Michaelmas term

Lent term

Summer term

1. Properties of Number

1. Properties of Number

1. Properties of Number

2. Multiplication and Division

2. Multiplication and Division

2. Calculations

3. Fractions

3. Area and Perimeter

3. Percentages, Decimals, Fractions

4. Addition and Subtraction

4. Fractions

4. Measurement and Time

5. Angles

5. Decimals

5. Movement Geometry and 3D

6. Measurement

6. Angles and Polygons

6. Frequency Tables and Data Tables

7. Line Graphs

Y5 SCHEME OF WORK

1: Properties of Number

Requirement

Notes

Numbers 2, 3

read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit

Ordering 4

Place Value 5

Counting in 6

count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000

Multiples 24

identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers

Common Factors 25

2: Multiplication and Division

Facts 29, 30

multiply and divide numbers mentally drawing upon known facts

Pupils practise and extend their use of the formal written methods of short multiplication and short division. They apply all the multiplication tables and related division facts frequently, commit them to memory and use them confidently to make larger calculations

Strategies 32

by 10, 100, 1000 33

Short Multiplication 36, 37

multiply numbers up to 4 digits by a one -digit number using a formal written method

Division 41, 42

divide numbers up to 4 digits by a one-digit number using the formal written method of short division

3: Fractions

Equivalent 53

identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths

Comparing 54, 55

compare and order fractions whose denominators are all multiples of the same number

Mixed Numbers 56, 57

recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number

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

Decimals and Fractions 65 – 67

read and write decimal numbers as fractions

recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

They extend their knowledge of fractions to thousandths and connect to decimals and measures

4: Addition and Subtraction

Mental 12 – 14

add and subtract numbers mentally with increasingly large numbers

They practise mental calculations with increasingly large numbers to aid fluency (for example, 12 462 – 2300 = 10 162)

Written 15- 17

add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)

Pupils practise using the formal written method of columnar addition and subtraction with increasingly large numbers to aid fluency

5: Angles

Quarter, half, whole turns 110

know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles

Comparing 111

Measuring 112 – 115

draw given angles, and measure them in degrees

Drawing 118

6: Measurement

Metric Units 84, 85

convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)

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

Length, Weight, Capacity 88 -90

use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling

Mental measures 101, 102

Pupils use their knowledge of place value and multiplication and division to convert between standard units

+ / – Measures 104, 105

7: Line Graphs

Interpreting 132 – 135

solve comparison, sum and difference problems using information presented in a line graph

…

Lent Term

1: Properties of Number

Rounding whole numbers 7

round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000

Rounding Decimals 68

round decimals with two decimal places to the nearest whole number and to one decimal place

Rounding to Estimate 18

use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy

Prime Numbers 26

know and use the vocabulary of prime numbers, prime factors and composite (nonprime) numbers

They use and understand the terms factor, multiple and prime, square and cube numbers

Square Numbers 34

recognise and use square numbers and cube numbers, and the notation for squared and cubed

Cube Numbers 35

2: Multiplication and Division

Long Multiplication 39, 40

multiply numbers up to 4 digits by a two-digit number using including long multiplication for two-digit numbers

Rounding Remainders 45

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

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

Word Problems 50

solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign

3: Area and Perimeter

Area and Perimeter 91 – 93

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 and square metres and estimate the area of irregular shapes

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

Comparing Areas 94,95

4: Fractions

+ / – Fractions 58 – 60

add and subtract fractions with the same denominator and denominators that are multiples of the same number

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

Fraction of whole number 61

multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams

Pupils connect multiplication by a fraction to using fractions as operators (fractions of), and to division

Fraction Problems 62

Multiplying Fractions 63

Fraction of an amount 64

5: Decimals

Comparing 69

read, write, order and compare numbers with up to three decimal places

Ordering 70

Mental Decimals 71

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

Counting in 72 – 74

count using decimals and fractions including bridging zero, for example on a number line

Pupils continue to practise counting forwards and backwards in simple fractions

6: Angles and Polygons

Angles and Straight Lines 116, 117

identify: angles at a point and one whole turn (total 360 ^o); angles at a point on a straight line and half a turn; other multiples of 90^o

Pupils use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems

Rectangles 119

use the properties of rectangles to deduce related facts and find missing lengths and angles

Quadrilaterals 120, 121

draw lines with a ruler to the nearest millimetre, and are accurate measuring with a protractor; 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

Regular / Irregular 124

distinguish between regular and irregular polygons based on reasoning about equal sides and angles

…

Summer Term

1: Properties of Number

Roman Numerals 10, 11

read Roman numerals to 1000 (M) and recognise years written in Roman numerals

Rounding to check 19

Prime Factors 27

establish whether a number up to 100 is prime and recall prime numbers up to 19

Find the number 52

2: Calculations

+ / – Problems 20, 21

solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

Written × / ÷ 48

Missing number problems 49

Word Problems 51

3: Percentages, Decimals, Fractions

Percentages 80, 81

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

Converting 82

Percentage of amount 83

solve problems which require knowing percentage and decimal equivalents of half, quarter, fifth, two fifths, and four fifths, and those fractions with a denominator of a multiple of 10 or 25

Pupils should make connections between percentages, fractions and decimals (for example, 100% represents a whole quantity and 1% is one hundredth, 50% is fifty hundredths, 25% is twenty-five hundredths) and relate this to finding ‘fractions of’

4: Measurement and Time

Calculations 103, 107, 108

use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling

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)

Imperial Units 86

understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints

Time Units 100

solve problems involving converting between units of time

Timetables 142, 143

complete, read and interpret information in timetables

5: Movement Geometry and 3D

Reflection 125 – 127

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 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.

Pupils connect their work on coordinates and scales to their interpretation of graphs

Translation 129 – 131

3D shapes 122, 123

identify 3-D shapes, including cubes and other cuboids, from 2-D representations

Volume 98, 99

estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water]

6: Frequency Tables and Data Tables

Frequency Tables 136, 137

complete, read and interpret information in tables

They begin to decide which representations of data are most appropriate and why

Data Tables 138 – 141