Swavesey Primary School Calculation Policy. Addition and Subtraction


 Hubert Cain
 1 years ago
 Views:
Transcription
1 Addition and Subtraction
2 Key Objectives KS1 Foundation Stage Say and use number names in order in familiar contexts Know that a number identifies how many objects in a set Count reliably up to 10 everyday objects Estimate how many objects they can see and check by counting Use language such as more or less to compare two numbers Use ordinal numbers in different contexts Recognise numerals 1 to 9 Observe number relationships and patterns in the environment and use these to derive facts. Find one more or less than a number from 1 to 10 Select two groups of objects to make a given total of objects Begin to relate addition to combining two groups of objects and subtraction to taking away. In practical activities and discussion begin to use the vocabulary involved in adding and subtracting Year 1 Count reliably at least 20 objects, recognising that when rearranged the number of objects stays the same; estimate a number of objects that can be checked by counting Compare and order numbers, using the related vocabulary; use the equals ( ) sign Read and write numerals from 0 to 20 then beyond; use knowledge of place value to position these numbers on a number track and number line Say the number that is 1 more or less than any given number, and 10 more or less for multiples of 10 Derive and recall all pairs of numbers with a total of 10 and addition facts for totals to at least 5; work out the corresponding subtraction facts Recall the doubles of all numbers to at least 10 Relate addition to counting on; recognise that addition can be done in any order; use practical and informal written methods to support the addition of a onedigit number or a multiple of 10 to a onedigit or twodigit number Understand subtraction as 'take away' and find a 'difference' by counting up; use practical and informal written methods to support the subtraction of a onedigit number from a onedigit or twodigit number and a multiple of 10 from a twodigit number Use the vocabulary related to addition and subtraction and symbols to describe and record addition and subtraction number sentence Year 2 Read and write twodigit and threedigit numbers in figures and words; describe and extend number sequences and recognise odd and even numbers Count up to 100 objects by grouping them and counting in tens, fives or twos; explain what each digit in a twodigit number represents, including numbers where 0 is a place holder; partition twodigit numbers in different ways, including into multiples of 10 and 1 Order twodigit numbers and position them on a number line; use the greater than ( ) and less than ( ) signs Estimate a number of objects; round twodigit numbers to the nearest 10 Derive and recall all addition and subtraction facts for each number to at least 10, all pairs with totals to 20 and all pairs of multiples of 10 with totals up to 100 Use knowledge of number facts and operations to estimate and check answers to calculations Add or subtract mentally a onedigit number or a multiple of 10 to or from any twodigit number Use practical and informal written methods to add and subtract twodigit numbers Understand that subtraction is the inverse of addition and vice versa; use this to derive and record related addition and subtraction number sentences Use the symbols,  and to record and interpret number sentences involving all four operations; calculate the value of an unknown in a number sentence (e.g , 3024)
3 The default method for carrying out and recording addition problems will be the use of number lines to count on. As children move through the school they will be encouraged to use the number lines in a more efficient way. Development of Addition KS1 In the foundation stage children will be taught to relate addition to grouping sets of objects and counting on, this may be done using a variety of models and images: Counting on in familiar contexts such as number rhymes or stories. Count on in 1 s from any given number. Find lots more on a number line/number track by counting on. Find lots more by counting on using bead strings Children will be encouraged to start with the largest number when counting on and teachers will use the image of putting this starting number in their head using their hand. This will be reinforced throughout the school as children begin to use numbers of different sizes. As children begin to move through KS1 they will be encouraged to use number lines and number tracks more frequently as a means of carrying out their addition calculations by counting on = As confidence increases children will be asked to use the + and = symbols to record mental calculations. Children will continue to use practical equipment in their maths lessons to continue to support them in understanding addition as counting on, such as: Bead strings; Practical counting equipment; Coins; Board games. Once children have displayed clear understanding they will be taught how to record their calculations by: Using a blank number line to jump on in 1 s = Using a blank number line to jump in 10 s and 1 s = As understanding of place value and partitioning begins to play a greater importance in children s ability to calculate efficiently they will be taught to partition numbers starting with the highest place value.
4 Development of Subtraction KS1 The default method for carrying out and recording subtraction problems will be the use of number lines to find the difference by counting on from the smaller to the larger number. As children move through the school they will be encouraged to use the number lines in a more efficient way. In the foundation stage children will be taught to relate subtraction to takingaway by using practical counting equipment alongside the following models and images: Counting back in familiar contexts such as number rhymes or stories. Count back in 1 s from any given number. Find lots less on a number line/number track. Find lots less by using bead strings to takeaway. Teachers will begin to link subtraction to finding the difference, using this vocabulary to help children understand the concept. This will be reinforced throughout the school as children begin to use informal and formal jottings to record their calculations. As children begin to move through KS1 they will be encouraged to use number lines and number tracks more frequently as a means of carrying out their subtraction calculations by counting on to find the difference between the smaller and larger number. 53 = As children increase in confidence they will be asked to use the  and = symbols to record mental calculations. Children will continue to use practical equipment in their maths lessons to continue to support them in understanding subtraction as taking lots away, such as: Practical counting equipment; Bead strings; Coins; Board games. Once children have displayed clear understanding they will be taught how to record their calculations by: Using a blank number line to jump on in 1 s to find the difference. 5 3 = Using a blank number line to jump in 10 s and 1 s = As understanding of place value and partitioning begins to play a greater importance in children s ability to calculate efficiently they will be taught to partition numbers starting with the highest place value.
