### Place Value

Counting

- Count to 5.

Counting to 6,7,8, 9, 10.

Counting to 20

Comparing Numbers

- Comparing quantities of identical and then non-identical objects.
- Comparing groups up to 10.

### Addition and Subtraction

Number Bonds

- Number bonds to 5
- Number bonds to 10

Mental Calculation

- Sorting into groups
- Change within 5: one more and one less
- Adding by counting on
- Take away by counting back

### Multiplication and Division

Multiplication & Division Facts

- Numerical Patterns
- Doubling
- Halving
- Odds and Evens

### Measurement

Comparing and Estimating

- Comparing length, height, distance, weight and capacity.
- Time – next, later, yesterday, today, tomorrow.

Measuring and Calculating

- How many jumps in 10 seconds, 1 minute.

### Geometry Properties of Shapes

Identifying Shapes and their Properties

- Are encouraged to see 2D shapes on the surface of 3D shapes.
- To begin to name common shapes; circles, triangles, rectangles including squares.

### Geometry – Position and Direction

Position, Direction and Movement

- Spatial awareness: Over, under, around, through.

### Place Value

Counting

- count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number
- count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens
- given a number, identify one more and one less

Comparing Numbers

- use the language of: equal to, more than, less than (fewer), most, least

Identifying, Representing and Estimating Numbers

- identify and represent numbers using objects and pictorial representations including the number line

Reading and Writing Numbers (including Roman Numerals)

- read and write numbers from 1 to 20 in numerals and words.

### Addition and Subtraction

Number Bonds

- represent and use number bonds and related subtraction facts within 20

Mental Calculation

- add and subtract one-digit and two-digit numbers to 20, including zero
- read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs (appears also in Written Methods)

Written Methods

- read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs (appears also in Mental Calculation)

Problem Solving

solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = – 9

### Multiplication and Division

Multiplication & Division Facts

- count in multiples of twos, fives and tens (copied from Number and Place Value)

Problem Solving

- solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher

### Fractions

Recognising Fractions

- recognise, find and name a half as one of two equal parts of an object, shape or quantity
- recognise, find and name a quarter as one of four equal parts of an object, shape or quantity

### Algebra

Equations

- solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = – 9 (copied from Addition and Subtraction)
- represent and use number bonds and related subtraction facts within 20 (copied from Addition and Subtraction)

Sequences

- sequence events in chronological order using language such as: before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening (copied from Measurement)

### Measurement

Comparing and Estimating

compare, describe and solve practical problems for:

- lengths and heights [e.g. long/short, longer/shorter, tall/short, double/half]
- mass/weight [e.g. heavy/light, heavier than, lighter than]
- capacity and volume [e.g. full/empty, more than, less than, half, half full, quarter]
- time [e.g. quicker, slower, earlier, later]

sequence events in chronological order using language [e.g. before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening]

Measuring and Calculating

measure and begin to record the following:

**lengths and heights****mass/weight****capacity and volume****time**(hours, minutes, seconds)

recognise and know the value of different denominations of **coins and notes**

Telling the Time

- tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.
- recognise and use language relating to dates, including days of the week, weeks, months and years

### Geometry Properties of Shapes

Identifying Shapes and their Properties

recognise and name common 2-D and 3-D shapes, including:

- 2-D shapes [e.g. rectangles (including squares), circles and triangles]
- 3-D shapes [e.g. cuboids (including cubes), pyramids and spheres].

### Geometry – Position and Direction

Position, Direction and Movement

- Over, under, around, through. describe position, direction and movement, including half, quarter and three-quarter turns.

