National Curriculum for the teaching of Mathematics.

Place Value 
Addition/Subtraction 
Multiplication/Division 
Fractions/Decimals 
Year 1 
 Count to and across 100, forwards, backwards, from any number and recognise those numbers in numerals.  Count in 2s, 5s and tens.  Represent numbers as objects and on number line.  Understand 'equal to', 'more than', 'less than', 'fewer', 'most' and 'least'.  Read & write numbers in numerals and words from 1 to 20.  Understand '+' & '' and '='. 
 Identify 1 more/less.  Know number bonds and related subtraction facts to 20 e.g. 9+7=16; 167=9.  Add/Subtract 1digit and 2digit numbers to 20, including 0.  Solve 1step problems involving Addition/Subtraction using concrete objects and pictures.  Solve missing number problems e.g. 7 = c  9 
 Solve 1step problems involving multiplication/division using objects, pictures and arrays with support. 
 Use shapes, quantities and sets of objects to recognise and name:

Year 2 
 Count in 2s, 3s and 5s from 0.  Count in 10s from any number, forwards and backwards.  Recognise place value of each digit in 2digit numbers.  Compare and order numbers up to 100  Use the symbols <, > and = correctly.  Identify, estimate and represent numbers using different representations including number lines.  Read & write numbers in numerals and words from 1 to 100.  Recognise 0 as a placeholder. 
 Use place value and number facts to solve problems.  Recall and use addition and number facts to 20 fluently and derive and use related facts to 100 e.g. 3+7=10 so 30+70=100  Add/Subtract numbers using concrete objects, pictures and mentally including: TU+U, TU+T, TU+TU, U+U+U.  Show that addition of 2 numbers can be done in any order (commutative) and subtraction cannot.  Solve problems with Addition/Subtraction using concrete objects and pictures.  Recognise and use the inverse relationship between Addition/Subtraction and use to check calculations and solve missing number problems.  Partition numbers in different ways. e.g. 23=20+3 23=10+13 
 TIMES TABLES: 2, 5, 10.  Recognise odd and even numbers.  Write numbers sentences for 2, 5 and 10 times tables and their related division facts.  Show that multiplication of 2 numbers can be done in any order but division cannot.  Solve problems involving x/÷ using materials, arrays, repeated addition, mental methods and x/÷ facts. 
 Recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity.  Write simple fraction calculations. e.g. 1/2 of 6 = 3  Recognise the equivalence of 2/4 and 1/2.  Count in fractions to 10 e.g. 1, 1 ½, 2, 2 ½... 

Measures 
Money 
Time 
Year 1 
 Compare, describe and solve practical problems for length/height, weight/mass, capacity/volume and time.  Measure and begin to record length/height, weight/mass, capacity/volume and time. 
 Recognise and know the value of different denominations of coins and notes. 
 Sequence events in chronological order using language. e.g. before, after, next, today, etc.  Recognise and use language relating to days of the week, weeks, months and years.  Tell the time to the nearest hour & half past the hour & draw the hands on clock face. 
Year 2 
 Choose and use appropriate standard units to measure; length/height (m/cm); mass (kg/g); temperature (^{0}C); capacity (litres/ml).  Estimate all the above to the nearest appropriate unit, using equipment.  Compare and order lengths, mass, column/capacity and record the results using >, < and = 
 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 +/ of money  Calculate change to be given. 
 Compare and sequence intervals of time.  Tell and write the time to 5 minutes including quarter past/to the hour and draw the hands on a clock face to show these times.  Know the number of minutes in an hour & hours in a day. 
Shape 


Properties of Shape 
Angles 
Position & Direction 
Year 1 
 Recognise and name common 2d shapes e.g. Square, circle, triangle.  Recognise and name common 3d shapes e.g. Cube, cuboids, pyramids and sphere. 