5 Key Objectives KS2 Year 3 Counting and understanding number Read, write and order whole numbers to at least 1000 and position them on a number line; count on from and back to zero in singledigit steps or multiples of 10 Partition threedigit numbers into multiples of 100, 10 and 1 in different ways Round twodigit or threedigit numbers to the nearest 10 or 100 and give estimates for their sums and differences Derive and recall all addition and subtraction facts for each number to 20, sums and differences of multiples of 10 and number pairs that total 100 Use knowledge of number operations and corresponding inverses to estimate and check calculations Add or subtract mentally combinations of onedigit and twodigit numbers Develop and use written methods to record, support or explain addition and subtraction of twodigit and threedigit numbers Year 4 Year 5 Counting and understanding number Recognise and continue number sequences formed by counting on or back in steps of constant size Partition, round and order fourdigit whole numbers; use positive and negative numbers in context and position them on a number line; state inequalities using the symbols and (e.g. 35, 1 1) Use decimal notation for tenths and hundredths and partition decimals; relate the notation to money and measurement; position oneplace and twoplace decimals on a number line Use knowledge of addition and subtraction facts and place value to derive sums and differences of pairs of multiples of 10, 100 or 1000 Use knowledge of rounding, number operations and inverses to estimate and check calculations Add or subtract mentally pairs of twodigit whole numbers (e.g , 91 35) Refine and use efficient written methods to add and subtract twoand threedigit whole numbers and.p Use a calculator to carry out one and two step calculations involving all 4 operations, recognise negative numbers on the display, correct mistaken entries and interpret display correctly in the context of money Counting and understanding number Count from any given number in wholenumber and decimal steps, extending beyond zero when counting backwards; relate the numbers to their position on a number line Explain what each digit represents in whole numbers and decimals with up to two places, and partition, round and order these numbers Use knowledge of place value and addition and subtraction of twodigit numbers to derive sums and differences of decimals (e.g ) Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations Extend mental methods for whole number calculations, for example to subtract one near multiple of 1000 from another (eg ) Use efficient written methods to add and subtract whole numbers and decimals with up to two places Use a calculator to solve problems including those involving decimals and interpret the display correctly in the context of measurement Year 6 Counting and understanding number Find the difference between a positive and a negative integer, or two negative integers, in context Use decimal notation for tenths, hundredths and thousandths; partition, round and order decimals with up to three places, and position them on the number line Calculate mentally with integers and decimals: U.t U.t, Use efficient written methods to add and subtract integers and decimals. Use a calculator to solve problems involving multi step calculations
6 The default method for carrying out and recording addition problems will be the use of number lines to count on. As children move through the school they will be encouraged to use the number lines with increasing efficiency, however practical resources such as bead strings may still be used to support children s understanding. If children show the required level of understanding through their own application of these methods they will be taught how to use column methods, however they will still be encouraged to use number lines when faced with different sized numbers which make calculations difficult for them and to use invisible number lines for their mental calculations. To develop their understanding and reinforce correct application of methods children will be encouraged to record their calculations by: Using a blank number line to jump on in 1 s. As children s understanding develops and their confidence improves children will be taught how to use number lines more efficiently by: Adding the units on in one jump Once children have displayed a full level of understanding they will be taught how to use column methods to increase the efficiency of their calculations. This will be taught in steps, which begins by using their understanding of partitioning: Development of Addition KS = Using a blank number line to jump in 10 s and 1 s = = Adding the tens in one jump = Bridging through ten = Horizontal expansion: = = 552 Vertical expansion Units 12 (7+5) Tens 140 ( ) Hundreds 400 (30000) Before moving onto the next stage it is important that children revisit their understanding of partitioning and recognise that they are now required to partition by starting with the digit with the lowest place value. Vertical
7 Development of Subtraction KS2 The default method for carrying out and recording subtraction problems will be the use of number lines to find the difference by counting on. As children move through the school they will be encouraged to use the number lines with increasing efficiency. If children show the required level of understanding through their own application of these methods they will be taught how to use column methods, however they will still be encouraged to use number lines when faced with different sized numbers which make calculations difficult for them. To develop their understanding and reinforce correct application of methods children will be encouraged to record their calculations by: Using a blank number line to jump on in 1 s to find the difference. 5 3 = Using a blank number line to jump in 10 s and 1 s = As children s understanding develops and their confidence improves children will be taught how to use number lines more efficiently by: Adding the units on in one jump = Adding the tens in one jump = Bridging through ten = Before moving onto the next stage it is important that children revisit their understanding of partitioning and recognise that they are now required to partition by starting with the digit with the lowest place value. Once children have displayed a full level of understanding they will be taught how to use column methods to increase the efficiency of their calculations. This will be taught in steps, which begins by using their understanding of partitioning: Horizontal expansion: Horizontal expansion with adjustment: Vertical * * Please note that children should be encouraged to explain their understanding of place value by using the language of exchanging a ten for ten units.
