Adio a Thynnu Addition and Subtraction CA2/KS2 S 2.1 S 2.2 S 2.4 CymraegSaesneg

Adio a Thynnu

Addition and Subtraction

CA2/KS2

S2.1

S2.2

S2.4

Cymraeg

Saesneg

2

DARLITHOEDD DIWETHAF

TASG CYCHWYNNOL

1) Disgrifiwch beth yw’r gwahaniaeth rhwng data arwahanol a di-

dor.

2) Defnyddiwch dull lluosi byr i ddatrys:

i. 237 x 7

ii. 634 x 6

3) Defnyddiwch dull rhannu hir i ddatrys:

i. 767 ÷ 27

ii. 986 ÷ 36

3

AMCANION

RHANNU

• Sut mae rhannu yn cael ei addysgu yn CA 2.

• I ail-ymgyfarwyddo gyda dulliau ysgrifennedig

• I fod yn ymwybodol or camsyniadau a sydd

gen rhai disgyblion o rannu

4

O Dan pa amgylchiadau mae rhannu yn briodol?

Mae yna dri strwythyr ble mae rhannu yn amlygu ei hyn.

Y ddau strwythyr yma yw:

Nid ‘Rhannu rhwng’ yw’r unig fodel o rannu. Rhannu yn gyfartal yw un strwythyr.

Dylid dim rhoi gormod o bwysa ar y cysyniad a iaith i rannu gan anghofio am dan rhannu fod yn

Gwrth-wyneb i lluosi

Dysgu ac Addysgu

• Strwythyr rhannu cyfartal;• Gwrthidro i Lluosi• Strwythyr Cymhareb.

5

Beth yw’r strwythyr rhannu cyfartal?

Mae’r Strwythyr Rhannu Cyfartal yma yn cyfeirio at sefyllfa ble mae maint yn cael ei rannu yn gyfartal I rhif briodol ac yna rydym yn ceisio darganfod faint sydd ty mewn i pob rhan.

e.e. 20 marble yn cael ei rannu’n gyfartal rhwng 4 plentyn mewn gêm.

Y termau a geiriau allweddol yma yw; ‘rhannu’n gyfartal’ ag ‘faint ym mhob rhan’.

Dysgu ac Addysgu

6

Strwythyr gwrthdro i lluosi

Gwrthdro I Lluosi yn dehongli yn wahanol.

Nawr y cwestiwn yw: ‘Faint o grwpiau o 4 sydd yn y set o 20??’

Rhannu 20 yn hafal I 4 grwp, faint sydd ym mhob grwp?

Nawr yn rhannu 20 i bedwar grwp, faint o grwpiau?

7

Strwythyr cymhareb

Pan rydym yn cymharu dau rhif;drwy ysgrifennu cymhareb

20:80

.

Dysgu ac Addysgu

CYNNYDD MEWN RHANNU3 4 5 6

Bydd y camau a sydd yn datblygu tuag at rhannu hir yn cwmpasu blynyddoedd 4-6 drwu ddechrau ag:

Bl 4 - DU ÷ UBL 5- CDU ÷ U BL 6- CDU ÷ TU

Dechrau adio

Ymarferol, cyfri gwrthrychau a gwneud cysylltiadau gyda cyplysu grwpiau o wrthrychau.

Dechrau defnyddio llinell rhif

Defnyddio cychwyn – neidio – a cofnodi.(a) 2 adio 3 = 5 0 1 2 3 4 5 6 7 8 9 10

Dulliau adio pen

Er mwyn adio yn llwyddiannus rhaid:

• Galw i gof ffeithiau allweddol (bondiau rhif hyd at 10, 20 & 100, dwblu

a.y.y.b) a cymhwyso hyn i gyfrifiadau.

• Adnabod fod all adio mewn unrhyw drefn a defnyddio hyn i adio

cyfuniadau gwahanol. DDd + DDd

• Dosrannu DDd mewn ffurf gwahanol ac bod yn fentrus a creadigol.

