National Curriculum for the teaching of Mathematics.
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Place Value |
Addition/Subtraction |
Multiplication/Division |
Fractions/Decimals |
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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; 16-7=9. - Add/Subtract 1-digit and 2-digit numbers to 20, including 0. - Solve 1-step problems involving Addition/Subtraction using concrete objects and pictures. - Solve missing number problems e.g. 7 = c - 9 |
- Solve 1-step problems involving multiplication/division using objects, pictures and arrays with support. |
- Use shapes, quantities and sets of objects to recognise and name:
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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 2-digit 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... |
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Measures |
Money |
Time |
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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. |
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Year 2 |
- Choose and use appropriate standard units to measure; length/height (m/cm); mass (kg/g); temperature (0C); 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. |
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Shape |
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Properties of Shape |
Angles |
Position & Direction |
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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. |
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- 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. |
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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. |
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- 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 & anti-clockwise. - Use programmable robots, giving turning instructions in right angles. |
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Data handling |
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Drawing |
Interpreting |
Extracting |
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Year 1 |
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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. |
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Place Value |
Addition/Subtraction |
Multiplication/Division |
Fractions/Decimals |
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- 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 3-digit 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 1-digit 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 non-unit fractions with small denominators. - Recognise and use fractions as numbers - unit fractions and non-unit 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. |
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- Count in 6s, 7s, 9s, 25s and 1000s. - Find 1000 more or less than any number. - Recognise place value of each digit in 4-digit 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 4-digits using formal written methods of columnar Addition/Subtraction. - Estimate and use inverse operations to check answers to calculations. - Solve Addition/Subtraction 2-step 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 2-digit and 3-digit numbers by a 1-digit number using formal written layout. - Solve problems involving multiplying and adding including using the distributive law to multiply 2-digit numbers by 1-digit. - 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 non-unit 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 2-digit 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. |
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Measure |
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Measures |
Money |
Time |
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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. |
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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. |
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- 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. |
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Shape |
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Properties of Shape |
Angles |
Position & Direction |
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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. |
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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 1800. |
- 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. |
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Handling Data |
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Drawing |
Interpreting |
Extracting |
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Year 3 |
- Present data using bar charts, pictograms and tables. - Use scales progressing in 2s, 5s and 10s.
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- 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. |
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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. |