# Mathematics

At The Vale Academy, we believe it is never too early to explore numbers. In order to ensure that all content is covered from the New National Curriculum, the school uses White Rose Maths Hub for yearly and medium-term plans, as well as mastery content. This is then adapted where necessary to suit each learner's needs. This will often be paired or individual work for children, following the whole-class teaching.

We believe it is never too early to explore numbers. Real life often provides the best opportunities to develop early maths skills like counting and recognising numbers. We provide learning opportunities through exploration, songs, rhymes and fun activities. We continue to build upon these learning experiences through daily teaching of mastery maths throughout the year phrases. Children have lots of opportunities for revisiting, embedding and extending their knowledge and understanding across the whole of our curriculum. Our aim is to enable every child to achieve success and build on their prior learning so that they can utilise these new skills in all aspects of their future lives.

## Reception

At The Vale Academy in Reception, your child will be introduced to numbers and counting, and will start to use basic mathematical language. An interest in maths and problem-solving will be encouraged through maths games and fun activities.

Much of your children’s learning will come from exploring and talking about maths in the world around them.

In Reception, your child will learn to:

- Count reliably with numbers from 1 to 20, place them in order and say which number is one more or one less than a given number.
- Use quantities and objects to add and subtract 2 single-digit numbers and count on or back to find the answer.
- Use everyday language to talk about size, weight, capacity, position, distance, time, and money to compare quantities and objects and to solve problems.
- Recognise, create, and describe patterns.
- Explore characteristics of everyday objects and shapes and use mathematical language to describe them.

## Year 1

In Year 1, children will start to build confidence working with numbers, through developing their counting and calculation skills. They will also gain an understanding of halves and quarters, start to measure, and tell the time, and learn about some 2D and 3D shapes.

Children will be taught to count forwards and backwards to 100, add and subtract numbers to 20, and be introduced to the idea of multiplying and dividing. They will be encouraged to use objects to help them solve simple problems in a practical way.

Much of the children’s learning will come from exploring and talking about maths in the world around them.

Child will learn:

**Place value**

In Year 1, children will be expected to:

- work with numbers up to 100, counting on or back from any number and in steps of 2, 5 or 10. This includes:
- reading and writing numerals to 100 and number names to 20 in words
- using objects and number lines to represent numbers
- finding one more and one less than any number.

**Addition & subtraction**

In Year 1, children will be expected to:

- be able to read, write and understand mathematical ideas using addition (+), subtraction (–) and equals (=) signs. This includes:
- making and using number bonds to 10 and then to 20
- adding and subtracting one-digit and two-digit numbers to 20, including 0
- solving simple problems using objects, drawings, diagrams and symbols, including missing number problems such as 7 = ? – 9.

**Multiplication & division**

In Year 1, children will be expected to:

- be able to solve simple multiplication and division problems using objects, drawings and arrays to help them. This includes:
- counting in steps of 2, 5 and 10 and understanding that, for example 3 × 2 is the same as 2 + 2 + 2
- using sharing and grouping to solve division problems
- beginning to understand the relationship between multiplication and division.

**Fractions**

In Year 1, children will be expected to:

- be recognise, find and name halves and quarters of objects, shapes and quantities. This includes:
- understanding halving as sharing equally into two parts or groups
- understand finding a quarter as sharing into four equal parts or groups
- understanding that finding a half is the same as dividing by 2 and finding a quarter is the same as dividing by 4.

**Geometry**

In Year 1, children will be expected to:

- be able to identify simple flat (2D) and solid (3D) shapes and use mathematical vocabulary to describe position, direction and movement. This includes:
- recognising and name common 2D shapes, such as circles, triangles, rectangles and squares
- recognising and name common 3D shapes, such as spheres, pyramids, cones, cuboids and cubes
- describing whole, half, quarter and three-quarter turn

**Measurement**

In Year 1, children will be expected to:

- be explore measurement in relation to length, height, weight, volume, time and money. This includes:
- measuring and comparing lengths, heights, weights and capacities
- telling the time to the hour and half hour
- recognising and knowing the value of different coins and notes.

## Year 2

In Year 2, children will continue to develop their counting and calculation skills, learning different ways to multiply and divide. They will also extend their understanding of fractions. They will measure length, weight, volume, temperature, time and money, discover more about 2D and 3D shapes, and begin to learn about statistics.

