Written methods for addition of whole numbers


 Linda Dalton
 1 years ago
 Views:
Transcription
1 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 accurately and with confidence. Children are entitled to be taught and to acquire secure mental methods of calculation and one efficient written method of calculation for addition which they know they can rely on when mental methods are not appropriate. These notes show the stages in building up to using an efficient written method for addition of whole numbers by the end of Year 4. To add successfully, children need to be able to: recall all addition pairs to and complements in 10; add mentally a series of onedigit numbers, such as ; add multiples of 10 (such as ) or of 100 (such as ) using the related addition fact, 6 + 7, and their knowledge of place value; partition twodigit and threedigit numbers into multiples of 100, 10 and 1 in different ways. Note: It is important that children s mental methods of calculation are practised and secured alongside their learning and use of an efficient written method for addition. At Byker we are using the terms units and ones throughout the school. Stage 1: The empty number line Jumping forwards in single steps. (See example) The mental methods that lead to column addition generally involve partitioning, e.g. adding the tens and ones separately, often starting with the tens. Children need to be able to partition numbers in ways other than into tens and ones to help them make multiples of ten by adding in steps. 1
2 The empty number line helps to record the steps on the way to calculating the total. Stage 2 Steps in addition can be recorded on a number line. The steps often bridge through a multiple of 10. Stage 2: Partitioning The next stage is to record mental methods using partitioning. Add the ones and then the tens to form partial sums and then add these partial sums. Partitioning both numbers into tens and ones mirrors the column method where ones are placed under ones and tens under tens. This also links to mental methods. 2
3 Stage 3: Adding using partitioning Partitioned numbers are written under one another: = When totals are more than 10, it is recorded like this =123 At Byker we have decided to add units first ready for the column method. 3
4 Stage 4: Column method In this method, recording is reduced further. Carry digits are recorded below the line, using the words carry ten or carry one hundred, not carry one. Later, extend to adding three twodigit numbers, two threedigit numbers and numbers with different numbers of digits. Stage 4  Example Column addition remains efficient when used with larger whole numbers and decimals. Once learned, the method is quick and reliable. The decimal point should be aligned in the same way as the other place value columns, and must be in the same column in the answer. 4
5 Say 6 tenths add 7 tenths to reinforce place value. 5
6 Written methods for subtraction 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 accurately and with confidence. Children are entitled to be taught and to acquire secure mental methods of calculation and one efficient written method of calculation for subtraction, which they know they can rely on when mental methods are not appropriate. These notes show the stages in building up to using an efficient method for subtraction of twodigit and threedigit whole numbers by the end of Year 4. To subtract successfully, children need to be able to: recall all addition and subtraction facts to 20; subtract multiples of 10 (such as ) using the related subtraction fact, 16 7, and their knowledge of place value; partition twodigit and threedigit numbers into multiples of one hundred, ten and one in different ways (e.g. partition 74 into or ). Note: It is important that children s mental methods of calculation are practised and secured alongside their learning and use of an efficient written method for subtraction. Stage 1: Using a number line counting backwards (subtracting) Jumping backwards in single steps. Count back in ones on a numbered number line to take away, with numbers up to 20 When children fully understand this method introduce them to a blank numberline. 6
7 Stage 2: subtraction with 2 digit numbers, using a blank numberline = 24 Partition the second number and subtract it in tens and units, as below: Move towards more efficient jumps back, as below: 7
8 The empty number line helps to record or explain the steps in mental subtraction. A calculation like can be recorded by counting back 27 from 74 to reach 47. The empty number line is also a useful way of modelling processes such as bridging through a multiple of ten. The steps can also be recorded by counting up from the smaller to the larger number to find the difference, for example by counting up from 27 to 74 in steps totalling 47. With practice, children will need to record less information and decide whether to count back or forward. It is useful to ask children whether counting up or back is the more efficient for calculations such as 57 12, or The notes below give more detail on the Counting up method using an empty number line. Stage 3 Steps in subtraction can be recorded on a number line. The steps often bridge through a multiple of = = 47 worked by counting back: The steps may be recorded in a different order or combined:
