Maths
At Coleridge Primary School we aim to equip all pupils with the skills and confidence to solve a range of problems through fluency with numbers and mathematical reasoning.
We started our journey to improve the teaching and learning of mathematics for every child in September 2018. There are several elements which have influenced improvements in attainment and progress in mathematics for our children. Mathematics is led by Mrs J. Shaw who is a maths mastery specialist and is working to support other schools and is travelling to Shanghai to further our research into the mastery approach. This document sets out our approach and the reasons behind our approach to maths at Coleridge.
The three aims of the NC should be addressed every day (not just in the maths lesson):
Fluency – Reasoning – Problem Solving.
Mathematics Planning
 Whole class together – we teach mathematics to whole classes and do not label children. Lessons are planned based on formative assessment of what students already know and we include all children in learning mathematical concepts. Therefore children are taught in mixed ability groups and are supported in moving along at the same pace. Children are then further supported through concrete resources or consolidation tasks whilst quick graspers move onto more challenging problem solving and reasoning. At the planning stage, teachers consider the scaffolding that may be required for children struggling to grasp concepts in the lesson and suitable challenge questions for those who may grasp the concepts rapidly. Staff have been heavily supported in planning in small steps using the White Rose planning support tools and S plans to ensure small steps of progression are made. Teachers follow a six part lesson structure which is as follows:
Most lessons will incorporate concrete resources at the beginning of each session and these are available to the children in all lessons in the ‘Brain Boxes’ on their tables which contain a range of resources which they may need for their lesson.
 Longer but deeper – in order to ensure children have a secure and deep understanding of the content taught, our plans have been adjusted to allow longer on topics and we move more slowly through the curriculum. We use the White Rose Hub small steps planning and the NCETM spine materials to support this progression within each maths lesson. Teachers adapt each lesson to meet the needs of their children and add extra questioning / tasks which will allow children to learn the content more deeply. The learning will focus on one key conceptual idea and connections are made across mathematical topics. To outsiders it may appear that the pace of the lesson is slower, but progress and understanding is enhanced.
 Questions will probe pupil understanding throughout, taking some children’s learning deeper. Responses are expected in full sentences, using precise mathematical vocabulary, talk frames and sentence stems. Teachers use questioning throughout every lesson to check understanding – a variety of questions are used, but you will hear the same ones being repeated: How do you know? Can you prove it? Are you sure? Can you represent it another way? What’s the value? What’s the same/different about? Can you explain that? What does your partner think? Can you imagine? Listen out for more common questions you hear.
 Rapid intervention – in mathematics new learning is built upon previous understanding, so in order for learning to progress and to keep the class together pupils need to be supported to keep up and areas of difficulty must be dealt with as and when they occur. Ideally this would happen on the same day but this is not always possible so it may be the following morning but will be before new learning is introduced.
 Discussion and feedback – pupils have opportunities to talk to their partners and explain/clarify their thinking. They use APE sheets and sentence stems and talk frames on the board to support them in their discussion.
 Recording the learning – not just pages of similar calculations – Maths books are used across the school. In books you will see a range of activities including those requiring written explanations of the children’s understanding. Often orange pen will be used to show a child needs further explanation or blue pen will be used to show a misconception.
 Marking – A next step is given daily to ensure that children either consolidate their learning or a challenge is given to move their learning forward. Children respond to these next steps in green pen in reflection time.
Basic skills
 Maths Mash Ups – As we are teaching in longer blocks, we wanted to ensure children still have consolidation of key skills to ensure they were embedded over time. This rapid recall and practise of these fluency skills are vital so that we can address gaps in learning and ensure that key objectives are embedded.
 Maths Mash Ups incorporate 4 main strands: Addressing key skills, mental maths strategies, arithmetic and
Prelearning. The Key skills that are addressed are: Calendar Maths, Statistics, Number, Fractions, Decimals and Percentages (Year Group dependent), Geometry, Measure and Time. Within these key skills there are nonnegotiables. For example in Year 6 Roman Numerals are a nonnegotiable as this has been determined as a particular area of weakness. There are done 1015 minutes daily and are in segments of 23 minutes. They are fun engaging sessions and children are encouraged to all participate and pace is kept at all times.
 Maths Mash Ups are a vital part of our Maths Mastery approach to teaching. They are used to ensure key objectives are covered continuously to make sure they are retained; this means gaps in learning are addressed throughout any block of learning.
 ‘Number Talks’ can also be included to practise mental strategies explicitly which enables children to recall on a range of strategies when answering arithmetic questions and when solving problems. During ‘Number Talks’ arithmetic can also be practised during these sessions: giving children the opportunity to practise basic skills they have learnt in fluency sessions. Because of this constant practise of skills, children will become more fluent and should be able to recall answers quickly. Children are asked to discuss one strategy for the question with their partner and then are asked in silence to generate as many strategies as they can. After giving children the appropriate amount of time, these strategies should be discussed as a class.