They’ll count in steps of 2, 3, 5 and 10 and learn number bonds to 20. They’ll partition numbers into 10s and 1s to add and subtract one-digit and two-digit numbers. They will be taught the 2, 5 and 10 times tables and how to find 1/2, 1/3, 1/4, 3/4 of quantities and shapes.

Much of their learning will come from exploring with objects to solve problems practically.

Children will learn:

**Place value**

In Year 2, children will be expected to:

- recognise tens and ones in 2-digit numbers (for example 23 has 2 tens and 3 ones) and use these to order numbers to 100. This includes:
- counting in steps of 2, 3, 5 and 10
- using more than (>), less than (<) and equals (=) symbols to compare numbers
- using place value and number facts to solve problems.

**Addition & subtraction**

In Year 2, children will be expected to:

- be able to solve addition and subtraction problems using numbers with one and two digits. This includes:
- knowing and using addition and subtraction facts up to 20 and working out related addition and subtraction facts to 100
- adding and subtracting numbers using objects, pictures and drawings, and also solving these problems mentally
- understanding that addition and subtraction have an inverse relationship, i.e. they undo each other, and using this to check their calculations.

**Geometry (shape)**

In Year 2, children will be expected to:

- be able to compare and sort common 2D and 3D shapes and everyday objects and continue patterns of shapes. This includes:
- describing 2D shapes including number of sides and lines of symmetry
- describing 3D shapes including number of faces, edges and vertices
- describing turns using clockwise, anti-clockwise and right angles.

**Measurement**

In Year 2, children will be expected to:

- use standard units to measure length, mass (weight), capacity and temperature, compare intervals of time and solve simple problems with money. This includes:
- comparing and ordering measures such as metres (m), centimetres (cm), kilograms (kg), grams (g), degrees Celsius (°C), litres (l) and millilitres (ml)
- telling the time to five minutes, including quarter to and quarter past
- choosing coins or notes to make a given amount of money and working out change.

**Multiplication & division**

In Year 2, children will be expected to:

- use a range of methods to solve multiplication and division problems, including using practical resources and mental methods. This includes:
- knowing and using multiplication and division facts for the 2, 5 and 10 times tables
- recognising and identifying odd and even numbers
- using the symbols ×, ÷ and = to record multiplication and division calculations.

**Fractions**

In Year 2, children will be expected to:

- be able to recognise and use the fractions
- finding fractions of lengths, shapes, sets of objects and quantities
- writing simple fractions, such as 1/2 of 6 = 3
- recognising that 2/4 and 1/2 mean the same.

**Statistics**

In Year 2, children will begin to:

- record, collate, organise, and compare information using simple ways to present data. This includes:
- interpreting and constructing simple pictograms, tally charts, block diagrams, and tables
- counting objects in categories to sort data
- asking and answering simple questions about data.

## Year 3

In Year 3, children will continue to develop their understanding of numbers and start to calculate using formal written methods. They will learn a lot more about fractions, including tenths. They will find perimeters of 2D shapes, use the 24-hour clock, recognise angles, and start to use bar charts.

They’ll count in steps of 4, 8, 50 and 100 and order numbers to 1000. They’ll partition numbers into 100s, 10s and 1s, add and subtract three-digit numbers, and multiply two-digit by one-digit numbers. They will be taught the 3, 4, and 8 times tables and begin to add and subtract fractions.

Children will learn:

**Place Value**

In year 3 children will be expected to:

- recognise hundreds, tens and ones in 3-digit numbers (for example 423 has 4 hundreds, 2 tens and 3 ones). This includes:
- counting in steps of 4, 8, 50 and 100
- reading, writing, comparing, and ordering numbers to 1000
- finding 10 or 100 more or less than a number.

**Addition & subtraction**

In Year 3, children will be expected to:

- be able to use a range of strategies to solve problems mentally and learn formal written methods for column addition and column subtraction.

This includes:

- adding and subtracting numbers with up to three digits
- estimating answers to problems before working them out accurately and checking using the inverse operation, i.e. using addition to check subtraction and vice versa
- explaining how they have solved a problem and why they chose a particular method.

**Geometry**

In Year 3, children will be expected to:

- use accurate mathematical language to describe properties of a wider range of symmetrical and non-symmetrical shapes. This includes:
- drawing 2D shapes and making 3D shapes
- identifying angles greater or less than a right angle
- identifying horizontal, vertical, parallel, and perpendicular lines.

