Key Skills
EYFS Year 1 Year 2
Counting Count reliably with numbers to 20 and place them in order. Count an irregular amount of objects. Identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least.
Subitise up to 10 (recognise number patterns without counting) Composition of numbers up to 10
Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number. www.ictgames.com/numberSquare/index.html Count, read and write numbers to 100 in numerals. www.ictgames.com/sharkNumbers/appDetails/sharkNumbersDemo_online/index.html Count in multiples of twos, fives and tens. www.ictgames.com/saucerSorter.html Represent and use number bonds and related subtraction facts within 20. www.topmarks.co.uk/Flash.aspx?b=maths/addition Add and subtract one-digit and two-digit numbers to 20, including zero .
Count from 0 in multiples of 4, 8, 50 and 100; finding 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 100. Identify, represent and estimate numbers using different representations. Read and write numbers to at least 100 in numerals and in words.
www.ictgames.com/numberSquare/index.html www.ictgames.com/arrowCards_revised_v6.html
Know the place value of a 2- digit number (tens and ones).
www.ictgames.com/partition.html www.topmarks.co.uk/place-value/place-value-charts Count in steps of 2, 3, and 5 from 0 from any number, forward and backward.
www.ictgames.com/fairyfog_random.html Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100.
www.topmarks.co.uk/maths-games/hit-the-button Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and ones.
Lead and write numbers from 1 to 20 in numerals and word. Count, recognise and order numbers to twenty. www.topmarks.co.uk/maths- games/3-5-years/ordering-and- sequencing
Identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least. Partition numbers into two or more parts. Add two or more of these parts in any order (commutativity). Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: two two-digit numbers. Add or subtract by counting on or back in ones BUT knowing the order of sums can help add or subtract by calculation.
Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward.
Can say which number is one more or one less than a given number.
Identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least
Comparing Numbers Identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least.
+ and – = means ‘equivalent’, ‘the same as’ or ‘balances’. Understanding this before other symbols are introduced helps children make sense of equations written with = in different positions. We can compare numbers using > or <
Compare and order numbers from 0 up to 100; use and = signs. Compare and order numbers from 0 up to 100; use <, > and = signs Identify, represent and estimate numbers using different representations, including the number line. Compare and order numbers from 0 up to 100 use and = signs
Identifying, representing and estimating numbers Select the correct numeral to represent numbers to 20. Estimate how many objects they can see and checks by counting.
Identify and represent numbers using objects and pictorial representations including the number line.
Identify, represent and estimate numbers using different representations, including the number line.
Reading and writing numbers (including Roman Numerals) Read and write numbers from 1 to 20 in numerals and words.
Read and write numbers from 1 to 100 in numerals and words. Read and write numbers to at least 100 in numerals and in words.
Understanding Place Value Relating numbers to 5 and 10 can add by calculating, using bonds. Form digit 0-9 correctly. Say one more and one less than numbers to twenty. Add and subtract 2 single digit
numbers.
Use a whole-part model (Dienes) to picture addition and subtraction. Relating numbers to 5 and 20 can help us to add by calculating, using bonds. Understand number system is base 10. The tens numbers must be seen as ten and one, ten and two and so on. The position (place) of a digit in a number determines its value. Partition numbers into two or more parts. Add two or more of these parts in any order (commutativity). Add or subtract by counting on or back in ones BUT knowing the order of sums can help add or subtract by calculation.
Recognise the place value of each digit in a two-digit number (tens, ones) Count in steps of 2, 3, and 5 from 0, and count in tens from any number, forward or backward. Recognise the place value of each digit 2-digit,10, 1s. Recognise the place value of each digit in a 2- digit number (tens, ones). Identify, represent and estimate numbers using. Use a whole-part model (Dienes) to picture addition and subtraction. Relating numbers to 5 and 100 can help us to add by calculating, using bonds.
Problem Solving Begin to identify own mathematical problems based on own interests and fascinations.
Use drawings, diagrams, or symbols to represent numbers. Write numbers up to 100 using numerals and words, learning by playing matching games. Compare and order numbers, that one number is bigger or smaller than another: Use more than (>) and less than (<) symbols when comparing numbers e.g. can write 32 < 76 or 76 > 32. Estimate how many there are before counting.
Partition numbers in different ways Reinforce understanding of number, finding everyday opportunities to use known number facts to solve problems.
Use place value and number facts to solve problems. Use more than (>) and less than (<) symbols when comparing numbers e.g. can write 32 < 76 or 76 > 32. Estimate how many there are before counting.
Partition numbers in different ways Reinforce understanding of number, finding everyday opportunities to use known number facts to solve problems.
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Greater depth-GLD Greater depth Greater depth Estimate a number of objects and check quantities by counting up to 20. Solve practical problems that involve combining groups of 2, 5 or 10.
Count reliably well beyond 100. Count on and back in 3’s from any given number to beyond 100. Say the number that is ten more or ten less than a number to 100. Know the signs < and >.
Reason with numbers showing an understanding of place value. Read and write numbers to at least 100 in numerals and in words. Use place value and number facts to solve problems
Key vocabulary Key vocabulary Key vocabulary Zero, number, one, two, three….to twenty and beyond, count, count on, count back, is the same as, more, less, pattern, digit, the same number as, more, larger, bigger, greater, fewer, smaller, less, fewest, smallest, least, most, biggest, largest, greatest, one more, one less, compare, order, size, first, second, third…twentieth, last, before, after, next, between. Guess, estimate, nearly, close, about the same as, just over, just under, too many, too few, enough, not enough.
Numeral, twenty one, twenty two…one hundred, forwards, backwards, equal to, equivalent to, most, least, many, multiple of, half way between, above, below, roughly, equal to, more than, less than (fewer), most, least
Two hundred….one thousand, threes, fours, tally, sequence, continue, predict, rule, >greater than,
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KEY SKILLS
Year 3 Year 4 Year 5 Year 6
Mental Calculation Add and subtract numbers mentally, including: * a three-digit number and ones * a three-digit number and tens * a three-digit number and hundreds Multiply by 50 by multiplying by 100 and halving e.g. 8 x 50= 8 x 100 divided by 2. Children must rapidly recall the related division facts as well. For example, for 4 x 6 = 24, children should know 24 ÷ 6 = 4 and 24 ÷ 4 = 6.
Know the value of digit and explore place value through partitioning. Solve addition and subtraction two-step problems in contexts. Count in multiples of 6, 7, 9, 25 and 1000. Count backwards through zero to include negative numbers and solve number and practical problems that involve all of the above and with increasingly large positive numbers Addition and subtraction of multiples of 10 (e.g. 70 + 30 = 100, 50 + 60 = 110, 20 + 40 = 60); Addition and subtraction of multiples of 100 where the answer is 1,000 or less (e.g. 300+400=700, 400+600=1,000); Double and halves of multiples of 10+100 (e.g. double 60=120, half 50=25); Multiplying two-digit numbers by 10 (e.g. 24x10=240); halves of any even number to 100 (e.g. half of 22=11); Multiplying any two and three-digit number by 10 and 100 (e.g. 24x100=2400.
Interpret negative numbers in context, count forwards and backwards with positive and negative whole number through zero. Understand place value and its overall value, as well as its position relative to other numbers, including tenths and hundredths. Add and subtract numbers mentally with increasingly large numbers. Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers. Addition and subtraction of multiples of 10 (e.g.70+30=100, 50+60=110, 20+40=60; Addition and subtraction of multiples of 100 (e.g.300+400=700, 400+600=1,000, 800+500=1,300); Addition and subtraction of multiples of 1000 (e.g. 3000+4000=7000).