### Place Value

Counting

- count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward

Comparing Numbers

- compare and order numbers from 0 up to 100; use <, > and = signs

Identifying, Representing and Estimating Numbers

- identify, represent and estimate numbers using different representations, including the number line

Reading and Writing Numbers (including Roman Numerals)

- read and write numbers to at least 100 in numerals and in words

Understanding Place Value

- recognise the place value of each digit in a two-digit number (tens, ones)

Problem Solving

- use place value and number facts to solve problems

### Addition and Subtraction

Number Bonds

- recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100

Mental Calculation

add and subtract numbers using concrete objects, pictorial representations, and mentally, including:

- a two-digit number and ones
- a two-digit number and tens
- two two-digit numbers
- adding three one-digit numbers

show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot

Inverse Operations, Estimating and Checking Answers

- recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.

Problem Solving

solve problems with addition and subtraction:

- using concrete objects and pictorial representations, including those involving numbers, quantities and measures
- applying their increasing knowledge of mental and written methods

solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change (copied from Measurement)

### Multiplication and Division

Multiplication & Division Facts

- count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward (copied from Number and Place Value)
- recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers

Mental Calculation

- show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot

Written Calculation

- calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs

Problem Solving

- solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts

### Fractions

Counting in Fractional Steps

- Pupils should count in fractions up to 10, starting from any number and using the 1/2 and 2/4 equivalence on the number line (Non Statutory Guidance)

Recognising Fractions

- recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity

Equivalence (Including Fractions, Decimals and Percentages)

- write simple fractions e.g. 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2.

### Algebra

Equations

- recognise and use the inverse relationship between addition and subtraction and use this to check calculations and missing number problems. (copied from Addition and Subtraction)
- recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 (copied from Addition and Subtraction)

Sequences

- compare and sequence intervals of time (copied from Measurement)
- order and arrange combinations of mathematical objects in patterns (copied from Geometry: position and direction)

### Measurement

Comparing and Estimating

- compare and order lengths, mass, volume/capacity and record the results using >, < and =
- compare and sequence intervals of time

Measuring and Calculating

- choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels
- recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value
- find different combinations of practical contexts coins that equal the same amounts of money
- solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change

Telling the Time

- tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times.
- know the number of minutes in an hour and the number of hours in a day. (appears also in Converting)

Converting

- know the number of minutes in an hour and the number of hours in a day. (appears also in Telling the Time)

### Geometry Properties of Shapes

Identifying Shapes and their Properties

- identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line
- identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces
- identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]

Comparing and Classifying

- compare and sort common 2-D and 3-D shapes and everyday objects

### Geometry – Position and Direction

Position, Direction and Movement

- use mathematical vocabulary to describe position, direction and movement including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise)

Pattern

- order and arrange combinations of mathematical objects in patterns and sequences

### Statistics

Interpreting, Constructing and Presenting Data

- interpret and construct simple pictograms, tally charts, block diagrams and simple tables
- ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity
- ask and answer questions about totalling and comparing categorical data

### Place Value

Counting

- count from 0 in multiples of 4, 8, 50 and 100;
- find 10 or 100 more or less than a given number

Comparing Numbers

- compare and order numbers up to 1000

Identifying, Representing and Estimating Numbers

- identify, represent and estimate numbers using different representations

Reading and Writing Numbers (including Roman Numerals)

- read and write numbers up to 1000 in numerals and in words
- tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks (copied from Measurement)

Understanding Place Value

- recognise the place value of each digit in a three-digit number (hundreds, tens, ones)

Problem Solving

- solve number problems and practical problems involving these ideas.

### Addition and Subtraction

Mental Calculation

add and subtract numbers mentally, including:

- a three-digit number and ones
- a three-digit number and tens
- a three-digit number and hundreds

Written Method

add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction

Inverse Operations, Estimating and Checking Answers

- estimate the answer to a calculation and use inverse operations to check answers

Problem Solving

solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction

### Multiplication and Division

Multiplication & Division Facts

- count from 0 in multiples of 4, 8, 50 and 100 (copied from Number and Place Value)
- recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables

Mental Calculation

- write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times

one-digit numbers, using mental and progressing to formal written methods (appears also in Written Methods)

