Goodrich Church of England Primary School

Maths Curriculum Statement

What Maths looks like in Goodrich CE Primary School

Our aim is to equip all pupils with the skills and confidence to solve a range of problems through fluency with numbers and mathematical reasoning. Our ultimate aim is to ensure that children are given a visual/concrete representation of the maths being taught and set in a real-life context to make it meaningful to the children.

Throughout the school all classes are mixed age. We use a flexible mastery approach which is taught with the lesson objective chosen from each year group which closely match and are a continuation of each other being developed throughout the lesson or series of lessons. Where lesson objectives for differing year groups cannot be closely match, objectives are taught to the whole class ensuring that support and/or depth of learning opportunities are provided. When necessary and appropriate, children are taught in smaller groups for precision teaching.

CURRICULUM INTENT

Curriculum Intent

What Maths looks like in our school.

❖ A curriculum which caters for the needs of all individuals

❖ A flexible approach is adopted to the grouping of children based on their needs relating to the particular objective(s) being taught. Where appropriate children are given the opportunity to choose the level of their challenge based on their need and thus providing opportunities for them to develop as independent learners.

❖ Daily basic skills practise (Mastering number/Minute Maths/ 9 Quick Questions / Times Tables) to ensure fluency and develop long term recall

❖ We use a concrete, pictorial, abstract approach (see Calculation Policy)

❖ Regular Reasoning & Problem-solving opportunities are provided

❖ Questioning is a key part of the maths lesson – letting the children demonstrate what they know and challenging them every step

❖ Pupils are required to explore maths in depth, using mathematical vocabulary to reason and explain their workings

❖ A well planned lessons using ready-to-progress criterion for each year group which links to pupils’ prior knowledge and future applications.

❖ Structured interventions to help close the gaps for targeted children.

This is our philosophy:

❖ To become fluent in the fundamentals of mathematics so that children develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.

❖ To be able to solve problems by applying their mathematics to a variety of problems with increasing sophistication, including in unfamiliar contexts and to model real-life scenarios

❖ To reason mathematically by following a line of enquiry and develop and present a justification, argument or proof using mathematical language.

❖ To have an appreciation of number and number operations, which enables mental calculations and written procedures to be performed efficiently, fluently and accurately to be successful in mathematics.

This is the knowledge and understanding gained at each stage:

By the end of EYFS pupils will:

❖ Have a deep understanding of number to 10, including the composition of each number

❖ Subitise (recognise quantities without counting) up to 5

❖ Automatically recall (without reference to rhymes, counting or other aids) number bonds up to 5 (including subtraction facts) and some number bonds to 10, including double facts

❖ Verbally count beyond 20, recognising the pattern of the counting system

❖ Compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or the same as the other quantity

❖ Explore and represent patterns within numbers up to 10, including evens and odds, double facts

❖ Develop their spatial reasoning skills across all areas of mathematics including shape, space and measures

❖ Have an ability to look for patterns and relationships, spot connections, ‘have a go’, talk to adults and peers about what they notice and not be afraid to make mistakes.

By the end of Key Stage 1 pupils will:

❖ Develop confidence and mental fluency with whole numbers, counting and place value.

❖ Use numerals, words and the four operations, including with practical resources.

❖ Recognise, describe, draw, compare and sort different shapes and use the related vocabulary.

❖ a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money.

❖ know the number bonds to 20 and be precise in using and understanding place value. An emphasis on practice at this early stage will aid fluency.

❖ Read and spell mathematical vocabulary, at a level consistent with their increasing word reading and spelling knowledge at key stage 1

By the end of Lower Key Stage 2 pupils will:

❖ Be increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value.

❖ Develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers.

❖ Develop their ability to solve a range of problems, including with simple fractions and decimal place value.

❖ Draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties and confidently describe the relationships between them.

❖ Use measuring instruments with accuracy and make connections between measure and number.

❖ By the end of year 4, memorised their multiplication tables up to and including the 12 multiplication table.

❖ Read and spell mathematical vocabulary correctly and confidently, using their growing word reading knowledge and their knowledge of spelling.

By the end of Key Stage 2 pupils will:

❖ Understand the number system and place value to include larger integers.

❖ Make connections between multiplication and division with fractions, decimals, percentages and ratio.

❖ Develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation.

❖ Use the language of algebra as a means for solving a variety of problems.

❖ Classify shapes with increasingly complex geometric properties and use the vocabulary they need to describe them.

❖ Be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages.