8 Multiplication and Division
9 Key Objectives KS1 Foundation Stage Say and use number names in order in familiar contexts Know that a number identifies how many objects in a set Count reliably up to 10 everyday objects Estimate how many objects they can see and check by counting Count aloud in ones, twos, fives and tens Use language such as more or less to compare two numbers Use ordinal numbers in different contexts Recognise numerals 1 to 9 Observe number relationships and patterns in the environment and use these to derive facts. Select two groups of objects to make a given total of objects Count repeated groups of the same size Share objects into equal groups and count how many in each group Year 1 Count reliably at least 20 objects, recognising that when rearranged the number of objects stays the same; estimate a number of objects that can be checked by counting Compare and order numbers, using the related vocabulary; use the equals ( ) sign Read and write numerals from 0 to 20 then beyond; use knowledge of place value to position these numbers on a number track and number line Use the vocabulary of halves and quarters in context Count on and back in ones, twos, fives and tens and use this knowledge to derive the multiplies of 2, 5 and 10 to the tenth multiple Recall the doubles of all numbers to at least 10 Solve practical problems that involve combining groups of 2, 5 and 10, or sharing into equal groups Counting in equal groups using real life objects and pictures 3 lots of 2 or 2 lots of 3 Year 2 Read and write twodigit and threedigit numbers in figures and words; describe and extend number sequences and recognise odd and even numbers Count up to 100 objects by grouping them and counting in tens, fives or twos; explain what each digit in a twodigit number represents, including numbers where 0 is a place holder; partition twodigit numbers in different ways, including into multiples of 10 and 1 Order twodigit numbers and position them on a number line; use the greater than ( ) and less than ( ) signs Estimate a number of objects; round twodigit numbers to the nearest 10 Find one half and three quarters of shapes and sets of objects Understand that halving is the inverse of doubling and derive and recall doubles of all numbers to 20, and the corresponding halves Derive and recall multiplication facts for the 2,5 and 10 times tables and the related division facts, recognise multiplies of 2,5 and 10 Use knowledge of number facts and operations to estimate and check answers to calculations Represent repeated addition and arrays as multiplication and sharing and repeated subtraction (grouping) as division, use practical and informal methods and related vocabulary to support multiplication and division, including calculations with remainders. Use the symbols =  x and to record and interpret number sentences involving all four operations; calculate The value of an unknown in i a number sentence e.g. 2 = 6
10 The default method for carrying out and recording multiplication problems in KS1 is the use of arrays. This method not only develops understanding of multiplication as grouping but also reinforces the commutative nature. Development of Multiplication KS1 In the foundation stage children will be introduced to the idea of multiplication by setting up groups in role play using a wide range of practical models and images. These may include: Setting the table with knives, forks and plates for 4 people; Putting 5 flowers in each vase; Giving 5 children 2 apples each. This practical approach will also be use to introduce the children to the concept of doubling as finding 2 lots of. This will lead the children into using arrays to represent multiplication problems. Peg boards, counters or other practical equipment may be used to show this practically before children begin to record this themselves. Children will also be encouraged to develop their understanding of multiplication as lots of by counting on in 2 s, 10 s and then 5 s. As children s understanding develops they will be taught how to record arrays by drawing dots to carry out calculations for themselves: x 3 = x 5=15 At this stage children will begin to record their answer in a number sentence. As their ability of counting on improves children will be introduced to the idea of using number lines to carry out repeated addition: Use of number lines to carry out repeated addition will naturally progress to using a blank number line to count on in familiar steps: 5 x 3 = = = Throughout KS1 children will continue to use practical equipment to create arrays and link their multiplication calculations to grouping. 5 x 3 = = =
11 The default method for carrying out and recording division problems is using repeated subtraction. This will be recorded on a number line once the children have been taught how to use them and will provide a link to their understanding of division as grouping. In the foundation stage children will be introduced to the concept of division as sharing or grouping. Firstly, children will be taught to practically share objects out between 2: Through KS1 children will continually reinforce their of sharing and grouping by using practical examples and will begin to record their calculations in number sentences using the symbol. Development of Division KS1 6 sweets are shared between 2 people, how many do they get each? As their understanding of the concept of sharing deepens children will begin to use larger numbers as their divisor. The second way children will be taught to divide is by grouping: There are 6 sweets, how many children can have 2 sweets each? By grouping children are beginning to think about division as taking away lots of the divisor, which will be useful as they begin to use written methods. The concept of division as grouping will be used to introduce children to using written methods for their calculations through repeated subtraction. This will be done initially using vertical number lines and as the children s confidence increases, using blank number lines: 12 3 = To help develop their understanding of division by counting back, firstly in 10 s, then 2 s and then 5 s. Towards the end of KS1 the children may be introduced to the idea that sometimes objects cannot be shared or grouped equally. They will be taught that the word for anything which has been left over is remainder.
12 Key Objectives KS2 Year 3 Year 4 Year 5 Year 6 Read, write and order whole numbers to at least 1000 and position them on a number line; count on from and back to zero in singledigit steps or multiples of 10 Partition threedigit numbers into multiples of 100, 10 and 1 in different ways Round twodigit or threedigit numbers to the nearest 10 or 100 and give estimates for their sums and differences Read and write proper fractions (e.g. ¾ ) interpreting the denominator as the parts of a whole and the numerator as the number of parts: identify and estimate fractions of shapes, use diagrams to compare fractions and establish equivalence. Derive and recall multiplication facts for the 2,3,4,5,6 and 10 times tables and the corresponding division facts; recognise multiplies of 2,5 or 10 up to 1000 Multiply one digit and two digit numbers (e.g. 13 x 3, 50 4) round remainders up or down depending on the context Understand that division is the inverse of multiplication and vice versa, use this to derive and record related multiplication and division number sentences Find unit fractions of numbers and quantities e.g. 1/2 1/3 1/4 and 1/6 of 12 litres Recognise and continue number sequences formed by counting on or back in steps of constant size Use decimal notation for tenths and hundredths and partition decimals; relate the notation to money and measurement; position oneplace and twoplace decimals on a number line Recognise the equivalence between decimal and fraction forms of one half, quarters, tenths and hundredths Use diagrams to identify equivalent fractions e.g. ¾ and 6/8 interpret mixed numbers and position them on a number line e.g. 3 ½ Use the vocabulary of ratio and proportion to describe the relationship between two quantities e.g. There are two red beads to every 3 blue beads or 2 in every 5 beads are red. Estimate a proportion about one quarter of the apples in the box are green Identify the doubles of twodigit numbers; use these to calculate doubles of multiples of 10 and 100 and derive the corresponding halves Derive and recall multiplication facts up to 10 x 10, the corresponding division facts and multiples of numbers up to 10 up to the tenth multiple Use knowledge of