Written Calculation

- write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times

one-digit numbers, using mental and progressing to formal written methods (appears also in Mental Methods)

Inverse Operations, Estimating and Checking Answers

- estimate the answer to a calculation and use inverse operations to check answers (copied from Addition and Subtraction)

Problem Solving

- solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects

### Fractions

Counting in Fractional Steps

- count up and down in tenths

Recognising Fractions

- recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
- recognise that tenths arise from dividing an object into 10 equal parts and in dividing one – digit numbers or quantities by 10.
- recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators

Comparing Fractions

- compare and order unit fractions, and fractions with the same denominators

Equivalence (Including Fractions, Decimals and Percentages)

- recognise and show, using diagrams, equivalent fractions with small denominators

Addition and Subtraction of Fractions

- add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)

Problem Solving

- solve problems that involve all of the above

### Algebra

Equations

- solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction. (copied from Addition and Subtraction)
- solve problems, including missing number problems, involving multiplication and division, including integer scaling (copied from Multiplication and Division)

### Measurement

Comparing and Estimating

- compare durations of events, for example to calculate the time taken by particular events or tasks
- estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, hours and o’clock; use vocabulary such as a.m./p.m., morning, afternoon, noon and midnight (appears also in Telling the Time)

Measuring and Calculating

- measure, compare, add and subtract:
**lengths**(m/cm/mm);**mass**(kg/g);**volume/capacity**(l/ml) - measure the
**perimeter**of simple 2-D shapes - add and subtract amounts of money to give change, using both £ and p in practical contexts

Telling the Time

- tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks
- estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, hours and o’clock; use vocabulary such as a.m./p.m., morning, afternoon, noon and midnight (appears also in Comparing and Estimating)

Converting

- know the number of seconds in a minute and the number of days in each month, year and leap year

### Geometry Properties of Shapes

Drawing and Constructing

- draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them

Angles

- recognise angles as a property of shape or a description of a turn
- identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle
- identify horizontal and vertical lines and pairs of perpendicular and parallel lines

### Statistics

Interpreting, Constructing and Presenting Data

- interpret and present data using bar charts, pictograms and tables

Problem Solving

- solve one-step and two-step questions [e.g. ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts and pictograms and tables.

### Place Value

Counting

- count backwards through zero to include negative numbers
- count in multiples of 6, 7, 9, 25 and 1000
- find 1000 more or less than a given number

Comparing Numbers

- order and compare numbers beyond 1000
- compare numbers with the same number of decimal places up to two decimal places (copied from Fractions)

Identifying, Representing and Estimating Numbers

- identify, represent and estimate numbers using different representations

Reading and Writing Numbers (including Roman Numerals)

- 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.

Understanding Place Value

- recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
- 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 units, tenths and hundredths (copied from Fractions)

Rounding

- round any number to the nearest 10, 100 or 1000
- round decimals with one decimal place to the nearest whole number (copied from Fractions)

Problem Solving

- solve number and practical problems that involve all of the above and with increasingly large positive numbers

### Addition and Subtraction

Written Method

- add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate

Inverse Operations, Estimating and Checking Answers

- estimate and use inverse operations to check answers to a calculation

Problem Solving

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

### Multiplication and Division

Multiplication & Division Facts

- count in multiples of 6, 7, 9, 25 and 1 000 (copied from Number and Place Value)
- recall multiplication and division facts for multiplication tables up to 12 × 12

Mental Calculation

- use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers
- recognise and use factor pairs and commutativity in mental calculations (appears also in Properties of Numbers)

Written Calculation

- multiply two-digit and three-digit numbers by a one-digit number using formal written layout

Properties of Numbers: Multiples, Factors, Primes, Square and Cube Numbers

- recognise and use factor pairs and commutativity in mental calculations (repeated)

Inverse Operations, Estimating and Checking Answers

- estimate and use inverse operations to check answers to a calculation (copied from Addition and Subtraction)