❖ Read, spell and pronounce mathematical vocabulary correctly

CURRICULUM IMPLEMENTATION

Curriculum Implementation

Please refer to:

Our Long Term Overview to demonstrate the progression of knowledge and skills within the whole school
Our Calculation Policy

This is how it works:

Children in EYFS have a daily mathematical focus based on acquiring knowledge of basic mathematical facts and concepts within the EYFS Curriculum using the Mastering Number Programme. Mathematical concepts are also woven throughout their continuous provision.
Teachers use a Concrete, Pictorial, Abstract (CPA) approach to support learning.
Teachers take time to think carefully about the small step nature of learning within their lessons and select questions which moe children on to the next step.
Lessons incorporate a ‘ping/pong’ approach i.e. the use of mid-point reflections to explore misconceptions/difficult points and allow ‘in the moment feedback’ which maximises progress.
Daily basic skills practise (Mastering Number/Minute Maths/ 9 Quick Questions / Times Tables) to ensure fluency and develop long term recall
There are frequent opportunities for children to explain their thinking promote reasoning, explanation and depth of thought.
We use mistakes and misconceptions as an essential part of learning.
Teachers use their professional judgement, and AfL strategies, to ensure that children have a depth of understanding before moving on, whilst ensuring that all key areas are covered across the year.
Children falling behind are given rapid, same day/next day intervention time to quickly reinforce the learning and give quick opportunities to reinforce understanding.
Support is determined during each lesson to ensure secure understanding based on the needs of the child
Pre-teaching and/or immediate interventions to prepare children for learning the next day.
123Maths used for daily intervention for the lowest achieving pupils in all year groups from Year 2 and across KS2

This is what the adults do:

Plan progressive lessons which build on prior knowledge.
Support, encourage and nurture a love of Maths.
Create a learning environment that supports learning and engages children’s interest.
Use Bloom’s Questioning in class to assess conceptual knowledge and skills and allow pupils to develop strategies for questioning and thinking.
Regular book scrutiny, learning walks, pupil meetings and planning audits.
Use data to identify strengths and weaknesses and develop/implement plans to address areas of concern.
Identify those children who need extra support in order to provide them with urgent, catch-up sessions
Whole school professional development.
Network with other schools and Maths coordinators, e.g. though the WVLN.

This how we support:

We use teacher and self-assessment to quickly identify any child who requires additional support in specific areas
Differentiated ability tasks enabling children to progress at their own pace.
We make cross curricular links whenever possible.
Provide visual and practical prompts
Provide additional targeted support where necessary

This is how we support staff:

Identification of CPD needed
Curriculum Groups – share expertise throughout the school
Use of staff meetings
Small sessions and immediate support as and when required
Work in conjunction with other local school through Maths network meeting and South Herefordshire Maths Hub

This how we challenge:

Lessons will be differentiated or adapted though challenge or support.
Though challenging questions e.g. Prove it! Convince me! Why? How do you know?
Additional activities/targets to stretch the learning within the lesson.
Activities with alternative/extended discussion points.
Teachers will adapt their questioning to support or challenge

This how we ensure all children can access the curriculum:

Children with SEND are taught within the daily mathematics lesson and are encouraged to take part when and where possible
Teaching lessons using the CPA approach.
Targeted intervention for those that need extra support with their basic maths skills
More frequent repetition and revisiting to help make it stick

Cultural Capital/Enrichment

The mathematics curriculum allows our pupils to develop lifelong skills that are essential for succeeding in all aspects of school life and beyond.

Cultural Capital is the essential knowledge that children need to prepare them for their future success – in the world of work, in relationships forged throughout life and as a valued contributor to society.

Therefore, our aim is to give children the knowledge and skills to prepare them for what comes next in their lives. This includes the relevant vocabulary needed throughout their education and the opportunity to link maths to real-world problem solving.

Cultural Capital is the accumulation of knowledge, behaviours, and skills that a child gains over time through different experiences and opportunities. They draw upon these to demonstrate their cultural awareness, knowledge and competence. It is one of the key ingredients a child will draw upon to be successful in society, their career and the world of work.

Cultural Capital gives a child power. It helps them achieve goals, become successful, and rise up the social ladder without necessarily having wealth or financial capital.

We recognise that for a child to aspire and be successful academically and in the wider areas of their lives, they need to be given rich and sustained opportunities to develop. Within Maths, we engage in; Careers Information, Growth mindset, Resilience development strategies and Pupil Voice to empower pupils.

CURRICULUM IMPACT

Curriculum Impact

This is what you might typically see:

Happy, confident and engaged learners
Children practising and applying knowledge to different situations.
Confident children talking positively about maths, sharing and reflecting on their learning and being able to justify their mathematical ideas
Specific gaps in learning addressed through daily interventions
A classroom environment with displays including vocabulary, to support learning.
TIPTOP learning

This is how we know how well our children are doing:

We have identified substantive and disciplinary knowledge which is fundamental to the children’s development and understanding as mathematicians. They accumulate this as they move through our school which then gives them a firm foundation to build on when they move on to KS3 and beyond.

