Dare to Discover
Strands 
EYFS 
Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
Year 6 
Place Value 
 Recognise some numbers of personal significance.  Read and write numerals 1 to 20.  Count objects to 20.  Begin to count backwards.  Say and select the correct numeral to represent the total number of objects counted up to 20.  Count up to 10 objects from a larger group.  Count an irregular arrangement of up to 20 objects. Estimate how many objects you can see and check by counting.  Represent numbers using objects, including Numicon and Base 10. 
 Count to and across 100, forwards and backwards, from any given number.  Count, read and write numbers to 100 in numerals.  Represent numbers using objects and pictures eg Dienes and Numicon  Recognise odd and even numbers.

 Read and write numbers to at least 100 in numerals and in words.  Recognise the place value of each digit in a two digit number (tens, ones)  Identify, represent and estimate numbers, including on a number line.  Compare and order numbers from 0 up to 100; use <, > and = signs.  Count in tens from any number, forward and backward.

 Read, write, identify, represent and estimate numbers up to 1000.  Find 10 or 100 more or less than a given number.  Recognise the place value of each digit in a threedigit number.  Compare and order numbers up to 1000.

 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.  Identify, represent and estimate numbers using different representations.  Round any number to the nearest 10, 100 or 1000.  Count backwards through zero to include negative numbers.  Read Roman numerals to 100 (I to C). 
 Read, write, order and compare numbers to at least 1000000 and say the value of each digit.  Count forwards or backwards in steps of powers of 10 from any number.  Multiply and divide whole numbers by 10, 100 and 1000.  Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers including through zero.  Round any number up to 1000000 to the nearest 10, 100, 1000, 10000 and 100000  Read Roman numerals to 1000 (M) and recognise years written in Roman numerals. 
 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.

Addition and Subtraction (see calculation policy, ‘Progression in Calculation’, for detailed teaching sequences) 
 Use the words ‘more’ or ‘fewer’ to compare two sets of objects.  Find the total number of objects in two groups by counting all of them.  Say the number that is one more than a given number.  Find one more or one less from a group of up to 20 objects.  Begin to use the vocabulary involved in adding and subtracting.  Add and subtract two single digit numbers, using concrete objects.  Count on or back to find the solution to additions and subtractions within 20.

 Identify the number one more or less than a given number.  Represent and use number bonds and related subtraction facts within 20.  Read, write and interpret mathematical statements involving addition, subtraction and equals signs.  Add and subtract one digit numbers to 20, including 0.  Solve one step problems and missing number problems, using concrete resources and pictures.

 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.  Show that the addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot.  Solve problems with addition and subtraction.  Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems. 
 Add and subtract numbers with up to three digits mentally.  Add and subtract numbers with up to three digits, using column method.  Estimate the answer to a calculation and use inverse operations to check answers. 
 Add and subtract numbers mentally with increasingly large numbers.  Add and subtract numbers with up to 4 digits using the formal written methods of 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. 
 Add and subtract numbers mentally with increasingly large numbers.  Add and subtract whole numbers with more than 4 digits using the column method.  Use rounding to check answers to calculations.  Decide which operations and methods to use and why to solve multistep problems. 
 Solve addition and subtraction multi step problems in contexts, deciding which operations and methods to use and why.  Use their knowledge of the order of operations.  Use estimation to check answers to calculations and determine in the context of a problem, an appropriate degree of accuracy. 
Multiplication and Division (see calculation policy, ‘Progression in Calculation’, for detailed teaching sequences) 
 Share objects out equally.  Solve problems including doubling and halving. 
 Count in multiples of twos, fives and tens.  Use grouping to solve one step multiplication and division problems using concrete resources and pictures. 
 Count in threes.  Recall and use multiplication and division facts for the 2, 5 and 10 times tables.  Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (x), division (÷) and equals (=) sign.  Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods and multiplication and division facts.  Show that the multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot.

 Count from 0 in multiples of 4, 8, 50 and 100.  Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables.  Write and calculate mathematical statements for multiplication and division using the multiplication tables they know, including for twodigit numbers times onedigit numbers.  Solve problems, including missing number problems, involving multiplication and division. 
 Count in multiples of 6, 7, 9, 25 and 1000.  Recall and use multiplication and division facts for multiplication tables up to 12 × 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.  Multiply two digit and three digit numbers by a one digit number using formal written layout.  Divide three digit numbers by one digit numbers using short division.

 Multiply and divide numbers mentally drawing upon known facts.  Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.  Recognise and use square numbers and cube 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 2 digit numbers.  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.  Understand the use of the equals sign and be able to solve missing number problems. 
 Multiply multidigit number up to 4 digits by a 2digit number using the formal written method of long multiplication.  Divide numbers up to 4 digits by 2digit whole number using the formal written method of short and long division, and interpret remainders as whole number remainders, fractions, or by rounding as appropriate for the context.  Identify common factors, common multiples and prime numbers.  Scale quantities up and down using whole numbers.

Fractions, Decimals (from Y4) and Percentages (from Y5) 
 Recognise, find and name a half as one of two equal parts of an object, shape or quantity.

 Recognise, find, name and write fractions 1/3, ¼ , 2/4 and 3/4 of a length, shape, set of objects or quantity.  Write simple fractions for example, ½ of 6 = 3.  Recognise the equivalence of 2/4 and ½. 
 Count up and down in tenths; know the value of a tenth.  Recognise and use fractions as numbers.  Recognise, find and write fractions of a discrete set of objects.  Recognise and show, using diagrams, equivalent fractions with small denominators.  Compare and order unit fractions, and fractions with the same denominators.  Add and subtract fractions with the same denominator within one whole. 
 Recognise and show, using diagrams, families of common equivalent fractions.  Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.  Add and subtract fractions with the same denominator.  Recognise and write decimal equivalents of any number of tenths or hundredths.  Find the effect of dividing a one or two digit number by 10 or 100, identifying the value of the digits in the answer as ones, tenths and hundredths.  Compare numbers with the same number of decimal places up to two decimal places.  Round decimals with one decimal place to the nearest whole number.  Recognise and write decimal equivalents to ¼, ½ and ¾.