Problem Solving

- 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

### Fractions

Counting in Fractional Steps

- count up and down in hundredths

Recognising Fractions

- recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten

Comparing Fractions

- compare numbers with the same number of decimal places up to two decimal places

Rounding Including Decimals

- round decimals with one decimal place to the nearest whole number

Equivalence (Including Fractions, Decimals and Percentages)

- recognise and show, using diagrams, families of common equivalent fractions
- recognise and write decimal equivalents of any number of tenths or hundredths
- recognise and write decimal equivalents to 1/4; 1/2; 3/4

Addition and Subtraction of Fractions

- add and subtract fractions with the same denominator

Multiplication and Division of Decimals

- 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

Problem Solving

- 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
- solve simple measure and money problems involving fractions and decimals to two decimal places.

### Algebra

Formulae

- Perimeter can be expressed algebraically as 2(a + b) where a and b are the dimensions in the same unit. (Copied from NSG measurement)

### Measurement

Comparing and Estimating

- estimate, compare and calculate different measures, including money in pounds and pence (also included in Measuring)

Measuring and Calculating

- estimate, compare and calculate different measures, including money in pounds and pence (appears also in Comparing)
- measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres
- find the area of rectilinear shapes by counting squares

Telling the Time

- read, write and convert time between analogue and digital 12 and 24-hour clocks (appears also in Converting)
- solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days (appears also in Converting)

Converting

- convert between different units of measure (e.g. kilometre to metre; hour to minute)
- read, write and convert time between analogue and digital 12 and 24-hour clocks (appears also in Converting)
- solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days (appears also in Telling the Time)

### Geometry Properties of Shapes

Identifying Shapes and their Properties

- identify lines of symmetry in 2-D shapes presented in different orientations

Drawing and Constructing

- complete a simple symmetric figure with respect to a specific line of symmetry

Comparing and Classifying

- compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes

Angles

- identify acute and obtuse angles and compare and order angles up to two right angles by size

### Geometry – Position and Direction

Position, Direction and Movement

- describe positions on a 2-D grid as coordinates in the first quadrant
- describe movements between positions as translations of a given unit to the left/right and up/down
- plot specified points and draw sides to complete a given polygon

### Statistics

Interpreting, Constructing and Presenting Data

- interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs

Problem Solving

- solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.

### Place Value

Counting

- interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero
- count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000

Comparing Numbers

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

Reading and Writing Numbers (including Roman Numerals)

- read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit (appears also in Comparing Numbers)
- read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

Understanding Place Value

- read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit (appears also in Reading and Writing Numbers)
- recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents (copied from Fractions)

Rounding

- round any number up to 1 000 000 to the nearest 10, 100, 1 000, 10 000 and 100 000
- round decimals with two decimal places to the nearest whole number and to one decimal place (copied from Fractions)

Problem Solving

- solve number problems and practical problems that involve all of the above

### Addition and Subtraction

Mental Calculation

add and subtract numbers mentally with increasingly large numbers

Written Methods

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

Inverse Operations, Estimating and Checking Answers

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

Problem Solving

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

### Multiplication and Division

Multiplication & Division Facts

- count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000 (copied from Number and Place Value)

Mental Calculation

- multiply and divide numbers mentally drawing upon known facts
- multiply and divide whole numbers and those involving decimals by 10, 100 and 1000

Written Calculation

- 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
- 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

Properties of Numbers: Multiples, Factors, Primes, Square and Cube Numbers

- 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
- recognise and use square numbers and cube numbers, and the notation for squared (
^{2}) and cubed (^{3})

Problem Solving

- 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

### Fractions

Recognising Fractions

- recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents (appears also in Equivalence)

Comparing Fractions

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

Comparing Decimals

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

Rounding Including Decimals

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

Equivalence (Including Fractions, Decimals and Percentages)

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

Addition and Subtraction of Fractions

- add and subtract fractions with the same denominator and multiples of the same number
- recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number (e.g. 2/5 + 4/5 = 6/5 = 1 1/5)

Multiplication and Division of Fractions

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

Problem Solving

- solve problems involving numbers up to three decimal places
- solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those with a denominator of a multiple of 10 or 25.