rounding, number operations and inverses to estimate and check calculations Identify pairs of fractions that total one Multiply and divide numbers to 1000 by 10 and then 100 (whole number answers) understanding the effect, relate to scaling up or down Develop and use written methods to record, support and explain multiplication and division of two digit numbers by a one digit number including division and remainders (e.g. 15x9, 98 6 ) Find fractions of numbers, quantities or shapes e.g. 1/3 of plums Use a calculator to carry out one and two step calculations involving all four operations recognising negative numbers in the display, correct mistaken entries and interpret the display correctly in the context of money Count from any given number in wholenumber and decimal steps, extending beyond zero when counting backwards; relate the numbers to their position on a number line Explain what each digit represents in whole numbers and decimals with up to two places, and partition, round and order these numbers Express a smaller number as a fraction of a larger one ( recognise 5 out of 8 is 5/8 ) find equivalent fractions 7/10 = 14/20 and relate fractions to their decimal representations Understand percentages as the number of parts in every hundred and express tenths and hundredths as percentages Use sequences to scale numbers up or down, solve problems involving proportions of quantities e.g. decrease quantities in a recipe designed to feed 6 people Recall quickly multiplication facts up to 10 x10 and use them to multiply pairs of multiples of 10 and 100; derive quickly corresponding division facts Identify pairs of factors of two digit whole numbers and find common multiples (e.g. for 6 and 9) Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations Use understanding of place value to multiply and divide whole numbers and decimals by 10,100 or 1000 Refine and use efficient written methods to multiply and divide htu x u tu x tu u.t x u and htu u Find fractions using division e.g. 1/100 of 5kg and percentages of numbers and quantities 10% of 80 Use a calculator to solve problems involving decimals and fractions and interpret the display in the context of measures Express a larger whole number as a fraction of a smaller one e.g. recognise that 8 slices of a 5 slice pizza represents 8/5 or 1 3/5 pizza. Simplify fractions by cancelling common factors; order a set of fractions by converting them to fractions with a common denominator Express one quantity as a percentage of another e.g. express 400 as a percentage of 1000; find equivalent percentages, decimals and fractions Solve simple problems involving direct proportion by scaling quantities up or down Use knowledge of place value and multiplication facts to 10 x 10 to drive related multiplication and division facts involving decimals e.g. 0.8 x Use knowledge of multiplication facts to derive quickly squares of numbers to 12 x 12 and the corresponding squares of multiples to 10 Recognise that prime numbers have only two factors and identify prime numbers less than 100, find the prime factors of two digit numbers Use approximations, inverse operations and tests of divisibility to estimate and check results Calculate mentally with integers and decimals TU x U, TU U, U.t x U, U.t U Use efficient methods to multiply and divide integers and decimals by a one digit integer and to multiply two digit and three digit integers by a two digit integer Relate fractions to multiplication and division e.g. 6 2 = ½ of 6 = 6 x ½ express a quotient as a fraction or decimal e.g = 13.4 or 13 and 2/5. Find fractions and percentages of whole number quantities e.g 5/8 of 96 65% of 260 Use a calculator to solve problems involving multi step calculations
13 Development of Multiplication KS2 The default method for carrying out and recording multiplication problems is using the grid method. This method builds on children s prior knowledge of the use of arrays and ensures the understanding of the calculation they are carrying out. As children s mental recall of multiplication facts Once full understanding of the concept of improves they will be introduced to using the grid multiplication has been met the children may be method. This may be linked to their use of arrays in introduced to expanded vertical methods of their teaching to draw on prior learning: multiplication: x 20 4 In KS2 children will continue to use arrays to represent their calculations and some children may still use practical representations of this: x 3 = x 5=15 Understanding of multiplication of finding lots of will be reinforced by using number lines to represent repeated addition, either with or without the numbers shown depending on how familiar the children are with the steps required: 5 x 3 = = = x 3 = = Children will first be taught to use this method for multiplying UxTU: 4 x 24 = 76 x This will then naturally progress to multiplying UxHTU: 3 x 124 = 372 x And continuing to multiplying TUxTU: 72 x 38 = 2736 x =80 dots + 16 dots 38 x 7 56 x x 7 56 (8x7) (30x7) x (6x7) 350 (50x7) 120 (6x20) 000 (30x7) 1512 Some children may be introduced to using the full vertical method: 136 x x The children must have a secure knowledge of times table facts and a deep understanding of place value to be able to carry out the parts of the calculation.
14 Development of Division KS2 The default method for carrying out and recording division problems is the vertical number line method. This links closely to children s understanding of division as grouping through repeated subtraction and provides a visual representation of the calculation they are carrying out. As children move into KS2 practical equipment will be used to carry out division problems to reinforce their understanding of division as sharing and grouping. The use of number lines to carry out division by repeated subtraction will be reinforced and children will continue to use this method until their understanding is secure. Some children will need to continue to use numbered vertical number lines where as some children s understanding may be clear enough to use blank vertical number lines: 12 3 = The idea that sometimes division problems may have a remainder will be reintroduced, firstly using practical equipment and then by recording on a number line. It is here that we see the importance of counting back, rather than counting on as we would do to find the difference: 7 3 = 2r As children s recall of multiplication facts improves they will be able to use the vertical number line method to carry out division problems with larger numbers and with greater efficiency: 52 4 = = x 4 3 x 4 Finally they will use this method using their times table facts to jump efficiently for division problems involving remainders: = r2 = 31r x4 10x4 10x4 1x4 While the vertical number line method will still be used as a default method some children may be introduced to using chunking as an introduction to short division: 72 3 = = (10x3) (10x3) (4x3) 0 The children will be taught to take away the chunks that they feel confident with. This method may also be used to carry out calculations with remainders: r (30x12) (2x12) 3 Finally the children may be shown how to use the short division bus stop method. Please note this should only be taught to children whose understanding is very secure
Knowing and Using Number Facts
Knowing and Using Number Facts Use knowledge of place value and Use knowledge of place value and addition and subtraction of twodigit multiplication facts to 10 10 to numbers to derive sums and derive
More informationAddition Subtraction Multiplication Division. size. The children develop ways of 5s and 10s. recording calculations using pictures etc.
Rec Children are encouraged to develop Children will experience equal a mental picture of the number groups of objects. system in their heads to use for Count repeated groups of the same calculation. size.
More informationTopic Skill Homework Title Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number.
Year 1 (Age 56) Number and Place Value Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number. Count up to 10 and back (Age 56) Count up to 20 objects (Age 56)
More informationMultiplication & Division. Years 3 & 4
Multiplication & Division Years 3 & 4 A booklet for parents Help your child with mathematics Multiplication & Division Year 3 Current Objectives Pupils should be taught to: Derive and recall multiplication
More informationYear 1. Use numbered number lines to add, by counting on in ones. Encourage children to start with the larger number and count on.
