Numbersaurus

What we teach

Numbersaurus teaches the number strand of the National Curriculum for England: 66 skills from Reception to Year 6, covering counting, early number sense, number bonds, place value, addition and subtraction, multiplication and division, and first fractions.

The National Curriculum starts at Year 1. The Reception skills below come from the Early Years Foundation Stage, which is the framework schools follow before Year 1, and each guide names the framework its year group sits in.

Not covered yet: the rest of fractions, decimals, percentages, ratio, algebra, measurement, geometry and statistics. We add skills in the order a child needs them.

Every skill is listed below under the year group where schools usually expect it to be secure, with a sentence saying what it is. The year group is guidance rather than a deadline: children reach these skills at different ages. Where a skill has a longer guide, the guide is linked. A guide covers what the skill looks like when it goes wrong, and how to help at home.

Jump to: Reception · Year 1 · Year 2 · Year 3 · Year 4 · Year 5 · Year 6

Reception

  • One-to-one correspondence — Giving each object one number while counting, so the same thing is not counted twice and none is skipped.
  • Stable number-word order — Saying the numbers in the same order every time, without missing a number out or putting two in the wrong order.
  • Cardinality — Knowing that the last number said when counting is how many there are, so there is no need to count again.
  • Conservation & order-irrelevance — Knowing that spreading a group out, or counting it from the other end, does not change how many there are.
  • Perceptual subitising (1-5) — Seeing at a glance how many there are, up to about five, the way a dice is read without counting the dots.
  • Comparing quantities — Saying which of two groups has more, fewer or the same, such as which plate has more biscuits, and putting small groups in order.
  • Numeral-word-quantity link — Connecting the written figure 5, the word five, and five actual things as the same number.
  • Part-whole / bonds within 5 — Knowing the pairs of numbers that make five, so five counters with two showing means three are hidden.

Year 1

  • Conceptual subitising — Seeing a larger group as smaller groups, so six dots look like four and two instead of six things to count.
  • One more / one less — Finding one more or one less than a number without going back to the start and counting again.
  • Counting fluency — Counting forwards and backwards past twenty, starting from any number rather than always from one.
  • Counting in 10s, 2s, 5s — Counting in equal jumps of two, five and ten, the counting used for pairs of socks and for 10p and 5p coins.
  • Number bonds to 10 — Knowing straight away which pairs of numbers make ten, such as seven and three, without working it out. Guide: Number bonds to 10
  • Number bonds within 20 — Using the pairs that make ten to work out pairs that make any number up to twenty, such as eight and nine making seventeen. Guide: Number bonds within 20
  • Add & subtract within 10 — Adding and taking away numbers up to ten, at first by counting on from the larger number and later straight from the pairs already known.
  • Subtraction as difference — Working out how many more one person has than another, which counts as subtraction even though nothing is taken away.
  • Add & subtract within 20 — Adding and taking away numbers up to twenty, such as 14 + 3 and 18 - 5, starting with calculations that do not cross ten.
  • Teen numbers as 10 + n — Seeing a teen number as a ten and some ones, so thirteen is ten and three.
  • Unitising (a ten as one unit) — Counting a group of ten as one ten rather than as ten separate things, so thirty is three tens.
  • Halves and quarters — Finding half or a quarter of a shape or an amount by splitting it into equal parts, such as folding paper in half or sharing eight cubes between four. Guide: Halves and quarters

Year 2

  • Inverse of + and - — Knowing that adding and taking away undo each other, so 3 + 4 = 7 also gives 7 - 4 = 3.
  • Bridging through 10 — Crossing ten by stopping at it on the way, so 8 + 5 is worked as 8 + 2 + 3, and 13 - 5 as 13 - 3 - 2. Guide: Bridging through 10
  • Two-digit numbers as tens & ones — Splitting any two-digit number into tens and ones, and knowing the 4 in 47 stands for forty, not four.
  • Ten more / ten less — Finding ten more or ten less by changing the tens digit, so ten more than 36 is 46.
  • Numbers to 100 — Reading, writing and ordering numbers up to a hundred, and saying which of two numbers is the larger.
  • 2-digit addition & subtraction — Adding and taking away two-digit numbers that cross a ten, such as 36 + 27 and 53 - 18.
  • Equal groups (x and ÷) — Making equal groups and sharing an amount out equally, seeing three groups of four as twelve altogether.
  • Commutativity of x — Knowing that 3 x 4 gives the same answer as 4 x 3, because it is the same set of objects counted a different way round.
  • Recall x2, x5, x10 (and ÷) — Knowing the 2, 5 and 10 times tables from memory, and the division facts that go with them, such as 20 ÷ 5.
  • Fractions of shapes — Recognising halves, thirds and quarters of a shape, and knowing the parts must be equal in size for it to be a half or a third.
  • Fractions of a quantity — Finding a fraction of an amount, such as a quarter of 12 sweets, by sharing it into the right number of equal groups. Guide: Fractions of an amount