AFL at the beginning and throughout eery lesson.
Marking and feedback which also includes peer assessment
Lesson planned based on work done in previous year groups to ensure children are progressing
Formative assessment though questioning throughout the lesson
Photographic/ideo evidence
Observations of children during investigation and exploration
Next step marking and feedback by teacher and peers.
Book scrutiny, pupil meetings and planning audits.
Regularly monitoring of the standards of children’s work and the quality of teaching and learning in lessons
Assessment tracked at the end of each term and entered onto our summative assessment tracking system.

This is the impact of the teaching:

Children who are confident talking about maths.
Children who enjoy their learning in maths.
Inquisitive learners who make observations and ask questions.
Depth of understanding/application in different contexts
Pupils use acquired vocabulary in maths lessons.
Reflective learners.
Children will be ready for the next stage in their education. Pupils with SEND will achieve the best possible outcomes.
Children ready for their next step in learning.
Pupils are able to apply their mathematical knowledge.

Maths Progression Document

Overview Goldcrests

MATHS

Wk 1

Wk 2

Wk 3

Wk 4

Wk 5

Wk 6

Wk 7

Wk 8

Wk 9

Wk 10

Wk 11

Wk 12

Autumn

Spatial Awareness

Number songs/rhymes/stories

Pattern

(Families)

Number and Measure

(Covered through the themes of Senses Healthy Eating and Harvest)

Number, Measure and Pattern

(Harvest)

Shape

(Diwali)

Number and Shape

(Bonfire Night)

Number

(Hibernation and Christmas)

Spring

Spatial Awareness

Number songs/rhymes/stories

Pattern

(Winter)

Number and Measure

(Seasons, Rhyme and Story Telling)

Shape and Pattern

(Chinese New Year)

Number

(Friends and Pets)

Number and Measure

(Mother’s Day)

Pattern and Shape

(Volcanoes)

Number, Measure and Pattern

(Easter)

Spatial Awareness

Number songs/rhymes/stories

Summer

Spatial Awareness

Number songs/rhymes/stories

Pattern

(Frogs)

Number, Shape and Measure

(Size)

Number

(Life Cycles, Insects and Wild animals)

Number and Measure

(Pets and Growing)

Shape

(Other Cultures)

Pattern

(Transition)

Number and Measure

(Three Billy Goats Gruff)

Number

(Emotions)

Overview Wrens– Reception

MATHS

Wk 1

Wk 2

Wk 3

Wk 4

Wk 5

Wk 6

Wk 7

Wk 8

Wk 9

Wk 10

Wk 11

Wk 12

Autumn

Number: song/rhymes

Spatial Awareness

Baseline assessments

Number:

Weeks 1 – 6 mastering Number (4 days per week)

Spatial awareness, Pattern, Shape and Measure: on going through continuous provision and focused teaching one day per week.

Consolidation

Spring

Number:

Weeks 7 – 16 mastering Number (4 days per week)

Spatial awareness, Pattern, Shape and Measure: on going through continuous provision and focused teaching one day per week.

Consolidation

Summer

Number:

Weeks 17 – 25 mastering Number (4 days per week)

Spatial awareness, Pattern, Shape and Measure: on going through continuous provision and focused teaching one day per week.

Consolidation

Overview Wren/Robins – Year 1 and 2

MATHS

Wk 1

Wk 2

Wk 3

Wk 4

Wk 5

Wk 6

Wk 7

Wk 8

Wk 9

Wk 10

Wk 11

Wk 12

Autumn

Number: Place value

Y1 – Numbers to 20

Y2 – Numbers to 100

Number: Addition and Subtraction

Y1 – Numbers within 20 (including recognising money)

Y2 – Numbers within 100 (including money)

Number:

Y1 – Place value to 50 and Multiplication

Y2 - Multiplication

Spring

Number:

Y1 Division and consolidation

Y2 Division

Number:

Y1 – place value to 100

Statistics

Y2 - Statistics

Measurement:

Length and Height

Geometry:

Y1 – Shape and consolidation

Y2 – Properties of Shape

Number:

Y1 - Fraction and consolidation

Y2 - Fraction

Consolidation

Statistics

Y2 - Statistics

Summer

Geometry:

Position and Direction

Measurement:

Time

Number:

Y1 – Place Value recap

Number:

Y1 – Four operations consolidation

Measurement:

Y1 - Weight and Volume

Y2 - Mass, Capacity and Temperature

Geometry:

Y1 – Properties of Shape (Y2 objectives)

