End of Year Expectations

Year 3

Year 4

Year 5

Year 6

Place Value:

Counting

Children will:

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

Children will:

• count in multiples of 6, 7, 9, 25 and 1000.
• Children will count backwards through zero to include negative numbers.

Children will:

• count forwards or backwards in steps of powers of 10 for any given number up to 1000000
• count forwards and backwards with positive and negative whole numbers, including through zero.

Place Value:

Represent

Children will:

• identify, represent and estimate numbers using different representations
• read and write numbers up to 1000 in numerals and in words

Children will:

• identify, represent and estimate numbers using different representations
• 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.

Children will:

• read, write (order and compare) numbers to at least 1000000 and determine the value of each digit
• read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

Children will:

• read, write (order and compare) numbers up to
• 10 000 000 and determine the value of each digit.

Place Value:

Use Place Value and Compare

Children will:

• recognise the place value of each digit in a three-digit number (hundreds, tens, ones)
• compare and order numbers up to 1000

Children will:

• find 1000 more or less than a given number
• recognise the place value of each digit in a four-digit number (thousands, hundreds, tens and ones)
• order and compare numbers beyond 1000

Children will:

• (read, write) order and compare numbers up to

1 000 000 and determine the value of each digit.

Children will:

• (read, write) order and compare numbers up to

10 000 000 and determine the value of each digit.

Place Value:

Problems and Rounding

Children will:

• solve number problems and practical problems involving these ideas.

Children will:

• 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.

Children will:

• Interpret negative numbers in context.
• Round any number up to
• 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000.
• solve number problems and practical problems that involve all of the above.

Children will:

• 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 and Subtraction: Recall, Represent, Use

Children will:

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

Children will:

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

Children will:

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

Addition and Subtraction:

Calculations

Children will:

• 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.

Children will:

• add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate.

Children will:

• add and subtract whole numbers with more than 4 digits, including formal written methods (columnar addition and subtraction)
• add and subtract numbers mentally with increasingly large numbers.

Children will:

• perform mental calculations, including with mixed operations and large numbers.
• use their knowledge of the order of operations to carry out calculations involving the four operations.

Addition and Subtraction:

Solve Problems

Children will:

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

Children will:

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

Children will:

• 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 and a combination of these, including understanding the meaning of the equals sign.

Children will:

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

Multiplication and Division:

Recall, Represent, Use

Children will:

• recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables.

Children will:

• 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 commutativity in mental calculations.

Children will:

• identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.
• know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers.
• establish whether a number up to 100 is a prime and recall prime numbers up to 19.
• recognise and use square numbers and cube numbers, and the notation for squared and cubed.

Children will:

• identify common factors, common multiples and prime numbers.
• use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

Multiplication and Division:

Calculations

Children will:

• 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.

Children will:

• multiply two-digit and three-digit numbers by a one-digit number using formal written layout.

Children will:

• 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.

Children will:

• multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication.
• divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context.
• divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context/
• perform mental calculations, including with mixed operations and large numbers.

Multiplication and Division:

Solve Problems

Children will:

• solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects and connected to m objects.

Children will:

• 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 and connected to m objects.

Children will:

• solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes.
• solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.

Children will:

• solve problems involving addition, subtraction, multiplication and division.

Multiplication:

Combined Operations

Children will:

• solve problems involving addition, subtraction, multiplication and division and a combination of these including understanding the meaning of the equals sign.

Children will:

• use their knowledge of the order of operations to carry out calculations involving the four operations.

Fractions:

Recognise and Write

Children will:

• count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10.
• recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators.
• recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators.

Children will:

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

Children will:

• 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.

Fractions:

Compare

Children will:

• recognise and show, using diagrams, equivalent fractions with small denominators.
• compare and order unit fractions, and fractions with the same denominators.

Children will:

• recognise and show, using diagrams, families of common equivalent fractions.

Children will:

• compare and order fractions whose denominators are all multiples of the same number.

Children will:

• use common factors to simplify fractions; use common multiples to express fractions in the same denomination.
• compare and order fractions, including fractions >1.

Fractions:

Calculations

Children will:

• add and subtract fractions with the same denominator within one whole.

Children will:

• add and subtract fractions with the same denominator.

Children will:

• add and subtract fractions with the same denominator and denominators that are multiples of the same number.
• multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams.

Children will:

• 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.

Fractions:

Solve Problems

Children will:

• solve problems that involve all of the above.

Children will:

• 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.

Decimals: Recognise and Write

Children will:

• recognise and write decimal equivalents of any number of tenths or hundredths.
• recognise and write decimal equivalents to ¼ ½ ¾

Children will:

• read and write decimal numbers as fractions.
• recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents.

Children will:

• identify the value of each digit in numbers given to three decimal places.