• Deall y iaith a sydd yn gysylltiedig ac adio sef: mwy nag, swm, plws,

cyfanswm, cyfanrhif, i gyd at ei gilydd a.y.y.b

Dulliau ysgrifennedig o adio

CAM 1: Llinell rhif gwagMae’r linell rhif gwag yn help i gofnodi pan yn anelu tuag at rhif. Mae’r camau yn aml yn pontio ac yn pasio lluosrifau o ddeg

8 + 7 = 15

48 + 36 = 84 neu:

Drosodd i chi!

Defnyddiwch linell rhif i ddarganfod.

53 + 24

86 + 17

149 + 38

Dulliau ysgrifennedig o adioCAM 2: Dosrannu

Y cam nesaf yw i gofnodi dosrannu rhifau.

Mae dosrannu degau ac unedau yn adlewyrchu y dull colofn yn yr ystyr maent yn cael eu paru unedau gydag unedau a.y.y.b

Mae hyn hefyd yn ddull pen.

e.e: 47 + 76 = 47 + 70 + 6 = 117 + 6 = 123

neu 47 + 76 = 40 + 70 + 7 + 6 = 110 + 13 = 123

Mae rhifau wedi ei dosrannu yna yn cael eiYsgrifennu uwchben ei gilydd i gysylltu a dull colofn.

Drosodd i chi!

Defnyddiwch dosrannu i ddarganfod:

65 + 38

71 + 26

94 + 45

Dulliau ysgrifennedig o adioCAM 3: Dull colofn ehangach

Gall ddisgyblion yn awr symyd yn eu blaenau gan dosrannu yn eu penau ac ysgrifennu dull colofn.Dylie disgyblion gychwyn gan adio yr unedau.

NODER: Mae adio y degau 47 + 76 yma yngyfesur ag 40 + 70 = 110 yn hytrach nag4 + 7 = 11.

Drosodd i chi!

Defnyddiwch y dull colofn ehangach i ddatrys:

65 + 38

123 + 59

315 + 172

Dulliau ysgrifennedig o adio

CAM 4: Dull Colofn

Yn y dull llawn yma, mae cofnodi wedi ei leihau.Cofnodir rhifau a sydd yn cario o dan y linell, drwy gyfeirio at ‘cario 10’ a ‘cario 100’ yn hytrach nag cario 1.Yna maent yn datblygu i TriDd + DDd a TriDd + TriDd ac yna ddegolion.

Tynnu

21

BETH YW’R GWAHANOL CYD-DESTYNAU MAE TYNNU YN CAEL EI DDEFNYDDIO?

MAE YNA LLAWER O GYD DESTYNAU BLE RHAID I NI ADNABOD MAI TYNNU YW’R DULL BRIODOL. Mae’r rhain wedi ei dosbarthu i 4 grwp:

•    Strwythur Dosrannu•    Strwythur Lleihau•    Strwythur Cymharu•    Strwythur Gwrth-wyneb i Adio

22

What are the different kinds of situation to which the operation subtraction applies?

Mae’n bwysig fod athrawon yn adnabod ac yn rhoi cyfle i ddisgyblion arbrofi a phob un or strwythurau, yn hytrach nag dim ond gofyn 56 – 10..

e.e, I ddarganfod faint yn fwy mae geneth sydd yn 167 cm yn fwy na hogyn sy’n 159 cm (Strwythur Cymharu), gellir disgybl adnabod fod angen gwneud ‘167 − 159’, ond wedyn dehongli hyn gan feddwl ‘Faint sydd rhaid adio i 159 er mwyn cael 167?’ (Strwythur Gwrth-wyneb i Adio).

23

Mae ymgyfarwyddo gyda’r amrediad yma o strwythurau yn mynd i alluogi disgyblion i ddehongli cyfrifiad tynnu mewn sawl ffurf ac o ganlyniad cefnogi ei gallu i ymdrin a ystod eang o gyfrifiadau a cyd-destynau.

Dysgu ac Addysgu

24

Beth yw y Strwythurau Tynnu?

StrwythurDosrannu

StrwythurLleihau

StrwythurCymharu

StrwythurGwrth-wyneb i

AdioYn y strwythur dosrannuBu maint yn cael eidosrannu, ac mae rhaidtynnu i ddarganfodfaint sydd ar ol.

e.e. Mae 17 marbl mewn bocs, mae 5 yn cael eiTynnu allan; faint sydd ar ol?