Y2 – Properties of Shape (Y3 objectives)

Number:

Y2 – problem Solving

Number:

Y2 – Four operations problems solving and investigations

Overview Woodpeckers – Year 3 and 4

MATHS

Wk 1

Wk 2

Wk 3

Wk 4

Wk 5

Wk 6

Wk 7

Wk 8

Wk 9

Wk 10

Wk 11

Wk 12

Aut

Number:

Place value

Number:

Addition and Subtraction

Number:

Multiplication and Division

Spring

Number: Multiplication and Division

Measurement:

Length, Perimeter and Area

(+ Fractions recap)

Number:

Fractions

Number:

Decimals (including money)

Consolidation

Summer

Measurement:

Time, Mass and Capacity

Statistics

Assessments and consolidation

Geometry:

Properties of Shape including Position and Direction (current year groups objectives plus following year’s objectives)

Consolidation of any objectives from the year/ moving onto following year’s objectives

Overview Owls - Year 4 and 5

MATHS

Wk 1

Wk 2

Wk 3

Wk 4

Wk 5

Wk 6

Wk 7

Wk 8

Wk 9

Wk 10

Wk 11

Wk 12

Autumn

Number:

Place value

Number:

Addition and Subtraction

Number:

Multiplication and Division

Measurement:

Length, Perimeter and Area

(+ Fractions recap)

Spr

Number:

Multiplication and Division

Number:

Fractions and Decimals

Summer

Statistics

Number:

Fractions, Decimals and Percentages

Assessments and consolidation

Geometry:

Properties of Shape (current year groups objectives plus following year’s objectives)

Consolidation of any objectives from the year/ moving onto following year’s objectives

Overview Peregrines – Year 5 and 6

MATHS

Wk 1

Wk 2

Wk 3

Wk 4

Wk 5

Wk 6

Wk 7

Wk 8

Wk 9

Wk 10

Wk 11

Wk 12

Autumn

Number:

Place value

Number:

All Four Operations

Number:

Fractions, Decimals and Percentages

Measurement:

Area, Perimeter and Volume

Spring

Number:

Multiplication and Division

Number:

Algebra

Geometry:

Properties of Shape

Statistics

Measurement:

Time and Money

Ratio and Proportion

Summer

Consolidation

Y5

Properties of shape

Y5 consolidate

All four operations

Y5 Measurement - Angles

Consolidation of any objectives from the year/ moving onto following year’s objectives

Y6: SATS

Y6 Cross Curricular topic work

Progression in Calculations

Addition

Objective and Strategies

Concrete

Pictorial

Abstract

Combining two parts to make a whole: part- whole model

Use cubes to add two numbers together as a group or in a bar.

Use pictures to add two numbers together as a group or in a bar.

4 + 3 = 7

10= 6 + 4

Use the part-part whole diagram as shown above to move into the abstract.

Starting at the bigger number and counting on

Start with the larger number on the bead string and then count on to the smaller number 1 by 1 to find the answer.

12 + 5 = 17

Start at the larger number on the number line and count on in ones or in one jump to find the answer.

5 + 12 = 17

Place the larger number in your head and count on the smaller number to find your answer.

Regrouping to make 10.

6 + 5 = 11

Start with the bigger number and use the smaller number to make 10.

Use pictures or a number line. Regroup or partition the smaller number to make 10.

7 + 4= 11

If I am at seven, how many more do I need to make 10. How many more do I add on now?

Adding three single digits

4 + 7 + 6= 17

Put 4 and 6 together to make 10. Add on 7.

Following on from making 10, make 10 with 2 of the digits (if possible) then add on the third digit.

Add together three groups of objects. Draw a picture to recombine the groups to make 10.

Combine the two numbers that make 10 and then add on the remainder.

Column method- no regrouping

24 + 15=

Add together the ones first then add the tens. Use the Base 10 blocks first before moving onto place value counters.

After practically using the base 10 blocks and place value counters, children can draw the counters to help them to solve additions.

Column method- regrouping

Make both numbers on a place value grid.

Add up the units and exchange 10 ones for one 10.

Add up the rest of the columns, exchanging the 10 counters from one column for the next place value column until every column has been added.

This can also be done with Base 10 to help children clearly see that 10 ones equal 1 ten and 10 tens equal 100.

As children move on to decimals, money and decimal place value counters can be used to support learning.

Children can draw a pictoral representation of the columns and place value counters to further support their learning and understanding.

Start by partitioning the numbers before moving on to clearly show the exchange below the addition.

As the children move on, introduce decimals with the same number of decimal places and different. Money can be used here.

Subtraction

Objective and Strategies

Concrete

Pictorial

Abstract

Taking away ones

Use physical objects, counters, cubes etc to show how objects can be taken away.

