# Subtraction. Fractions

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1 Year 1 and across 100, forwards and backwards, beginning with 0 or 1, or from any given number write numbers to 100 in numerals; count in multiples of twos, fives and tens Children continue to combine groups of real objects. They learn and use number bonds within 20, including adding 0. They begin to learn the strategy of counting on from the larger number. They begin to interpret and write addition number sentences, using + and =. They begin to use a marked number line to add a small number. Children continue to take away objects from a group, then count how many are left. They learn and use number bonds within 20, including subtracting 0. They begin to interpret and write subtraction number sentences, using - and =. They begin to use a marked number line to count back. They learn to solve missing number problems such as: 7 = - 2 Children put objects into groups of equal size, and count the number of groups and the total number of objects. Children share objects out fairly and investigate practically which numbers can/cannot be shared into groups of different sizes. They use concrete objects, pictorial representations and arrays to solve 1-step problems. E.g. Tom has 4 bags of marbles. Each bag has 3 marbles in it. How many marbles does he have altogether? identify one more and one less sent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least They learn to solve missing number problems such as: 9 = + 2 Number range: 0-20 More able children: 0-50 They learn to count up and find the difference between numbers, using objects or visual models to support their understanding. Number range: 0-20 More able children: 0-50 Fractions They make connections between arrays, number patterns and counting in 2s, 5s and 10s Number range: 0-20 More able children: 0-50 Recognise and find 1/2 of an object, shape or quantity. numbers from 1 to 20 in numerals and words. Recognise and find 1/4 of an object, shape or quantity.

2 Year 2 count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward place value of each digit in a two-digit number (tens, ones) sent and estimate numbers using different representations, including the number line der numbers from 0 up to 100; use <, > and = signs Children learn and use number bonds within 20, and use these to derive bonds to 100 Children add: TU + U TU + T0 TU + TU U + U + U using concrete objects (numicon, beadstrings, base 10), pictorial representations (including empty number lines ) and mentally. They begin to partition numbers to add efficiently using hundred squares and mental methods. They understand that addition is commutative. They understand how to use the inverse to check calculations. Children learn and use number bonds within 20, and use these to derive bonds to 100 Children subtract: TU U TU T0 TU TU U U U using concrete objects (numicon, beadstrings, base 10), pictorial representations (including empty number lines) and mentally. They begin to partition numbers to add efficiently using hundred squares and mental methods. They learn to count up to find the difference between numbers when this is a more efficient subtraction strategy. They understand how to use the inverse to check calculations. Children learn their 2,5 and 10 times tables. They write and solve multiplication number sentences and know that multiplication is commutative. They solve multiplication problems using concrete objects, arrays, repeated addition, mental methods and known number facts. They solve multiplication problems working with a variety of materials and contexts. Bananas cost 7p each. How much will 4 bananas cost? They understand that multiplication and division are inverses of each other and can derive related number facts. Children learn the division facts for the 2,5 and 10 times tables. They write and solve division number sentences, and understand that division can be modelled using grouping or sharing. They solve division problems using concrete objects, arrays, repeated addition, mental methods and known number facts. Eggs are packed in boxes of 6. How many boxes will be needed for 26 eggs? They understand that multiplication and division are inverses of each other and can derive related number facts. numbers to at least 100 in numerals and in words and number facts to solve problems. Fractions Children recognise and find 1/3, 1/4, 2/4 and 3/4 of objects, shapes or quantities. They count in fraction steps up to 10. They begin to understand equivalence by learning that 2/4 = 1/2.