Pan fydd maint wedi ei leihau ac mae’n rhaiddarganfod beth yw gwerth sydd ar ol.

e.e. Os yw pris beic yn £149 ac mae’n cael ei leihau gan £25, beth yw’r pris newydd?

Pan mae dau rhif yn cael ei gymharu ac mae’n gwneud synnwyr i dynnu er mwyn cymharu y ddau rhif.

Lle bum yn ceisio darganfod faint rydym angen adio ar ben rhif er mwyn cyrraedd targed o riw fath.

Mae’n tanlinellu y ffaith for y gwrth-wyneb i tynnu yw adio.

e.e. Gan fod 28+52 = 80, felly maen gwneud synnwyr fod 80-52 yn gwneud 52.

25

Beth yw y Strwythurau Tynnu?

StrwythurDosrannu

StrwythurLleihau

StrwythurCymharu

StrwythurGwrth-wyneb i

AdioLle bynag rydym yn dechrau gyda rhif, ac yna mae yna rhif yn cael ei dynnu oddi-wrtho .

GwrthrychauPresSiopGwaith Mesur

Pan fydd cost yn cael ei leihau, neu fesur tymheredd yn cael ei leihau.

PresTymheredd

Pan yr ydym yn gosod ddau rif wrth ei gilydd ac yn dymuno ei cymharu.

Mesur

Pan rydym yn cychwyn o rhif ac yn gofyn faint dwi angen i gyrraedd y targed

PresMesurMabolgampau

26

FFOCWS YMCHWIL: ADIO A THYNNU

Greer (1997),

Reviewing research into children’s responses to word problems in mathematics, identifies a widespread tendency for children to disregard the reality of the situations described by the text of the problem.

His analysis suggests that an explanation is not to be found in some cognitive deficit of the children, but rather in the culture of the classroom where word problems are presented in a stereotyped fashion.

Children learn that the solution involves the application of one of the basic arithmetical operations to the numbers mentioned in the text and look for clues as to which operation they should use.

Cyflwyno Tynnu

Dechrau gyda enghreifftiau ymarferol sy’n dilyn i ‘tynnu’.‘ Defnyddio gwrthrychau lluniau numicon, blociau canaeuon. (1,2,3 mam yn dal y pry, 6 crocodeil yn nofio yn yr afon..)

Dulliau Pen o Tynnu

• Er mwyn tynnu yn effeithiol rhaid :

• Galw i gof ffeithiau tynnu yn sydyn (bondiau rhif 10, 20 & 100, haneri

a.y.y.b) a chymhwyso’r rhain mewn cyfrifiadau.

• Tynnu rhifau un digid a dau ddigid yn y pen

• Deall fod tynnu yn gwrth-wyneb i adio, ac fod y drefn mewn tynnu yn

holl bwysig. (dechrau gyda’r rhif mwyaf)

• Deall y iaith o tynnu sef: llai, minws, tynnu, gwahaniaeth a.y.y.b

PROBLEM GYDA TYNNUCwestiynau cyffredin

• Mae Sam wedi cynilo 57c. Mae ei chwaer wedi casglu 83c

Faint yn fwy sydd gan Sam nag ei chwaer?

Mae Samir yn rhedeg 50m mewn ras tatw. Mae’n tynnu’n ol ar ol 18m

Faint yn fwy sydd ganddo ei fynd?

• Mae Nisha a Charlie yn pwyso ffrwythau. Mae Nisha’s gyda 38g. Mae gan Charlies 50g.

Faint yn drymach yw ffrwythau Charlies nag rhai Nisha?

• Mae blodyn haul yn 38cm o uchder. Mae un arall yn 83cm.

Beth yw’r gwahaniaeth mewn uchder rhwng y ddau flodyn?

Written methods for Subtraction

CAM 1: LLINELL RHIFMae’r dull yma yn helpu wrth gyfrif i fynnu:

• Cyfri i fynnu- gall camau gael ei cofnodi wrth gyfri i fynnu oddi wrth y rhif lleiaf tuag at y rhif mwyaf.

neu

Dull ysgrifenedig o Tynnu

CAM 1: LLINELL RHIFGyda ymarfer dylie disgyblion gofnodi llai a phenderfynnu i gyfri yn ol neu ymlaen. Mae’n hanfodol fod trafodaeth pam bryd ac beth yw’r gorau yn y sefyllfa…

Gyda rhif tri digid gall cofnodi gael ei leihau ond mae angen gallu cyfrifo 178 + ? = 200 ag 200 + ? = 326 yn y pen.

neu

Drosodd i chi!