Year 1 Add with numbers up to 20 Use numbered number lines to add, by counting on in ones. Encourage children to start with the larger number and count on. +1 +1 +1 Children should: Have access to a wide
More informationWritten methods for addition of whole numbers
Written methods for addition of whole numbers The aim is that children use mental methods when appropriate, but for calculations that they cannot do in their heads they use an efficient written method
More informationThe Crescent Primary School Calculation Policy
The Crescent Primary School Calculation Policy Examples of calculation methods for each year group and the progression between each method. January 2015 Our Calculation Policy This calculation policy has
More informationProgression in written calculations in response to the New Maths Curriculum. September 2014
Progression in written calculations in response to the New Maths Curriculum This policy has been written in response to the New National Curriculum, and aims to ensure consistency in the mathematical written
More informationAddition Methods. Methods Jottings Expanded Compact Examples 8 + 7 = 15
Addition Methods Methods Jottings Expanded Compact Examples 8 + 7 = 15 48 + 36 = 84 or: Write the numbers in columns. Adding the tens first: 47 + 76 110 13 123 Adding the units first: 47 + 76 13 110 123
More informationCalculations Policy. Introduction
Thousands Hundreds Tens Units Tenth Hundredth thousandth Calculations Policy Introduction This Calculations Policy has been designed to support teachers, teaching assistants and parents in the progression
More informationSubtraction. Fractions
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
More informationRepton Manor Primary School. Maths Targets
Repton Manor Primary School Maths Targets Which target is for my child? Every child at Repton Manor Primary School will have a Maths Target, which they will keep in their Maths Book. The teachers work
More informationObjectives. Key Skills Addition. Subtraction
Objectives read, write and interpret mathematical statements involving addition (+), subtraction () and equals (=) signs represent and use number bonds and related subtraction facts within 20 add and
More informationPROGRESSION THROUGH CALCULATIONS FOR SUBTRACTION
PROGRESSION THROUGH CALCULATIONS FOR SUBTRACTION Knowing and using number facts Foundation Find one more or one less than a number from 1 to 10 Stage Year 1 Derive and recall all pairs of numbers with
More informationObjectives. Key Skills Addition. Subtraction
Objectives read, write and interpret mathematical statements involving addition (+), subtraction () and equals (=) signs represent and use number bonds and related subtraction facts within 20 add and
More informationYear 4 overview of calculations and calculation objectives in context of overall objectives for each year group. N.B. CONNECTIONS should be made
Year 4 overview of calculations and calculation objectives in context of overall objectives for each year group. N.B. CONNECTIONS should be made between these objectives in order for children to use and
More informationAbercrombie Primary School Progression in Calculation 2014
Abercrombie Primary School Progression in Calculation 204 What you need to know about calculations Mathematics will be at the core of your child s schooling from the moment they start to the moment they
More informationQueens Federation Maths Calculation Policy
Queens Federation Maths Calculation Policy Draft v3b This document describes the progression in methods of calculation taught within the Queens Federation. It has been developed in line with the 2013 National
More informationMultiplication. Year 1 multiply with concrete objects, arrays and pictorial representations
Year 1 multiply with concrete objects, arrays and pictorial representations Children will experience equal groups of objects and will count in 2s and 10s and begin to count in 5s. They will work on practical
More informationAddition. They use numbered number lines to add, by counting on in ones. Children are encouraged to start with the larger number and count on.
Year 1 add with numbers up to 20 Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways of recording calculations using pictures,
More informationMental calculations: expectations for years 1 to 6 Year 1
Rapid recall  Children should be able to recall rapidly: all pairs of numbers with a total of 10, e.g. 3 + 7 (L2) addition and subtraction facts for all numbers to at least 5 (L1) addition doubles of
More informationPUTTERIDGE PRIMARY SCHOOL
Calculations policy Version 3 PUTTERIDGE PRIMARY SCHOOL Autumn 2015 Authored by: Rob Weightman Written Methods& Mental Methods & A D D I T I O N FOUNDATION STAGE YEAR 1 YEAR 2 Count with 1:1 correspondence
More informationYear 1 Procedural Fluency Subtract numbers from up to 20
Year 1 Procedural Fluency Subtract numbers from up to 20 Children consolidate understanding of subtraction practically, showing subtraction on bead strings, using cubes etc. and in familiar contexts, and
More informationCount back in ones on a numbered number line to take away, with numbers up to 20
SUBTRACTION Stage 1 Subtract from numbers up to 20 Children consolidate understanding of subtraction practically, showing subtraction on bead strings, using cubes etc. and in familiar contexts, and are
More informationPROGRESSION THROUGH CALCULATIONS FOR MULTIPLICATION
PROGRESSION THROUGH CALCULATIONS FOR MULTIPLICATION By the end of year 6, children will have a range of calculation methods, mental and written. Selection will depend upon the numbers involved. Children
More informationMathematics Calculation and Number Fluency Policy. Curriculum MMXIV. Chacewater School. +  x
Mathematics Calculation and Number Fluency Policy Curriculum MMXIV Chacewater School +  x Autumn 2014 Introduction The purpose of this document is to build on the successes of the Calculation Policy which
More informationProgression towards a standard written method of Calculation
Progression towards a standard written method of Calculation Introduction Children are introduced to the process of Calculation through practical, oral and mental activities. Through these activities they
More informationSimonside Primary School Progression in Multiplication
Simonside Primary School Progression in Multiplication Year Objective Method Pictorial/ EYFS Chanting of counting in 2s Repeated ing Counting in pairs Doubling / recorded using ICT (eg digital photos /
More informationNumeracy Targets. I can count at least 20 objects
Targets 1c I can read numbers up to 10 I can count up to 10 objects I can say the number names in order up to 20 I can write at least 4 numbers up to 10. When someone gives me a small number of objects
More informationPROGRESSION THROUGH CALCULATIONS FOR SUBTRACTION
PROGRESSION THROUGH CALCULATIONS FOR SUBTRACTION By the end of year 6, children will have a range of calculation methods, mental and written. Selection will depend upon the numbers involved. Children should
More informationMULTIPLICATION. Present practical problem solving activities involving counting equal sets or groups, as above.