Use negative numbers in context, and calculate intervals across zero Understand negative numbers as positions on a number line. Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals (reciprocals will be described in the form 1 and not -1. Counting on or back in tens from any number– e.g. working out 27 + 60= ? by counting on in tens from 27. Counting on or back in fives from any multiple of 5– e.g. 35+15=? by counting on in steps of 5 from 35. Counting on or back in hundreds from any number e.g. 570 + 300= ? by counting on in hundreds from 570. Counting on or back in tenths and/or hundredths- e.g. 3.2 + 0.6 = ? by counting on in tenths. 1.7 + 0.55=? by counting on in tenths and hundredths.
Read and write numbers up to 1000 in numerals and in words. Solve number problems and practical problems involving these ideas. Addition and subtraction of multiples of 10 where the answer is between 0 and 100 (e.g. 70+30=100, 20+40=60);
Multiply a 2-digit number by a single digit by partitioning– e.g. 26 x 3 = 20 x 3 + 6 x 3. Multiply a decimal number with up to 2 decimal places by a single digit by partitioning– e.g. 3.42 x 4 = 3 x 4 + 0.4 x 4 + 0.02 x 4. Find the doubles and halves of any two-digit number and any multiple of 10 or 100– e.g. half 680 or double 73.
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. Add and subtract whole numbers with more than 4 digits, including using efficient written methods (columnar addition and subtraction).
Use their knowledge of the order of operations to carry out calculations involving the four operations. Calculations with whole numbers which do not involve crossing place value boundaries- e.g. 23 + 45= ? by 40 + 5 +20 + 3 or 40 + 23 + 5. Calculations with whole numbers which involves crossing place value
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Double and halves of multiples of 10 to 100 (e.g. double 60=120); Multiplying two-digit number by 10 (e.g. 24x10=240).
Multiply and divide by 4 by doubling/halving twice and 8 by doubling/halving again. – e.g. 34 x 4 = 34 x 2 x 2. Find the doubles and halves of any number up to 10,000 by partitioning – e.g. half of 32,202 by halving 3,000, 2000, 200 and 2. Mentally find fractions of numbers in the 2,3,4,5 and 10 times table using known multiplication and division facts– e.g. 3/5 of 45 by 45 ÷ 5 x 3. Recall percentage equivalents to ½, 1/3, , , 1/10 and 1/100 – e.g. ¼ = 25%. Find 10% or multiples of 10% of whole numbers and quantities- e.g. 30% of 50 by 50 ÷ 10 x 3. Mentally find 50% by halving and 25% by dividing by 4 or 2 of numbers and quantities- e.g. 25% of 150 by 150 ÷ 4. Year 4 mental maths with only 38 new multiplications (and related division) facts left that children need to develop the ability to rapidly recall.
Double and halves of multiples of 10 to 100 (e.g. double 60=120, half 50=25); quadruples (x4) of all numbers to 10 (e.g. 6x4=24); Multiplying two-digit number by 10 (e.g. 24x10=240); Halves of any number to 100 (e.g. half of 22=11, half of 51=25.5); Multiplying and dividing any number of 10 and 100 (e.g. 24x100=24000, 45 divided 100=0.45, 3.4x10=34); Squares of all number up to 12; and cubes of 2,3,4 and 5. Near doubles to numbers under 20 e.g. 18 + 16 is double 18 and subtract 2 or double 16 and add 2. Near doubles to multiples of 10 e.g. 60 + 70 is double 60 and add 10 or double 70 and subtract 10 or 75 + 76 is double 76 and subtract 1 or double 75 and add 1. Decimal near doubles to whole numbers e.g. 2.5 + 2.6 is double 2.5 add 0.1 or double 2.6 subtract 0.1. Divide a multiple of 25 by 25 dividing by 100 then multiplying by 4 (by doubling and doubling again) e.g. 350 ÷ 25 = 350 ÷ 100 x 2 x2. Divide a multiple of 50 by 50 by dividing by 100 then doubling- e.g. 450 ÷ 50= 450 ÷ 10 x 2.
boundaries e.g. 49 – 32= ? by 49 – 9 – 23 or 57 + 34=? by 57 + 3 + 31. Calculations with decimal numbers which do not involve crossing place value boundaries 5.6 + 3.7= ? by 5.6 + 3 +0.7 or 540 + 380= ? by 540 + 300 + 80 or 540 + 360 + 20. Calculations with decimal numbers which involve crossing place value boundaries e.g. 1.4 + 1.7= ? by 1.4 + 0.6 + 1.1 and 0.8 + 0.35= ? by 0.8 + 0.2 + 0.15. Compensating and adjusting to 10– e.g. 34 + 9=? by 34 + 10 – 1 or 34 – 11= ? by 34 – 100 – 1 = ?. Compensating and adjusting multiples of 10 e.g. 38 + 68= ? by 38 + 70 – 2 or 45 – 29 = 45 – 30 + 1. Compensating and adjusting multiples of 10 or 100 e.g. 138 + 69= ? by 138 + 70 – 1 or 299 – 48 = 300 – 48 – 1. Compensating and adjusting multiples with decimals e.g 2 ½ + 1 ¾ by 2½ + 2 – ¼ or 5.7 + 3.9 by 5.7 + 4.0 – 0.1.
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Written Methods Add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction. Solve problems involving all four operations including missing number problems, using number facts and place value. Focus on calculations rather than counting on in ones. Relate numbers to their parts (partitioning) and to multiples of 10 to bridge multiples of ten. Understand the concept of ‘difference’ between numbers.
Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate. Solve addition and subtraction two-step problems in contexts.
Accurately use formal written methods: column addition, column subtraction, formal written multiplication, short division, chunking, long division and apply this knowledge to solve problems. Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction). Solve addition and subtraction multi- step problems in contexts, deciding which operations and methods to use and why. Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy. Solve problems involving numbers up to three decimal places. Number of digits in a number does not necessarily make it larger or smaller e.g. 0.35 < 0.5. Read, write, order and compare numbers at least to 1,000,000 and determine the value of each digit.
Order, add and subtract positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, ≤, ≥ . Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative. Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures].
Inverse operations, estimating and checking answers Estimate the answer to a calculation and use inverse operations to check answers. Use inverse operations to estimate and check answers. Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables.
Estimate and use inverse operations to check answers to a calculation
Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
Use estimation to check answers to calculations and determine, in the context of a problem, levels of accuracy. Recognise and use relationships between operations including inverse operations.
Problem Solving Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction
Solve addition and subtraction twostep problems in contexts, deciding which operations and methods to use and why
Solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why
Solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why Solve problems involving addition, subtraction, multiplication and division.
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Greater Depth Greater Depth Greater Depth Greater Depth Add and subtract numbers with any number of digits using formal written methods. Solve integer scaling problems and correspondence problems in which n objects are connected to m objects
Use tenths, hundreds and thousandths when solving addition and subtraction problems. Solve multi-step problems involving more than one of the operations.
Calculate number problems algebraically for example 2x-3=5.
Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations (Square and cube roots and powers up to 5 may be tested.