 Describe position, direction and movement including whole, 1/2, 1/4 and 3/4 turns.  Relate ‘clockwise’ to the clock face.  Use vocabulary such as left, right, top, bottom, above, between, near to etc. 
Year 2 
 Identify and describe the properties of 2d shapes including:  number of sides  line symmetry in a vertical line.  Compare and sort 2d and 3d shapes and everyday objects.  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. e.g. circle on a cylinder  Read and write the names of shapes appropriate to their reading and speaking ability.  Draw lines and shapes using a ruler. 

 Order and arrange combinations of mathematical objects in patterns and sequences.  Use mathematical vocabulary to describe position, direction and movement including movement in a straight line.  Distinguish between rotation as a turn and in terms of right angles for 1/4, 1/2 and 3/4 turns.  Understand the terms clockwise & anticlockwise.  Use programmable robots, giving turning instructions in right angles. 
Data handling 


Drawing 
Interpreting 
Extracting 
Year 1 



Year 2 
 Construct simple pictograms, tally charts, block diagrams and tables.  Draw pictograms where one symbol represents multiple units. 
 Interpret simple pictograms, tally charts, block diagrams and tables in a variety of contexts. 
 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 data. 
Place Value 
Addition/Subtraction 
Multiplication/Division 
Fractions/Decimals 
 Count in 4s, 8s, 50s and 100s from 0.  Find 10 or 100 more or less than any number.  Recognise place value of each digit in 3digit numbers.  Compare and order numbers up to 1000.  Identify, estimate and represent numbers using different representations.  Read & write numbers in numerals and words up to 1000.  Recognise and read Roman numerals to 12 (I to XII) 
 Add and subtract numbers mentally including: HTU+U, HTU+T, HTU+H  Add/Subtract numbers with up to 3 digits using formal written methods of columnar addition and subtraction.  Estimate answers to calculations and use inverse operations to check answers.  Solve problems, including missing number problems using number facts, place value and more complex Addition/Subtraction.  Partition numbers in different ways e.g. 146=100+46 146=130+16 
 TIMES TABLES: 3, 4, 8.  Write number sentences for 3, 4 and 8 times tables and related division facts.  Use times tables to work out more complex calculations. e.g. 4x12x5 = (4x5)x12 = 20x12 = (2x12)x10= 24x10= 240  Progress to formal written method calculations of short multiplication/division.  Solve problems, including missing number problems, involving x/÷.  Solve problems of positive integer scaling and correspondence. i.e. n objects are connected to m objects. e.g. 3 hats, 4 coats, how many different outfits? 
 Count up and down in tenths.  Recognise that tenths arise from dividing an object into ten equal parts and dividing 1digit numbers or quantities by 10.  Compare and order unit fractions including on a number line going beyond 1.  Compare and order fractions with the same denominators.  Recognise, and show with diagrams, equivalent fractions with small denominators.  Recognise, find and write fractions of a discrete set of objects  unit fractions and nonunit fractions with small denominators.  Recognise and use fractions as numbers  unit fractions and nonunit fractions with small denominators.  Add and subtract fractions with the same denominator within a whole. e.g. 5/7 + 1/7 = 6/7  Solve problems using all fractions knowledge.  Understand the relation between unit fractions and division. 
 Count in 6s, 7s, 9s, 25s and 1000s.  Find 1000 more or less than any number.  Recognise place value of each digit in 4digit numbers.  Compare and order numbers beyond 1000.  Identify, estimate and represent numbers using different representations including measures.  Count backwards through 0 to include negative numbers.  Read Roman numerals to 100 (I to C) and know that over time the numeral system changed to include the concept of 0 and place value.  Round any number to the nearest 10, 100 or 1000. 
 Add and subtract numbers up to 4digits using formal written methods of columnar Addition/Subtraction.  Estimate and use inverse operations to check answers to calculations.  Solve Addition/Subtraction 2step problems in contexts.  Decide which operations and methods to use and why. 
 TIMES TABLES: Up to 12x12.  Use place value, known and derived facts to x/÷ mentally, including multiplying by 0 & 1, dividing by 1, multiplying 3 numbers together. 2x3=6 so 600÷3=200  Recognise and use factor pairs and commutativity in mental calculations. e.g. 39x7=(30x7)+(9x7) e.g. 2x3x4=(2x4)x4 and 2x(3x4)  Multiply 2digit and 3digit numbers by a 1digit number using formal written layout.  Solve problems involving multiplying and adding including using the distributive law to multiply 2digit numbers by 1digit.  Solve problems of integer scaling and correspondence i.e. n objects are connected to m objects. e.g. number of meal choices on a menu e.g. 3 cakes shared between 10 children. 
 Count up and down in hundredths.  Recognise that hundredths arise from dividing an object into one hundred equal parts, dividing by one hundred and dividing tenths by ten.  Recognise and show families of common equivalent fractions.  Simplify simple fractions e.g. 2/8=1/4  Solve problems involving increasingly harder fractions to calculate quantities, fractions to divide quantities, including nonunit fractions where the answer is a whole number.  Addition/Subtraction fractions with the same denominator including beyond 1.  Recognise and write decimal equivalents of any number of tenths or hundredths and 1/4, 1/2 and 3/4.  Find the effect of ÷ a 1 or 2digit number by 10 or 100, identifying the value of the digits in the answer as ones, tenths and hundredths.  Round decimals with 1dp to the nearest whole number.  Compare numbers with the same number of decimal places up to 2dp.  Solve simple measure and money problems involving fractions and decimals to 2dp. 
Measure 