9 Stage 4: The counting on method Mental strategy  subtract numbers close together by counting on: The mental method of counting up from the smaller to the larger number can be recorded using either number lines. The number of rows (or steps) can be reduced by combining steps. With twodigit numbers, this requires children to be able to work out the answer to a calculation such as 30 +? = 74 mentally
10 74 27 = With threedigit numbers the number of steps can again be reduced, provided that children are able to work out answers to calculations such as 178 +? = 200 and 200 +? = 326 mentally. The most compact form of recording remains reasonably efficient = 148 Children can use addition calculations to add up the jumps if needed, although they should be encouraged to add tem mentally. 10
11 The method can be used with decimals where no more than three columns are required. However, it becomes less efficient when more than three columns are needed. This counting up method can be a useful alternative for children whose progress is slow, whose mental and written calculation skills are weak and whose projected attainment at the end of Key Stage 2 is towards the lower end of level = 4.6 Stage 4: Expanded layout, leading to column method Subtraction can be recorded using partitioning to write equivalent calculations that can be carried out mentally. For this involves partitioning the 27 into 20 and 7, and then subtracting from the 74 the 20 and the 7 in turn
12 Expanded layout leading to the standard written method of decomposition. Partitioned numbers are then written under one another: Example: Example Stage 5 Subtraction written methods The Standard method. Record using the standard method. Example
13 13
14 Written methods for multiplication 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 accurately and with confidence. Children are entitled to be taught and to acquire secure mental methods of calculation and one efficient written method of calculation for multiplication, which they know they can rely on when mental methods are not appropriate. Stage 2: Expanded layout, leading to column method Partitioning the numbers into tens and ones, mirroring the early stages of addition and subtraction.. It also relies on secure mental skills. Children need to be secure in their times tables. The expanded method leads children to the more compact method so that they understand the digit s value and efficiency. The amount of time that should be spent teaching and practising the expanded method will depend how secure the children are in their recall of number facts and with partitioning. These notes show the stages in building up to using an efficient method for twodigit by onedigit multiplication by the end of Year 4, two digit by twodigit multiplication by the end of Year 5, and threedigit by twodigit multiplication by the end of Year 6. Multiplying decimal numbers by a single digit in years 5 and 6. To multiply successfully, children need to be able to: recall all multiplication facts to 10 10; To know the inverse operation in relation to multiplication and division partition number into multiples of one hundred, ten and one; work out products such as 70 5, 70 50, or using the related fact 7 5 and their knowledge of place value; add two or more singledigit numbers mentally; add multiples of 10 (such as ) or of 100 (such as ) using the related addition fact, 6 + 7, and their knowledge of place value; add combinations of whole numbers using the column method (see above). Note: It is important that children s mental methods of calculation are practised and secured alongside their learning and use of written methods for multiplication. 14
15 Stage 1: Multiply with concrete objects, arrays and pictorial representations There are 3 sweets in one bag. How many sweets are in 5 bags altogether? = 15 Give children experience of counting equal group of objects in 2s, 5s and 10s. Present practical problem solving activities involving counting equal sets or groups, as above. Stage 2: To multiply using arrays and repeated addition 15
16 5 x 3 = Stage 3: Mental multiplication using Mental methods for multiplying TU U can be based on the distributive law of multiplication over addition. This allows the tens and ones to be multiplied separately to form partial products. These are then added to find the total product. Either the tens or the ones can be multiplied first but it is more common to start with the tens. Note: These methods are based on the distributive law. Children should be introduced to the principle of this law (not its name) in Years 2 and 3, for example when they use their knowledge of the 2, 5 and 10 times tables to work out multiples of 7: The Partitioning Method This is based on the distributive law and links directly to the mental method.. The partitioning method we have chosen at Byker encourages the children to understand the value of the digits and increase their mental maths skills. Example 1 24 x 7 20 x 7 = x 7 = = 168. Children should be encouraged to add the two numbers mentally 16
17 Stage 4 : Short multiplication The recording is reduced further, with carry digits recorded below the line. If, after practice, children cannot use the compact method without making errors, they should return to the pationing method of stage 1. Example: 38 x Stage 5: Twodigit by twodigit products Extend to TU TU, asking children to estimate first. Stage 5 example is approximately = X The aim is for most children to use this long multiplication method for TU TU by the end of Year 5. 1 Stage 4: Threedigit by twodigit products Extend to HTU TU asking children to estimate first. Example is approximately = Children are then taught the long multiplication method 17