**Measurement**

In Year 3, children will be expected to:

- be able to add and subtract measurements, tell the time to the nearest minute, and compare durations of time. This includes:
- measuring and adding to find the perimeter of 2D shapes
- telling the time using 12-hour and 24-hour clocks, including Roman numerals I to XII for 1 to 12
- adding and subtracting amounts of money to give change.

**Multiplication & division**

In Year 3, children will be expected to:

- use a range of strategies to solve problems mentally and begin to learn formal written methods for short multiplication and short division. This includes:
- knowing and using multiplication and division facts for the 3, 4 and 8 times tables
- multiplying two-digit by one-digit numbers
- understanding that multiplication and division have an inverse relationship, i.e. they undo each other, and using this to check their calculations.

**Fractions**

In Year 3, children will be expected to be able to:

- compare and order fractions and begin to add and subtract fractions with the same denominator. This includes:
- counting up and down in tenths and connecting tenths to dividing by 10
- using unit and non-unit fractions
- understanding equivalent fractions, that is fractions that have the same value such as 2/5 = 4/10

**Statistics**

In Year 3, children will interpret and present data in a range of ways. This includes:

- interpreting and making bar charts, pictograms, and tables
- understanding information presented using scales
- solving one-step and two-step problems using data.

## Year 4

In Year 4, children will develop their mental and written calculation skills using larger positive numbers and fractions. They will meet negative and decimal numbers, as well as some Roman numerals. They will convert between units of measurement, find perimeters and areas, and learn more about angles and symmetry. They will plot shapes on coordinate grids and start to use timeline graphs.

They’ll count in steps of 6, 7, 9, 25 and 1000, add and subtract four-digit numbers and multiply three-digit by one-digit numbers. They will know all the times tables up to 12 x 12 and be able to divide by 10 and 100 to give decimal answers. They’ll round numbers to the nearest 10, 100 and 1000, or whole number for decimals.

Children will learn:

**Place value**

In Year 4, children will be expected to:

- order and compare numbers beyond 1000 using place value in 4-digit numbers (for example 1423 has 1 thousand, 4 hundreds, 2 tens and 3 ones). This includes:
- counting in steps of 6, 7, 9, 25 and 1000
- counting backwards through zero to include negative numbers
- rounding any number to the nearest 10, 100 or 1000.

**Addition & subtraction**

In Year 4, children will be expected to:

- be able to solve addition and subtraction problems involving numbers up to four digits. This includes:
- choosing from a variety of methods, including mental calculations, using objects, diagrams, or drawings such as number lines, models such as the area/grid method or written column addition and column subtraction
- estimating answers before calculating accurately and checking answers by understanding that addition and subtraction are inverse operations
- solving two-step word problems which require them to solve two different calculations before coming to the answer.

**Multiplication & division**

In Year 4, children will be expected to:

- be able to use formal written methods of short multiplication and short division confidently. This includes:
- knowing and using multiplication and division facts for all times tables up to 12 × 12
- multiplying three-digit by one-digit numbers
- multiplying three numbers together.

**Measurement**

In Year 4, children will be expected to:

- be able convert between some units of measurement, such as kilometres to metres and calculate measurements in relation to shapes.

This includes:

- working out the perimeter and area of rectilinear shapes
- solving problems involving converting units of time
- adding, subtracting, multiplying, and dividing measurements including money.

**Fractions & decimals**

In Year 4, children will be expected to:

- explore the link between fractions and multiplication/division and begin to learn about decimals. This includes:
- solve simple measure and money problems involving fractions and decimals
- recognising and writing tenths and hundredths as decimals
- rounding decimal numbers with one decimal place to the nearest whole number.

**Geometry**

In Year 4, children will be expected to:

- extend their knowledge of properties of shapes and be able to describe the position of shapes on a coordinate grid. This includes:
- comparing shapes such as quadrilaterals and triangles based on their properties and sizes
- drawing mirror images of shapes in lines of symmetry
- plotting points and describing how shapes move up/down/left/right on a coordinate grid.

**Statistics**

In Year 4, children will be expected to:

- interpret and present data in bar charts, pictograms, tables, and other graphs. They will begin to understand how data can show changes over time. This includes:
- interpreting and presenting discrete and continuous data using graphs
- interpreting and making time graphs (a type of line graph)
- solving problems by comparing, adding, and subtracting data from tables, charts, and graphs.