Cross out drawn objects to show what has been taken away.

18 -3= 15

8 – 2 = 6

Counting back

Make the larger number in your subtraction. Move the beads along your bead string as you count backwards in ones.

13 – 4

Use counters and move them away from the group as you take them away counting backwards as you go.

Count back on a number line or number track

Start at the bigger number and count back the smaller number showing the jumps on the number line.

This can progress all the way to counting back using two 2 digit numbers.

Put 13 in your head, count back 4. What number are you at? Use your fingers to help.

Find the difference

Compare amounts and objects to find the difference.

Use cubes to build towers or make bars to find the difference

Use basic bar models with items to find the difference.

Count on to find the difference.

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Draw bars to find the difference between 2 numbers.

Hannah has 23 sandwiches, Helen has 15 sandwiches. Find the difference between the number of sandwiches.

Part Part Whole Model

Link to addition- use the part whole model to help explain the inverse between addition and subtraction.

If 10 is the whole and 6 is one of the parts. What is the other part?

10 - 6 =

Use a pictorial representation of objects to show the part part whole model.

Move to using numbers within the part whole model.

Make 10

14 – 9 =

Make 14 on the ten frame. Take away the four first to make 10 and then takeaway one more so you have taken away 5. You are left with the answer of 9.

Start at 13. Take away 3 to reach 10. Then take away the remaining 4 so you have taken away 7 altogether. You have reached your answer.

16 – 8=

How many do we take off to reach the next 10?

How many do we have left to take off?

Column method without regrouping

Use Base 10 to make the bigger number then take the smaller number away.

Show how you partition numbers to subtract. Again make the larger number first.

Draw the Base 10 or place value counters alongside the written calculation to help to show working.

This will lead to a clear written column subtraction.

Column method with regrouping

Use Base 10 to start with before moving on to place value counters. Start with one exchange before moving onto subtractions with 2 exchanges.

Make the larger number with the place value counters

Start with the ones, can I take away 8 from 4 easily? I need to exchange one of my tens for ten ones.

Now I can subtract my ones.

Now look at the tens, can I take away 8 tens easily? I need to exchange one hundred for ten tens.

Now I can take away eight tens and complete my subtraction

Show children how the concrete method links to the written method alongside your working. Cross out the numbers when exchanging and show where we write our new amount.

Draw the counters onto a place value grid and show what you have taken away by crossing the counters out as well as clearly showing the exchanges you make.

When confident, children can find their own way to record the exchange/regrouping.

Just writing the numbers as shown here shows that the child understands the method and knows when to exchange/regroup.

Moving forward the children use a more compact method.

This will lead to an understanding of subtracting any number including decimals.

Multiplication

Objective and Strategies

Concrete

Pictorial

Abstract

Doubling

Use practical activities to show how to double a number.

Draw pictures to show how to double a number.

Partition a number and then double each part before recombining it back together.

Counting in multiples

Count in multiples supported by concrete objects in equal groups.

Use a number line or pictures to continue support in counting in multiples.

Count in multiples of a number aloud.

Write sequences with multiples of numbers.

2, 4, 6, 8, 10

5, 10, 15, 20, 25 , 30

Repeated addition

Use different objects to add equal groups.

Write addition sentences to describe objects and pictures.

Arrays- showing commutative multiplication

Create arrays using counters/ cubes to show multiplication sentences.

Draw arrays in different rotations to find commutative multiplication sentences.

Link arrays to area of rectangles.

Use an array to write multiplication sentences and reinforce repeated addition.

Grid Method

Show the link with arrays to first introduce the grid method.

4 rows of 10

4 rows of 3

Move on to using Base 10 to move towards a more compact method.

4 rows of 13

Move on to place value counters to show how we are finding groups of a number.We are multiplying by 4 so we need 4 rows.

Fill each row with 126.

Add up each column, starting with the ones making any exchanges needed.

Then you have your answer.

Children can represent the work they have done with place value counters in a way that they understand.

They can draw the counters, using colours to show different amounts or just use circles in the different columns to show their thinking as shown below.

Start with multiplying by one digit numbers and showing the clear addition alongside the grid.

Moving forward, multiply by a 2 digit number showing the different rows within the grid method.

Column multiplication

Children can continue to be supported by place value counters at the stage of multiplication.

It is important at this stage that they always multiply the ones first and note down their answer followed by the tens which they note below.

Bar modelling and number lines can support learners when solving problems with multiplication alongside the formal written methods.

Start with long multiplication, reminding the children about lining up their numbers clearly in columns.

If it helps, children can write out what they are solving next to their answer.

This moves to the more compact method.