 Maths Mash Ups should occur daily for 1015 minutes. They should cover several blocks and should be broken down into short segments; each segment should take approximately 23 minutes.
Number facts
 Children use a range of resources to help them improve their multiplication knowledge as this is the basis of much of their learning for their further education and life skills. Using TT Rockstars, maths frame and mash ups children are continuously supported with their knowledge of times tables. Children in Y3 and 4 are given weekly intervention using flash cards to further their knowledge and this is tracked weekly.
 Number facts are supported particularly in Year 1 and 2 using addition fact cards.
 Practising – not drill and practice but practice characterised by variation – years 16 use White Rose Hub small step planning and Maths No Problem textbooks to provide children with carefully chosen questions and are essential in assessing how the children have understood the concept taught. You will also see another level of differentiation within these books as some children rapidly grasp the concepts and therefore complete the pages quickly and move onto questions or activities where their understanding can be developed to a greater depth. Some children will work very hard in the lesson to complete the pages independently, some children will need additional support to complete the pages and some children will sometimes be provided with different tasks and questions appropriate to their understanding of a concept.
 SEND pupils – may be supported by additional adults, different resources, differentiated activities. They will also complete additional activities outside of the mathematics lesson if necessary.
 Children in EYFS explore mathematical concepts through active exploration and their everyday play based learning. Children are taught key concepts and application of number using a hands on practical approach. EYFS practitioners provide opportunities for children to manipulate a variety of objects which supports their understanding of quantity and number. The CPA approach is used when teaching children key mathematical skills. Practitioners allow children time for exploration and the use of concrete objects helps to support children’s mathematical understanding. Maths in the early years provides children with a solid foundation that will enable them to develop skills as they progress through their schooling and ensures children are ready for the Nation Curriculum.
NB: We do not label our children. We have high expectations of all children and strongly believe that all children are equally able in mathematics. Some may take longer to grasp concepts and may need careful scaffolding or extra time/support (guided groups, same day catchup, additional homework, preteaching, intervention group, specific parental support).
The New Times Tables Tests Explained
All Y4 children will have their multiplication skills formally tested in the summer term of Year 4 from 2020. The Multiplication Tables Check (MTC) was officially announced by the Department for Education (DfE) in September 2017. It will be administered for children in Year 4, starting in the 201920 academic year.
Times tables test / multiplication tables check
Primaryschool children are expected to know all their times tables up to 12×12. Under the current National Curriculum, children are supposed to know their times tables by the end of Year 4, but they are not formally tested on them other than through multiplication questions in the Year 6 maths SATs.
The DfE says that the check is part of a new focus on mastering numeracy, giving children the skills and knowledge they need for secondary school and beyond. The purpose of the MTC is to determine whether Y4 pupils can recall their multiplication tables fluently.
The times tables test will be introduced in English schools only. It will be taken by children in Year 4, in the summer term (during a threeweek period in June; schools will decide which day to administer the check).
In June 2019 the multiplication check will be voluntary (schools will be able to decide whether to administer it or not). In June 2020 it will become compulsory. Children with special educational needs will be provided for when taking the MTC.
How will the children be tested?
 Children will be tested using an onscreen check (on a computer or a tablet), where they will have to answer multiplication questions against the clock.
 The test will last no longer than 5 minutesand is similar to other tests already used by primary schools. Their answers will be marked instantly.
 Children will have 6 seconds to answer each question in a series of 25.
 Questions will be selected from the 121 number facts that make up the multiplication tables from 2 to 12, with a particular focus on the 6, 7, 8, 9 and 12 times tablesas they are considered to be the most challenging. Each question will only appear once in any 25question series, and children won’t be asked to answer reversals of a question as part of the check (so if they’ve already answered 3 x 4 they won’t be asked about 4 x 3).
 Once the child has inputted their answer on the computer / device they are using, there will be a threesecond pause before the next question appears.
How can you help your children at home?
 Encouraging your children to practice using TT Rockstars at home!
 Practising times tables in order or in a song.
 Asking your child multiplication questions out of order – such as ‘What’s 11×12? What’s 5×6?’
 Using arrays to help your child memorise times tables – you can use fun objects like Smarties or Lego bricks to make it more entertaining.
 Use the practice books given to your child.
Mathematics – Number and Place Value.  
Year 1  Year 2  Year 3  Year 4  Year 5  Year 6 
Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number.