MULTIPLICATION Stage 1 Multiply with concrete objects, arrays and pictorial representations How many legs will 3 teddies have? 2 + 2 + 2 = 6 There are 3 sweets in one bag. How many sweets are in 5 bags
More informationSubtraction. Year 1 subtract from numbers up to 20
Year 1 subtract from up to 20 Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways of recording calculations using pictures,
More informationOur Lady of the Visitation Catholic Primary School. CalculationDivision Policy Years 16
Our Lady of the Visitation Catholic Primary School CalculationDivision Policy Years 16 Date of Ratification: Signed: Miss K. Coll (HEAD TEACHER) Review date: Mrs H.McKenzie (CHAIR OF GOVERNORS) Signed:
More informationMultiplication & Division. Years 5 & 6. A booklet for parents. Help your child with mathematics 9 9 =
Q1.Write these in order of size, starting with the smallest. 0.5 0.65 Multiplication & Division Q2. Calculate of 288 Years 5 & 6 Q3.Write the two missing digits in this multiplication. 9 9 = 2001 Q4. Find
More informationAdd and subtract 1digit and 2digit numbers to 20, including zero. Measure and begin to record length, mass, volume and time
Year 1 Maths  Key Objectives Count to and across 100 from any number Count, read and write numbers to 100 in numerals Read and write mathematical symbols: +,  and = Identify "one more" and "one less"
More informationOral and Mental calculation
Oral and Mental calculation Read and write any integer and know what each digit represents. Read and write decimal notation for tenths and hundredths and know what each digit represents. Order and compare
More informationMaths Targets Year 1 Addition and Subtraction Measures. N / A in year 1.
Number and place value Maths Targets Year 1 Addition and Subtraction Count to and across 100, forwards and backwards beginning with 0 or 1 or from any given number. Count, read and write numbers to 100
More informationSummary Of Mental Maths Targets EYFS Yr 6. Year 3. Count from 0 in multiples of 4 & 8, 50 & 100. Count back in 100s, 10s, 1s eg.
Autumn 1 Say the number names in order to 10. Read and write from 1 to 20 in numerals and words. Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward. Count from 0 in
More informationEYFS. Learning Objectives Success criteria Method. Mickleover Primary School Calculation Policy Division. Solve problems involving halving and sharing
Mickleover Primary School Calculation Policy Division Learning Objectives Success criteria Method Solve problems involving halving and sharing Using concrete apparatus, children will be able to find a
More informationMaths Area Approximate Learning objectives. Additive Reasoning 3 weeks Addition and subtraction. Number Sense 2 weeks Multiplication and division
Maths Area Approximate Learning objectives weeks Additive Reasoning 3 weeks Addition and subtraction add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar
More informationCALCULATION POLICY NEW CURRICULUM 2014 MENTAL AND WRITTEN CALCULATIONS
CALCULATION POLICY NEW CURRICULUM 2014 MENTAL AND WRITTEN CALCULATIONS 1 This policy outlines both the mental and written methods that should be taught from Year 1 to Year 6. The policy has been written
More informationCALCULATIONS. Understand the operation of addition and the associated vocabulary, and its relationship to subtraction
CALCULATIONS Pupils should be taught to: Understand the operation of addition and the associated vocabulary, and its relationship to subtraction As outcomes, Year 4 pupils should, for example: Use, read
More informationNumber: Multiplication and Division
MULTIPLICATION & DIVISION FACTS count in steps of 2, 3, and 5 count from 0 in multiples of 4, 8, 50 count in multiples of 6, count forwards or backwards from 0, and in tens from any and 100 7, 9, 25 and
More informationYear 3 End of year expectations
Number and Place Value Count in 4s, 8s, 50s and 100s from any number Read and write numbers up to 1000 in numbers and words Compare and order numbers up to 1000 Recognise the place value of each digit
More informationPROGRESSION THROUGH CALCULATIONS FOR MULTIPLICATION
PROGRESSION THROUGH CALCULATIONS FOR MULTIPLICATION THE FOLLOWING ARE STANDARDS THAT WE EXPECT THE MAJORITY OF CHILDREN TO ACHIEVE BY THE END OF THE YEAR. YR Related objectives: Count repeated groups of
More informationAddition Year 1 Year 2 Year 3
Year 1 Year 2 Year 3 24 29 Understanding addition and subtraction 24 Understand the operation of addition and use the related vocabulary. Begin to recognise that addition can be done in any order. Begin
More informationDetailed breakdown of changes in the core subjects. Maths
Detailed breakdown of changes in the core subjects Maths Changes to the Maths Curriculum: Year 1 Maths Curriculum Contents This document contains details breakdown comparisons of the new curriculum against
More informationBonneygrove Primary School Calculations Policy
Bonneygrove Primary School Calculations Policy Rationale At Bonneygrove, we strongly encourage children to independently use a variety of practical resources to support their learning for each stage of
More informationCalculation Policy Version 1 January 2015
2015 Calculation Policy Version 1 January 2015 NATIONAL CURRICULUM 2014 ABBOTSMEDE PRIMARY SCHOOL CASTOR C OF E PRIMARY SCHOOL DISCOVERY PRIMARY SCHOOL DOGSTHORPE INFANTS EYE C OF E PRIMARY SCHOOOL NENE
More informationCALCULATIONS. Understand the operation of addition and the related vocabulary, and recognise that addition can be done in any order
CALCULATIONS Pupils should be taught to: Understand the operation of addition and the related vocabulary, and recognise that addition can be done in any order As outcomes, Year 1 pupils should, for example:
More informationNumber: Fractions (including Decimals and Percentages) COUNTING IN FRACTIONAL STEPS Year 1 Year 2 Year 3 Year 4 Year 5 Year 6
Pupils should begin to count in halves, using practical resources to support Number: Fractions (including Decimals and Percentages COUNTING IN FRACTIONAL STEPS Pupils should count in count up and down
More informationSubtraction Year 1 6 2 = 4
Subtraction Year 1 Key Vocabulary Key skills for subtraction at Y1: Given a number, say one more or one less. Count to and over 100, forward and back, from any number. Represent and use subtraction facts
More informationMultiplication Year 1
Multiplication Year 1 A range of concrete and pictorial representations should be used with teacher support. Examples: Using songs/rhythms to begin counting in 2 s, 5 s and 10 s Using pictures of shoes/socks
More informationadd and subtract onedigit and twodigit numbers to 20, including zero
LEEK EDUCATION PARTNERSHIP ADDITION AND SUBT PLACE VALUE MENTAL METHODS WRITTEN METHODS R Y1 represent and use number bonds and related subtraction facts within 20 count to and across 100, forwards and
More informationYear 6 Maths Objectives
Year 6 Maths Objectives Place Value COUNTING COMPARING NUMBERS IDENTIFYING, REPRESENTING & ESTIMATING NUMBERS READING & WRITING NUMBERS UNDERSTANDING PLACE VALUE ROUNDING PROBLEM SOLVING use negative numbers
More informationYear 5. Pupils should identify the place value in large whole numbers.
