**2018-19**

Select the appropriate year below

# Year 1

### Number

*Number and place value *

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

count, read and write numbers to 100 in numerals

count in multiples of twos, fives and tens

given a number, identify one more and one less

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

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

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

*Addition and subtraction*

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

carry out formal methods of addition, introduce = sign.

carry out addition of two digit numbers and ones with no carrying.

read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs.

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

add a two digit number and ones up to 20, including zero.

subtract ones from a two digit number (no carrying).

*Multiplication and division*

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

*Measurement*

compare, describe and solve practical problems for:

lengths and heights (eg: long, short, longer/shorter, tall/short, double/half).

mass or weight (eg: heavy/light, heavier than, lighter than).

capacity/volume (full/empty, more than, less than, quarter)

time (quicker, slower, earlier, later).

measure and begin to record the following:

lengths and heights (m, cm)

mass and weight (g)

capacity and volume (practical skills)

time (hours, minutes, seconds).

recognise and know the value of denominations of coins and notes.

sequence events in chronological order, using language such as: before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening.

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

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

### Geometry

*Properties of shapes *

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

2D shapes, eg: rectangles (including squares), circles and triangles.

# Year 2

### Number

*Number and place value *

Count in steps of 2, 3, and 5 from 0, and in 10s from any number, forwards up to 50

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

compare and order numbers from 0 up to 100

read and write numbers to at least 100 in numerals.

use the language of less than and greater than, introduce “fewer than”

use place value and number facts to solve problems.

count from 100 to 200.

*Addition and subtraction*

solve problems with addition and subtraction:

using concrete objects and pictorial representations, including those involving numbers, quantities and measures.

apply their increasing knowledge of mental and written methods.

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

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

addition and subtraction of 2 two digit numbers, using formal columnar written methods.

as above, with carrying

adding three 1 digit numbers.

decomposition of 2 two digit numbers.

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

missing number problems; eg – 7 = 9 – ? and 7 = ? – 9.

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

*Multiplication and division*

recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers (extension of Year 1).

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

show that multiplication of two numbers can be done in any order (commutative) solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.

*Fractions *

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

write similar fractions, 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2.

### Measurement

choose and use appropriate standard units to estimate and measure length/height in any direction (M/cm); mass (kg/g); temperature (degrees C); capacity (litres/ml) to the nearest appropriate unit, using rulers, (scales,thermometers where all divisions are shown)and measuring vessels.

compare and order lengths, mass, volume/capacity and record results.

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

find different combinations of coins that equal the same amounts of money.

solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change.

compare and sequence intervals of time.

tell and write the time, including quarter past/ to the hour and draw the hands on a clock face to show these times.

### Geometry

*Properties of shapes *

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

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

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

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

*Position and direction*

order and arrange combinations of mathematical objects in patterns.

### Statistics

interpret and construct simple pictograms, tally charts, block diagrams and simple tables.

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

ask and answer questions about totalling and comparing categorical date.

# Year 3

### Number

*Number and place value *

count from 0 in multiples of 3, 4, 8, 50 and 100; find 10 or 100 more or less than a given number.

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

compare and order numbers up to 1000.

identify, represent and estimate numbers using different representations.

read and write numbers up to 1000 in numerals and words.

solve number problems and practical problems involving these ideas.

*Addition and subtraction*

add and subtract numbers mentally, including:-

a three digit number and ones

a three digit number and tens

a three digit number and hundreds

add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction estimate the answer to a calculation and use inverse operations to check answers.

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

*Multiplication and division*

recall and use multiplication and division facts for the 3, 4 and 6 multiplication tables.

show that division of two numbers can only be done in one order e.g 8/2 is not the same as 2/8

write and calculate mathematical statements for multiplication and division, using the multiplication tables that they know, including for two digit numbers times one digit numbers, using mental and progressing to formal written methods.

solve problems, including missing number problems, involving multiplication and division, including integer scaling problems and correspondence problems eg. Adapt a recipe for more or less people

Multiply 2 digit and 3 digit numbers by a one digit number using formal written methods.

*Fractions *

count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal part5s and in dividing a one digit number by 10.

recognise, find and write fractions of a discrete set of objects; unit fractions and no unit fractions with small denominators.eg. 1/5 of 25 pencils by dividing the pencils into 5 pots.

recognise and use fractions as numbers; unit fractions and non unit fractions with small denominators.

begin to recognise other denominators; eg: 1/3, 1/7 and 1/9 etc.

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

add and subtract fractions with the same denominat or within one whole, eg: 5/7, + 1/7 = 8/7.

compare and order unit fractions, and fractions with the same denominators going across whole number, ie:1/4, 2/4, 3/4, 4/4, 1 1/4, etc. solve problems that involve all of the above.

fraction of a quantity.

### Measurement

measure, compare, add and subtract lengths (m/cm/mm), mass (kg/g), volume/capacity (l/ml).

measure the perimeter of simple 2D shapes.

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

tell and write the time from a 12 hour analogue clock.

estimate and read time with increasing accuracy to the nearest minute and five minutes; understand minutes, hours o’clock; use vocabulary such as am/pm, morning, afternoon, noon and midnight.

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

compare durations of events, for example to calculate the time taken by particular events or tasks.