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

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

Count in multiples of 6, 7, 9, 25 and 1000.
Count backwards through zero to include negative numbers.

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

Use negative numbers in context, and calculate intervals across zero.

Count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens.

Recognise the place value of each digit in a twodigit number (tens, ones) and use number facts to solve problems

Recognise the place value of each digit in a threedigit number (hundreds, tens, ones) and use number facts to solve problems

Recognise the place value of each digit in a fourdigit number (thousands, hundreds, tens, and ones) and solve problems with increasingly large positive numbers.  Read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit and solve number problems.

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

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.

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

Identify, represent and estimate numbers using different representations.

Identify, represent and estimate numbers using different representations.


Given a number, identify one more and one less  Compare and order numbers from 0 up to 100; use <, > and = signs.

Compare and order numbers up to 1000.

Order and compare numbers beyond 1000.
Round any number to the nearest 10, 100 or 1000.

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

Round any whole number to a required degree of accuracy.

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.

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


Mathematics – Addition and Subtraction  
Year 1  Year 2  Year 3  Year 4  Year 5  Year 6 
Represent and use number bonds and related subtraction facts within 20.

Recall and use addition and subtraction facts to 20 fluently  
Add and subtract onedigit and twodigit numbers to 20, including zero.

Add and subtract numbers using concrete objects, pictorial representations, and mentally two twodigit numbers

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

Add and subtract numbers with up to 4 digits using the written methods of addition and subtraction where appropriate.

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


Solve onestep problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ? – 9.

Using concrete objects and pictorial representations, including those involving numbers, quantities and measures;

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

Solve addition and subtraction twostep problems in contexts, deciding which operations and methods to use and why.

Solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why.

Solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why.

Applying their increasing knowledge of mental and written methods.

Add and subtract numbers mentally including a threedigit numbers and ones, a threedigit number and tens and a threedigit number and hundreds.  Add and subtract numbers mentally with increasingly large numbers [for example, 12,462 – 2300 = 10,162].


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

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

Estimate and use inverse operations to check answers to a calculation.

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

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

Mathematics – Multiplication and Division  
Year 1  Year 2  Year 3  Year 4  Year 5  Year 6  

Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers.  Recall and use multiplication and division facts for the
3, 4 and 8 times table 
Recall multiplication and division facts for multiplication tables up to 12 x 12.

Perform mental calculations, including with mixed operations and large numbers.



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

Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for twodigit numbers times onedigit numbers, using mental and progressing to written methods.

Multiply twodigit and threedigit numbers by a onedigit number using formal written layout

Multiply numbers up to 4 digits by a one or twodigit number using a formal written method, including long multiplication for twodigit numbers.

Multiply multidigit numbers up to 4 digits by a twodigit whole number using the formal written method of long multiplication.


Divide numbers up to 4 digits by a onedigit number using the formal written method of short division and interpret remainders appropriately for the context.  Divide numbers up to 4 digits by a twodigit 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.  
Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot.  Recognise and use factor pairs and commutativity in mental calculations.

Solve problems by Identifying multiples and factors, common factors of two numbers and identifying square and cube numbers.  Identify common factors, common multiples and prime numbers.


Solve onestep problems by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

Solve problems using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in context.  Solve problems, including missing number problems, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.  Solve problems using the distributive law to multiply twodigit numbers by one digit, using integer scaling and correspondence problems such as n objects are connected to m objects.  Solve problems involving multiplication and division and a combination of these, including understanding the meaning of the equals sign.  Solve problems involving multiplication and division and check using estimation.


