## Subject Lead: Mrs Candlish

The Maths curriculum at Denbigh strives to equip children with the number and problem solving skills that they will need to succeed in, and beyond their school years. We use a variety of teaching and learning skills to support our children’s learning throughout the Maths curriculum which encompasses calculation methods, measure, fractions, data handling, shape, counting and using and applying skills in real life contexts.

Our staff aim to enthuse and inspire a love of Maths through a range of activities which include practical Maths sessions, providing children with relevant problem solving opportunities and supporting children to see how Maths is woven throughout our everyday lives.

A cross curricular approach to Maths is in place to allow children have the opportunity to apply the skills learned in Maths lessons through other areas, such as STEM, Topic, Art, DT etc. Educational trips work alongside our Maths curriculum to support the teaching and learning, and give children real-life experiences to draw on in school.

In Nursery and Reception we embrace the ‘Early Years Big Ideas’ concepts to support children in their development towards attaining the Mathematics Early Learning Outcome and prepare them with the foundation knowledge and skills to engage with our KS1 curriculum.

In Nursery, children explore mathematical concepts and learn mathematical vocabulary through play. We begin to develop the children’s mathematical understanding through their own interests within their play. We build on this by then introducing concepts in small groups and further develop their understanding through adult support in child initiated activities. As children move into Reception, we support their development through differentiated small group teacher led learning which focuses on the mathematical concepts and vocabulary of Shape, Space, Measurement and Number. In addition to teacher led learning, children learn through the provision of an exciting and stimulating learning environment which embraces the characteristics of effective learning.

Within Years 1 and 2 the children are taught using the ‘Maths No Problem’ scheme of work which allows children to develop their thinking and reasoning skills from the off. Every day a lesson begins with an anchor task (a hook) which prompts the children to think and discuss how a solution to the problem can be reached. All the methods the children suggest are given due consideration before we explore the most efficient method to use. The children then practice the required skill before applying this in solving more problems and challenges. Lessons build upon previous skills taught to ensure children have a secure knowledge of all areas of maths and can use a range of calculation methods fluently. In Years 3 to 6 teachers follow a similar lesson structure but plan their own activities for the children to undertake. In KS2 Maths lessons are ‘set’ so that all learners are accessing Maths at their level with support and challenge built in throughout. Children of all ages are challenged to extend their learning and to ensure they can reason about number. Indeed a great deal of Maths lessons involve a lot of discussion, giving children the opportunity to share their thinking and explain how they reached a conclusion. At Denbigh we feel that ‘a quiet Maths lesson is a suspicious Maths lesson’. We actively encourage our pupils to discuss, to question, to debate, to reason and to consider ‘what if?’.

Throughout all strands of Maths, ICT is used to engage, enthuse, present and document the children’s learning.

Staff at Denbigh know that good Maths occurs in our school when:

- It is led by the children, interests them and is memorable to them.
- Children are talking, laughing, engaged and enjoying Maths through a range of interactive and practical activities.
- Children are actively involved in their own learning, asking questions, looking for the answers and keen to challenge themselves further.
- Maths is differentiated and inclusive with children making progress throughout the lesson.
- Good quality assessment and Assessment for Learning is used to inform planning and builds on children’s prior learning.

If you would like to support your child with their learning journey, then please take the time to read our ‘Maths Parents Booklets’. For more information please ask to speak to Mrs Candlish.

# Progression Threshold Concepts in Maths

## Threshold Concept :To add and subtract

### Milestone 1: Solve one step problems with addition and subtraction .

## Threshold Concept : To add and subtract

### Milestone 2:Solve two step addition and subtraction problems in contexts, deciding which operations and methods to use and why

## Threshold Concept : To add and subtract

### Milestone 3: Solve multi step addition and subtraction problems in contexts, deciding which operations and methods to use and why.

## Threshold Concept :To multiply and divide

### Milestone 1: To solve one step problems using multiplication and division.

## Threshold Concept :To multiply and divide

### Milestone 2: To solve two step problems using multiplication and division.

## Threshold Concept :To multiply and divide

### Milestone 3: To solve multi step problems using multiplication and division.

## Threshold Concept :To use algebra

### Milestone 1: Know that a symbol can represent a value

## Threshold Concept :To use algebra

### Milestone 2: Use symbols to represent a value and identify the value of given symbols.

## Threshold Concept :To use algebra

### Milestone 3: Enumerate possibilities of combinations of two variables.

## Threshold Concept :To use fractions

### Milestone 1: To solve simple problems finding half and quarter of a given number.

__Year 1__

__Year 1__

Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number

Count and read numbers to 100 in numerals

Count and write numbers to 100 in numerals

Count in multiples of twos, fives and tens from 0

Identify one more and one less of a given number

Identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least

Read and write numbers from 1 to 20 in numerals

Read and write numbers from 1 to 20 in words

Count in twos, fives and tens to solve problems e.g. count the number of chairs in a diagram when the chairs are organised in 7 rows of 5 by counting in fives