Year 5 Year 5 programme of study (statutory requirements) Number, place value, approximation and estimation Number, place value, approximation and estimation Pupils should identify the place value in large
More informationCharlesworth School Year Group Maths Targets
Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve
More informationAddition and subtraction
Addition and subtraction numbers using concrete objects, pictorial representations. All number facts 10 are secure by the end of Year 1 in order to progress and consolidate decimal numbers in KS2. From
More informationHow we teach calculations in Maths A Parent s Guide
How we teach calculations in Maths A Parent s Guide Belmont Maths Department 2011 1 Contents Introduction...Page 3 Maths at Belmont...Page 4 Addition...Page 5 Subtraction...Page 7 Multiplication...Page
More informationCalculation strategies for subtraction
Calculation strategies for subtraction 1 Year 1 Subtract numbers up to 20. Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways
More informationTeaching programme: Reception
Teaching programme: Reception Counting and recognising numbers 2 8 2 2, 3 4, 5 5 6 7 7 8 Counting Say and use the number names in order In familiar contexts such as number rhymes, songs, stories, counting
More informationArithmetic 1 Progress Ladder
Arithmetic 1 Progress Ladder Maths Makes Sense Foundation Endofyear objectives page 2 Maths Makes Sense 1 2 Endofblock objectives page 3 Maths Makes Sense 3 4 Endofblock objectives page 4 Maths Makes
More informationLevel Descriptors Maths Level 15
Level Descriptors Maths Level 15 What is APP? Student Attainment Level Descriptors APP means Assessing Pupil Progress. What are the APP sheets? We assess the children in Reading, Writing, Speaking & Listening,
More informationAdults to use fraction vocabulary of halves, quarters, thirds etc when describing the number of groups).
DEVELOPING UNDERSTANDING OF FRACTIONS, DECIMALS AND PERCENTAGES Year NC Objectives Examples Models and Images EYFS Share objects, shapes and count how many are in each group (early division) Solve problems
More informationTeaching Pupils to calculate
Teaching Pupils to calculate It is vital that all schools have a calculation policy that is followed throughout the school. The calculation policy should allow the methods to build upon prior learning
More informationPrimary Curriculum 2014
Primary Curriculum 2014 Suggested Key Objectives for Mathematics at Key Stages 1 and 2 Year 1 Maths Key Objectives Taken from the National Curriculum 1 Count to and across 100, forwards and backwards,
More informationCalculation Policy for Year 5: Calshot Primary School
ADDITION Add numbers mentally with increasingly large numbers, e.g. 12,462 + 2300 = 14,762 Add 10, 100 and 1000 onto fivedigit numbers Mentally add tenths and onedigit numbers and tenths Add decimals,
More informationYear 1 Maths Expectations
Times Tables I can count in 2 s, 5 s and 10 s from zero. Year 1 Maths Expectations Addition I know my number facts to 20. I can add in tens and ones using a structured number line. Subtraction I know all
More informationWithin each area, these outcomes are broken down into more detailed stepbystep learning stages for each of the three terms.
MATHEMATICS PROGRAMME OF STUDY COVERAGE all topics are revisited several times during each academic year. Existing learning is consolidated and then built upon and extended. Listed below are the end of
More informationThe Penryn Partnership Mathematics Calculation Policy 2014
The Penryn Partnership Mathematics Calculation Policy 2014 1 Contents Introduction... 3 Addition... 4 Subtraction... 6 Multiplication... 8 Division... 10 Progression Ladders...12 Useful links/websites...14
More informationNumber: Multiplication and Division with Reasoning
count in multiples of twos, fives and tens (copied from Number and Number: Multiplication and Division with Reasoning MULTIPLICATION & DIVISION FACTS Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 count in
More information2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Vertical Alignment Chart Kindergarten Algebra I 1
2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Vertical Alignment Chart Kindergarten Algebra I 1 The materials are copyrighted (c) and trademarked (tm)
More informationYear 2 Maths Objectives
Year 2 Maths Objectives Counting Number  number and place value Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward Place Value Comparing and Ordering Read and write
More informationAddition and Subtraction
Year 2 Addition and Subtraction Recall and use addition and subtraction facts up to 20 fluently, and derive and use related facts up to 100. Add and subtract with concrete objects, representations and
More informationAddition Subtraction Multiplication Division Stage E. Stage E
Addition Subtraction Division Stage E HTU + TU, then HTU + HTU. Cross 10s, 100s boundary. Add least significant figures first. Check for mental approach first before written method. Record steps in brackets
More informationHerts for Learning Primary Maths Team model written calculations policy Rationale The importance of mental mathematics
Herts for Learning Primary Maths Team model written calculations policy Rationale This policy outlines a model progression through written strategies for addition, subtraction, multiplication and division
More information+ Addition + Tips for mental / oral session 1 Early addition. Combining groups of objects to find the total. Then adding on to a set, one by one
+ Addition + We encourage children to use mental methods whenever possible Children may not need to be taught every step STEP Tips for mental / oral session Counting Concept & images Comments Early addition
More informationYear 5 Mathematics Programme of Study Maths worksheets from mathsphere.co.uk MATHEMATICS. Programme of Study. Year 5 Number and Place Value
MATHEMATICS Programme of Study Year 5 Number and Place Value Here are the statutory requirements: Number and place value read, write, order and compare numbers to at least 1 000 000 and determine the value