Key vocabulary Key vocabulary Key vocabulary Key vocabulary Tens boundary, hundreds boundary, complex, operations.
tenths, hundredths, thousandths, partitioning, inverse operation, integer
Units boundary, tenths boundary, algebraic, significant figures
integer powers, decimal approximations
Multiplication and division facts Solve one-step problems involving multiplication
and division Able to count in steps of 2, 5, and 10. Start linking this to the idea of multiplication as ‘repeated addition’ e.g. they will know that 3 × 2 is the same as 2 + 2 + 2. They will begin to understand the relationship between multiplication and division, and will calculate with concrete objects, pictorial representations and arrays with support.
Count in multiples of twos, fives and tens (copied from Number and Place Value). Expect to solve simple division problems through sharing and grouping. For example: 10 ÷ 2 can be thought of as sharing 10 objects into 2 equal groups. This gives us 5 in each group. 10 ÷ 2 can be thought of as finding how many groups of 2 there are in 10. This gives us 5 groups of 2. Division can be explored as the inverse through ‘grouping’, as well as ‘sharing’. Inverse relationship can also be explored through arrays
Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward (copied from Number and Place Value)
. Recall and use multiplication and division facts for the 2, 5 and 10
multiplication tables, including recognising odd and even numbers
Mental Calculation Count in multiples of twos, fives and tens –
understanding that this is repeated addition. Doubling as ‘two groups of’ and counting in other ‘groups of’ numbers.
Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot. Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot. By the end of Year 2, and by the time children reach KS2, they should have developed rapid recall in mental maths for their basic addition and subtraction facts, including number bonds to 20, and doubles to 20.
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Written Calculation Understand adding objects that are grouped in 2s, 5s, and 10s. Provide lots of opportunities to do this using things around your home. Use pairs of shoes or socks to practise counting in twos, gloves to count in fives, and ice cube trays to practise counting in tens. Draw pictures of the items counted and use these to practise counting in steps of 2, 5, or 10 at any time.
Solve problems using concrete objects or pictorials. Division can be seen as ‘how many groups of…in…’. Use objects and drawings to help them understand multiplication and division. They will make and use arrays to solve problems. Arrays are sets of objects arranged in rows and columns to make a rectangle e.g. egg boxes, muffin trays, ice cube trays, and chocolate bars with rows of pieces are all arrays.
Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
Problem Solving Solve problems , including doubling, halving and sharing.
Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays.
Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts
Greater depth-GLD Greater depth Greater depth
Solve practical problems that involve combining groups of 2, 5 or 10, or sharing into equal groups.
Apply knowledge of number to solve a one-step problem involving simple multiplication and division. Solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems.
Recall and use multiplication and division facts for 2, 5 and 10, and make deductions outside known multiplication facts. Solve unfamiliar word problems that involve more than one step.
Key vocabulary Key vocabulary Key vocabulary Sharing, doubling, halving, number patterns. Multiplication, multiply, multiplied by, multiple,
division, dividing, grouping, array Groups of, times, once, twice, three times…ten times, repeated addition, divide, divided by, divided into, share, share equally, left over, one each, two each…group in pairs, threes…equal groups of, row, column, multiplication table, fact
KEY SKILLS
Year 3 Year 4 Year 5 Year 6 Multiplication and division facts 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. Solve number and practical problems that involve all of the above and with increasingly larger positive numbers
Count in multiples of 6, 7, 9, 25 and 1 000 Recall multiplication facts for multiplication and division tables up to 12 × 12. Solve multiplication and division. Recognise and use factors. Multiply and divide two-digit and three-digit numbers using formal written layout and solve problems involving multiplying and adding and harder multiplication problem. Consolidate number and place value 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.
Count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000 (copied from Number and Place Value) 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, 1000, 10,000 and 100,000. Solve number problems and practical problems that involve all of the above. Read numerals to 1000 (M) and recognise years written in Roman numerals. Use rounding to check answers to calculations for accuracy. Solve problems involving numbers up to three decimal places. Recognise and use square numbers and cube numbers, and the notation for squared and cubed. Calculate and compare the area of squares and rectangles including using standard units, square.
Use Venn and Carroll diagrams e.g. sorting numbers into multiples of 8 and multiples of 6. Create and interpret line graphs where the intermediate values. Understand and use the mean of discrete data. Use the concepts of fractions, multiples, primes and special number patterns. Use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property.
Read Roman numerals to 100 (I to C) and understand how, over time, the numeral system changed to include the concept of zero and place value.
Multiply and divide numbers mentally using known facts. Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000. Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.
Count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000
Mental Calculation 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
Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1-2 digits; multiplying together three numbers using long and short calculation
Mental methods to solve problems where appropriate, modelling mental partitioning. Rounding can help to get a sense of the size of the answer or to find an equivalent calculation, then adjust. Numbers should be looked at before a method is chosen to decide which will be most efficient.
Perform mental calculations, including with mixed operations and large numbers. Consolidate and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings; solve simple word problems mentally.
Recognise and use factor pairs of number for mental calculations
Recognise and use factor pairs and commutativity in mental calculations (in Properties of Nos)
Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000
Associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. 3 /8)
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Written Calculation 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
Multiply two-digit and three-digit numbers by a one-digit number using formal written layout. Ideas to be explored are partitioning, scaling and recombining formal multiplication. Multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit number.
Numbers should be looked at before a method is chosen to decide which will be most efficient. Accurately use formal written methods: column addition, column subtraction, formal written multiplication, short division, chunking, long division and apply this knowledge to solve problems
Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication Use written division methods in cases where the answer has up to two decimal places (copied from Fractions (including decimals)) Use a range of written and mental methods using the four operations applied to integers, both positive and negative.
Decide best method to be most efficient to solve problems. Solve missing number problems
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
Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign.
Divide numbers up to 4-digits by a two-digit whole number using the formal written method of short division where appropriate for the context 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.
Properties of numbers: Multiples, factors, primes, square and cube numbers Recognise and use factor pairs and commutativity in mental calculations (repeated).
Recognise and use factor pairs and commutativity in mental calculations with increasing difficulty (repeated). 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 prime and recall prime numbers up to 19
Identify common factors, common multiples and prime numbers Use common factors to simplify fractions; use common multiples to express fractions in the same denomination (copied from Fractions). Recognise the symbol for square root and work out square roots for numbers up to 100.
Understand what are factors, multiples, composite and prime numbers. Solve simple problems using 1- 2 digit numbers.
Understand the links between factors, multiples, composite and prime numbers. Solve and calculate factors and prime numbers using the four operations.
Understand the links between factors, multiples, composite and prime numbers, rather than seeing these as separate facts to be learnt. Solve word problems using factors, multiples and prime numbers.
Calculate, estimate and compare volume of cubes and cuboids using standard units, including centimetre cubed (cm 3 ) and cubic metres (m 3 ), and extending to other units such as mm 3 and km 3.
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which operations and methods to use and why.
Rec BIDMAS rule, using only parentheses. · Carryout combined operations using BIDMAS rules. Use standard column procedures to add and subtract whole numbers
and decimals with up to two places.
Use their knowledge of the order of operations to carry out calculations involving the four operations. Solve word problems and investigate in a range of contexts: compare and evaluate solutions.
Inverse operations, estimating and checking answers Estimate the answer to a calculation and use inverse operations to check answers. Multiplication is related to times tables as repeated addition and children count in ‘groups of’ a number. Division can be seen as ‘how many groups of’. The inverse relationship will also be explored through arrays.
Estimate and use inverse operations to check answers to a calculation. 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. Add and subtract numbers with up to four digits using written methods, estimate and use inverse operations to check answers.
Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes. Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign. Round positive whole numbers to the nearest 10, 100 or 1000 and decimals to the nearest whole number or one decimal place Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.
Use estimation to check answers to calculations and determine, in the context of a problem, levels of accuracy solve problems involving addition, subtraction, multiplication and division Round numbers and measures to an appropriate degree of accuracy [e.g.to a number of decimal places or S.F. Make and justify estimates and approximations of calculations. Enter numbers and interpret the display in different contexts (decimals, percentages, money, metric measures). Appreciate the infinite nature of the sets of integers, real and rational numbers
Greater Depth Greater Depth Greater Depth Greater Depth Know all multiplication facts up to 12x12 and be able to instantaneously answer questions such as how many 7’s in 42. Multiply and divide any two digit number by a single digit number and have an understanding of remainder.
Solve multi-step problems involving more than one of the operations. Rapidly recall answer when multiplying and diving a whole or decimal number by 10.
Divide whole numbers (up to 4 digits) by 2 digit numbers using preferred method. Understand addition, subtraction, multiplication and division as they apply to whole numbers and decimals; know how to use the laws of arithmetic and inverse operations. Know and use the order of operations, including brackets. Consolidate and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings; solve simple word problems mentally
Multiply all integers (using efficient written methods) including mixed numbers and negative numbers. Move beyond squared and cubed numbers to calculate problems such as X x 10n where n is positive. Consolidate the rapid recall of number facts, including positive integer complements to 100 and multiplication facts to 12 × 12, and quickly derive associated division facts. Know and use the order of operations, including brackets.
Key vocabulary Key vocabulary Key Vocabulary Key vocabulary Factor, product, remainder. Inverse, square, squared, cube,
cubed. inverse operations, BIDMAS, brackets, negative integers, jottings, scaling, composite numbers
Integers, negative, positive, terms
Key Skills
EYFS Year 1 Year 2
Counting in fractional steps Fractions of shapes and quantities & fractions as numbers. Fractions are equal parts of a whole which can be a whole shape.
Fractions can also be counted like any other numbers. Recognise and find half of objects, shapes and quantities.
Pupils should count in fractions up to 10, starting from any number and using the1/2 and 2/4 equivalence on the number line (Non Statutory Guidance).
Recognising fractions Recognise, find and name a half as one of two equal parts of an object, shape or quantity.
Recognise, find and name a half as one of two equal parts of an object, shape or quantity. Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.
Recognise, find, name and write fractions 1 / 3 , 1 / 4 , 2 / 4 and 3 / 4 of a length, shape, set of objects or quantity equivalence is started to be introduced e.g. 2/4 and ½
Equivalence (including fractions, decimals and percentages) Fractions of shapes and quantities & fractions as numbers. Recognise and match the simple fractions as numbers.
Fractions of shapes and quantities & fractions as numbers Fractions are equal parts of a whole which can be a whole shape Fractions can also be counted like any other numbers Recognise and find half of objects, shapes and quantities
Write simple fractions e.g. 1 / 2 of 6 = 3 and recognise the equivalence of 2 / 4 and 1 / 2. Understand that finding a tenth is the same as dividing by ten (by dividing objects, sets of objects, and numbers into ten equal parts. See the connection between fractions and division. Start to introduce to decimals at this stage.
Greater depth- GLD Greater depth Greater depth Recognise, find and name a half as one of two equal parts of an object, shape or quantity. Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.
Recognise and create thirds and fifths. Identify and create halves and quarters. Recognise and create halves, quarters, thirds, fifths and eights.
Find and compare fractions of amounts. Solve simple word problems involving fractions
Key vocabulary Key vocabulary Key vocabulary Parts of a whole, half, quarter. Fraction, equal part, equal grouping, equal sharing, one
of two equal parts, one of four equal parts Equivalent fraction, numerator, denominator, two halves, two quarters, three quarters, one third, two thirds, one of three equal parts
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KEY SKILLS
Year 3 Year 4 Year 5 Year 6
Counting in fractional steps Count up and down in tenths Count up and down in hundredths Writing one number as a fraction of
another. Finding fractions which are equivalent.
Cancelling a fraction to its lowest terms.
Recognising fractions Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators. Recognise that tenths arise from dividing an object into 10 equal parts and in dividing one – digit numbers or quantities by 10. Know that fractions are equal parts of a whole and they represent a relationship between a whole and parts of a whole.
Recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten. Know that fractions are equal parts of a whole and they represent a relationship between a whole and parts of a whole. Understand that fractions that look very different in their notation may be equal. Know that fractions can be added and subtracted with different denominated.
Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents. Read, write, order and compare numbers with up to three decimal places. Read and write decimal numbers as fractions.
Secured understand and use place value, ordering and rounding. Understand addition, subtraction, multiplication and division as they apply to whole numbers and decimals; know how to use the laws of arithmetic and inverse operations. Know and use the order of operations, including brackets
Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators.
Can add or subtract 2 fractions with the same denominator
Finding fractions which are equivalent. Changing between mixed numbers and improper fractions.
Comparing fractions Compare and order unit fractions, and fractions with the same denominators. Compare and order fractions whose denominators are all multiples of the same number. Solve problems that involving halving. Find and write fractions of a given number of objects e.g.
Find of 15. First, your child can find of 15 by dividing the total by the denominator: 15 ÷ 5 = 3. Then, they can multiply this result by the numerator to find the correct fraction:
If of 15 is 3, then of 15 is 3 × 2 = 6.
Consolidate prior learning and 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. Recognise and show, using diagrams, families of common equivalent fractions. Add and subtract fractions with the same denominator. Add and subtract fractions with the same or different denominator and multiples of the same number.
Recognise mixed numbers and improper fractions and convert from one form to the other. Write mathematical statements > 1 as a mixed number. Add and subtract fractions with different denominator and mixed numbers, using the concept of equivalence.
Compare and order fractions, including fractions >1 Examples of Solving Fractions and Decimals Solve:
Solution:
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of 15 is therefore 6. Able to do this with unit and non-unit fractions. Learn that: A unit fraction is any fraction with a
numerator of 1 (for example, ) A non-unit fraction is any fraction with a
numerator larger than 1 (for example, ). Use fractions as number in their own right e.g. find ½ on a number line and show that it is a number halfway between 0 and 1.
Arrange the following in descending order: (i)29,23,821(ii)15,37,710
Comparing decimals Compare numbers with the same number of
decimal places up to two decimal places Read, write, order and compare numbers to 3 deciplaces
Changing between fractions and decimals.
Identify the value of each digit in numbers given to three decimal places.
Rounding including decimals Round decimals with one decimal place to
the nearest whole number. Round decimals with two decimal places to the nearest whole number and to one decimal place. Recognise and write decimal equivalents of any number of tenths or hundredths and 1/4; 1/2; 3/4. 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.
Recognise and use thousandths and relate them to tenths, hundredths and decimals equivalents. Solve problems involving number up to three decimal places.
Solve problems which require answers to be rounded to specified degrees of accuracy Perform calculations using the four operations applied to decimals and fractions. Work interchangeably with terminating decimals and their corresponding fractions (e.g. 3.5 and 7 2 or 0.375 and 3 8 ). Round numbers and measures to an appropriate degree of accuracy e.g dp or sig fig. Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation.