Mathematics – Fractions  
Year 1  Year 2  Year 3  Year 4  Year 5  Year 6  
Recognise, find and name a half as one of two equal parts of an object, shape or quantity.  Recognise, find, name and write fractions 1⁄3, 1⁄4, 2⁄4, and 3⁄4 of a length, shape, set of objects or quantity.  Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing onedigit numbers or quantities by 10.  Recognise and show, using diagrams, families of common equivalent fractions.  Compare and order fractions whose denominators are all multiples of the same number.  Use common factors to simplify fractions; use common multiples to express fractions in the same denomination.  
Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.  Write simple fractions for example, ½ of 6 = 3 and recognise the equivalence of 2⁄4 and ½.  Recognise, find and write fractions of a discrete set of objects: unit fractions and nonunit fractions with small denominators.  Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.  Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths.  Compare and order fractions, including fractions > 1.  
Recognise and use fractions as numbers: unit fractions (numerator of 1) and nonunit fractions with small denominators.  Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including nonunit fractions where the answer is a whole number.  Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 2⁄5 + 4⁄5 = 6⁄5 = 11⁄5].  Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions.  
Recognise and show, using diagrams, equivalent fractions with small denominators.  Add and subtract fractions with the same denominator.  Add and subtract fractions with the same denominator and denominators that are multiples of the same number.  Multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1⁄4 × 1⁄2 = 1⁄8].  
Add and subtract fractions with the same denominator within one whole [for example, 5⁄7 + 1⁄7 = 6⁄7].  Recognise and write decimal equivalents of any number of tenths or hundredths.  Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams.  Divide proper fractions by whole numbers [for example, 1⁄3 ÷ 2 = 1⁄6].  
Compare and order unit fractions, and fractions with the same denominators.  Recognise and write decimal equivalents to 1⁄4, 1⁄2, 3⁄4.  Read and write decimal numbers as fractions [for example, 0.71 = 71⁄100].  Associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3⁄8].  
Solve problems that involve all of the above.  Find the effect of dividing a one or twodigit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths.  Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents.


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

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.  
Compare numbers with the same number of decimal places up to two decimal places.  Read, write, order and compare numbers with up to three decimal places.

Multiply onedigit numbers with up to two decimal places by whole numbers.  
Solve simple measure and money problems involving fractions and decimals to two decimal places.  Solve problems involving number up to three decimal places.

Use written division methods in cases where the answer has up to two 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 answers to be rounded to specified degrees of accuracy.  
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.  Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts. 
Mathematics – Measurement  
Year 1  Year 2  Year 3  Year 4  Year 5  Year 6  
Compare, describe and solve practical problems for:
lengths and heights [for example, long/short, longer/shorter, tall/short, double/half]; mass/weight [for example, heavy/light, heavier than, lighter than]; capacity and volume [for example, full/empty, more than, less than, half, half full, quarter]; time [for example, quicker, slower, earlier, later]. 
Choose and use appropriate standard units to estimate and measure to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels:
– Length/height in any directions. – Mass (kg/g) – Temperature (oc) – Capacity (litres/ml) 
Measure, compare, add and subtract:
– Length (m/cm/mm) – Mass (kg/g) – Volume/capacity (l/ml) 
Convert between different units of measure [for example, kilometre to metre; hour to minute]  Convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre).

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


Measure and begin to record the following:
lengths and heights; mass/weight; capacity and volume; time (hours, minutes, seconds). 
Compare and order lengths, mass, volume/capacity and record the results using >, < and =.  Measure the perimeter of simple 2D shapes.

Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres.  Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints.  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.


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


Add and subtract amounts of money to give change, using both £ and p in practical contexts.

Find the area of rectilinear shapes by counting squares.

Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres.  Convert between miles and kilometres.


Sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening].  Find different combinations of coins that equal the same amounts of money. 

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

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.

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


Recognise and use language relating to dates, including days of the week, weeks, months and years.  Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change.  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. 
Read, write and convert time between analogue and digital 12 and 24hour clocks.

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

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


Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times. 
Compare and sequence intervals of time.

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

Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days.  Solve problems involving converting between units of time.

Calculate the area of parallelograms and triangles.


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.  Compare durations of events [for example to calculate the time taken by particular events or tasks].

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

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 [for example, mm3 and km3].