Pryd y bysech yn defnyddio llinell rhif?

1) 59 - 11

2) 86 – 68

3) 142 – 35

4) 92-9

Dull ysgrifenedig o Tynnu

CAM 2: Dull Colofn EhangachGall ei cymwyso ar gyfer rhifau tri digid.

      Esiampl: 741 - 367

Dull ysgrifenedig o Tynnu

CAM 3: Dull Colofn EhangachMae’r dull yma yn pontio ynesaf gyda’e dull flaenorol, ac yn gallu bod yn feuchys.

Drosodd i chi!

Defnyddiwch y dull colofn ehangach i ddarganfod.

73 - 39

123 - 58

315 - 177

Dull ysgrifenedig i Tynnu

CAM 4: Dull ColofnMae’r dull ehangach yn cael ei fireinio i:

Drosodd i chi!

Defnyddiwch y dull colofn i ddarganfod y canlynol.

83 - 58

166 - 47

402 - 175

SYNIADAU GWERSI

SYNIADAU GWERSI

Be ydan ni wedi addysgu?

Sut?

Pa effaith y caiff ar dysgu ac addysgu?

Mwy?

NNS documents Dudley i mewn yn google.

SAFONAUS1.1 Deall anghenion dysgu pawb, gwneud y gorau o botensial a dangos ymrwymiadS1.2 Ystyried y dysgwyr a pharch at ei gilyddS1.3 Ysbrydoli dysgwyrS1.4 Cyfathrebu â rhieni a gofalwyrS1.5 Hybu’r ysgol fel rhan o’r gymuned ehangachS1.6 Gweithio gydag eraillS1.7 Ymrwymiad i ddatblygiad proffesiynolS1.8 Gweithio o fewn y gyfraith

S2.1 Gwybodaeth am bynciau(a) Y Cyfnod Sylfaen(b) Cyfnod Allweddol 2

S2.2 Nodau a chanllawiau’r Cwricwlwm CenedlaetholS2.3 Cynnydd rhwng cyfnodauS2.4 Sut y mae datblygiad yn effeithio ar ddysguS2.5 Defnyddio technoleg gwybodaeth a chyfathrebu (TGCh)S2.6 Anghenion Addysgol Arbennig (AAA)S2.7 Hybu ymddygiad daS3.1.1 Gosod amcanionS3.1.2 Cynllunio gwersiS3.1.3 Defnyddio adnoddauS3.1.4 Gweithio mewn timoeddS3.1.5 Dysgu y tu allan i’r ysgol

S3.2.1 Strategaethau asesuS3.2.2 Asesu i gefnogi dysguS3.2.3 Asesu o fewn gofynion cenedlaetholS3.2.4 Diwallu anghenion y dysgwyrS3.2.5 Cymraeg neu Saesneg fel iaith ychwanegolS3.2.6 Cofnodi cynnyddS3.2.7 Adrodd i rieni ac i eraillS3.3.1 Disgwyliadau uchelS3.3.2 [Addysgu sgôp / ystod oed arbenigol]S3.3.3 Rhoi gwersi effeithiolS3.3.4 Gwahaniaethu wrth addysguS3.3.5 Cymorth i ddysgu Cymraeg neu Saesneg fel

iaith ychwanegolS3.3.6 Ystyried amrywiaethS3.3.7 Rheoli amserS3.3.8 Defnyddio adnoddau’n ddiogel ac yn effeithiolS3.3.9 Rheoli ymddygiadS3.3.10 Defnyddio TGChS3.3.11 Hyd a lled y profiad addysguS3.3.12 Rhoi gwaith cartrefS3.3.13 Gweithio gydag eraillS3.3.14 Cyfle cyfartalS3.3.15 Datblygu cynaliadwy a dinasyddiaeth fyd-eang

http://wales.gov.uk/docs/dcells/publications/090915becomingateacheren.pdf

Addition andSubtraction

CA2/KS2

S2.1

S2.2

S2.4

English

44

PREVIOUS LECTURES

STARTER1) Describe the difference between discrete and continuous

data.