18 286 X Children who are already secure with multiplication for TU U and TU TU should have little difficulty in using the same method for HTU TU. Carry digits should again be placed beneath the answer. Stage 6: Short multiplication involving decimals. Encourage children to make an estimate first. For example: 7.2 x 8 7 x 8 = 56 When children progress to the final stage, ensure that numbers are in correct column, particularly the units. 7.2 x X Progress to 2 decimal places, using the same principle x X
19 Written methods for division 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 accurately and with confidence. Children are entitled to be taught and to acquire secure mental methods of calculation and one efficient written method of calculation for division which they know they can rely on when mental methods are not appropriate. These notes show the stages in building up to long division through Years 4 to 6 To divide successfully in their heads, children need to be able to: understand and use the vocabulary of division for example in 18 3 = 6, the 18 is the dividend, the 3 is the divisor and the 6 is the quotient; partition twodigit and threedigit numbers into multiples of 100, 10 and 1 in different ways; recall multiplication and division facts to 10 10, recognise multiples of onedigit numbers and divide multiples of 10 or 100 by a singledigit number using their knowledge of division facts and place value; know how to find a remainder working mentally for example, find the remainder when 48 is divided by 5; understand and use multiplication and division as inverse operations. Note: It is important that children s mental methods of calculation are practised and secured alongside their learning and use of an efficient written method for division. To carry out written methods of division successful, children also need to be able to: understand division as repeated subtraction; estimate how many times one number divides into another for example, how many sixes there are in 47, or how many 23s there are in 92; multiply a twodigit number by a singledigit number mentally; subtract numbers using the column method. To know the inverse operation To know times tables 19
20 Stage 1: To group and share quantities How many groups of 4 can be made with 12 stars? Pupils should : use lots of practical apparatus, arrays and picture representations Be taught to understand the difference between grouping objects (How many groups of 2 can you make?) and sharing (Share these sweets between 2 people) Be able to count in multiples of 2s, 5s and 10s. Find half of a group of objects by sharing into 2 equal groups 20
21 Stage 2: To group and share using and = sign. Use objects, arrays, diagrams and pictorial representations, and grouping on a number line. This represents 12 3, posed as how many groups of 3 are in 12? Pupils should also show that the same array can represent 12 4 = 3 if grouped horizontally. Stage 2: Grouping using a number line: Group from zero in equal jumps of the divisor to find out How many groups of _ in _? Pupils could and using a bead string or practical apparatus to work out problems like, A CD costs 3. How many CDs can I buy with 12? This is an important method to develop understanding of division as grouping. 21
22 Stage 3: grouping on a number line Children continue to work out unknown division facts by grouping on a number line from zero. They are also now taught the concept of remainders, as in the example. This should be introduced practically and with arrays, as well as being translated to a number line. 4 r1 Stage 3: Short division for TU U and HTU U Example Stage 4: Short division for TU U and HTU U with carry numbers Ensure that the children understand that the carry digit (2) represents the 2 tens that have been exchanged for 20 ones / units. 22
23 Stage4: Long division The next step is to tackle HTU TU, which for most children will be in Year 6. 23
Using objects, diagrams and pictorial representations to solve problems involving both grouping. and sharing.
Using objects, diagrams and pictorial representations to solve problems involving both grouping and sharing. Grouping: How many groups of 4 can be made with 12 stars? = 3 Example division problem in a
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 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 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 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 informationSt. Joseph s Catholic Primary School. Calculation Policy April 2016
St. Joseph s Catholic Primary School Calculation Policy April 2016 Information The following calculation policy has been devised to meet requirements of the National Curriculum 2014 for the teaching 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 informationWritten methods for division of whole numbers
Written methods for division 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 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 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 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 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 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 informationWritten methods for addition of whole numbers
Stage 1: The empty number line Mathematics written methods at the Spinney Written methods for addition of whole numbers The mental methods that lead to column addition generally involve partitioning, e.g.