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Equivalence (including fractions, decimals and percentages) Recognise and show, using diagrams, equivalent fractions with small denominators. Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
Recognise and show, using diagrams, families of common equivalent fractions recognise and write decimal equivalents of any number of tenths or hundredths. Recognise and write decimal equivalents to 1 / 4 ; 1 / 2 ; 3 / 4
Read and write decimal numbers as fractions (e.g. 0.71 = 71 / 100); Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents. Recognise the per cent symbol (%) and understand that per cent relates to “number of parts per hundred”, and write percentages as a fraction with denominator 100 as a decimal fraction. Solve problems with percentage and decimal equivalents.
Use common factors to simplify fractions; use common multiples to express fractions in the same denomination. Associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. 3 / 8 ). Recall and use equivalences between simple fractions, decimals and percentages, including in different context.
Addition and Subtraction of fractions
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 and use fractions as numbers: unit fractions and non-unit fractions with small denominators. Recognise and show, using diagrams, equivalent fractions with small denominators.
Add and subtract fractions with the same denominator.
Add and subtract fractions with the same denominator and multiples of the same number. Recognise mixed numbers and improper fractions and convert from one form to the other. Write mathematical statements > 1 as a mixed number: Recognise mixed numbers and improper fractions and convert from one form to the other. Add and subtract whole numbers with more than 4 digits, including using efficient written methods (columnar addition and subtraction). Solve addition and subtraction multi- step problems in contexts, deciding which operations and methods to use and why.
Continue embedding adding and subtracting fractions with different denominators and mixed numbers, using the concept of equivalent fractions.
Add and subtract fractions with the same denominator within one whole (5/7 + 1/7 = 6/7). To solve problems that involve all of the above.
Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number (e.g. 2 / 5 + 4 / 5 = 6 / 5.
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Multiplication and division of fractions
Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
Multiply simple pairs of proper fractions, writing the answer in its simplest form (e.g. 1 / 4 × 1 / 2 = 1 / 8 ) Divide proper fractions by whole numbers (e.g. 1 / 3 ÷ 2 = 1 / 6 )
Multiplication and division of decimals Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators. To solve problems that involve all of the above. Compare and order fractions whose denominators are all multiples of the same number.
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.
Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths. Read, write, order and compare numbers with up to three decimal places. Read and write decimal numbers as fractions.
Multiply one-digit numbers with up to two decimal places by whole numbers. Multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places.
Identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places. Associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. 3 /8) Use written division methods in cases where the answer has up to two decimal places.
Problem Solving Solve problems that involve all of the above 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.
Solve problems involving numbers up to three decimal places. Solve problems involving multiplication and division, including scaling by simple fractions. Estimate volume and capacity.
Make the largest possible quotient. Write numerical expressions for word problems. Multi-step addition and subtraction word problems. Multi-step word problems involving remainders.
Solve simple measure and money problems involving fractions and decimals to two decimal places.
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.
Multi-step word problems: identify reasonable answers. Word problems with extra or missing information. Use Venn diagrams to solve problems.
Greater Depth Greater Depth Greater Depth Greater Depth Can find fractional values (from ½ to 1/10) of amounts up to 1000. Understand that fractions that look very different in their notation may be equal. Know that fractions can be added and subtracted with different denominated. Can add or subtract 2 fractions with the same or different denominator. Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities.
Relate tenths and hundredths to fractional values. Work out simple percentage values of whole numbers. Compare and add fractions whose denominators are all multiples of the same number.
Compare, order and convert between fractions, decimals and percentages in contexts. Understand percentages in a range of contexts. Arrange the number cards to create a calculation and identify the cards which are not needed. Includes multiplying one-digit numbers with two decimal
places by one digit whole numbers. Explain the mistake made in a multiplication calculation and find the correct answer. Includes multiplying one-digit numbers with two decimal places by one-digit whole numbers.
Identify and explain the odd one out of 3 calculations. Includes multiplying one-digit numbers with three decimal places by one-digit whole numbers and zeroes in decimal places. Arrange the number cards to create a calculation and identify the cards which are not needed. Includes multiplying one-digit numbers with three decimal places by one-digit whole numbers and zeroes in decimal places. Explain the mistake made in a multiplication calculation and find the correct answer. Includes multiplying one-digit numbers with three decimal places by one digit whole numbers and zeroes in decimal places.
Key vocabulary Key vocabulary Key vocabulary Key vocabulary Sixths, sevenths, eighths, tenths. Hundredths, decimal, decimal fractions,
decimal point, decimal place, decimal equivalent, proportion.
Proper/improper fraction, equivalent, reduced to, cancel, thousandths, in every, for every, percentage, per cent.
Ratio and Proportion
KEY SKILLS Statements only appear in Years 5 and 6 but should be connected to previous learning, particularly fractions and multiplication and division
Year 3 Year 4 Year 5 Year 6 The concept of ratio is used in many daily activities such as cooking, using maps, or reading scale drawings.
Solve ratio problems involving missing values
Solve problems involving the calculation of
percentages, using fractions, division,
and multiplication to calculate percentages.
Compare quantities using ratios, rates, and proportions. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Find an unknown in a proportion. Solve application problems using proportions.
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 ratio and proportion. Equivalent ratios, simplifying ratios and sharing in given ratio. Use ratio notation and divide in a given ratio. Proportion inverse and direct.
Solve problems involving shapes and a scale
factor. Solve problems involving ‘similar shapes’; shapes with the same proportions that are not necessarily in the same orientation or the same size e.g.
Solve problems where the scaler factor between two shapes is known or can be found. Scale factor means the amount by which you increase the size of the shape e.g. in the picture above there is a scale factor of 2, which you can work out by comparing the lengths of the sides.
Find possible combinations of two variables in
an equation. Able to find numerical solutions to equations where two of the values are unknown e.g. able to find the values of a and b that make this equation correct: 2a + b = 28. Use trial and error to explore different possibilities: In the equation 2a + b = 28, you may take the value of a to be 4. Using ratios by talking about the difference between ratio and proportion. Ratio tells us how much of one thing there is in relation to another thing e.g. ‘For every 2 apples we have 3 bananas’. Proportion tells us about how much of one thing there is in relation to the whole amount of something e.g. ‘There are 50
Solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison. Understanding formula for Percent Proportion is Parts /whole = percent/100. Use formula to find the percent of a given ratio and to find the missing value of a part or a whole. Learn the three main methods for determining whether two fractions (or ratios) are equivalent. 1st method - Vertical
2nd Method - Horizontal
3rd Method- Cross-products
and grouping, using their knowledge of fractions,
division, and multiplication to solve unequal
sharing or grouping problems. Express
remainders as fractions and decimals e.g.
children can express the solution to 27divided by
5 as 5 remainder 2. Express this remainder as a
fraction 5 2/5) or decimal (5.4).
Use percentages to explore everywhere in the real world e.g. what percentage of your child’s class are girls? If there is 25% off the cost of something at the shops, how much money are you saving? Can you then subtract this to find out the new price?
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
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Greater Depth Greater Depth Greater Depth Greater Depth Solve ratio word problems involving the
calculation of percentages,
using fractions, division,
percentages.
Using ratios and talking about the difference between ratio and proportion. Help child’s maths skills later on: Ratio tells us how much of one thing there is in relation to another thing e.g. ‘For every 2 apples we have 3 bananas’. Proportion tells about how much of one thing there is in relation to the whole amount of something e.g. ‘There are 50 pieces of fruit, and 1 in every 5 of those is an apple.’