Partition and combine numbers using apparatus if required e.g. partition 76 into tens and ones; combine 6 tens and 4 ones

Read and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs

Write mathematical statements involving addition (+), subtraction (-) and equals (=) signs

Demonstrate an understanding of the commutative law (e.g. 3 + 2 = 5, therefore 2 + 3 = 5)

Demonstrate an understanding of inverse relationships involving addition and subtraction (e.g. if 3 + 2 = 5, then 5 – 2 = 3)

Recall at least four of the six number bonds for 10 and reason about associated facts (e.g. 6 + 4 = 10 , therefore 4 + 6 = 10 and 10 – 6 = 4)

Represent and use number bonds within 20

Represent and use subtraction facts within 20

Represent and use subtraction facts within 20

Add one-digit and two-digit numbers to 20, including zero

Subtract one-digit and two-digit numbers to 20, including zero

Solve one-step problems that involve addition, subtraction and missing numbers using concrete objects and pictorial representations

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

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

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

Compare, describe and solve practical problems for lengths and heights e.g. long/short, longer/shorter, tall/short, double/half

Compare, describe and solve practical problems for mass/weight e.g. heavy/light, heavier than, lighter than

Compare, describe and solve practical problems for capacity and volume e.g. full/empty, more than, less than, half, half full, quarter

Compare, describe and solve practical problems for time e.g. quicker, slower, earlier, later

Measure and begin to record mass/weight

Measure and begin to record capacity and volume

Measure and begin to record time (hours, minutes, seconds)

Recognise and know the value of different denominations of coins and notes

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

Recognise and use language relating to dates, including days of the week, weeks, months and years

Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times

Measure and begin to record length/height

Recognise and name common 2-D shapes e.g. rectangles (including squares), circles and triangles

Recognise and name common 3-D shapes e.g. cuboids (including cubes), pyramids and spheres

Describe position, direction and movement, including whole, half, quarter and three-quarter turns

__Year 2__

__Year 2__

Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward

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

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

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

Read and write numbers to at least 100 in numerals

Read and write numbers to at least 100 in words

Use place value and number facts to solve problems

Partition two-digit numbers into different combinations of tens and ones using apparatus if needed e.g. 23 is the same as 2 tens and 3 ones which is the same as 1 ten and 13 ones

Use reasoning about numbers and relationships to solve more complex problems and explain his/her thinking e.g. 29 + 17 = 15 + 4 + ?; ‘Together Jack and Sam have £14. Jack has £2 more than Sam. How much money does Sam have?’ etc.

Recall the multiples of 10 below and above any given 2 digit number e.g. say that for 67 the multiples are 60 and 70

Solve problems with addition and subtraction using concrete objects and pictorial representations, including those involving numbers, quantities and measures

Solve problems with addition and subtraction applying his/her increasing knowledge of written methods and mental methods where regrouping may be required

Recall all number bonds to and within 10 and use these to reason with and calculate bonds to and within 20, recognising other associated additive relationships (e.g. If 7 + 3 = 10, then 17 + 3 = 20; if 7 – 3 = 4, then 17 – 3 = 14; leading to if 14 + 3 = 17, then 3 + 14 = 17, 17 – 14 = 3 and 17 – 3 = 14)

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

Add and subtract numbers where no regrouping is required, using concrete objects, pictorial representations, and mentally, including a two-digit number and ones

Add and subtract numbers using concrete objects, pictorial representations, and mentally, including a two-digit number and tens

Add and subtract numbers using concrete objects, pictorial representations, and mentally, including two two-digit numbers

Add and subtract numbers using concrete objects, pictorial representations, and mentally, including 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

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

Recall doubles and halves to 20 e.g. knowing that double 2 is 4, double 5 is 10 and half of 18 is 9

Use estimation to check that his/her answers to a calculation are reasonable e.g. knowing that 48 + 35 will be less than 100

Solve missing number problems using addition and subtraction

Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers

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

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

Solve problems involving multiplication and division, using concrete materials and mental methods