More informationSwavesey Primary School Calculation Policy. Addition and Subtraction
Addition and Subtraction 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
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 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 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 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 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 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 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 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 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 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 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 informationMaths methods Key Stage 2: Year 3 and Year 4
Maths methods Key Stage 2: Year 3 and Year 4 Maths methods and strategies taught in school now are very different from those that many parents learned at school. This can often cause confusion when parents
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 informationMaths Calculation Policy September 2014
Maths Calculation Policy September 2014 Addition and Subtraction Progression Policy Adapted March 2014 to incorporate Years 12 and 7+ Visual Images??? Children should be selecting one of these three visual
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 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 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 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 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 informationCalculations Year 2 What We Do and How We Do It
Calculation Policy Calculations Year 2 What We Do and How We Do It The following calculation policy has been devised to meet requirements of the calculation strand of the National Curriculum 2014 for the
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 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 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 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 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 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 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 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 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 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 informationDartington Church of England Primary School and Nursery
Dartington Church of England Primary School and Nursery Maths calculation policy Mental and written strategies for: * addition * subtraction * multiplication * division Dartington C of E Primary School
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 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 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 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 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 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 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 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 informationSummary of the Steps for Written Calculation Division 1
Summary of the Steps for Written Calculation Division 1 Steps 114 lead children through the necessary stages for mastering the traditional column method of short division and begin to prepare them for
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 informationProgression for Subtraction
Progression for Subtraction Written methods for subtraction 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
More informationMake your child a Maths Star!
Make your child a Maths Star! A parents guide to helping your children with Maths Booklet 2 of 3: Key Stage 2 Year 3 to Year 4 It wasn t like this when I was AT school! Have you ever wished that you understood
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 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 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 informationA guide to how your child learns division
This series of leaflets are designed to help parents understand how we teach calculation at our school. Methods of calculating have changed over the years and hopefully this leaflet will help to alleviate
More information23 33 43 To bridge through a multiple of 10 eg 36 + 8 = 44 +4 +4
ADDITION Foundation Stage Year 1 Year 2 Year 3 Begin to represent numbers using fingers, marks on paper or pictures. Begin to relate addition to combining 2 groups of objects. Eg. Practical activities,
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 informationScholastic Do The Math
Scholastic correlated to the Grades K  7 2011 TM & Scholastic Inc. All rights reserved. SCHOLASTIC,, and associated logos are trademarks and/or registered trademarks of Scholastic Inc. Scholastic Correlated
More informationWootton Wawen C.E. Primary School. A Guide to Mental Maths
Wootton Wawen C.E. Primary School A Guide to Mental Maths Why is it important that children recall maths facts? Calculators should not be used as a substitute for good written and mental arithmetic. (National
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 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 informationCommon Core State Standards for Math Grades K  7 2012
correlated to the Grades K  7 The Common Core State Standards recommend more focused and coherent content that will provide the time for students to discuss, reason with, reflect upon, and practice more
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 informationProgression in calculation. Division. Children need to understand the concept of division, that it is: Repeated subtraction
Progression in calculation Division Children need to understand the concept of division, that it is: Repeated subtraction They also need to understand and work with certain principles: Inverse of multiplication
More informationOakhurst Community Primary School Maths Workshop for Parents. November 2009
Oakhurst Community Primary School Maths Workshop for Parents November 2009 Stages in Recording Mathematical Thinking Although this booklet is divided up into two educational stages Foundation Stage and
More informationWelcome to the Key Stage 1 curriculum evening for Maths.