Problems involving ratio and proportion can be solved using knowledge. Equivalent ratios, simplifying ratios and sharing in given ratio
Compare, order and convert between fractions, decimals and percentages in
contexts. Able to write ratios in three different forms. Able to use ratios to solve real-world problems. Secure understanding of the 3- methods: 1.Numerator and denominator are related (by multiplying or dividing by 2), we know these two ratios are equivalent. 2.The numerators are related (by multiplying or dividing by 3) to each other and the denominators are related to each other, we know these two ratios are equivalent. 3. The cross-products are equal to each other; the two ratios are equivalent.
Key vocabulary Key vocabulary Key vocabulary Key vocabulary Ratio, proportion, relationship, quantities,
simplifying, integer
EYFS Year 1 Year 2
Comparing and estimating Orders two or three items by length or height orders two items by weight or capacity Everyday language to talk about: *size [e.g. long/short, longer/shorter, tall/short] * weight [e.g. heavy/light, heavier than, lighter than] *capacity [e.g. full/empty, more than, less than, half, half full, quarter] * position [e. g. behind, next to] *distance *time [e.g. quicker, slower, earlier, later] *money
Compare, describe and solve practical problems to secure understanding and conceptualization for: * lengths and heights [e.g. long/short, longer/shorter, tall/short, double/half] * mass/weight [e.g. heavy/light, heavier than, lighter than] * capacity and volume [e.g. full/empty, more than, less than, half, half full, quarter] time [e.g. quicker, slower, earlier, later] Recognise and know the value of different denominations of coins.
Compare and order lengths, mass, volume/capacity and record the results using >, < and = Consolidate and secure full understanding to compare, describe and solve practical problems for: * lengths and heights [e.g. long/short, longer/shorter, tall/short, double/half] * mass/weight [e.g. heavy/light, heavier than, lighter than] * capacity and volume [e.g. full/empty, more than, less than, half, half full, quarter] time [e.g. quicker, slower, earlier, later] Recognise and know the value of different denominations of coins
Orders and sequences familiar events measures Sequence events in chronological order using language such as: before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening.
Sequence events in chronological order using language [e.g. before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening].
Compare and sequence intervals of time. Solve real life word problems.
Measuring and calculating Measures short periods of time in simple ways. Measure and begin to record the following:
* lengths and heights * mass/weight * capacity and volume * time (hours, minutes, seconds)
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) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels
Everyday language to talk about: *money. Begin to compare and understand different measurements for: lengths and heights (long/short, longer/shorter, tall/short, double/half);mass or weight (heavy/light, heavier than, lighter than); capacity/volume (full/empty, more than, less than, quarter); time (quicker, slower, earlier, later). Begin to recognise and know the value of different denominations of coins.
Recognise and know the value of different denominations of coins and notes. 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
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 with larger numbers. Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change.
Know how different units of time relate to one another.
Know that there are 60 seconds in a minute, know the number of
days in each month and the number of days in a year (including
leap years).
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Telling the time Everyday language to talk about: *time [e.g. quicker, slower, earlier, later] Sequence events in chronological order using language such as: before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening. Tell the time to the hour and half past the hour. Draw the hands on a clock face to show these times
Tell and write the time to five minutes including quarter past / to the hour. Draw the hands on a clock to show these times. Know the number of minutes in an hour and hours in a day. Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times. Recognise and use language relating to dates, including days of the week, weeks, months and years. 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, hours and o’clock; use vocabulary such as am/pm, morning, afternoon, noon and midnight. Know the number of seconds in a minute, number of days in month, year and leap year.
Tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times. Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times. Calculate the time that an event or task takes. Identify the start and end time of an event. Use these times to work out how long an event lasted. Understand this is the duration of an event. Use individual clocks and number lines to work out the duration. Count in steps of 5 minutes to help them. Make a timetable including the time they get up, the time school begins, and the time they go to bed. Record these times in four different ways: in analogue clock form in digital clock form using the 12-hour clock (remember to use am or pm)in digital clock form using the 24-hour clock in words.
Converting Using standard and non-standard measurements to measure objects or capacity.
Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
Understand how different units of time (seconds, minutes, hours, and so on) relate to each other e.g. know there are 60 seconds in a minute, 24 hours in a day, and 12 months in a year.
Greater depth- GLD Greater depth Greater depth
Estimate, measure, weigh and compare and order objects. Talk about properties, position and time. Use knowledge of time-key periods of the day happen, lunchtime, home time etc.
Recognise all coins and notes, and know their value. Use coins to pay for items bought up to £1. Review all number work and focus in on essentials.
Read scales where not all numbers on the scale are given, and estimate points in between. Read the time on a clock to the nearest 5 minutes. Solving one or two steps time word problems.
Key vocabulary Key vocabulary Key vocabulary Measure, size, compare, guess, estimate, enough, too much, too little, too many, too few, nearly, close to, about the same as. Length, height, long, short, tall, wide, narrow, thick, thin, longer, shorter, taller… longest, shortest, tallest, highest… Weigh, weighs, balances, heavy, light, heavier than, lighter then, scales, non-standard units. Full empty, half full, holds, container. Time, days of the week, birthday, morning, afternoon, evening, night, bedtime, dinner time, playtime, today, yesterday, tomorrow, before, after, next, last, quick, quicker, quickest, quickly, slow, slower, slowest, slowly, old, new, hour, o’clock, watch, clock, hands. .
Measurement, roughly, centimetre, metre, standard units, wide, narrow, ruler, metre stick, kilogram, litre, capacity, volume, more than, less than, quarter full. Months of the year, January, February…, seasons, Autumn, Winter, Spring, Summer, weekend, month, year, earlier, later, first, midnight, date, always, never, often, sometimes, usually, once, twice, half past, clock face, hour hand, minute hand, hours, minutes. Money, coin, penny, pence, pound, price, cost, buy, sell, spend, spent, pay
Measuring scales, further, furthest, tape measure, gram, millimetre, temperature, degree, 5, 10, 15 minutes past/ to, fortnight, quarter past, digital, analogue, timer, seconds, bought, sold.
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Measurement
Year 3 Year 4 Year 5 Year 6
Comparing and estimating Add and subtract amounts of money to give change, using both £ and p in practical contexts. Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml).
Estimate, compare and calculate different measures, including money in pounds and pence (also included in Measuring)
Calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm 2 ) and square metres (m 2 ) and estimate the area of irregular shapes.
Calculate, estimate and compare volume of cubes and cuboids using standard units, including centimetre cubed (cm 3 ) and cubic metres (m 3 ), and extending to other units such as mm 3 and km 3 .
Compare durations of events, for example to calculate the time taken by particular events or tasks.
Convert between different units of measure. Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres.
Estimate volume (e.g. using 1 cm 3 blocks to build cubes and cuboids) and capacity (e.g. using water)
Understand and apply Pythagoras’ Theorem Understand and use three figure bearings to define direction. Understand that measurement expressed to a given unit.
Estimate and read time with increasing accuracy to the nearest minute. Record and compare time in terms of seconds, minutes, hours and o’clock. Use vocabulary such as a.m./p.m., morning, afternoon, noon and midnight.
Calculate areas and perimeters of shapes, regular and simple composite shapes using cm, m and mm.
Calculate the area of parallelograms and triangles; calculate, estimate and compare volume of cubes and cuboids using standard units-cm, m, mm and km.
Calculate the area of parallelograms and triangles; calculate, estimate and compare volume of cubes and cuboids using standard units. Solving multi-steps word problems using formulae for area and volume of shapes.