Solve problems involving multiplication and division, using arrays, repeated addition and multiplication and division facts, including problems in contexts e.g. knowing that 2 × 7 = 14 and 2 × 8 = 16, explains that making pairs of socks from 15 identical socks will give 7 pairs and one sock will be left

Use multiplication and division facts for 2, 5 and 10 to make deductions outside known multiplication facts e.g. know that multiples of 5 have one digit of 0 or 5 and use this to reason that 18 × 5 cannot be 92 as it is not a multiple of 5

Solve word problems involving multiplication and division with more than one step e.g. which has the most biscuits, 4 packets of biscuits with 5 in each packet or 3 packets of biscuits with 10 in each packet

Recognise the relationships between addition and subtraction and rewrite addition statements as simplified multiplication statements e.g. 10 + 10 + 10 + 5 + 5 = 3 × 10 + 2 × 5 = 4 × 10

Recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity and demonstrate understanding that all parts must be equal parts of the whole

Write simple fractions for example, 1/2 of 6 = 3 and recognise the equivalence of 2/4 and ½

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

Compare and order lengths, mass, volume/capacity and record the results using >, < and =

Recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value

Find different combinations of 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

Compare and sequence intervals of 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

Remember the number of minutes in an hour and the number of hours in a day

Read scales in divisions of ones, twos, fives and tens

Read scales where not all numbers on the scale are given and estimate points in between

Read the time on a clock to the nearest 15 minutes

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

Name some common 2-D and 3-D shapes from a group of shapes or from pictures of the shapes and describe some of their properties (e.g. triangles, rectangles, squares, circles, cuboids, cubes, pyramids and spheres)

Identify 2-D shapes on the surface of 3-D shapes e.g. a circle on a cylinder and a triangle on a pyramid

Compare and sort common 2-D and 3-D shapes and everyday objects describing similarities and differences e.g. find 2 different 2-D shapes that only have one line of symmetry; that a cube and a cuboid have the same number of edges, faces and vertices and describe what is different about them

Order and arrange combinations of mathematical objects in patterns and sequences

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)

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

__Year 3__

__Year 3__

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

Compare and order numbers up to 1000

Identify, represent and estimate numbers using different representations

Read and write numbers up to 1000 in numerals

Read and write numbers up to 1000 in words

Solve number problems and practical problems involving these ideas

Add and subtract numbers mentally, including a three-digit number and ones

Add numbers with up to three digits using the formal method of columnar addition

Add and subtract numbers mentally, including a three-digit number and tens

Subtract numbers with up to three digits using the formal method of columnar subtraction

Add and subtract numbers mentally, including a three-digit number and hundreds

Estimate the answer to a calculation and use inverse operations to check answers

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

Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables

Write and calculate mathematical statements for multiplication and division using the multiplication tables that he/she knows, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods

Recognise and show, using diagrams, families of common equivalent fractions

Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10

Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

Add fractions with the same denominator within one whole e.g. 5/7 + 1/7 = 6/7

Subtract fractions with the same denominator within one whole e.g. 6/7 – 1/7 = 5/7

Compare and order unit fractions, and fractions with the same denominators

Solve fraction problems

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

Write the time using 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 and hours; use vocabulary such as o’clock, a.m./p.m., morning, afternoon, noon and midnight

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

Compare durations of events e.g. to calculate the time taken by particular events or tasks

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

Recognise angles as a property of shape or a description of a turn

Identify right angles and identify whether other angles are greater or less than a right angle

Recognise that two right angles make a half turn, three make three quarters of a turn and four a complete turn

Identify horizontal and vertical lines and pairs of perpendicular and parallel lines

Interpret and present data using bar charts, pictograms and tables

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

__Year 4__

__Year 4__

Count in multiples of 6, 7, 9, 25 and 1000

Find 1000 more or less than a given number

Count backwards through zero to include negative numbers

Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)

Order and compare numbers beyond 1000

Identify, represent and estimate numbers using different representations including measures

Round any number to the nearest 10, 100 or 1000

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

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

Add numbers with up to four digits using the formal method of columnar addition

Estimate and use inverse operations to check answers to a calculation

Subtract numbers with up to four digits using the formal method of columnar subtraction

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

Recall multiplication and division facts for multiplication tables up to 12 × 12

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

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

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

Recognise and show, using diagrams, families of common equivalent fractions

Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten

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

Add and subtract fractions with the same denominator

Recognise and write decimal equivalents of any number of tenths or hundredths

Recognise and write decimal equivalents to 1/4, 1/2, ¾

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

Round decimals with one decimal place to the nearest whole number

Compare numbers with the same number of decimal places up to two decimal places

Solve simple measure and money problems involving fractions and decimals to two decimal places