2) Use the short multiplication method to find:

i. 237 x 7

ii. 634 x 6

iii. Use long division to find:

iv. 767 ÷ 27

v. 986 ÷ 36

AIMS

To have an overview of the skills children need to calculate.

To understand how to support your child with maths. To be more aware of the models, images and

resources used to support the teaching and learning of maths.

Think about the progression from mental towards written methods.

ADDITION

47

What are the different kinds of situation to which the operation of division applies?

There are two basic categories of real-life problems that are modeled by the mathematical operation we call addition. The problems in each of these categories may vary in terms of their content and context, but essentially they all have the same structure.

•    The Aggregation structure

•    The Augmentation structure

I find it is useful in teaching to have these in mind to ensure that children have opportunities to experience the full range of situations and, most importantly, the associated language that they have to learn to connect with addition.

48

What is the aggregation structure of addition?

I use the term aggregation to refer to a situation in which two (or more) quantities are combined into a single quantity and the operation of addition is used to determine the total.

For example:There are 15 marbles in one circle and 17 in another: how many marbles altogether?

The key language to be developed in the aggregation structure of addition includes: How many altogether? How much altogether? The total? The sum of.

Teaching and Learning

49

What is the augmentation structure of addition?

I use the term augmentation to refer to a situation where a quantity is increased by some amount and the operation of addition is required in order to find the augmented or increased value.

For example, the price of a bicycle costing £149 is increased by £25: what is the new price?

The key language to be developed in the augmentation structure of addition includes: Start at and count on, increase by, go up by.Start on notches and then count!

Teaching and Learning

It should just be mentioned at this stage that if the number added were a negative number, then the addition would not result in an increase, but in a decrease.

50

What are some of the contexts in which children will meet addition in the aggregation and augmentation structures?

AGGREGATION

Problems involved with moneyand measurement, wherever a summative answer is needed.A concept of summing quantities together.

AUGMENTATION

Problems involved with moneyand temperature, specifically when money is increased or decreased. Children’s age is a good example. Augmentation is a concept that connects with the use of number lines.

PROGRESSION OF ADDITION METHODS

Beginning to add

Practical, counting objects and relating addition to combining two groups of objects

Beginning to use a number track

Use of the number track- hopping and recording.(a) 2 and 3 makes 5 0 1 2 3 4 5 6 7 8 9 10

Mental Strategies for Addition

• Secure mental addition requires the ability to:

• Recall key number facts instantly (number pairs to 10, 20 & 100,

doubles etc) and to apply these to similar calculations

• Recognise that addition can be done in any order and use this to

add mentally different combinations of one and two digit numbers

• Partition two-digit numbers in different ways, including adding the

tens and units separately before recombining

• Understand the language of addition including more than, sum,

plus, greater than, total, altogether etc)

Written methods for Addition

Stage 1: The empty number lineThe empty number line helps to record the steps on the way to calculating the total. The steps often bridge through a multiple of 10.

8 + 7 = 15

48 + 36 = 84 or:

Over to you!

Use a number line to find answers to these sums.

53 + 24

86 + 17

149 + 38

Written methods for AdditionStage 2: Partitioning

The next stage is to record mental methods using partitioning.

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.

eg: 47 + 76 = 47 + 70 + 6 = 117 + 6 = 123

or 47 + 76 = 40 + 70 + 7 + 6 = 110 + 13 = 123

Partitioned numbers are then written under one another:

Over to you!

Use Partitioning to find answers to these sums.

65 + 38

71 + 26

294 + 145

Written methods for AdditionStage 3: Expanded method in columns

Children can now move on to a layout showing the addition of the tens to the tens and the ones to the ones separately. Children should start by adding the ones digits first.

The addition of the tens in the calculation 47 + 76 is described as 40 + 70 = 110 as opposed to 4 + 7 = 11.

Over to you!

Use the expanded column method to find answers to these sums.

65 + 38

123 + 59

315 + 172

Written methods for Addition

Stage 4: Column method

In this method, recording is reduced further.Carry digits are recorded below the line, using the words 'carry 10' or 'carry 100', not 'carry 1'. Later, extend to adding three two-digit numbers, two three-digit numbers, numbers with different numbers of digits and decimals.