## year 5

In Year 5, children will develop their mental and written calculation skills using the four operations. They will meet six-digit numbers and develop their decimal and Roman numerals knowledge further. They will convert between units of measurement, identify 3-D shapes from 2-D representations and solve problems using line graph in greater detail.

They will count in steps powers of 10 for any given number up to 1,000,000. They will meet, know and use the vocabulary of prime numbers and factors. They will develop their prior learning about angles and shape.

Children will learn:

**Place value**

In Year 5, children will be expected to:

- read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit.
- counting 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, 1,000, 10,000 and 100,000.
- solve number problems and practical problems that involve all of the above
- read Roman numerals to 1,000 (M) and recognise years written in Roman Numerals.

**Addition & subtraction**

In Year 5, children will be expected to:

- 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

**Multiplication & division**

In Year 5, children will be expected to:

- identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.
- solve problems involving multiplication and division where larger numbers are used by decomposing them into their factors
- 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 cube numbers, and the notation for squared (
^{2}) and 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.

**Fractions, decimals & percentages**

In Year 5, children will be expected to:

- compare and order fractions whose denominators are all multiples of the same number
- identify, name and 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 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) - 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 hundred, and as a decimal fraction
- solve problems which require knowing percentage and decimal equivalents of
^{1}/2,^{1}/4,^{1}/5,^{2}/5,^{4}/5 and those with a denominator of a multiple of 10 or 25.

**Geometry (properties of shapes)**

In Year 5, children will be expected to:

- 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 (
^{o}) - identify:
- angles at a point and one whole turn (total 360
^{o}) - angles at a point on a straight line and ½ a turn (total 180
^{o}) - other multiples of 90
^{o} - 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.

**Position and direction**

In Year 5, children will be expected to:

- 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

**Measurement**

In Year 5, children will be expected to:

- convert between different units of metric measure (e.g. kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)
- understand and use 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 squares and rectangles including using standard units, square centimetres (cm
^{2}) and square metres (m^{2}) and estimate the area of irregular shapes - estimate volume (e.g. using 1 cm
^{3}blocks to build cubes and cuboids) 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.

**Statistics**

In Year 5, children will be expected to:

- solve comparison, sum and difference problems using information presented in a line graph
- complete, read and interpret information in tables, including timetables.

## year 6

In Year 6, children will develop their learning about larger numbers and will work with 7-digit numbers. They will continue to develop their number and practical problem solving using the four operations. They will meet algebra and develop this knowledge further through the generating and describing of linear number sequences.

The children will prepare for their End of Key Stage 2 Assessments. In the summer term, they will demonstrate their skills and knowledge that they have learnt during their Maths journey at The Vale through thematic projects.

Children will learn:

**Place value**

In Year 6, children will be expected to:

- 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 all of the above.

**Addition, subtraction, multiplication and division.**

In Year 6, children will be expected to:

- 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
- perform mental calculations, including with mixed operations and large numbers.
- identify common factors, common multiples and prime numbers
- use their 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, levels of accuracy.

**Fractions, decimals & percentages**

In Year 6, children will be expected to:

- 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. 0.375) for a simple fraction (e.g.
^{3}/8) - identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places
- 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.

**Algebra**

In Year 6, children will be expected to:

- express missing number problems algebraically
- use simple formulae expressed in words
- generate and describe linear number sequences
- find pairs of numbers that satisfy number sentences involving two unknowns
- enumerate all possibilities of combinations of two variables.

**Ratio**

In Year 6, children will be expected to:

- solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
- solve problems involving the calculation of percentages (e.g. of measures) 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.

**Measurement**

In Year 6, children will be expected to:

- 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 centimetre cubed (cm
^{3}) and cubic metres (m^{3}), and extending to other units such as mm^{3}and km^{3}.

**Statistics**

In Year 6, children will be expected to:

- interpret and construct pie charts and line graphs and use these to solve problems
- calculate and interpret the mean as an average.

**Geometry (properties of shapes)**

In Year 6, children will be expected to:

- 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.

** Position and direction**

In Year 6, children will be expected to:

- describe positions on the full coordinate grid (all four quadrants)
- draw and translate simple shapes on the coordinate plane, and reflect them in the axes.
- 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 centimetre cubed (cm
^{3}) and cubic metres (m^{3}), and extending to other units such as mm^{3}and km^{3}.