Know the number of minutes in an hour and number of hours in a day. 
Mathematics – Geometry  
Year 1  Year 2  Year 3  Year 4  Year 5  Year 6  
Recognise and name common 2D and 3D shapes, including:
– 2D shapes [for example, rectangles (including squares), circles and triangles] – 3D shapes [for example, cuboids (including cubes), pyramids and spheres.

Identify and describe the properties of 2D shapes, including the number of sides and line symmetry in a vertical line.

Draw 2D shapes and make 3D shapes using modelling materials.

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

Identify 3D shapes, including cubes and other cuboids, from 2D representations.

Draw 2D shapes using given dimensions and angles.


Describe position, direction and movement, including whole, half, quarter and threequarter turns.

Identify and describe the properties of 3D shapes, including the number of edges, vertices and faces.

Recognise 3D shapes in different orientations and describe them.

Identify acute and obtuse angles and compare and order angles up to two right angles by size.  Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles.

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



Identify 2D shapes on the surface of 3D shapes [for example, a circle on a cylinder and a triangle on a pyramid].

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

Identify lines of symmetry in 2D shapes presented in different orientations.  Draw given angles, and measure them in degrees ().

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


Compare and sort common 2D and 3D shapes and everyday objects.

Identify right angles, recognise that two right angles make a halfturn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle.

Complete a simple symmetric figure with respect to a specific line of symmetry. 
– angles at a point on a straight line and 1⁄2 a turn (total 180); – other multiples of 90. 
Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius.


Order and arrange combinations of mathematical objects in patterns and sequences.  Identify horizontal and vertical lines and pairs of perpendicular and parallel lines.

Describe positions on a 2D grid as coordinates in the first quadrant.

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

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


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 threequarter turns (clockwise and anticlockwise).

Describe movements between positions as translations of a given unit to the left/right and up/down.

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

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


Plot specified points and draw sides to complete a given polygon.  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.

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

Mathematics – Statistics  
Year 1  Year 2  Year 3  Year 4  Year 5  Year 6 
Interpret and construct simple pictograms, tally charts, block diagrams and simple tables.

Interpret and present data using bar charts, pictograms and tables.

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 a line graph.

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


Ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity.

Solve onestep and twostep questions [for example, ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts and pictograms and tables.

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

Complete, read and interpret information in tables, including timetables.

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


Ask and answer questions about totalling and comparing categorical data.