Year 3

  • Counting in multiples (3, 4, 8, 25, 50, 1000) — Counting in steps of three, four, eight, twenty-five, fifty and a thousand, forwards and backwards, from any starting number.
  • Numbers to 1000 (hundreds, tens, ones) — Reading, writing and ordering numbers up to a thousand, and saying what each digit is worth, so the 4 in 462 is four hundred. Guide: Place value
  • Mental add/subtract with 3-digit numbers — Doing 462 + 30 or 462 - 200 as mental arithmetic, adding or taking away ones, tens or hundreds from a three-digit number.
  • Column method to 3 digits — Setting out additions and subtractions up to three digits in columns, lining up the places and carrying or exchanging when needed. Guides: Column addition · Column subtraction
  • Multiplication and division as inverses — Knowing that multiplying and dividing undo each other, so 3 x 7 = 21 also gives 21 ÷ 3 and 21 ÷ 7.
  • Recall x3, x4, x8 — Knowing the 3, 4 and 8 times tables from memory, and the division facts that go with them, rather than counting up to reach an answer.
  • Multiply and divide by 10 and 100 — Multiplying and dividing by 10 and 100 by moving every digit one place left or right for 10 and two for 100, rather than by adding or taking off a zero. Guide: Multiplying and dividing by 10 and 100
  • Multiply 2-digit by 1-digit — Multiplying a two-digit number by a single digit, such as 24 x 6, by splitting it into tens and ones or by short multiplication.
  • Unit and non-unit fractions — Naming and writing fractions such as 1/5 and 3/5, where the bottom number is how many equal parts the whole was split into and the top number is how many of those parts are counted. Guide: Understanding fractions
  • Comparing fractions — Comparing fractions that share a bottom number, such as 2/7 and 5/7, and comparing single parts such as 1/3 and 1/5, where splitting a whole into more parts makes each part smaller. Guide: Comparing fractions
  • Fractions on a number line — Reading fractions as numbers on a line, counting on in steps such as fifths or tenths, and carrying on past 1, so 5/4 sits between 1 and 2.

Year 4

  • Round to the nearest 10 and 100 — Rounding two- and three-digit numbers to the nearest ten or hundred, using the digit that decides which way it goes. Guide: Rounding to the nearest 10 and 100
  • Numbers to 10000 — Reading, writing and ordering numbers up to ten thousand, and saying what each digit is worth, including one with a zero in the middle like 3040. Guide: Four-digit numbers
  • Round to the nearest 1000 — Rounding to the nearest ten, hundred or thousand, so 3486 becomes 3500 or 3000 depending on which is asked for.
  • Roman numerals — Reading Roman numerals up to a hundred, including the ones on a clock face, and knowing IV is four, not six. Guide: Roman numerals
  • Column method to 4 digits — Setting out additions and subtractions up to four digits in columns, including subtractions that have to exchange across a zero, like 4002 - 1547.
  • Estimate and check with rounding and inverse — Estimating an answer by rounding first, then checking the exact answer by doing the opposite calculation.
  • Two-step problems (+ and -) — Solving word problems that need two steps, deciding at each step whether to add or take away.
  • All tables to 12 x 12 — Knowing every times table up to 12 x 12 quickly — what England's year 4 multiplication tables check tests — and the matching division facts. Guides: The Multiplication Tables Check · Times tables
  • Short multiplication (3-digit by 1-digit) — Multiplying three-digit numbers by a single digit in columns, such as 346 x 7, carrying between the columns. Guide: Short multiplication
  • Short division — Dividing two- and three-digit numbers by a single digit using the bus stop method, where the number shares out exactly with nothing left over. Guide: Short division
  • Factor pairs — Finding the pairs of numbers that multiply together to make a number, such as 3 and 8 for 24.

Year 5

  • Numbers to 1,000,000 — Reading, writing and ordering numbers up to a million, including ones where a zero holds an empty column, like 200,450.
  • Round to any power of ten — Rounding any whole number to whichever place is asked for, from the nearest ten up to the nearest hundred thousand.
  • Negative numbers — Reading negative numbers and counting back through zero, such as saying how cold it is when three degrees falls by seven.
  • Add & subtract numbers with more than 4 digits — Adding and subtracting numbers with more than four digits in columns, keeping the places lined up when the two numbers are different lengths.
  • Factors, multiples and primes — Finding the factors and multiples of a number, spotting which factors two numbers share, and working out whether a number up to a hundred is prime. Guide: Factors, multiples and prime numbers
  • Square and cube numbers — Knowing what square and cube numbers are and how they are written, so 6 squared is 36 rather than 12.
  • Long multiplication — Multiplying by a two-digit number using long multiplication, such as 342 x 27, working out two rows and adding them together. Guide: Long multiplication
  • Short division with remainders — Dividing numbers of up to four digits by a single digit using the bus stop method, and saying what the amount left over means in the question.

Year 6

  • Numbers to 10,000,000 — Reading, writing and ordering numbers up to ten million, and rounding them to whichever place is asked for.
  • Intervals across zero — Working out the gap between a negative number and a positive one, so the difference between -4 and 3 is 7.
  • Order of operations — Doing brackets, then multiplying and dividing, before adding and subtracting, so 5 + 2 x 3 is 11 and not 21. Guide: Order of operations
  • Long division — Dividing by a two-digit number, such as 2647 ÷ 23, using long division and dealing with what is left over. Guide: Long division
  • Common factors, common multiples, primes — Finding the factors two numbers have in common and the multiples they have in common, such as the highest number that divides into both 24 and 36.