Convert between different units of measure e.g. kilometre to metre; hour to minute

Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres

Find the area of rectilinear shapes by counting squares

Estimate, compare and calculate different measures, including money in pounds and pence

Read, write and convert time between analogue and digital 12- and 24-hour clocks

Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days

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

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

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

Complete a simple symmetric figure with respect to a specific line of symmetry

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

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

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

__Year 5__

__Year 5__

Read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit e.g. what is the value of the ‘7’ in 276,541? Find the difference between the largest and smallest whole numbers that can be made from using three digits

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

Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero

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

Solve number problems and practical problems that involve ordering and comparing numbers to 1 000 000, counting forwards or backwards in steps, interpreting negative numbers and rounding

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

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

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 the notation for squared (2)

Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes

Recognise and use cube numbers and the notation for cubed (3)

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

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

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

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 e.g. 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

Read and write decimal numbers as fractions e.g. 0.71 = 71/100, 8.09 = 8 + 9/?

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 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25

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 e.g. using 1 cm³ blocks to build cuboids (including cubes) and capacity e.g. using water

Solve problems involving converting between units of time

Use all four operations to solve problems involving measure e.g. length, mass, volume, money using decimal notation, including scaling

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 (°)

Identify angles at a point and one whole turn (total 360°)

Identify angles at a point on a straight line and 1/2 a turn (total 180°)

Identify other multiples of 90°

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

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

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

Complete, read and interpret information in tables, including timetables

__Year 6__

__Year 6__

Read, write, order and compare numbers up to 10 000 000 and determine the value of each digit

Round any whole number to a required degree of accuracy

Use negative numbers in context, and calculate intervals across zero

Solve number and practical problems that involve ordering and comparing numbers to 10 000 000, rounding to a required degree of accuracy, using negative numbers and calculating intervals across zero

Demonstrate an understanding of place value including decimals e.g. 28.13 = 28 + ? + 0.03

Perform mental calculations with mixed operations to carry out calculations involving the four operations

Solve multi-step problems in contexts, deciding which operations and methods to use and why e.g. find the change from £20 for three items that cost £1.24, £7.92 and £2.55; a roll of material is 6m long: how much is left when 5 pieces of 1.15m are cut from the roll?; a bottle of drink is 1.5 litres, how many cups of 175ml can be filled from the bottle, and how much drink is left?

Solve problems involving addition and subtraction

Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

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 long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context

Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context

Perform mental calculations, including with mixed operations and large numbers

Identify common factors, common multiples and prime numbers

Use his/her knowledge of the order of operations to carry out calculations involving the four operations

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

Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

Use common factors to simplify fractions; use common multiples to express fractions in the same denomination

Compare and order fractions, including fractions > 1

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

Multiply simple pairs of proper fractions, writing the answer in its simplest form e.g. 1/4 × 1/2 = 1/8

Divide proper fractions by whole numbers e.g. 1/3 ÷ 2 = 1/6

Associate a fraction with division and calculate decimal fraction equivalents e.g. know that 7 divided by 21 is the same as 7/21 and that this is equal to 1/3 and e.g. 0.375 is equivalent to 3/8

Identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places

Multiply one-digit numbers with up to two decimal places by whole numbers

Use written division methods in cases where the answer has up to two decimal places

Solve problems which require answers to be rounded to specified degrees of accuracy

Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts e.g. one piece of cake that has been cut into 5 equal slices can be expressed as 1/5 or 0.2 or 20% of the whole cake

Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate

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

Convert between miles and kilometres

Recognise that shapes with the same areas can have different perimeters and vice versa

Recognise when it is possible to use formulae for area and volume of shapes

Calculate the area of parallelograms and triangles

Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units e.g. mm³ and km³

Draw 2-D shapes using given dimensions and angles

Recognise, describe and build simple 3-D shapes, including making nets

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

Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

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

Describe positions on the full coordinate grid (all four quadrants)

Draw and translate simple shapes on the coordinate plane, and reflect them in the axis

Interpret and construct pie charts and line graphs and use these to solve problems

Calculate and interpret the mean as an average

Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts e.g. find 7/9 of 108

Solve problems involving the calculation of percentages e.g. 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

Use simple formulae e.g. perimeter of a rectangle or area of a triangle

Generate and describe linear number sequences

Express missing number problems algebraically

Find pairs of numbers that satisfy an equation with two unknowns

Enumerate possibilities of combinations of two variables