More informationSubtraction. Subtraction September 2015. Learning Intention Strategy Resources End of year expectation. Year Group
Subtraction Group Learning Intention Strategy Resources End of year expectation Early s 1:1 correspondence with objects Recognising correct Counting backwards Taking away from a set of objects Counting
More informationHigh Coniscliffe CE Primary School. Calculation Strategies Booklet. +  x. Guidance for Staff, Parents and Governors
High Coniscliffe CE Primary School Calculation Strategies Booklet +  x Guidance for Staff, Parents and Governors 20152016 Contents About this booklet.3 School Aims..3 Problem Solving..3 Reasons for using
More informationOperations on Decimals
Operations on Decimals Addition and subtraction of decimals To add decimals, write the numbers so that the decimal points are on a vertical line. Add as you would with whole numbers. Then write the decimal
More informationNational Curriculum for England 2014 Abacus Year 4 Medium Term Plan
National Curriculum for England 2014 Year 4 always covers the content of the National Curriculum within the paired age range (i.e. Y1/2, Y3/4, 5/6). Very occasionally postpones something from the first
More informationSUBTRACTION CALCULATION GUIDANCE
SUBTRACTION CALCULATION GUIDANCE Year 1 read, write and interpret mathematical statements involving, subtraction () and equals (=) signs represent and use number bonds and related subtraction facts within
More informationCurriculum overview for Year 1 Mathematics
Curriculum overview for Year 1 Counting forward and back from any number to 100 in ones, twos, fives and tens identifying one more and less using objects and pictures (inc number lines) using the language
More informationSaxon Math Home School Edition. September 2008
Saxon Math Home School Edition September 2008 Saxon Math Home School Edition Lesson 4: Comparing Whole Lesson 5: Naming Whole Through Hundreds, Dollars and Cent Lesson 7: Writing and Comparing Through
More informationAddition and subtraction. Key Stage 1:
Key Stage 1: The principal focus of mathematics teaching in key stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should involve
More informationRead and write numbers to at least 1000 in numerals and in words.
Year 1 Year 2 Year 3 Number, place value, rounding, approximation and estimation Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number. Count, read and write
More informationYear 2 Maths Objectives
Year 2 Maths Objectives Place Value COUNTING COMPARING NUMBERS IDENTIFYING, REPRESENTING & ESTIMATING NUMBERS count in steps of 1, 2, 3, and 5 from 0, and in tens from any twodigit number, forward or
More informationPROBLEM SOLVING, REASONING, FLUENCY. Year 6 Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Number and Place Value. Measurement Four operations
PROBLEM SOLVING, REASONING, FLUENCY Year 6 Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Number and Place Value Addition and subtraction Large numbers Fractions & decimals Mental and written Word problems,
More informationMaths Level Targets. This booklet outlines the maths targets for each sublevel in maths from Level 1 to Level 5.
Maths Level Targets This booklet outlines the maths targets for each sublevel in maths from Level 1 to Level 5. Expected National Curriculum levels for the end of each year group are: Year 1 Year 2 Year
More informationStudent Profile Name: Emergent to One to One Counting Date achieved
mergent to One to One Counting ledge Read The numerals 1 to 10 1 2 3 4 5 6 7 8 9 10 The numbers 1 to 10 forwards: 1 2 3 4 5 6 7 8 9 10 The numbers 10 to 1 backwards: 10 9 8 7 6 5 4 3 2 1 A Count The number
More informationMATHEMATICS LOWER KS2
MATHEMATICS LOWER KS2 The principal focus of mathematics teaching in lower key stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the four operations, including number facts
More informationContents. Block A Understanding numbers 7. Block C Geometry 53. Block B Numerical operations 30. Page 4 Introduction Page 5 Oral and mental starters
Contents Page 4 Introduction Page 5 Oral and mental starters Block A Understanding numbers 7 Unit 1 Integers and decimals 8 Integers Rounding and approximation Large numbers Decimal numbers Adding and
More informationDecimals and Percentages
Decimals and Percentages Specimen Worksheets for Selected Aspects Paul Harling b recognise the number relationship between coordinates in the first quadrant of related points Key Stage 2 (AT2) on a line
More informationMental Addition Using place value Count in 100s e.g. Know as 475, 575, 675. Using place value
Overview of Strategies and Methods Addition (Draft) Year 3 Using place value Using place value Count in 100s e.g. Know 475 + 200 as 475, 575, 675 Count in 1000s e.g. Know 3475 + 2000 as 3475, 4475, 5475
More informationOverview of Strategies and Methods Year 6 UPPER KEY STAGE 2
UPPER KEY STAGE 2 Children move on from dealing mainly with whole numbers to performing arithmetic operations with both decimals and fractions. Addition and subtraction: Children will consolidate their
More informationSt Luke s Primary School. Calculations Policy. Multiplication. Autumn 2007
St Luke s Primary School Calculations Policy Multiplication Autumn 2007 PROGRESSION THROUGH CALCULATIONS FOR MULTIPLICATION MENTAL CALCULATIONS (ongoing) These are a selection of mental calculation strategies:
More informationTeaching Guidance. For. Counting and Partitioning Numbers
Teaching Guidance For Counting and Partitioning Numbers (Overcoming Barriers Moving Levels 1 to 2, 2 to 3, 3 to 4, 4 to 5) 1 of 2 The National Strategies Primary Overcoming barriers in mathematics helping
More informationcount up and down in tenths count up and down in hundredths
Number: Fractions (including Decimals and Percentages COUNTING IN FRACTIONAL STEPS Pupils should count in fractions up to 10, starting from any number and using the1/2 and 2/4 equivalence on the number
More informationMental Calculation Progression and Guidance
KEY STAGE 1 Year 1 The principal focus of mathematics teaching in key stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. Ø count to and
More information