### Algebra

Equations

- use the properties of rectangles to deduce related facts and find missing lengths and angles (copied from Geometry: Properties of Shapes)

### Measurement

Comparing and Estimating

- calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm
^{2}) and square metres (m^{2}) andestimate the area of irregular shapes (also included in measuring) - estimate volume (e.g. using 1 cm
^{3}blocks to build cubes and cuboids) and capacity (e.g. using water)

Measuring and Calculating

- use all four operations to solve problems involving measure (e.g. length, mass, volume, money) using decimal notation including scaling.
- measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
- calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm
^{2}) and square metres (m^{2}) and estimate the area of irregular shapes - recognise and use square numbers and cube numbers, and the notation for squared (
^{2}) and cubed (^{3}) (copied from Multiplication and Division)

Telling the Time

- solve problems involving converting between units of time

Converting

- convert between different units of metric measure (e.g. kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)
- solve problems involving converting between units of time
- understand and use equivalences between metric units and common imperial units such as inches, pounds and pints

### Geometry Properties of Shapes

Identifying Shapes and their Properties

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

Drawing and Constructing

- draw given angles, and measure them in degrees (
^{o})

Comparing and Classifying

- 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

Angles

- know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
- identify:
- angles at a point and one whole turn (total 360
^{o}) - angles at a point on a straight line and ½ a turn (total 180
^{o}) - other multiples of 90
^{o}

- angles at a point and one whole turn (total 360

### Geometry – Position and Direction

Position, Direction and Movement

- 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

### Statistics

Interpreting, Constructing and Presenting Data

- complete, read and interpret information in tables, including timetables

Problem Solving

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

### Place Value

Counting

- use negative numbers in context, and calculate intervals across zero

Comparing Numbers

- read, write, order and compare numbers up to 10 000 000 and determine the value of each digit (appears also in Reading and Writing Numbers)

Reading and Writing Numbers (including Roman Numerals)

- read, write, order and compare numbers up to 10 000 000 and determine the value of each digit (appears also in Understanding Place Value)

Understanding Place Value

- read, write, order and compare numbers up to 10 000 000 and determine the value of each digit (appears also in Reading and Writing Numbers)
- identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places (copied from Fractions)

Rounding

- round any whole number to a required degree of accuracy
- solve problems which require answers to be rounded to specified degrees of accuracy (copied from Fractions)

Problem Solving

- solve number and practical problems that involve all of the above

### Addition and Subtraction

Mental Calculation

- perform mental calculations, including with mixed operations and large numbers
- use their knowledge of the order of operations to carry out calculations involving the four operations

Inverse Operations, Estimating and Checking Answers

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

Problem Solving

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

### Multiplication and Division

Mental Calculation

- perform mental calculations, including with mixed operations and large numbers
- associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. 3/8) (copied from Fractions)

Written Calculation

- multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
- divide numbers up to 4-digits by a two-digit whole number using the formal written method of short division where appropriate for the context divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
- use written division methods in cases where the answer has up to two decimal places (copied from Fractions (including decimals))

Properties of Number: Multiples, Factors, Primes, Square and Cube Numbers

- identify common factors, common multiples and prime numbers
- use common factors to simplify fractions; use common multiples to express fractions in the same denomination (copied from Fractions)
- calculate, estimate and compare volume of cubes and cuboids using standard units, including centimetre cubed (cm
^{3}) and cubic metres (m^{3}), and extending to other units such as mm^{3}and km^{3}(copied from Measures)

Order of Operations

- use their knowledge of the order of operations to carry out calculations involving the four operations

Inverse Operations, Estimating and Checking Answers

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

Problem Solving

- solve problems involving addition, subtraction, multiplication and division
- solve problems involving similar shapes where the scale factor is known or can be found (copied from Ratio and Proportion)

### Fractions

Comparing Fractions

- compare and order fractions, including fractions >1

Comparing Decimals

- identify the value of each digit in numbers given to three decimal places

Rounding Including Decimals

- solve problems which require answers to be rounded to specified degrees of accuracy

Equivalence (Including Fractions, Decimals and Percentages)

- use common factors to simplify fractions; use common multiples to express fractions in the same denomination
- associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. 3/8)
- recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.

