MA2: Number



MA2: Number

| | |Calculating |

| |Counting and understanding numbers |Knowing and using number facts | |

| |Numbers and the number system |Fractions and decimals |Operations, relationships between |Mental methods |Solving numerical problems |Written methods |

| | | |them | | | |

|Leve|Pupils count, order, add and subtract numbers when solving problems involving up to 10 objects. They read and write the numbers involved. |

|l 1 | |

| |count up to 10 objects, e.g. |begin to use the fraction, |understand addition as finding the |add and subtract numbers of objects|solve addition and subtraction |record their work, e.g. |

| |estimate and check a number |one-half, e.g. |total of two or more sets of |to 10 |problems involving up to 10 |record their work with objects, |

| |read, write numbers to 10 |halve shapes including folding |objects |begin to add by counting on from |objects, e.g. |pictures or diagrams |

| |perhaps with some reversal |paper shapes, lengths of string |understand subtraction as ‘taking |the number of objects in the first |given a number work out how many |begin to use the symbols ‘+’ and |

| |order numbers to 10 |put water in a clear container so |away’ objects from a set and |set |more to make…’ |‘=’ to record additions |

| |say what number comes next, is one |that it is about ‘half-full’ |finding how many are left |begin to know some addition facts, |choose which of given pairs of | |

| |more/less |halve an even number of objects | |e.g. |numbers add to a given total | |

| |count back to zero | | |doubles of numbers to double 5 |solve measuring problems such as | |

| |place 1-10 into ascending order | | | |how many balance with… | |

| |point to first, second, etc. in a | | | |solve problems involving 1p or £1 | |

| |line | | | |coins | |

| |begin to count in twos | | | | | |

|Leve|Pupils count sets of objects reliably, and use mental recall of addition and subtraction facts to 10. They begin to understand the place value of each digit in a number and use this to order numbers up to 100. They|

|l 2 |choose the appropriate operation when solving addition and subtraction problems. They use the knowledge that subtraction is the inverse of addition. They use mental calculation strategies to solve number problems |

| |involving money and measures. They recognise sequences of numbers, including odd and even numbers. |

| |count sets of objects reliably, e.g.|begin to use halves and quarters, |use the knowledge that subtraction |use mental recall of addition and |choose the appropriate operation |record their work in writing, e.g. |

| |group objects in tens, twos or fives|e.g. |is the inverse of addition, e.g. |subtraction facts to 10, e.g. |when solving addition and |record their mental calculations as|

| |to count them |use the concept of a fraction of a |begin to understand subtraction as |use addition/subtraction facts to |subtraction problems, e.g. |number sentences |

| |begin to understand the place value |number in practical contexts such |‘difference’ |10 and place value to add or |use repeated addition to solve | |

| |of each digit; use this to order |as sharing sweets between two to |given 14, 6 and 8, make related |subtract multiples of 10, e.g. know|multiplication problems | |

| |numbers up to 100, e.g. |get ½ each , among four to get ¼ |number sentences |3 + 7 = 10 and use place value to |begin to use repeated subtraction | |

| |know the relative size of numbers to|each |6 + 8 = 14, 14 – 8 = 6, |derive 30 + 70 = 100 |or sharing equally to solve | |

| |100 |work out halves of numbers up to 20|8 + 6 = 14, 14 – 6 = 8 |use mental calculation strategies |division problems | |

| |use 0 as a placeholder |and begin to recall them |understand halving as a way of |to solve number problems including |solve number problems involving | |

| |demonstrate knowledge using a range |relate the concept of half of a |‘undoing’ doubling and vice versa |those involving money and measures,|money and measures, e.g. | |

| |of models/images |small quantity to the concept of | |e.g. |add/subtract two-digit and | |

| |recognise sequences of numbers, |half of a shape, e.g. | |recall doubles to 10 + 10 and other|one-digit numbers, bridging tens | |

| |including odd and even numbers, e.g.|shade one half or one quarter of a | |significant doubles, e.g. double |where necessary in contexts using | |

| |continue a sequence that increases |given shape including those divided| |50p is 100p or £1 |units such as pence, pounds, | |

| |/decreases in regular steps |into equal regions | |use knowledge of doubles to 10 + 10|centimetres | |

| |recognise numbers from counting in | | |to derive corresponding halves | | |

| |tens or twos | | | | | |

|Leve|Pupils show understanding of place value in numbers up to 1000 and use this to make approximations. They begin to use decimal notation and to recognise negative numbers, in contexts such as money and temperature. |