 Compare and order fractions whose denominators are multiples of the same number.  Identify, name and write equivalent fractions of a given fraction, represented visually.  Recognise mixed numbers and improper fractions and convert from one form to the other.  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.  Read and write decimal numbers as fractions.  Read, write, order and compare numbers with up to three decimal places.  Round decimals with two decimal places to the nearest whole number and to one decimal place.  Recognise the per cent symbol (%) and its meaning.

 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 denominations 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.  Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.  Identify the value of each digit in numbers given to 3 decimal places and multiply numbers by 10, 100 and 1,000 giving answers up to 3 decimal places.  Multiply onedigit numbers with up to 2 decimal places by whole numbers.


Geometry 
 Use mathematical names for 3D and 2D shapes.  Select a named shape.  Describe position using terms such as ‘behind’ or ‘next to’  Use familiar objects to create and copy patterns and build models.  Explore characteristics of everyday objects and use mathematical language to describe them. 
 Recognise and name common 2D shapes.  Recognise and name common 3D shapes.  Describe position, direction and movement, including whole, half, quarter and three quarter turns. 
 Identify and describe the properties of 2D shapes, including the number of sides and symmetry.  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.  Compare and sort common 2D and 3D shapes and everyday objects.  Use mathematical vocabulary to describe position, direction and movement including clockwise and anticlockwise.  Order and arrange combinations of mathematical objects in patterns and sequences. 
 Recognise angles as a property of shape or a description of a turn.  Use knowledge of right angles, to estimate other angles.  Identify horizontal and vertical lines and pairs of perpendicular and parallel lines.  Draw 2D shapes and make 3 D shapes using modelling materials.  Recognise 3D shapes in different orientations and describe them. 
 Identify acute and obtuse angles and compare and order angles up to two right angles by size.  Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes.  Identify lines of symmetry in 2D shapes presented in different orientations.  Complete a simple symmetric figure with respect to a specific line of symmetry.  Describe positions on a 2D grid as coordinates in the first quadrant.  Plot specified points and draw sides to complete a given polygon.  Describe movements between positions as translations of a given unit to the left/ right and up/ down. 
 Identify 3D shapes from 2D representations.  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.  Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles.  Draw given angles, and measure them in degrees.  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. 
 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.  Draw 2 D shapes using given dimensions and angles.  Compare and classify geometric shapes based on their properties and sizes and 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. 
Measurement 
Measures  Use everyday language to talk about size, weight, capacity and distance.  Order a set of items by length or height.  Order a set of items by weight or capacity. Time  Use everyday language related to time.  Measure short periods of time. Money  Use everyday language related to money.

Measures  Measure and begin to record lengths and heights.  Measure and begin to record mass/weight, capacity and volume.  Compare, describe and solve practical problems for: lengths, heights, mass/ capacity and volume. Time  Sequence events in chronological order using appropriate language.  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.  Compare, describe and solve practical problems for time [for example, quicker, slower, earlier, later]  Measure and begin to record time (hours, minutes, seconds) Money  Recognise and know the value of different denominations of coins and notes.

Measures  Choose and use appropriate standard units to estimate and measure: length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml).  Compare and order: lengths, mass, volume/capacity and record the results using >, < and =. Time  Tell and write the time to five minutes.  Know the number of minutes in an hour and the number of hours in a day. Money  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, including giving change.

Measures  Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml).  Measure the perimeter of simple 2D shapes. Time  Tell and write the time from an analogue clock, including using Roman numerals from I to XII and 12hour and 24hour clocks.  Estimate and read time with increasing accuracy to the nearest minute.  Use vocabulary such as o’clock, a.m./p.m., 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. Money  Add and subtract amounts of money to give change, using both £ and p in practical contexts. 
Measures  Measure and calculate the perimeter of a rectilinear figure in centimetres and metres  Convert between different units of measure.  Find the area of rectilinear shapes by counting squares. Time  Read, write and convert time between analogue and digital 12 and 24hour clocks.  Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days. Money Solve money problems involving fractions and decimals to two decimal places. 
Measures  Measure and calculate the perimeter of composite rectilinear shapes in cm and m.  Calculate and compare the area of rectangles and estimate the area of irregular shapes.  Convert between different units of metric measure [for example, km and m; cm and m; cm and mm; g and kg; l and ml]  Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints.  Estimate volume and capacity. Time  Solve problems involving converting between units of time. Money (included in calculations of four operations) 
 Use, read, write and convert between standard units of measure.  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 cm3 , m3 and extending to other units (mm3 , km3)  Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius. 
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, sorting the categories by quantity and totalling. 
 Interpret and present data using bar charts, pictograms and tables.  Solve onestep and twostep using information presented in scaled bar charts and pictograms and tables. 
 Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs.  Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs. 
 Solve comparison, sum and difference problems using information presented in a line graph.  Complete, read and interpret information in tables including timetables. 
 Interpret and construct pie charts and line graphs and use these to solve problems.  Calculate the mean as an average. 
Algebra 





 Describe simple linear number sequences.  Solve missing number problems expressed algebraically.

 Use simple formulae.  Generate and describe linear number sequences.  Express missing number problems algebraically.  Find pairs of numbers that satisfy an equation with two unknowns.  Enumerate possibilities of combinations of two variables. 