Addition and Subtraction of Fractions

- add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

Multiplication and Division of Fractions

- multiply simple pairs of proper fractions, writing the answer in its simplest form (e.g. 1/4 × 1/2 = 1/8)
- multiply one-digit numbers with up to two decimal places by whole numbers
- divide proper fractions by whole numbers (e.g. 1/3 ÷ 2 = 1/6)

Multiplication and Division of Decimals

- multiply one-digit numbers with up to two decimal places by whole numbers
- multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places
- identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places
- associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. 3/8)
- use written division methods in cases where the answer has up to two decimal places

### Ratio and Proportion

Statements only appear in Year 6 but should be connected to previous learning, particularly fractions and multiplication and division

- solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
- solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison
- solve problems involving similar shapes where the scale factor is known or can be found
- solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.

### Algebra

Equations

- express missing number problems algebraically
- find pairs of numbers that satisfy number sentences involving two unknowns
- enumerate all possibilities of combinations of two variables

Formulae

- use simple formulae
- recognise when it is possible to use formulae for area and volume of shapes (copied from Measurement)

Sequences

- generate and describe linear number sequences

### Measurement

Comparing and Estimating

- calculate, estimate and compare volume of cubes and cuboids using standard units, including centimetre cubed (cm
^{3}) and cubic metres (m^{3}), and extending to other units such as mm^{3}and km^{3}.

Measuring and Calculating

- solve problems involving the calculation and conversion of
**units of measure**, using decimal notation up to three decimal places where appropriate (appears also in Converting) - recognise that shapes with the same areas can have different
**perimeters**and vice versa - calculate the area of parallelograms and triangles
- calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm
^{3}) and cubic metres (m^{3}), and extending to other units [e.g. mm^{3}and km^{3}]. - recognise when it is possible to use formulae for area and volume of shapes

Converting

- use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places
- solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate (appears also in Measuring and Calculating)
- convert between miles and kilometres

### Geometry Properties of Shapes

Identifying Shapes and their Properties

- recognise, describe and build simple 3-D shapes, including making nets (appears also in Drawing and Constructing)
- illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

Drawing and Constructing

- draw 2-D shapes using given dimensions and angles
- recognise, describe and build simple 3-D shapes, including making nets (appears also in Identifying Shapes and Their Properties)

Comparing and Classifying

- compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

Angles

- recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles

### Geometry – Position and Direction

Position, Direction and Movement

- describe positions on the full coordinate grid (all four quadrants)
- draw and translate simple shapes on the coordinate plane, and reflect them in the axes.

### Statistics

Interpreting, Constructing and Presenting Data

- interpret and construct pie charts and line graphs and use these to solve problems

Problem Solving

- calculate and interpret the mean as an average

# Mental Maths Progression

Autumn 1

- Count numbers to 20, forwards and backwards
- Read and write numbers to 20 in numerals
- Number bonds to 5
- Related subtraction facts

Autumn 2

- Count numbers to 50, forwards and backwards
- Read and write numbers to 50 in numerals
- Number bonds to 10 (emphasise subitising to 5 e.g. 8 = 5 + 3)
- Related subtraction facts

Spring 1

- Count numbers to 100, forwards and backwards
- Read and write numbers to 100
- Number bonds to 20
- Related subtraction facts

Spring 2

- Count in multiples of 2
- Facts families to 20 (e.g. 8+7=15, 7+8=15, 15-7=8, 15-8=7)