|l 3 |Pupils use mental recall of addition and subtraction facts to 20 in solving problems involving larger numbers. They add and subtract numbers with two digits mentally and numbers with three digits using written |

| |methods. They use mental recall of the 2, 3, 4, 5 and 10 multiplication tables and derive the associated division facts. They solve whole number problems involving multiplication or division, including those that |

| |give rise to remainders. They use simple fractions that are several parts of a whole and recognise when two simple fractions are equivalent. |

| |understand place value in numbers |use simple fractions that are |derive associated division facts |add and subtract two-digit numbers|use mental recall of addition and |add and subtract three-digit numbers |

| |to 1000, e.g. |several parts of a whole and |from known multiplication facts, |mentally, e.g. |subtraction facts to 20 in solving|using written method, e.g. |

| |represent/compare numbers using |recognise when two simple |e.g. |calculate 36 + 19, 63 – 26, and |problems involving larger numbers,|use written methods that involve |

| |number lines, 100-squares, base 10 |fractions are equivalent, e.g. |given a number sentence, use |complements to 100 such as 100 – |e.g. |bridging 10 or 100 |

| |materials, etc. |understand and use unit fractions |understanding of operations to |24 |choose to calculate mentally, on |add and subtract decimals in the |

| |recognise that some numbers can be |such as 1/2, 1/4, 1/3, 1/5, 1/10 |create related sentences, e.g. |use mental recall of the 2, 3, 4, |paper or with apparatus |context of money, where bridging is |

| |represented as different arrays |and find those fractions of shapes|given 14 × 5 = 70, create 5 × 14 =|5 and 10 multiplication tables, |solve one-step whole number |not required |

| |use understanding of place value to|and sets of objects |70, 70 ÷ 5 = 14, 70 ÷ 14 = 5, 14 ×|e.g. |problems appropriately |multiply and divide two-digit numbers |

| |multiply/divide whole numbers by 10|recognise and record fractions |5 = 10 × 5 add 4 × 5 |multiply a two-digit number by 2, |solve two-step problems that |by 2, 3, 4 or 5 as well as 10 with |

| |(whole number answers) |that are several parts of the |use inverses to find missing whole|3, 4 or 5 |involve addition and subtraction |whole number answers and remainders, |

| |use place value to make |whole such as 3/4, 2/5 |numbers in problems such as ‘I |understand finding a quarter of a |solve whole number problems |e.g. |

| |approximations |recognise some fractions that are |think of a number, double it and |number of objects as halving the |including those involving |calculate 49 ÷ 3 |

| |recognise negative numbers in |equivalent to 1/2 |add 5. The answer is 35. What was |number and halving again |multiplication or division that | |

| |contexts such as temperature |begin to use decimal notation in |my number?’ |begin to know multiplication facts|may give rise to remainders, e.g. | |

| |recognise a wider range of |contexts such as money, e.g. |begin to understand the role of |for ×6, ×8, ×9 and ×7 tables |identify appropriate operations to| |

| |sequences, e.g. |order decimals with one decimal |‘=’, the ‘equals’ sign, e.g. | |use | |

| |recognise sequences of multiples of|place, or two decimal places in |solve ‘balancing’ problems such as| |round up or down after simple | |

| |2, 5 and 10 |context of money |7 × 10 = 82 – | |division, depending on context | |

| | |know that £3.06 equals 306p | | | | |

| | |Calculating |

| |Counting and understanding numbers |Knowing and using number facts | |

| |Numbers and the number system |

| |recognise and describe number |recognise approximate proportions |use inverse operations, e.g. |use a range of mental methods of |solve problems with or without a |begin to use simple formulae expressed|

| |patterns, e.g. |of a whole and use simple |use a calculator and inverse |computation with all operations, |calculator |in words |

| |continue sequences involving |fractions and percentages to |operations to find missing |e.g. |solve two-step problems choosing |use and interpret coordinates in the |

| |decimals |describe these |numbers, including decimals |calculate complements to 1000 |appropriate operations |first quadrant |

| |recognise and describe number |recognise simple equivalence |‘undo’ two-step problems |recall multiplication facts up to |deal with two constraints | |

| |relationships including multiple, |between fractions, decimals and |understand ‘balancing sums’ |10 × 10 and quickly derive |simultaneously | |

| |factor and square |percentages e.g. 1/2, 1/4, 1/10, |including those using division, |corresponding division facts, e.g.|interpret a calculator display of | |