Measuring and Calculating measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
Estimate, compare and calculate different measures, including money in pounds and pence (appears also in Comparing)
Use all four operations to solve problems involving measure (e.g. length, mass, volume, money) using decimal notation including scaling.
Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate (appears also in Converting)
Measure the perimeter of simple 2-D shapes.
Add and subtract amounts of
money, using both £ and p. Learn the value of coins and will be able to add and subtract amounts of money.
Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres.
Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres Convert between different units of measure (kilometre and metre; metre and centimetre; centimetre and millimetre; kilogram and gram; litre and millilitre). Understand and use basic equivalences between metric units and common imperial units such as inches, pounds and pints.
Recognise that shapes with the same areas can have different perimeters and vice versa. Measure and draw angles to the nearest degree, when constructing models or drawing. Read and interpret scales on a range of measurements.
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Able to give change using manageable amounts. Record money using the £ and p symbols separately (for example, ‘£2 and 35p’). Note that the decimal recording of money (for example, £2.35) is introduced.
Able to calculate the area of rectangles using standard units e.g. square centimetres (cm squared) and square metres (m squared). Calculate area from a scale drawing. Volume means the amount of space occupied by a 3D shape. It is measured in cubed units like cm³. Capacity means the amount a container can hold. Capacity is measured in metric units such as litres or imperial units such as pints. Estimate the volume and capacity of 3D shapes and containers.
Solve problems involving the conversion of units. Understand and use the formula to find the area and perimeter of shapes. Understand congruence of 2D shapes. Investigate properties of triangles and quadrilaterals and measure and draw angles up to 360 degrees with reasonable accuracy. Calculate areas, perimeter, volumes of cubes and cuboids.
Add and subtract amounts of money to give change, using both £ and p in practical contexts
Find the area of rectilinear shapes by counting squares
Calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm 2 ) and square metres (m 2 ) and estimate the area of irregular shapes. Recognise and use square numbers and cube numbers, and the notation for squared ( 2 ) and cubed ( 3 )
Use approximate equivalences between metric and
common imperial units. Use metric units such as metres, grams, and litres, and imperial units such as inches, pounds, and pints. They will also learn about approximate equivalences between metric and imperial units:
Conversions – for example, ‘Convert 24 days into weeks, expressing the answer as weeks and days.’ Scaling – for example, ‘If an item costs £28.40 and there is a 50% discount, what is the new price?’ Decimals – for example, ‘If one plank of wood measures 1·6 m and four planks of wood are needed, what is the total length of wood needed?’
Calculate the area of parallelograms and triangles. Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm 3 ) and cubic metres (m 3 ), and extending to other units [e.g. mm 3 and km 3 ]. Recognise when it is possible to use formulae for area and volume of shapes. Understand and use compound measures. Carry out calculations involving length and area of parallelograms, rhombuses, kites and circles. Areas of linear rectilinear figures.
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Telling the time 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, hours and o’clock; use vocabulary such as a.m./p.m., morning, afternoon, noon and midnight.
Read, write and convert time between analogue and digital 12 and 24-hour clocks (appears also in Converting) Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days.

Solve problems involving converting between units of time.
Speed, Distance and Time Other compound measures. Able to express speed as distance travelled per unit of time. Calculation SDT problems using the speed equation. How to calculate Speed, Distance and Time?
1. To calculate distance (D), we multiply time (T) by speed (S) or speed by time. D = S × T.
2. To calculate speed (S), we divide distance (D) by time (T). S = D ÷ T.
3. To calculate time (T), we divide distance (D) by speed (S). T = D ÷ S.
4.
Analyse ad interpret speed time and distance graphs.
Converting Know the number of seconds in a minute and the number of days in each month, year and leap year
Convert between different units of measure (e.g. kilometre to metre; hour to minute) Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres.
Convert between different units of metric measure (e.g. kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre). Solve problems involving converting between units of time
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
Read, write and convert time between analogue and digital 12 and 24-hour clocks.
Understand and use equivalences between metric units and common imperial units such as inches, lbs and pints. Use all four operations to solve problems involving measure (e.g. length, mass, volume, money) using decimal notation including scaling. Use all four operations to solve problems involving measure (e.g. length, mass, volume, money) using decimal notation including scaling.
Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate.
Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days (appears also in Telling the Time)
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.
Convert between miles and kilometres
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Greater Depth Greater Depth Greater Depth Greater Depth Use knowledge of number to solve problems related to money, time and measures. Can relate knowledge of time to problems related to timetables. Measure, compare, add and subtract more complex problems using common metric measures set out in kg, g, kl, l, m, km.
Use a 24 hour timetable to find out times for a journey between various places. Use knowledge of perimeter to work out the perimeter of large areas around school using metres and centimetres.
Use knowledge of measurement to create plans of areas around school, such as classroom, filed, play area etc. Relate imperial measures still used regularly in our society to their metric equivalent, e.g. miles to kilometres, pounds to kilograms. Use a range of timetables to work out journey times on a fictional journey around the world, e.g. how long would it take to reach the rainforests in the Amazon.
Use formula for measuring the area of shape such as cuboid and triangle to work out the area of an irregular shape in the school environment. Use four operations with mass, length, time, money and other measures, including with decimal quantities. Calculate costs and time involved to visit a destination in another part of the world.
Key vocabulary Key vocabulary Key vocabulary Key vocabulary Division, approximately, millimetre, kilometre, mile, distance apart, between, to, from, perimeter, centigrade, century, calendar, earliest, latest, a.m, p.m, roman numerals, 12 hour clock time, 24 hour clock time.
Unit, standard unit, metric unit, breadth, edge, area, covers, square centimetre, mass, measuring cylinder, leap year, millennium, date of birth, timetable, arrive, depart
Imperial unit, square metre, square millimetre, pint, gallon, discount, currency.
Yard, foot, feet, inch, inches, circumference, tonne, pound, ounce, centilitre, cubic centimetres, cubic metres, cubic millimetres, cubic kilometres, Greenwich Mean Time, British Summer Time, International Date Line, profit, loss.
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Key Skills
EYFS Year 1 Year 2 Identifying shapes and their properties Uses familiar objects and common shapes to create and recreate patterns and build models. Selects a particular named shape. Explore characteristics of everyday objects and shapes, and use mathematical language to describe them. Beginning to use mathematical names for ‘solid’ 3D shapes and ‘flat’ 2D shapes, and mathematical terms to describe shapes. Spot 2D shapes in everyday life, such as on buildings, cushions, clothes, curtains, or in picture books.
Recognise and name common 2D and 3D shapes including: * 2-D shapes [e.g. rectangles (including squares), circles and triangles] * 3-D shapes [e.g. cuboids (including cubes), pyramids and spheres]. Know that 2D shapes are completely flat shapes.
Identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line. Identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces. Identify 2-D shapes on the surface of 3-D shapes [for example, a circle on a cylinder and a triangle on a pyramid]. A polygon is a 2D shape that has three or more straight sides and angles (for example, a rectangle). A non-polygon is a 2D shape with sides that are not all straight (for example, a semicircle). Use language like straight, curved, side and corner ( or vertex/vertices) to describe them.
Comparing and classifying 3D shapes are made up of 2D faces and they have depth/volume. Recognise, find and name a half as one of two equal parts of an object, shape or quantity. Compare shapes using the correct mathematical language. Show two shapes, 2D or 3D (for example, building blocks, cereal boxes, cans). Name the shapes and to describe what is the same about them and what is different.