Division

Objective and Strategies

Concrete

Pictorial

Abstract

Sharing objects into groups

I have 10 cubes, can you share them equally in 2 groups?

Children use pictures or shapes to share quantities.

8 ÷ 2 = 4

Share 9 buns between three people.

9 ÷ 3 = 3

Division as grouping

Divide quantities into equal groups.

Use cubes, counters, objects or place value counters to aid understanding.

Use a number line to show jumps in groups. The number of jumps equals the number of groups.

Think of the bar as a whole. Split it into the number of groups you are dividing by and work out how many would be within each group.

28 ÷ 7 = 4

Divide 28 into 7 groups. How many are in each group?

Division within arrays

Link division to multiplication by creating an array and thinking about the number sentences that can be created.

Eg 15 ÷ 3 = 5 5 x 3 = 15

15 ÷ 5 = 3 3 x 5 = 15

Draw an array and use lines to split the array into groups to make multiplication and division sentences.

Find the inverse of multiplication and division sentences by creating four linking number sentences.

7 x 4 = 28

4 x 7 = 28

28 ÷ 7 = 4

28 ÷ 4 = 7

Division with a remainder

14 ÷ 3 =

Divide objects between groups and see how much is left over

Jump forward in equal jumps on a number line then see how many more you need to jump to find a remainder.

Draw dots and group them to divide an amount and clearly show a remainder.

Complete written divisions and show the remainder using r.

Short division

Use place value counters to divide using the bus stop method alongside

42 ÷ 3=

Start with the biggest place value, we are sharing 40 into three groups. We can put 1 ten in each group and we have 1 ten left over.

We exchange this ten for ten ones and then share the ones equally among the groups.

We look how much in 1 group so the answer is 14.

Students can continue to use drawn diagrams with dots or circles to help them divide numbers into equal groups.

Encourage them to move towards counting in multiples to divide more efficiently.

Begin with divisions that divide equally with no remainder.

Move onto divisions with a remainder.

Finally move into decimal places to divide the total accurately.

Maths Assessment

Children are assessed within lessons on a daily basis. Frequent opportunities are built into lessons to assess children’s retention of previous objectives taught to ensure that the objectives are securely achieved (the daily number skills sessions are ideal opportunities for this assessment.)

Progress through objectives are recorded on data sheets termly. Analysis of this data is completed shortly after each data point and used to inform teaching and learning.

Evidence for assessment could also include:

Children’s work
Marking codes and annotations
Teacher/TA observation notes
Photographs with annotations
Audio recordings
End of unit tasks

Essential Building Blocks

Knowledge of number facts and a fluency in using them is a vital part of Maths for each year group. Rapid recall of number facts can provide the basic knowledge required for most aspects of primary mathematics, including mental and written calculations, fractions, decimals and percentages and problem solving. Number facts learned in Maths can also be transferred to many other subjects across the curriculum and in ‘real life’ situations.

Year	Essential Building Blocks
EYFS	Count reliably with numbers from 1 to 10 Write numbers from 0-9 with correct formation Recognise numbers 1-10 and place numbers in order Say which number is one more or one less than a given number to 10 Count to over 100
1	Count to and across 100, forwards and backwards from any number Count on and back in 1s, 2s, 5s and 10s Can double up to 10 + 10 Read, write & order numbers from 0 to at least 100 Say what is one more & one less than a given number to 100 Add & subtract two numbers using the correct symbols within 20 Know addition and subtraction facts to 20 & use bonds to at least 20
2	Count to over 100 Explain value of digits (to 3 digits) Read, write & order numbers up to 100 Count on and back in twos, threes & tens from any number Know addition and subtraction facts to 20 & use all bonds to 10 Know all number pairs to 100 using ‘ten’ numbers Can double all numbers up to 10 and halve all even numbers up to 20 Know x2, x5 and x10 and division facts
3	Read, write and order numbers to 1000 and know value the of each digit Count from 0 in multiples of 4, 8, 50 and 100 Find 10 or 100 more or less than a given number Know addition & subtraction facts to 20 Add and subtract mentally up to 3-digit numbers Add and subtract one digit and two-digit numbers using the column method Know x2, x3, x4, x5, x8 and x10 (and division facts) Do simple divisions, e.g., 27 divided by 5 Find simple fractions, e.g., 1/2, 1/3, 1/4, 1/5, 1/10 of shapes & amounts Count up and down in tenths Use £. p and know value of amounts
4	Read, write and order numbers to 10,000, and know value of each digit Count in multiples of 6, 7, 9, 25 and 1000 Count up and down in tenths and hundredths Know all times tables to 12x12 (and division facts). New multiplication and division facts in Y4 are x6 x7 x9 x11 and x12 Round numbers (up to 3 digits) to nearest 10, 100 or 1000 Add and subtract mentally pairs of two-digit numbers Multiply and divide 2-digit numbers by 10 or 100 Divide (up to 4 digits) numbers by 10 or 100 Multiply and divide numbers up to 100 by 2, 3, 4 or 5 and find remainders Identify pairs of fractions that total 1 and equivalent fractions Solve problems including fractions and decimals to 2.d.p
5	Read, write and order numbers to 3dp; know value of each digit up to 1,000,000 Multiply & divide positive integers up to 1,000,000 by powers of 10 Order sets of positive and negative integers Round numbers up to 1 000 000 to the nearest 10, 100, 1000, 10 000, 100 000 Add and subtract whole numbers with more than 4 digits using formal column methods Multiply numbers up to 4 digits by one- or two-digit numbers using formal written method Divide numbers up to 4 digits by a one-digit number using formal method of short division. Mentally add and subtract increasingly large numbers Know all multiplication facts to 12x12 (& division facts) Identify multiples and factor pairs of a number and identify common factors of 2 numbers Find equivalent fractions Recognise mixed numbers and improper fractions and convert from one form to the other.
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 Multiply numbers up to 4 digits by one- or two-digit numbers using formal written method Divide numbers up to 4 digits by a one- or two-digits number using formal method of short division and long division and record the remainder as appropriate. Use knowledge of order of operations to carry out calculations involving four operations. Add, subtract, multiply and divide fractions Use common factors to simplify fractions Multiply or divide numbers by 10, 100, 1000 giving answers up to 3 decimal places. Find a percentage of a given number.