| |use place value to multiply and |3/4 |such as 20 + ? = 100 ÷ 4 |use their knowledge of tables and |4.5 as £4.50 in context of money | |

| |divide whole numbers by 10 or 100 |convert mixed numbers to improper |understand the use of brackets in |place value in calculations with |carry out simple calculations | |

| | |fractions and vice versa |simple calculations |multiples of 10 such as 30 × 7, |involving negative numbers in | |

| | |order decimals to three decimal |quickly derive division facts that|180 ÷ 3 |context | |

| | |places |correspond to multiplication facts|use efficient written methods of |check the reasonableness of | |

| | |begin to understand simple ratio |up to 10 × 10 |addition and subtraction and of |results with reference to the | |

| | | | |short multiplication and division |context or size of numbers | |

| | | | |e.g. | | |

| | | | |calculate 1202 + 45 + 367 or 1025 | | |

| | | | |– 336 | | |

| | | | |add and subtract decimals to two | | |

| | | | |places | | |

| | | | |multiply a simple decimal by a | | |

| | | | |single digit, e.g. | | |

| | | | |calculate 36.2 × 8 | | |

|Leve|Pupils use their understanding of place value to multiply and divide whole numbers and decimals by 10, 100 and 1000. They order, add and subtract negative numbers in context. They use all four operations with |

|l 5 |decimals to two places. They reduce a fraction to its simplest form by cancelling common factors and solve simple problems involving ratio and direct proportion. They calculate fractional or percentage parts of |

| |quantities and measurements, using a calculator where appropriate. Pupils understand and use an appropriate non-calculator method for solving problems that involve multiplying and dividing any three-digit number by|

| |any two-digit number. They check their solutions by applying inverse operations or estimating using approximations. They construct, express in symbolic form, and use simple formulae involving one or two operations.|

| |They use brackets appropriately. Pupils use and interpret coordinates in all four quadrants. |

| |use understanding of place value to|use equivalence between fractions,|use known facts, place value and |add and subtract negative numbers |solve simple problems involving |construct, express in symbolic form, |

| |multiply and divide whole numbers |e.g. |knowledge of operations to |in context |ordering, adding, subtracting |and use simple formulae involving one |

| |and decimals by 10, 100 and 1000 |convert fractions such as 2/5 into|calculate, e.g. |estimate using approximations |negative numbers in context |or two operations, e.g. |

| |and explain the effect |tenths or hundredths and express |calculate decimal complements to |use all four operations with |solve simple problems involving |understand simple expressions using |

| |round decimals to the nearest |them as decimals or percentages |10 or 100, such as 100 – 63.8 |decimals to two places, e.g. |ratio and direct proportion, e.g. |symbols e.g. ‘2 less than n’ can be |

| |decimal place |and vice versa |multiply a two-digit number by a |add and subtract numbers that do |begin to use multiplication rather|written as ‘n – 2’ |

| |order negative numbers in context |reduce a fraction to its simplest |single digit e.g. 39 × 7 |not have the same number of |than trial and improvement to |evaluate expressions by substituting |

| |recognise and use number patterns |form by cancelling common factors |calculate simple fractions or |decimal places |solve ratio problems |numbers into them |

| |and relationships, e.g. |order fractions and decimals, e.g.|percentages of a number/quantity, |multiply or divide decimal numbers|approximate to check answers to |use symbols to represent an unknown |

| |find two-digit prime numbers |order fractions with different |e.g. 3/8 of 400g or 60% of £300 |by a single digit, e.g. 31.62 × 7 |problems are of the correct |number or a variable |

| |make generalisations about |denominators |apply inverse operations |use a calculator where appropriate|magnitude |use and interpret coordinates in all |

| |sequences saying whether much |order decimals that have a mixture|use brackets appropriately, e.g. |to calculate fractions/percentages|check solutions by applying |four quadrants |

| |larger numbers will be in the |of one, two or three decimal |know and use the order of |of quantities/ measurements, e.g. |inverse operations or estimating | |

| |sequence or not |places |operations, including brackets |find fractions of quantities such |using approximations | |

| | |understand simple ratio | |as 3/8 of 980 | | |

| | | | |find percentages such as 15% of | | |

| | | | |360g | | |

| | | | |understand and use an appropriate | | |

| | | | |non calculator method for solving | | |

| | | | |problems that involve multiplying | | |

| | | | |and dividing any three digit | | |

| | | | |number by any two-digit number | | |

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