SUBTRACTION

63

What are the different kinds of situation to which the operation subtraction applies?

There is a daunting range of situations in which we have to learn to recognize that the appropriate operation is subtraction.

I find it helpful to categorize these into at least the following four categories:

•    The Partitioning structure;•    The Reduction structure;•    The Comparison structure; and•    The Inverse-of-addition structure.

64

What are the different kinds of situation to which the operation subtraction applies?

Each of these has its own characteristic language patterns, all of which have to be connected in the learner’s mind with subtraction.

It is important for teachers to be aware of this range of structures, to ensure that children get the opportunity to learn to apply their number skills to all of them.

Being able to connect subtraction with the whole range of these situations and to switch freely from one to the other is also the basis for being successful and efficient at mental and informal strategies for doing subtraction calculations.

For example, to find out how much taller a girl of 167 cm is than a boy of 159 cm (which is the comparison structure), a child may recognize that this requires the subtraction ‘167 − 159’, but then do the actual calculation by interpreting it as ‘what must be added to 159 to get 167?’ (which is the inverse of addition).

65

Familiarity with the range of subtraction structures and the associated language patterns will enable children to interpret a subtraction calculation in a number of ways and hence increase their ability to handle these calculations by a range of methods.

Teaching and Learning

66

What are the structures of subtraction?

PartitioningStructure

ReductionStructure

Comparison

Structure

Inverse–of-AdditionStructure

The partitioning structure refers to a situation in which a quantity is partitioned off in some way or other and subtraction is required to calculate how many or how much remains.

For example, there are 17 marbles in the box, 5 are removed, how many are left?

The reduction structure is similar to ‘take away’ but it is associated with different language. It is simply the reverse process of the augmentation structure of addition. It refers to a situation in which a quantity is reduced by some amount and the operation of subtraction is required to find the reduced value.

For example: if the price of a bicycle costing £149 is reduced by £25, what is the new price?

The comparison structure refers to a completely different set of situations, namely, those where subtraction is required to make a comparison between two quantities.

The inverse-of-addition structure refers to situations where we have to determine what must be added to a given quantity in order to reach some target. The phrase ‘inverse of addition’ underlines the idea that subtraction and addition are inverse processes.

For example, that since 28 + 52 comes to 80, then 80 − 52 must be 28. The subtraction of 52 undoes the effect of adding 52.

67

What are the most common contexts associated with the structures of subtraction?

PartitioningStructure

ReductionStructure

Comparison

Structure

Inverse–of-AdditionStructure

First, this structure is encountered whenever we start with a given number of things in a set and a subset is taken away (removed, destroyed, eaten, killed, blown up, lost or whatever).

Money and shopping. For example, we might plan to spend £72 from our savings of £240 and need to work out how much would be left (that is, carry out the subtraction, 240 − 72).Measurment

Realistic examples of the reduction structure mainly occur in the context of money. The key idea which signals the operation of subtraction is that of ‘reducing’, for example, reducing prices and costs, cutting wages and salaries.

For example, if a person’s council tax of £625 is cut by £59, the reduced tax is determined by the subtraction, 625 − 59.

Wherever two numbers occur we will often find ourselves wanting to compare them.

The first step in this is to decide which is the larger and which is the smaller and to articulate this using the appropriate language.

The process of comparison is a central idea in all measurement contexts

There are many commonplace situations where we encounter this structure: for example, any situation where we have a number of objects or a number of individuals and we require some more in order to reach a target.

The most convincing examples for many will be in the context of sport.

68

RESEARCH FOCUS: SUBTRACTION

Greer (1997),

Reviewing research into children’s responses to word problems in mathematics, identifies a widespread tendency for children to disregard the reality of the situations described by the text of the problem.

His analysis suggests that an explanation is not to be found in some cognitive deficit of the children, but rather in the culture of the classroom where word problems are presented in a stereotyped fashion.

Children learn that the solution involves the application of one of the basic arithmetical operations to the numbers mentioned in the text and look for clues as to which operation they should use.