Maths Vocabulary

Core Maths Vocabulary: All Classrooms to have these where relevant to learning.

Digit, integer, number, answer, solution, solve, work out, systematic, group, share, sort, diagram, represent, pattern, relationship, rule, sequence, explain, correct, incorrect, true, false, agree, disagree, same, different, bar model, part- whole model, formal method, equal to, more, less, greater than, fewer, less than, largest, greatest, least, most, estimate, approximately.

	Number- Place Value	Number- Addition and Subtraction	Number- Multiplication and Division	Number- Fractions	Measurement	Geometry- Shape	Geometry-Position and direction	Statistics
EYFS	Number; zero; numbers to 20; count, forwards, backwards; how many, more, fewer, equal, group; order, largest, smallest, less; even, odd	One more, one less, altogether, how many are left? Same, different, number bond, part-whole, add, take-away	Double, half, halve, halving, pairs, twice as many, share, equal, unequal, group, left over	Half, halve, halving	Now, before, soon, later, after, next, fastest; time, yesterday, today, tomorrow, day, week, weekend, month, year; Days of the week: Monday, Tuesday, etc. Seasons: spring, summer, autumn, winter; birthday, holiday; Morning, afternoon, evening, night, midnight bedtime, dinner/lunch time, playtime; length, height, breadth, tall, short, long, tallest, shortest, longest, longer/shorter, taller/shorter, wider/narrower, weigh, weight, heavy, heavier, heaviest, light, lighter, lightest, balance	Shape, circle, triangle, rectangle, square, side, straight, curved, cylinder, cube, cuboid, cone, sphere, pyramid, face, same, different, pattern.	On, next to, over, under, around, through.
Year 1	Numbers to 100; place value; digit, integer; symbol; compare; equal to, more, less, greater than, fewer, less than, greatest, smallest; first, second, third…last; ones, tens, partition, exchange; order, largest, smallest, biggest, least, most.	Number bonds, part, whole; plus; fact family, addition sentence, number sentence; how many more; number line; commutative; addition, more, make, sum, total, add together, altogether; calculation; Inverse equals, is the same as (including equals sign); subtract, , subtraction, take away, minus; difference between, what is the difference? how many more?, how many less? how much more is?	How many altogether? How may are there?; groups, groups of, equal groups, unequal groups; row, column, array; number sentence; double, doubles; equal groups of 2, equal groups of 5, equal groups of 10; share, sharing, equally, odd, even,	Whole, parts, equal parts, the same; split; groups; share; equally; quarter; four equal parts One half, two halves A quarter, two quarters	Length, measure, measuring; ruler, cm; mass; balance, scale; volume, full, half full, quarter full, empty; capacity; holds, Container; money; value; coin; note; amount; 1p, 2p, 5p, 10p, 20p, 50p, £1, £2, £5, £10; hour, o'clock, half past, clock, watch, hands; hour, minute, second; before, after next, last now, soon, early, late quick, quicker, quickest, quickly, fast, faster, fastest, slow, slower, slowest, slowly old, older, oldest, new, newer, newest	Polygon, 2D, 3D, group, sort, corner (point, pointed) Face, side, edge Make, build, draw.	Turn, full, half, quarter, three quarter; direction; movement, move; position; left, right, up, down; top, bottom, middle, above, below, between; in front, behind.