3 Year 3 multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number place value of each Children learn to mentally add: HTU + U HTU + T HTU + H Informal methods, such as empty number lines, are valued and encouraged alongside formal methods. Children learn to mentally subtract: HTU - U HTU - T HTU - H Informal methods, such as empty number lines, are valued and encouraged alongside formal methods. Children learn the 3,4 and 8 times tables. They develop efficient mental methods using commutativity and associativity E.g = = = 240 Children learn the division facts for the 3,4 and 8 times tables. They develop efficient mental methods, supported by jottings. They use empty number lines to count forward or back to solve divisions (including remainders), so: 15 3 is understood as How many 3s in 15? digit in a three-digit number (hundreds, tens, ones) numbers up to 1000 and estimate numbers using different representations numbers up to 1000 in numerals and in words They add and subtract 2 and 3-digit numbers using the expanded column method first: Then moving onto the compact method, learning to start with the least significant digit. Children learn to estimate their answers and use the inverse to check calculations. They use counting up to find the difference between 2 numbers where this is more efficient. They learn the expanded column method first, then the compact method, including decomposition. This is supported by the use of base 10 materials Children learn to estimate their answers and use the inverse to check calculations. They solve TU x U calculations using known facts and progressing towards formal written methods. They learn to use the grid method to multiply. They solve problems involving scaling (4 times as high, 8 times as long etc) and correspondence. ( I have 3 hats and 4 coats. How many different outfits can I make?) They use multiplication and division facts to derive related facts. They progress to using multiples (or chunks) of the divisor to divide bigger numbers. This could be on an empty number line or by subtracting chunks of the divisor = 54 (10x3) = 24 (10x3) = 0 (8x3) 84 3 = 28. They use multiplication and division facts to derive related facts. lems and practical problems involving these ideas. Count up and down in tenths and link this with dividing by 10. Fractions Recognise, find and write unit and non-unit fractions of a set of objects. Add and subtract fractions with the same denominator within 1. Recognise and show equivalent fractions using diagrams. Compare and order fractions with the same denominator. Solve problems involving all these fraction concepts.

4 Year 4 7, 9, 25 and 1000 than a given number through zero to include negative numbers value of each digit in a Children learn to add numbers up to 4-digits using formal column method where appropriate. Children learn to subtract numbers up to 4-digits using formal column method where appropriate. Children learn all multiplication facts up to 12 x 12. They multiply mentally using known and derived facts. They use their knowledge of the rules of multiplication to solve multiplications efficiently e.g. 2 x 6 x 5 = 10 x 6 = 60 Children learn all division facts up to 12 x 12. They divide mentally using known and derived facts. They continue to develop efficient mental methods, supported by jottings. They continue to use multiples (or chunks) of the divisor to divide bigger numbers. four-digit number (thousands, hundreds, tens, and ones) numbers beyond 1000 estimate numbers using different representations the nearest 10, 100 or 1000 They continue to practise mental methods with increasingly larger numbers and use these where more efficient. They estimate and use inverse operations to check calculations. They solve 2-step problems in a variety of contexts, deciding which operation to use. They apply their addition strategies to decimals, up to 2 decimal places. They continue to practise mental methods with increasingly larger numbers and use these where more efficient. (Eg counting up to find the difference between numbers for calculations like ) They estimate and use inverse operations to check calculations. They solve 2-step problems in a variety of contexts, deciding which operation to use. They apply their subtraction strategies to decimals, up to 2 decimal places. They know that, for example, = 200 can be derived from 2 x 3 = 6 They multiply HTU x U and TU x U using the formal written method where this is appropriate. They solve problems involving scaling (4 times as high, 8 times as long etc) and correspondence. ( I have 3 hats and 4 coats. How many different outfits can I make?) This could be on an empty number line or by subtracting chunks of the divisor = 54 (10x3) = 24 (10x3) = 0 (8x3) 84 3 = 28. They learn short division, dividing 2 and 3 digit numbers by a single digit. tical problems that involve all of the above and with increasingly large positive numbers Children learn to: Fractions and Decimals 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value. Know decimal equivalents of any number of tenths or hundredths, and of 1/2, 1/4 and 3/4. Round decimals with 1 d.p. to the nearest whole number. Compare numbers with the same number of decimal places up to 2 d.p. Understand the effect of dividing a number by 10 or 100 and link with tenths and hundredths. Recognise families of common equivalent fractions (using diagrams). Add and subtract fractions with the same denominator. Count up and down in hundredths, and link this with dividing by a hundred. Solve problems involving fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number. Solve simple measure and money problems involving fractions and decimals to 2 d.p.