Introducing ‘take away’

Begins with practical demonstrations of subtraction relating to ‘take away’. Use of number tracks, pictures and songs (10 green bottles, 5 little speckled frogs).

Beginning to take away

•Number tracks leading to number lines introduced for recording ‘jumps’ back.• 8 - 3=5

1 2 3 4 5 6 7 8

Mental Strategies for Subtraction

• Secure mental subtraction requires the ability to:

• Recall key subtraction facts instantly (inverse of number pairs to 10, 20 &

100, halves etc) and to apply these to similar calculations

• Mentally subtract combinations of one and two digit numbers

• Understand that subtraction is the inverse of addition and recognise that

subtraction can’t be done in any order (it has to start with the larger

number)

• Understand the language of subtraction including less, minus, take

away, difference between etc)

The problem with subtractionTypical Questions

• Sam has saved 57p. Her sister has saved 83p

How much more money does Sam have than his sister?

• Samir is running a 50 metre potato race. He drops out after 18 metres

How much further does he have to go?

• Nisha and Charlie weigh fruit. Nisha’s weighs 38g. Charlies weighs 50g.

How much heavier is Charlies fruit than Nishas?

• One sunflower is now 38cm high. Another is 83cm high.

What is the difference between the heights of the sunflowers?

Written methods for Subtraction

Stage 1: The empty number lineThe empty number line helps to record the steps in mental subtraction.

• Counting Up - the steps can also be recorded by counting up from the smaller number to find the difference

or

Written methods for Subtraction

Stage 1: The empty number lineWith 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, 86 - 77 or 43 - 28.

With three-digit 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.

or

Over to you!

When would you use a number line?

1) 59 - 11

2) 86 – 68

3) 142 – 35

4) 92-9

Written methods for Subtraction

Stage 2: Expanded column method It can also be applied to three and four digit numbers.

      Example: 741 - 367

Written methods for Subtraction

Stage 3: Expanded column method Depending on the numbers it can get quite complicated and this stage may need a lot of time and perseverance!

Over to you!

Use the expanded column method to find answers to these sums.

73 - 39

123 - 58

315 - 177

Written methods for Subtraction

Stage 4: Column methodThe expanded method is eventually reduced to:

Over to you!

Use the compact column method to find answers to these sums.

83 - 58

166 - 47

402 - 175

LESSON IDEAS

LESSON IDEAS

What have we learnt?

How?

What effect will this have on learning?

More?

NNS documents Dudley in google.

STANDARDSS1.1 Understanding everyone’s learning needs, maximizing potential and demonstrating commitmentS1.2 Consideration for learners and mutual respectS1.3 Inspiring learnersS1.4 Communication with parents and careersS1.5 Promoting the school in the wider communityS1.6 Working with othersS1.7 Commitment to professional developmentS1.8 Working within the law

S2.1 Subject knowledge(a) Foundation Phase(d) Key Stage 2

S2.2 National Curriculum aims and guidelinesS2.3 Progression between stagesS2.4 How development affects learningS2.5 Using information and communications technology (ICT)S2.6 Special Educational Needs (SEN)S2.7 Promoting good behaviourS3.1.1 Setting objectivesS3.1.2 Planning lessonsS3.1.3 Using resourcesS3.1.4 Working in teamsS3.1.5 Out-of-school learning

S3.2.1 Assessment strategiesS3.2.2 Assessment to support learningS3.2.3 Assessment against national requirementsS3.2.4 Meeting learners’ needsS3.2.5 English or Welsh as an additional languageS3.2.6 Recording progressS3.2.7 Reporting to parents and others

S3.3.1 High expectationsS3.3.2 [Teaching specialist scope / age range]S3.3.3 Delivering effective lessonsS3.3.4 Differentiating teachingS3.3.5 Supporting English or Welsh as an additional

languageS3.3.6 Taking account of diversityS3.3.7 Time managementS3.3.8 Using resources safely and effectivelyS3.3.9 Managing behaviourS3.3.10 Using ICTS3.3.11 Length and breadth of teaching experienceS3.3.12 Providing homeworkS3.3.13 Working with othersS3.3.14 Equal opportunitiesS3.3.15 Sustainable development and global citizenship

http://wales.gov.uk/docs/dcells/publications/090915becomingateacheren.pdf