Measures 
Money 
Time 
Year 3 
 Measure, compare, +/ lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml) including mixed units. e.g. 200g and 1kg  Measure the perimeter of simple 2d shapes 
 +/ amounts of money to give change using both £ & p in practical contexts. 
 Tell and write the time from an analogue clock to the nearest minute.  Read 12 hour & 24 hour clocks.  Record and compare time in terms of seconds, minutes and hours.  Use vocabulary such as o'clock, am/pm, morning, afternoon, noon, midnight.  Know the number of seconds in a minute & the number of days in each month, year & leap year.  Compare durations of events. 
Year 4 
 Convert between different units of measure.  Estimate, compare and calculate different measures including money in £ & p.  Measure and calculate the perimeter of a rectilinear figure (including squares) in cm & m.  Find the area of rectilinear shapes by counting squares.  Start to relate area to arrays. 

 Convert between different units of measure e.g. Hours to minutes.  Read, write and convert time between analogue and digital 12/24 hour.  Solve problems involving converting from hours to minutes, minutes to seconds, years to months and weeks to days. 
Shape 


Properties of Shape 
Angles 
Position & Direction 
Year 3 
 Draw 2d shapes.  Make 3d shapes using modelling materials.  Recognise 3d shapes in different orientations and describe them. 
 Recognise angles as a property of shape or a description of a turn.  Identify right angles.  Recognise that 2 right angles make 1/2 turn, 3 make 3/4 turn and 4 make a whole turn.  Identify whether angles are greater or less than a right angle. 
 Identify horizontal and vertical lines  Identify pairs of perpendicular and parallel lines. 
Year 4 
 Compare and classify geometric shapes including quadrilaterals and triangles based on 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. 
 Identify acute and obtuse angles.  Compare and order angles up to 180^{0}. 
 Describe positions on a 2d grid as coordinates in the 1st quadrant. e.g. (2,5)  Describe movements between positions as translations of a given unit to the left/right and up/down.  Plot specific points and draw sides to complete a given polygon.  Draw axes and label integer scales. 
Handling Data 


Drawing 
Interpreting 
Extracting 
Year 3 
 Present data using bar charts, pictograms and tables.  Use scales progressing in 2s, 5s and 10s.

 Interpret data using bar charts, pictograms and tables in a variety of contexts. 
 Solve 1 and 2 step questions e.g. How many more/fewer using information presented in scaled bar charts, pictograms and tables. 
Year 4 
 Present discrete and continuous data using appropriate graphical methods including bar charts and time graphs.  Use a greater range of scales. 
 Interpret 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. 