Summer 1

- Count in multiples of 2 and 10
- Doubles of numbers to 10 and corresponding halves

Summer 2

- Count in multiples of 2, 10 and 5
- Doubles of numbers to 20 and corresponding halves

Autumn 1

- Count in multiples of 2, 5, 10
- Number bonds from 20 to 100 (in multiples of 10)

Autumn 2

- Count in multiples of 2, 5 and 3
- Count in steps of 10 from any number
- Number bonds from 20 to 100 (in multiples of 5 and 10)

Spring 1

- Count in multiples of 3
- Count in even numbers up to 50 and odd numbers up to 30, forwards and backwards
- Number bonds from 20 to 100
- Add and subtract mentally: 3 one-digit numbers

Spring 2

- Count in steps of ½ and ¼ up to 10 (including context of time)
- Add and subtract mentally: Two-digit numbers and one-digit; Two-digit numbers and 10s

Summer 1

- Count in steps of 1/3 up to 10
- × and ÷ 2 and 10
- Add and subtract mentally: 2 two-digit numbers (initially without bridging followed by bridging)

Summer 2

- Revisit aspects from Y1 and Y2
- × and ÷ 2, 10 and 5

Autumn 1

- Count in multiples of 3
- Revise × and ÷ 2, 5 and 10
- Number bonds to 1000 (in multiples of 100 then 50)

Autumn 2

- Count from 0 in multiples of 4 and 8
- Add and subtract mentally: Three-digit numbers and one-digit; Three-digit numbers and 10s; Three-digit numbers and 100s

Spring 1

- Count from 0 in multiples of 50 and 100
- × and ÷ 3

Spring 2

- Revise counting in steps of ½, ¼ and 1/3
- Count in 1/10s, forwards and backwards
- × and ÷ 2, 4 and 8

Summer 1

- Count in decimal tenths

Summer 2

- Count in coin values (including 20)
- × and ÷ 5,10; 2, 4, 8

Autumn 1

- Count in steps of 10, 100 and 1000 from any number
- Revise × and ÷ 2, 4 and 8

Autumn 2

- Count from 0 in multiples of 6, 7 and 9
- × and ÷ 3, 6, 9 and 7

Spring 1

- Count from 0 in multiples of 25
- × and ÷ all to 12 x 12

Spring 2

- Count in multiples of 60 from 0 (to relate to time conversions)
- × and ÷ all to 12 x 12

Summer 1

- Revise counting in 1/10s and other unit fractions
- Count in 1/100s
- Know and use factor pairs

Summer 2

- Count in decimals, forwards and backwards

Autumn 1

- Count forwards and backwards in powers of 10 from any number
- Recall the prime numbers up to 19

Autumn 2

- Count backwards through 0 to negative numbers
- Square numbers to 15² and multiples of 10 to 100²
- Cube numbers to 5³ and also 10³

Spring 1

- Count forwards and backwards in powers of 10 from any number and through 0 to negative numbers
- Use place value to add and subtract large numbers mentally

Spring 2

- Count in unit fractions including 1/10s and 1/100s, bridging through zero.
- × and ÷ whole numbers and decimals by powers of 10

Summer 1

- Count in decimals, bridging through zero
- × and ÷ numbers mentally using known facts

Summer 2

- Counting in units of time(e.g. 7 days, 30 minutes)
- Counting forwards and backwards in minutes across o’clock)
- Bridge across 60 when calculating time

Autumn 1

- Revision from years 3 – 5
- Additive relationships for 90⁰, 180⁰ and 360⁰
- Complements to 1000, 100, 10 and 1

Autumn 2

- Use double number lines to count in approximate conversions for metric and Imperial measures including miles to kilometres
- Using known × and ÷ facts to support calculation
- Use knowledge of rules of divisibility

Spring 1

- Revision from years 3 – 5

Spring 2

- Revision from years 3 – 5