5 Year 5 and compare numbers to at least and determine the value of each digit backwards in steps of powers of 10 for any given number up to numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero Children add numbers with more than 4 digits, using a formal written method where necessary. They add increasingly large numbers mentally: Eg They use estimating and rounding to check calculations. They use addition to solve multi-step problems in a variety of contexts. Children subtract numbers with more than 4-digits using formal column method where appropriate. They continue to practise mental methods with increasingly larger numbers and use these where more efficient. Eg = They estimate and use inverse operations to check calculations. They solve multi-step problems in a variety of contexts, deciding which operation to use. They apply their subtraction strategies to decimals, up to 2 decimal places. Children learn to multiply whole numbers and decimals by 10, 100 and They multiply numbers up to 4 digits by a 1 or 2-digit number using the grid method and progressing to the formal written method where necessary. They continue to multiply numbers mentally drawing on known facts. They use square and cube numbers and their notation. Children learn to divide whole numbers and decimals by 10, 100 and They identify the multiples and all the factors of a number, and the common factors of two numbers. They understand prime numbers, and composite (non-prime) numbers and they recall primes up to 19; they can establish whether a number up to 100 is prime. They can find the prime factors of a number. They can divide numbers up to 4 digits by a 1-digit number, using short division, and interpret remainders appropriately for the context. They may express non-integer answers as a fraction, as a decimal or by rounding. to to the nearest 10, 100, 1000, Fractions, Decimals and Percentages and Children learn to: lems and practical problems that involve all of the above to 1000 (M) and recognise years written in Roman numerals. Read and write decimal numbers as fractions. Round decimals with 2 d.p. to the nearest whole number and to 1d.p. Recognise and use thousandths. Read, write, order and compare numbers with up to 3 d.p. and solve problems involving these numbers. Compare and order fractions whose denominators are multiples of the same number eg 2/6 and 10/12. Name equivalent fractions of a given fraction presented visually. Recognise mixed numbers and improper fractions and convert from one to the other. Add and subtract fractions with the same denominator or denominators that are multiples of the same number. Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams. Recognise and understand the % symbol, and write percentages as a fraction with the denominator 100, and as a decimal. Solve problems which involve knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 3/5 and those fractions with a denominator which is a multiple of 10 or 25.

6 Year 6, and Children learn to : and compare numbers up to and determine the value of each digit number to a required degree of accuracy bers in context, and calculate intervals across zero Solve multi-step problems in contexts, deciding which operation to use and why. Use their knowledge of the order of operations to carry out calculations involving the 4 operations. Perform mental calculations, including with large numbers and mixed operations. Multiply up to 4 digits by 2 digits using the formal written method of long multiplication, where necessary. Divide up to 4 digits by 2 digits using the formal written method of long division (where necessary), and interpret remainders as whole numbers, fractions, or by rounding depending on the context. Divide up to 4 digits by 2 digits using the written method of short division where appropriate. Identify common factors, common multiples and prime numbers. Solve problems where the answer has to be rounded to specified degrees of accuracy. practical problems that involve all of the above. Fractions, Decimals and Percentages solve simple measure and money problems involving fractions and decimals to two decimal places. Children learn to: Use common factors to simplify fractions and common multiples to express fractions in the same denomination. Compare and order fractions including fractions > 1. Add and subtract fractions with different denominators and mixed numbers by using the concept of equivalence. Multiply pairs of proper fractions, writing the answer in its simplest form. Divide proper fractions by whole numbers eg 1/3 2 = 1/6. Understand a fraction as a division and calculate the decimal equivalent of a fraction. Identify the value of each digit in numbers up to 3 d.p. Multiply and divide numbers by 10, 100 and 1000, giving answers up to 3d.p. Multiply 1-digit numbers with up to 2 d.p. by whole numbers. Use written division methods where the answer has up to 2 d.p. Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.

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