Decimals:

Compare

Children will:

• round decimals with one decimal place to the nearest whole number.
• compare numbers with the same number of decimal places up to two decimal places.

Children will:

• 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.

Decimals:

Calculations and Problems

Children will:

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

Children will:

• solve problems involving number up to three decimal places.

Children will:

• multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places.
• multiply one-digit numbers with up to two decimal places by whole numbers.
• use written division methods in cases where the answer has up to two decimal places.
• solve problems which require answers to be rounded to specified degrees of accuracy.

Fractions, Decimals and Percentages

Children will:

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

Children will:

• recognise the per cent symbol (%) and understand that per cent related to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal.
• solve problems which require knowing percentage and decimal equivalents of  ½, ¼, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25.

Children will:

• associate a fraction with division and calculate decimal fraction equivalents for a simple fraction.
• recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.

Ratio and Proportion

Children will:

• 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 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

Children will:

• solve problems, including missing number problems.

Children will:

• use simple formulae.
• generate and describe linear number sequences.
• express missing number problems algebraically.
• Find

Year 3

Year 4

Year 5

Year 6

Measurement:

Using Measures

Children will:

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

Children will:

• convert between different units of measure (eg. Kilometre to metre and hour to minute)
• estimate, compare and calculate different measures.

Children will:

• convert between different units of metric measure.
• understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints.
• use all four operations to solve problems involving measure using decimal notation, including scaling.

Children will:

• 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.

Measurement:

Money

Children will:

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

Children will:

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

Children will:

• use all four operations to solve problems involving measure.

Measurement:

Time

Children will:

• tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12 hour and 24 hour clocks.
• estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes and hours; use vocabulary such as o’clock, 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.

Children will:

• 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.

Children will:

• solve problems involving converting between units of time.

Children will:

• use, read, write and convert between standard units, converting measurements of time from a smaller unit of measure to a larger unit, and vice versa.

Measurement:

Perimeter, Area and Volume

Children will:

• measure the perimeter of the simple 2-D shapes.

Children will:

• measure and calculate the perimeter of a rectilinear figure in centimetres and metres.
• find the area of rectilinear shapes by counting squares.

Children will:

• measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres.
• calculate and compare the area of rectangles and including using standard units, square centimetres and square metres and estimate the area of irregular shapes.
• estimate volume and capacity.

Children will:

• recognise that shapes with the same areas can have different perimeters and vice versa.
• recognise when it is possible to use formulae for area and volume of shapes.
• calculate the area of parallelograms and triangles.
• calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres and cubic metres, and extending to other units.

Year 3

Year 4

Year 5

Year 6

Geometry:

2-D shapes

Children will:

• draw 2-D shapes

Children will:

• compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes.
• identify lines of symmetry in 2-D shapes presented in different orientations.

Children will:

• distinguish between regular and irregular polygons based on reasoning about equal sides and angles.
• use the properties of rectangles to deduce related facts and find the missing lengths and angles.

Children will:

• draw 2-D shapes using given dimensions and angles.
• compare and classify geometric shapes based on their properties and sizes.
• Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius.

Geometry:

3-D shapes

Children will:

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

Children will:

• identify 3-D shapes, including cubes and other cuboids, from 2-D representations.

Children will:

• recognise, describe ad build simple 3-D shapes, including making nets.

Geometry:

Angles and Lines

Children will:

• recognise angles as a property of shape of 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.

Children will:

• identify acute and obtuse angles and compare and order angles up to two right angles by size.
• identify lines of symmetry in 2-D shapes presented in different orientations.
• complete a simple symmetric figure with respect to a specific line of symmetry.

Children will:

• know angles are measure in degrees: estimate and compare acute, obtuse and reflex angles.
• draw given angles, and measure them in degrees.
• identify:

• angles at a point and one whole turn.
• angles at a point on a straight line and ½ a turn.
• other multiples of 90 degrees.

Children will:

• find unknown angles in any triangles, quadrilaterals, and regular polygons.
• recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.

Geometry:

Position and Direction

Children will:

• describe positions on a 2-D grid as coordinates in the first quadrant.
• describes movements between positions as translations of a given unit to the left/right and up/down.
• plot specified points and draw sides to complete a given polygon.

Children will:

• 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.

Children will:

• describe positions on the full coordinate grid.
• draw and translate simple shapes on the coordinate plane, and reflect them in the axes.

Year 3

Year 4

Year 5

Year 6

Statistics:

Present and Interpret

Children will:

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

Children will:

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

Children will:

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

Children will:

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

Statistics:

Solve Problems

Children will:

• solve one-step and two-step questions using information presented in scared bar charts and pictograms and tables.

Children will:

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

Children will:

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

Children will:

• calculate and interpret the mean as an average.