of the formal written methods of short multiplication and short division (see HYPERLINK \l "MathematicsAppendix1Examples" HYPERLINK \l "MathematicsAppendix1Examples" Mathematics Appendix 1). They apply all the multiplication tables and related division facts frequently, commit them to memory and use them confidently to make larger calculations.
They use and understand the terms factor, multiple and prime, square and cube numbers.
Pupils interpret non-integer answers to division by expressing results in different ways according to the context, including with remainders, as fractions, as decimals or by rounding (for example, 98 4 =EMBED Equation.3 = 24 r 2 = 24EMBED Equation.3 = 24.5 H" 25).
Pupils use multiplication and division as inverses to support the introduction of ratio in year 6, for example, by multiplying and dividing by powers of 10 in scale drawings or by multiplying and dividing by powers of a 1000 in converting between units such as kilometres and metres.
Distributivity can be expressed as a(b + c) = ab + ac.
They understand the terms factor, multiple and prime, square and cube numbers and use them to construct equivalence statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 92 x 10).
Pupils use and explain the equals sign to indicate equivalence, including in missing number problems (for example, 13 + 24 = 12 + 25; 33 = 5 x SHAPE \* MERGEFORMAT ).Calculation Policy MUST be followed
Children must be given a secure understanding of the effect of multiplying and dividing any positive integer up to 10,000 by 10 or 100. Apparatus, such as an abacus, may still need to be used to support this understanding.
All tables from 1-12 should continue to be revised (including division) regularly, so chn are able to recall facts at speed. As part of knowing several calculation methods, chn should practise using factors to mentally multiply.
As with addition and subtraction, it is vital that multiplication and division be contextualised, giving chn purpose and the ability to use and apply their skills. It is non-negotiable that they show their working out in a clear, neat and logical way, using formal written methods.
It is essential to give chn the opportunity to explain their methods and reasoning in an articulate way, modelling where necessary.
NUMBER FRACTIONS (INCLUDING DECIMALS AND PERCENTAGES)Pupils should be taught to:
compare and order fractions whose denominators are all 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, EMBED Equation.3+EMBED Equation.3 = EMBED Equation.3 = 1EMBED Equation.3]
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
read and write decimal numbers as fractions [for example, 0.71 = EMBED Equation.3]
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
read, write, order and compare numbers with up to three decimal places
solve problems involving number up to three decimal places
recognise the per cent symbol (%) and understand that per cent relates to number of parts per hundred, and write percentages as a fraction with denominator 100, and as a decimal
solve problems which require knowing percentage and decimal equivalents of EMBED Equation.3, EMBED Equation.3, EMBED Equation.3, EMBED Equation.3, EMBED Equation.3 and those fractions with a denominator of a multiple of 10 or 25. Pupils should be taught throughout that percentages, decimals and fractions are different ways of expressing proportions.
They extend their knowledge of fractions to thousandths and connect to decimals and measures.
Pupils connect equivalent fractions > 1 that simplify to integers with division and other fractions > 1 to division with remainders, using the number line and other models, and hence move from these to improper and mixed fractions.
Pupils connect multiplication by a fraction to using fractions as operators (fractions of), and to division, building on work from previous years. This relates to scaling by simple fractions, including fractions>1.
Pupils practise adding and subtracting fractions to become fluent through a variety of increasingly complex problems. They extend their understanding of adding and subtracting fractions to calculations that exceed 1 as a mixed number.
Pupils continue to practise counting forwards and backwards in simple fractions.
Pupils continue to develop their understanding of fractions as numbers, measures and operators by finding fractions of numbers and quantities.
Pupils extend counting from year 4, using decimals and fractions including bridging zero, for example on a number line.
Pupils say, read and write decimal fractions and related tenths, hundredths and thousandths accurately and are confident in checking the reasonableness of their answers to problems.
They mentally add and subtract tenths, and one-digit whole numbers and tenths.
They practise adding and subtracting decimals, including a mix of whole numbers and decimals, decimals with different numbers of decimal places, and complements of 1 (for example, 0.83 + 0.17 = 1).
Pupils should go beyond the measurement and money models of decimals, for example, by solving puzzles involving decimals.