Welcome to the Key Stage 1 curriculum evening for Maths. Whilst you are waiting, see if you can have a go at this maths problem. Please work with a friend if you would like to! How many different ways
More informationNumber Families By the end of Year 1 children should be able to recall and use facts within and to 20
Subtract from numbers up to 20 Immerse children in practical opportunities to develop understanding of addition and subtraction. Link practical representations to a number track and on a beadstring, to
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 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 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 informationCalculations at Holy Cross. Addition and Subtraction
Calculations at Holy Cross Addition and Subtraction Addition Mental strategies: Mental recall of number bonds 6 + 4 = 10 25 + 75 = 100 19 + = 20 Use near doubles 6 + 7 = double 6 + 1 = 13 Addition using
More informationMaths Calculation Booklet for parents
Maths Calculation Booklet for parents INTRODUCTION This booklet is intended to explain the ways in which your children are taught to write down their calculations. We have revised the school calculation
More informationAddition. Addition September 2015. Learning Intention Strategy Resources End of year expectation. Year Group. Early Years
Addition Group Learning Intention Strategy Resources End of year expectation Early s 1:1 correspondence with objects Recognising correct numbers Matching numbers to sets Counting Adding 2 sets together
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 informationYear 6 ADDITION. MENTAL CALCULATION. Many strategies, including: Mental recall of number bonds = = = = 20
Year 6 ADDITION MENTAL CALCULATION. Many strategies, including: Mental recall of number bonds 6 + 4 = 10 + 3 = 10 25 + 75 = 100 19 + = 20 Use near doubles 6 + 7 = double 6 + 1 = 13 Addition using partitioning
More informationStep 1 Representations Recordings Number count reliably with numbers from 1 to 20. Bead strings to 20 and 100 5+3=8 15+3=18. What else do you know?
Progression in calculation: Abbey Park Middle School NH 2013/2014 amended for APMS by IT June 2014, Addition and Subtraction Step 1 Representations Recordings count reliably with from 1 to 20 What number
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 informationCALCULATION POLICY FOR DIVISION THE FOLLOWING ARE STANDARDS THAT WE EXPECT THE MAJORITY OF CHILDREN TO ACHIEVE.
Foundation Stage CALCULATION POLICY FOR DIVISION THE FOLLOWING ARE STANDARDS THAT WE EXPECT THE MAJORITY OF CHILDREN TO ACHIEVE. Working vocabulary: compare, double, half, halve, share out, left, left
More informationParents Guide to mathematics in Year 4
Parents Guide to mathematics in Year 4 Ark Academy follows the Mathematics Mastery approach in Years R, 1,2,3 and 4. This will move up through the school with the children. In years 5 and 6 the National
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 informationPLACE VALUE MENTAL METHODS WRITTEN METHODS count in multiples of find half (from fractions)
LEEK EDUCATION PARTNERSHIP MULTIPLICATION AND DIVIS Y1 PLACE VALUE MENTAL METHODS WRITTEN METHODS count in multiples of find half (from fractions) twos, fives and tens Y2 count in steps of 2, 3, and 5
More informationPROGRESSION MAP Multiplication This must be viewed alongside the division map so that connections can be made. YR Y1 Y2 Y3 Y4 Y5 Y6
PROGRESSION MAP Multiplication This must be viewed alongside the division map so that connections can be made. YR Y1 Y2 Y3 Y4 Y5 Y6 Begin to understand multiplication by using concrete objects, pictorial
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 informationAddition. How is your child taught to add? Holy Trinity C.E. (C) Primary School. Introduction
Page 2 Introduction Holy Trinity C.E. (C) Primary School Addition How is your child taught to add? Mathematics is all around us; it underpins much of our daily lives and our futures as individuals and
More informationStandards Correlation: Symphony Math and the National Curriculum in England
Standards Correlation: and the National Curriculum in England National Curriculum Key and Year Key stage 1year 1: Numbernumber and place value count to and across 100, forwards and backwards, beginning
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 informationMake your child a Maths Star!
Make your child a Maths Star! A parents guide to helping your children with Maths Booklet 1 of 3: Key Stage 1 Year 1 to Year 2 It wasn t like this when I was AT school! Have you ever wished that you understood
More informationQuantile Textbook Report
Quantile Textbook Report My Math Grade 5 Volume 1 Author StateEdition Grade 5 1 Place Value 1.1 Place Value Through Millions 620Q 1.2 Compare and Order Whole Numbers Through Millions 600Q 1.3 Hands On:
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 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 informationProgression through the teaching of addition and subtraction
Progression through the teaching of addition and subtraction Maths has changed! The maths work your child is doing at school may look very different to the kind of sums you remember. This is because children
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 informationCedar Road Primary School Maths No Problem Calculation Policy
Cedar Road Primary School Maths No Problem Calculation Policy 201617 Textbooks and workbooks The textbooks allow teachers and pupils to explore each topic in real depth. From the 2500 handdrawn illustrations
More information