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Year 3
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Year 4
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Year 5
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Year 6
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Place Value:
Counting
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Children will:
- count from 0 in multiples of 4, 8, 50 and 100.
- find 10 or 100 more or less than a given number.
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Children will:
- count in multiples of 6, 7, 9, 25 and 1000.
- Children will count backwards through zero to include negative numbers.
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Children will:
- count forwards or backwards in steps of powers of 10 for any given number up to 1000000
- count forwards and backwards with positive and negative whole numbers, including through zero.
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Place Value:
Represent
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Children will:
- identify, represent and estimate numbers using different representations
- read and write numbers up to 1000 in numerals and in words
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Children will:
- identify, represent and estimate numbers using different representations
- read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value.
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Children will:
- read, write (order and compare) numbers to at least 1000000 and determine the value of each digit
- read Roman numerals to 1000 (M) and recognise years written in Roman numerals.
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Children will:
- read, write (order and compare) numbers up to
- 10 000 000 and determine the value of each digit.
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Place Value:
Use Place Value and Compare
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Children will:
- recognise the place value of each digit in a three-digit number (hundreds, tens, ones)
- compare and order numbers up to 1000
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Children will:
- find 1000 more or less than a given number
- recognise the place value of each digit in a four-digit number (thousands, hundreds, tens and ones)
- order and compare numbers beyond 1000
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Children will:
- (read, write) order and compare numbers up to
1 000 000 and determine the value of each digit.
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Children will:
- (read, write) order and compare numbers up to
10 000 000 and determine the value of each digit.
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Place Value:
Problems and Rounding
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Children will:
- solve number problems and practical problems involving these ideas.
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Children will:
- 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.
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Children will:
- Interpret negative numbers in context.
- 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.
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Children will:
- round any whole number to a required degree of accuracy.
- use negative numbers in context, and calculate intervals across zero.
- solve number and practical problems that involve all of the above.
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Addition and Subtraction: Recall, Represent, Use
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Children will:
- estimate the answer to a calculation and use inverse operations to check answers.
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Children will:
- estimate and use inverse operations to check answers to a calculation.
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Children will:
- use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy.
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Addition and Subtraction:
Calculations
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Children will:
- add and subtract numbers mentally, including:
- a three-digit number and ones
- a three- digit number and tens
- a three- digit number and hundreds
- add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction.
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Children will:
- add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate.
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Children will:
- add and subtract whole numbers with more than 4 digits, including formal written methods (columnar addition and subtraction)
- add and subtract numbers mentally with increasingly large numbers.
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Children will:
- perform mental calculations, including with mixed operations and large numbers.
- use their knowledge of the order of operations to carry out calculations involving the four operations.
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Addition and Subtraction:
Solve Problems
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Children will:
- solve problems, including missing number problems, using number facts, place value and more complex addition and subtraction.
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Children will:
- solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.
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Children will:
- solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.
- solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign.
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Children will:
- solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.
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Multiplication and Division:
Recall, Represent, Use
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Children will:
- recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables.
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Children will:
- recall multiplication and division facts for multiplication tables up to 12 x 12.
- 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.
- recognise and use factor pairs and commutativity in mental calculations.
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Children will:
- 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 a prime and recall prime numbers up to 19.
- recognise and use square numbers and cube numbers, and the notation for squared and cubed.
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Children will:
- identify common factors, common multiples and prime numbers.
- use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.
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Multiplication and Division:
Calculations
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Children will:
- 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, using mental and progressing to formal written methods.
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Children will:
- multiply two-digit and three-digit numbers by a one-digit number using formal written layout.
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Children will:
- multiply numbers up to 4 digits by a one or two-digit number using a formal written method, including long multiplication for two-digit numbers.
- multiply and divide numbers mentally drawing upon known facts.
- 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.
- multiply and divide whole numbers and those involving decimals by 10, 100 and 1000.
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Children will:
- multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication.
- 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.
- divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context/
- perform mental calculations, including with mixed operations and large numbers.
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Multiplication and Division:
Solve Problems
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Children will:
- solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects and connected to m objects.
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Children will:
- 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 and connected to m objects.
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Children will:
- solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes.
- solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.
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Children will:
- solve problems involving addition, subtraction, multiplication and division.
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Multiplication:
Combined Operations
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Children will:
- solve problems involving addition, subtraction, multiplication and division and a combination of these including understanding the meaning of the equals sign.
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Children will:
- use their knowledge of the order of operations to carry out calculations involving the four operations.
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Fractions:
Recognise and Write
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Children will:
- 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, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators.
- recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators.
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Children will:
- count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.
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Children will:
- identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths.
- recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements >1 as a mixed number.
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Fractions:
Compare
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Children will:
- recognise and show, using diagrams, equivalent fractions with small denominators.
- compare and order unit fractions, and fractions with the same denominators.
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Children will:
- recognise and show, using diagrams, families of common equivalent fractions.
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Children will:
- compare and order fractions whose denominators are all multiples of the same number.
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Children will:
- use common factors to simplify fractions; use common multiples to express fractions in the same denomination.
- compare and order fractions, including fractions >1.
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Fractions:
Calculations
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Children will:
- add and subtract fractions with the same denominator within one whole.
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Children will:
- add and subtract fractions with the same denominator.
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Children will:
- add and subtract fractions with the same denominator and denominators that are multiples of the same number.
- multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams.
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Children will:
- add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions.
- multiply simple pairs of proper fractions, writing the answer in its simplest form.
- divide proper fractions by whole numbers.
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Fractions:
Solve Problems
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Children will:
- solve problems that involve all of the above.
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Children will:
- 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.
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Decimals: Recognise and Write
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Children will:
- recognise and write decimal equivalents of any number of tenths or hundredths.
- recognise and write decimal equivalents to ¼ ½ ¾
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Children will:
- read and write decimal numbers as fractions.
- recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents.
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Children will:
- identify the value of each digit in numbers given to three decimal places.
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Decimals:
Compare
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Children will:
- 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.
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Children will:
- round decimals with two decimal places to the nearest whole number and to one decimal place.
- read, write, order and compare numbers with up to three decimal places.
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Decimals:
Calculations and Problems
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Children will:
- 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.
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Children will:
- solve problems involving number up to three decimal places.
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Children will:
- multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places.
- multiply one-digit numbers with up to two decimal places by whole numbers.
- use written division methods in cases where the answer has up to two decimal places.
- solve problems which require answers to be rounded to specified degrees of accuracy.
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Fractions, Decimals and Percentages
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Children will:
- solve simple measure and money problems involving fractions and decimals in two decimal places.
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Children will:
- recognise the per cent symbol (%) and understand that per cent related to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal.
- solve problems which require knowing percentage and decimal equivalents of ½, ¼, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25.
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Children will:
- associate a fraction with division and calculate decimal fraction equivalents for a simple fraction.
- recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.
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Ratio and Proportion
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Children will:
- 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 the calculation of percentages and the use of percentages for comparison.
- 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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Algebra
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Children will:
- solve problems, including missing number problems.
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Children will:
- use simple formulae.
- generate and describe linear number sequences.
- express missing number problems algebraically.
- Find
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