Properties of a shape inform and names of shapes - 2D and 3D shapes can be sorted by their properties. Compare and sort common 2D and 3D shapes and everyday objects. Seeing lots of real-world examples: shapes like cuboids and pyramids. Identify pyramids with different bases, such as triangular or square-based pyramids. Identify 2D shapes on the surface of 3D shapes, for example circle on a cylinder and a triangle on a pyramid.
Identify and describe the properties of 2D and 3D shapes, including the number of sides, symmetry in a vertical line, edges, vertices, and faces Identify 2D shapes on the surface of 3D shapes, for example circle on a cylinder and a triangle on a pyramid. Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures Solve one-step problems involving multiplication and division, using materials, arrays, repeated addition, mental methods and multiplication and division facts, including problems in contexts. See shapes in different orientations. For example:
Find certain shapes – a 3D shape with a square base, a 2D shape that has three sides, and so on. Understand exactly what all these maths words mean. Choose a cube and a cuboid, tell the shapes are similar in that they are both 3D shapes with 8 vertices, 12 edges and 6 faces. Shapes are different in that a cube has 6 square faces whereas the cuboid may have 6 rectangular faces (which could be a mixture of squares and rectangles).
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Greater depth-GLD Greater depth Greater depth Recognise and name a range of 2D and 3D shapes. Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.
Recognise different 2D and 3D shapes in the environment.
Describe similarities and differences of 2D and 3D shapes using their properties.
Key vocabulary Key vocabulary Key vocabulary Shape, pattern, flat, curved, straight, round, solid, sort, make, build, draw, size, bigger, larger, smaller, symmetrical, pattern, repeating pattern, match, 2D shape, corner, side, rectangle, square, circle, triangle, 3D shape, face, edge, corner, cube, pyramid, sphere, cone.
Point, pointed, cuboid, cylinder. Surface, line symmetry, rectangular, circular, triangular, pentagon, hexagon, octagon.
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Year 3 Year 4 Year 5 Year 6
Identifying shapes and their properties Draw a dotted line to show each line of symmetry. For example, if your child has folded an isosceles triangle in half in various ways, they will find that it has one line of symmetry.
Identify lines of symmetry in 2-D shapes presented in different orientations
Identify 3-D shapes, including cubes and other cuboids, from 2-D representations. Calculate and solve problems involving perimeters and areas of 2-D shapes.
Recognise, describe and build simple 3-D shapes, including making nets (appears also in Drawing and Constructing). Calculate and solve complex word problems involving perimeters and areas of 2-D shapes
Talk about common 3D shapes such as cuboids and prisms (a prism is a 3D shape that has two identical parallel bases, such as a cylinder). Point out 3D shapes in different orientations and sizes when out and about with your child. Describe the shapes to you using precise language like face, vertex(vertices), and edge.
Consolidate geometry and measure knowledge from previous terms, and begin to use protractors to construct and measure given angles. Children can translate shapes across quadrant form. Identify acute and obtuse angles and compare. Compare and classify geometric shapes, including quadrilaterals and triangles. Identify lines of symmetry and describe positions using coordinates
Use wider range of properties of 2d and 3 D shapes. Understand ‘parallel’ and begin to understand ‘perpendicular’ in relation to edges or faces. Classify quadrilaterals, including trapezium and kite, using their properties e.g. number of parallel sides. 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, (cm2) and (m2) and estimate the area of irregular shapes.
Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius. Be able to specify location and co-ordinates in all four quadrants. Enlarge a shape by a whole number scale factor through a given centre of enlargement. Understand and use language associated with the circle, such as circumference, radius, diameter, arc and chord. Understand and use the terms parallel, perpendicular, right-angle, tessellation, reflective and rotational symmetry, and apply this is a range of 2D and 3D shapes
Drawing and constructing Draw 2-D shapes and make 3-D shapes using modelling materials. Recognise 3-D shapes in different orientations and describe them with inaccurately. Used to describing the properties of a shape clearly and accurately. easing accuracy.
Complete a simple symmetric figure with respect to a specific line of symmetry. Consolidate knowledge and describe 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
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.
Draw 2-D shapes using given dimensions and angles. Use angle measure; distinguish between and estimate the size of acute, obtuse and reflex angles. Draw and measure line segments and angles in geometric figures, including interpreting scale drawings.
Identify horizontal, vertical, perpendicular and parallel lines in relation to other lines.
Recognise, describe and build simple 3-D shapes, including making nets.
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Comparing and classifying Describe shapes in terms of their properties, such as: the number of vertices/corners the number of sides/edges the number of faces types of angles within them the number of lines of symmetry (if any). Try to get into the habit of using accurate language, such as symmetrical, polygon, polyhedron (polyhe dra), vertical, horizontal, perpendicular, paral lel, and so on. You can practise by showing your child a shape like this and asking your child to describe it:
that this is a triangle, has 3 straight sides and 3 corners, that a triangle is a polygon, that there are 3 acute angles (angles that are smaller than right angles) and explain that the shape has 3 lines of symmetry.
Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes..
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. Use the properties of rectangles to deduce related facts and find missing lengths and angles. To identify 3D shapes including cubes and cuboids from 2D representations
Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons. Calculate problems using range of geometric shapes.
Angles Recognise angles as a property of shape or a description of a turn. Recognise angles as a property of shape and associate angles with turning. Identify right angles.
Consolidate geometry and measure knowledge from previous terms, and begin to use protractors to construct and measure given angles. Translate shapes across quadrant form.
Know angles are measured in degrees. Estimate and compare acute, obtuse and reflex angles. Use the properties of a rectangle to deduce related facts and find missing lengths and angles.
Circle and Properties Interior and exterior angles; sum of interior and exterior angles of polygon; sum of exterior angles of polygon; regular polygon; exterior angles of regular polygons.
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 acute and obtuse angles and compare and order angles up to two right angles by size.
Identify angles at a point and one whole turn (total 360 degree). Identify angles at a point on a straight line and ½ a turn (total 180 degree). Identify other multiples of 90degree.
Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles. Derive and use angle facts in triangles, on a straight line and at a point. Use geometric reasoning on parallel lines.
Identify horizontal and vertical lines and pairs of perpendicular and parallel lines
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Greater Depth Greater Depth Greater Depth Greater Depth Able to identify acute and obtuse angles and compare and order angles up to two right angles by size.
Know that the total internal angles of a triangle measure 180 degree and can measure each.
Recognise nets and show an understanding that they create 3D shapes. Solve problems involving angles. Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric
Use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles. Derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line.
Key vocabulary Key vocabulary Key vocabulary Key vocabulary Draw, perimeter, pentagonal, hexagonal, octagonal, quadrilateral, right angled, parallel, perpendicular, hemisphere, prism, triangular prism, orientations.
Line, construct, sketch, centre, angle, right angles, base, square based, reflect, reflection, regular, irregular, two dimensional, oblong, rectilinear, equilateral triangle, isosceles triangle, scalene triangle,
Radius, diameter, congruent, axis of symmetry, reflective symmetry, x-axis, y axis, quadrant, octahedron, heptagon, parallelogram, rhombus, trapezium, polygon, three dimensional, spherical, cylindrical, tetrahedron, polyhedron
Circumference, concentric, arc, net, open, closed, intersecting, intersection, plane, kite, dodecahedron, points, lines, parallel lines, perpendicular lines, right angles, regular polygons, reflectively and rotationally symmetric
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Key Skills
EYFS Year 1 Year 2 Position, di