### Geometry

*Properties of shapes *

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

recognise that angles are a property of shape or a description of a turn.

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

identify horizontal and vertical lines and pairs of perpendicular and parallel lines.

describe positions (co-ordinates) on a 2D grid in the 1st quadrant.

### Statistics

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

solve one step and two step questions such as “how ma ny more?” and “how many fewer?” using information presented in scaled bar charts and pictograms and tables.

# Year 4

### Number

*Number and place value *

count in multiples of 6, 7, 9, 25 and 1000.

find 1000 more or less than a given number.

count backwards through zero to include negative numbers.

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

order and compare numbers beyond 1000.

identify, represent and estimate numbers using different representations.

round any number to the nearest 10, 100 or 1000.

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

read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value.

*Addition and subtraction*

begin to recognise symbols and understand their meaning

add and subtract numbers with up to 4 digits

using the formal written methods or columnar addition and subtraction, where appropriate.

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

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

*Multiplication and division*

recall multiplication and division facts for multiplication tables up to 12 x 12.

use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers.

recognise and use factor pairs and communtativity in mental calculations.

solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems, such as n objects are connected to m objects.

divide numbers up to three digits by a one digit number using formal written methods of short division.

as above, but with remainders.

commence by dividing by 2 and 5. 1st steps 46 ÷2, where no “carrying”, then progress to 40 ÷2, 56 ÷2, 57 ÷2 etc

one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.

*Fractions *

recognise and show, using diagram, families of common equivalent fractions.

count up and down in hundredths; recognise that hundredths arise when dividing an object by a hundred and dividing tenths by ten.

solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number.

add and subtract fractions with the same denominator.

recognise and write decimal equivalents of any number of tenths or hundredths.

recognise and write decimal equivalents to 1/4, 1/2 and 3/4.

divide quantities (formal written) by a fraction; starting with 1/2, 1/5, 1/10, progressing onto 1/4, 1/3, 1/7 etc.

find the effect of dividing a one or two digit number by 10 and 100, identifying the value of digits in the answer as units, tenths and hundredths.

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

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

Division of whole quantities (formal methods), ½ of 36

Commence with ½ of, 1/5 of, 1/10 of and progress to 1/3 of, 1/7, of etc

Introduce 2/5, 2/10’s of a quantities, progress to 2/3’s

### Measurement

Volume practical comparisons of liquids and accurate measurements make practical comparisons in volume.

choose and use appropriate standard units to estimate and measure on scales/thermometers etc where there are different intervals of measurement

convert between different units of measure (eg: km to m, hour to minute).

measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres.

find the area of rectilinear shapes by counting squares

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

read, write and convert time between analogue and digital 12 and 24 hour clocks.

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

record and compare time in terms of seconds, minutes, hours and o’clock.

### Geometry

*Properties of shapes *

compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and size.

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

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

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

*Position and direction*

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

Plot specified points and draw sides of a given unit to the left/right and up/down.

### Statistics

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

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

# Year 5

### Number

*Number and place value *

read, write, order and compare numbers to at least 1,000,000, in numbers and words, and determine the value of each digit.

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

interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers 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 and subtraction*

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 and division*

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.

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 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.

use a decimal point in remainders.

multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000.

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.

*Fractions(including decimals and percentages) *

consolidate 2/5 of whole numbers etc. (2/5 of 1,005)

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 concert from one form to the other and write mathematical statements > 1 as a mixed number (eg: 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. (eg: 0.71 as 71/100)

recognise and use thousandths and relate them totenths, hundredths and decimal equivalents.

compare numbers with the same number of decimal places (up to two decimal places).

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.

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.

### Measurement

convert between different units of metric measure.

understand and use equivalences between metric units and common imperials 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 (cm²) and square metres (m²) and estimate the area of irregular shapes.

estimate volume and capacity, solve problems involving converting between units of time.

use all four operations to solve problems involving measure, musing decimal notation including scaling.

### Geometry

*Properties of shapes *

- identify 3D shapes, including cubes and other cuboids, from 2D 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 360º).

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

other multiples of 90º - 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*

- identify, describe and represent the position of a shape following a reflection or translation, musing the appropriate language, and know that the shape has not changed.

### Statistics

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

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

# Year 6

### Number

*Number and place value *

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*

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 up, as appropriate for the context.

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.

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, min the context of a problem, levels of accuracy

*Fractions(including decimals and percentages) *

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.

divide proper fractions by whole numbers.

associate a fraction with division and calculate decimal fraction equivalents for a simple fraction.

identify the value of each digit to three decimal places and multiply and divide numbers by 10, 10 and 1,000

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 up0 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.

### Ratio And Proportion

solve problems involving the relative size of two quantities where missing values can be found by using integer multiplication and division facts.

solve problems involving the calculation of percentages, such as 15% of 360 and the use of percentages for comparison.

solve problems involving similar shapes where the scale factor is known or can be found.

solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.

### Algebra

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.

### Geometry

*Properties of shapes *

draw 2D shapes using given dimensions and angles

recognise, describe and build simple 3D 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*

describe positions on the full co-ordinate grid (all four quadrants).

draw and translate simple shapes on the co-ordinate plane, and reflect them in the axes.

### Statistics

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

calculate and interpret the mean as an average.