Pupils should make connections between percentages, fractions and decimals (for example, 100% represents a whole quantity and 1% is EMBED Equation.3, 50% is EMBED Equation.3, 25% is EMBED Equation.3) and relate this to finding fractions of.Chn should, by this point, be able to confidently use fraction notation, including mixed numbers, and the vocabulary denominator and numerator. They should be taught to relate fractions to division in order for them to begin to convert between fractions, decimals and percentages.
To aid their understanding of the value of fractions, chn should be able to not only order a set of fractions but also place them on a number line (including in the context of measures).
Chn should be given opportunities to apply their knowledge of fractions and percentages in problem solving and investigating. It must be ensured that pupils are able to calculate 1% and 10% of numbers and amounts, using this to solve other percentage calculations.solve problems which require knowing percentage and decimal equivalents of EMBED Equation.3, EMBED Equation.3, EMBED Equation.3, EMBED Equation.3, EMBED Equation.3 and those fractions with a denominator of a multiple of 10 or 25.They practise adding and subtracting decimals, including a mix of whole numbers and decimals, decimals with different numbers of decimal places, and complements of 1 (for example, 0.83 + 0.17 = 1).
Pupils should go beyond the measurement and money models of decimals, for example, by solving puzzles involving decimals.
Pupils should make connections between percentages, fractions and decimals (for example, 100% represents a whole quantity and 1% is EMBED Equation.3, 50% is EMBED Equation.3, 25% is EMBED Equation.3) and relate this to finding fractions ofMEASUREMENTPupils should be taught to:
convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)
understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints
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) and estimate the area of irregular shapes
estimate volume [for example, using 1 cm3 blocks to build cuboids (including cubes)] and capacity [for example, using water]
solve problems involving converting between units of time
use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling. Pupils use their knowledge of place value and multiplication and division to convert between standard units.
Pupils calculate the perimeter of rectangles and related composite shapes, including using the relations of perimeter or area to find unknown lengths. Missing measures questions such as these can be expressed algebraically, for example 4 + 2b = 20 for a rectangle of sides 2 cm and b cm and perimeter of 20cm.
Pupils calculate the area from scale drawings using given measurements.
Pupils use all four operations in problems involving time and money, including conversions (for example, days to weeks, expressing the answer as weeks and days).As in other years, measures must always be taught within context, and practically wherever possible. There are obvious links to other areas of the curriculum, including Geography and Science, and these subjects should be used to reinforce chns concepts of measure.
All chn must, by the end of Year 5, be able to read and use notation to tell the time on a 24 hour digital clock and interpret timetables. Time must again be taught in context, with pupils carrying out open-ended investigations using different types of timetables.
In the teaching of perimeter and area, investigations should be given to the chn, allowing them to discover all possibilities.
GEOMETRY PROPS OF SHAPEPupils should be taught to:
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 EMBED Equation.3 a turn (total 180o)
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.Pupils become accurate in drawing lines with a ruler to the nearest millimetre, and measuring with a protractor. They use conventional markings for parallel lines and right angles.
Pupils use the term diagonal and make conjectures about the angles formed between sides, and between diagonals and parallel sides, and other properties of quadrilaterals, for example using dynamic geometry ICT tools.
Pupils use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems.Chn should understand area measured in square centimetres (being able to write its notation) and be able to use formula to find areas of rectangles and regular polygons.
They should recognise parallel and perpendicular lines in shapes and understand the term bisect .
Chn should be taught to classify and draw triangles using given criteria (isosceles, equilateral, scalene). They must know that the angles in a triangle total 180.
They should be able to recognise reflective symmetry in polygons of different orientations.
GEOMETRY POS AND DIRPupils should be taught to:
identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed. Pupils should be taught to:
Pupils recognise and use reflection and translation in a variety of diagrams, including continuing to use a 2-D grid and coordinates in the first quadrant. Reflection should be in lines that are parallel to the axes.STATISTICSPupils should be taught to:
solve comparison, sum and difference problems using information presented in a line graph
complete, read and interpret information in tables, including timetables.Pupils connect their work on coordinates and scales to their interpretation of time graphs.
They begin to decide which representations of data are most appropriate and why.Chn need to consider statistics in real contexts at all times. They should s234 .
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