Calculate and interpret the mean as an average. 
Jessica Shaw – China Exchange November 2019
At the beginning of November, after being selected as part of the DFE’s EnglandChina exchange, I spent two weeks in Shanghai analysing and experiencing mathematics teaching at first hand. I was given the opportunity to spend time in two schools. A local Shanghai school which used government implemented textbooks and scheme of work and an international which had devised its own textbooks around the accelerated progress of their children. We were welcomed into both schools and were immersed in their culture of learning and their continuous use of TRG discussions to analyse and improve the teaching of mathematics. This is a culture of learning and open door classrooms which has been developed over the last 10 years and is by no means a quick fix to rapidly improve the teaching of mathematics in the UK. I will discuss below some of the findings which were pertinent over the two weeks I spent in Shanghai.
Textbooks
All local schools in Shanghai follow the government implemented Shanghai textbooks which is given to teachers alongside ppts and a teacher guide. Children are given a practice book and text book which teachers use in most lessons. Because these lessons are so carefully structured, teachers are able to use these as a basis for their lesson and develop further challenge or support as is appropriate for their class. During our observations, many teachers would add reallife contexts and more complex problems to challenge their children. These textbooks always start at a low starting point and build to much more demanding content. One key concept is always introduced and maintained within each lesson so that teachers are not pressured to include too much: meaning children can concentrate on one key focus. There is a clear progression of skills throughout the textbooks so that teachers know exactly what has been taught before and where the learning is being taken. Because the same textbooks and ppts are used continuously over time, these lessons are stored and annotated and developed by each teacher so that they can be analysed and improved over time. I found it surprising that many teachers, who were part of the exchange, commented on identical lessons to the ones we had observed with small alterations or additions. We commented that going from school to school in the UK you may see a completely different topic or scheme of work in place and new lessons being created each year. Perhaps this is something to consider in creating a cohesive and progressive curriculum for the children in our communities.
TRG and lesson anaylsis
Throughout our specialist training, we have been coached and have facilitated TRG lesson analysis of which I can see the huge benefits for a more open and analytical study of lesson design around mathematics. However, to see this first hand showed me how a culture of shared learning and opendoor policy can really vastly improve the teaching of mathematics. The Chinese teachers were so used to being observed and even filmed, that in one observation with 50 students there was 30 observers – some of whom were even hanging in the window, that they were not perturbed by this as they are continuously using the observations as a way to continuously design and improve lessons over time. After each lesson, a discussion was had around the session, where the teacher described the lesson focus; any potential misconceptions; the teaching process and any additions and alterations they had made with their reasoning behind their choices. After this analysis, each observer would comment on something they had noticed about the mathematics within the session. Because these teachers will often watch the same lesson multiple times over their years in the profession, they are continuously ensuring that they are learning from one another and that their lessons are improved by a shared discussion of children’s learning and the improvements on lesson design. In one seminar, we took part in a lesson which looked at the use of the number line using fractions. In this study, two planning sessions took place, the lesson was taught twice and then the lesson was analysed and reviewed. This shows the real dedication to improvements of key structures and models that will support the children in their understanding of mathematics.
Lesson length
Each lesson was precisely timed to 38 minutes and this was stuck to with rigour. Each lesson would end and start with music and would begin with the Chinese ‘eye exercises.’ This happens in all schools and children are focused and ready to learn at the beginning of each session. The lesson progress quickly from a low starting point to very challenging content. Chinese maths teacher in primary only teach this subject and teach around 24 lessons per day. After this session, children are asked to complete independent work and homework in order to consolidate the learning done in class. Therefore, when the teachers are not in class they are marking books, adapting planning or observing as part of a TRG.
Lesson structure
Observations showed that all lessons began with a key lesson focus. Often lessons would begin with a reallife focus, especially in KS1, to ensure that children were engaged and that purpose was given to their learning. Most lessons involved a practical group activity which included rich mathematical talk. This was something I didn’t expect to see and was surprised how active and fast paced the sessions were. Children were asked to share their ideas by standing up and sharing it with the class if they were chosen after their hand was raised. The teachers always knew the answers they wanted and instead of praising answers that were incorrect they would move onto someone with the correct answer. This is something which is rather different in English schools and an interesting point to consider. Do we overpraise children when they give an answer which irrelevant or incorrect? Often key learning points and generalisations would be placed on the rightside of the board. These would be repeated by a child, then to their partner and then as a whole class. Any equations or jottings would be placed on the left of the board. At the end of each session, children would be asked what t had learnt and would use these generalisations to summarise what they had learnt. Most lessons included a reasoning question to consolidate and challenge learners and these would come in the form of true or false and multiple choice questioning. The visualiser was used in all lessons and was so important in children being able to share their ideas and for the teachers to address any misconceptions; it was also a great tool to show a variety of possibilities in problem solving.
Number sense
Something that really struck me during my time in Shanghai was the quick recall of number facts throughout our observations. Children were never held back by their ability to calculate mentally which meant that as the content became harder they were able to handle it with ease. The below table shows how Chinese children learn their multiplication facts. When I asked the maths lead why children knew their multiplication facts so well, he noted that often children start school and have already learnt these facts. Chinese children understand commutativity and number facts in such a deep way that they only need to learn 45 facts to know their tables instead of our 144 facts. The language is also much easier for them to learn. Instead of saying, ‘one times one is one’ the children will simply say ‘one, one, one.’ In Chinese, 22 (twentytwo) is said, ‘two tens and two,’ meaning place value is something that is far easier for the children to understand. In geometry, quadrilaterals are called quadrangles meaning children can more easily link them with triangles and their properties.
Although a culture of learning and the importance of education it clearly instilled into the people China, this should not be something that deters us from learning from the Shanghai teachers and their teaching of mathematics. The continuous analysis and development of mathematics that has taken place over the past 10 years is something that should be admired and I feel very privileged to have witnessed this firsthand. I know that the importance of number sense and our children’s knowledge of key facts should be paramount in ensuring that children can develop their understanding of mathematics. The culture of learning from one another and sharing best practices to analyse and carefully craft lessons is so important in moving the teaching of mathematics forward. Finally, small steps are so important to ensure all children are kept together, but this must build to a challenging point where children are able apply their knowledge to different reallife contexts. Their carefully crafted lesson design and the children’s secure understanding of key facts means that the children of China are receiving an in depth understanding from the teaching of mathematics.