Year 2	2-digit; base 10; pattern; sequence; Numbers to one hundred Hundreds Partition, recombine Hundred more/less	Bar model; operation, inverse operation; column; exchange; bridge; method;	Times-table; facts; multiples; repeated addition; lots of; of; multiply; multiplied by; times; commutative; twos, fives, tens, threes; array; go into; divide, divide between, division, dividing; grouping, sharing;	Two quarters, three quarters, one third, two thirds; unit fraction, numerator, denominator, vinculum; equivalence, equivalent.	Change, total; distance; metres; g/kg; ml/l; temperature, thermometer, degrees Celsius, increase, decrease, warmer, colder; quarter past/to, 5 past, 10 past, twenty to etc, start, duration, end, interval, how long…? When did it start /end /finish…?, seconds;	Pentagon, hexagon, octagon, quadrilateral; prism; vertices, vertex; rotate; Symmetry, symmetrical, line of symmetry; horizontal, vertical; Fold; pattern, repeating pattern.	Direction, forwards, backwards; right angle; rotation, Clockwise, anticlockwise.	Count, tally, tally chart, table; data, represent, sort; pictogram, symbol; block diagram, axis; label, title, scale; most popular, most common, least popular, least common; Venn diagram, Carrol diagram.
Year 3	Numbers to one thousand; 3-digit; thousand; ascending, descending;	Column, column addition and subtraction; regroup; efficient; estimate.	Fours, eights; remainder; divisor, dividend, quotient.	Non-unit fraction; tenths, two tenths, three tenths etc; two thirds; fifth, sixth, ninth; decimal, decimal point;	mm; perimeter; leap year; minutes past/to; a.m., p.m.; analogue, digital; twelve-hour /twenty-four- hour clock; Roman numerals I to XIII.	Parallel, perpendicular; surface; acute angle, obtuse angle.	North, South, East, West; angle, point, acute, obtuse; ninety degrees Orientation (same orientation, different orientation)	Chart, bar chart; frequency table, Carroll diagram, Diagram
Year 4	Numbers to ten thousand; Roman numerals to one hundred; round, nearest; approximately; negative, minus, count through zero; tenths, hundredths, 0.25, 0.5, 0.75.	Formal method.	Sixes, sevens, nines; produce, poduct; commutativity; factor, factor pair; formal method;	Proper fraction, improper fraction, mixed number; hundredths;	Km; rectilinear; area, square centimetres; warmest, coldest.	Isosceles, scalene, equilateral; rhombus, parallelogram, trapezium; regular polygon; mirror line, reflect.	Coordinates, translation, first quadrant, x-axis, y-axis.	Continuous data, discrete data; line graph, x axis, y-axis.
Year 5	Numbers to a million; Roman numerals to one thousand; powers of 10.	Place holder.	Common factor, prime number, composite number, prime factor, square number, cubed number; round up/down.	Common denominator; thousandth; simplify, simplified; convert; per cent, percentage, per hundred;	Imperial units, metric units, inches, lbs, pints; timetable; compound shape; volume, capacity, cm cubed/cubic cm.	Degrees, protractor, reflex angle; irregular polygon, dimensions; net.	Reflection, reflect.
Year 6	Numbers to ten million. Algebra: Function, input, output; algebra, algebraic, rule; expression; substitute; formula, formulae; equation; value, possible values..		Order of operations, BIDMAS; common multiple, lowest common multiple.	Cancel, highest common factor, common numerator. Ratio, proportion; for every ?_there are_, :(to); enlargement, scale factor.	Tonnes, ounces, stone, miles.	Vertically opposite (angles), internal angles; circumference, radius, diameter, centre.	Four quadrants.	Mean, pie chart.

Maths Recommended Reads/ Websites/ Apps

Early Years and Key Stage 1 Maths

A selection of great counting books and maths stories covering cardinal and ordinal numbers and place value.

The Great Pet Sale

by Mick Inkpen

One to Ten and Back Again

by Nick Sharratt

The Shopping Basket

by John Burningham

The Doorbell Rang

by Pat Hutchins

Ten Black Dots by Donald Crews

I Spy Numbers By Jean Marzollo

Mouse Count by Ellen Stoll Walsh

The Hueys in None the Number by Oliver Jeffers

Recommended reads for Key Stage 2 Maths

These books are a great way to introduce a range of mathematical concepts like pie charts, probability, ratio and simplifying fractions in a way which engages the children in a story.

A Remainder of One by Elinor Pinczes