Guidance on calculation methods for Parents Key Stage 2

Transcription

1 Guidance n calculatin methds fr Parents Key Stage 2

2 This bklet has been written in rder t help yu understand hw the fur rules f additin, subtractin, multiplicatin and divisin are taught in ur schl and t give yu sme ideas f hw t help yur child with their wrk. One f the mst valuable things yu can d with yur child is talk t them abut mathematics, when ut shpping, playing games invlving numbers, cking etc. This may include: 1. Talking abut any maths wrk that they bring hme frm schl. 2. Asking them t help yu when yu are ding things with mney, r measuring r weighing. Ensuring they have the pprtunity t handle mney (buying things and receiving change) and encuraging them t read a range f scales; weighing scales, tape measures, temperature scales, speedmeters. 3. Helping them t learn their multiplicatin tables: 7 year lds shuld knw the 2- and 10-times table 8 year lds shuld knw the 5-times table. 9 year lds shw the 3- and 4-times tables. 10 year lds shuld knw all their tables t 10 x 10 Encuraging them t recgnize the relatinship between different facts will help them t learn eg 9 x 6 = (10 x 6) 6 r 4 x 7 is duble 2 x 7 4. Helping them t learn their number bnds as these underpin much f the mathematical teaching that is dne at schl. Fr example, they need t understand the relatinship between grups f numbers up t 10 and beynd, such as: = = = = = = = = Telling the time, bth digital and analgue. Using magazines t find ut when a TV prgramme is n and helping t set the vide recrder. 7. Lking at the price f things in catalgues r when ut shpping and wrking ut if yu can affrd them. Discuss sale signs eg 20% ff r ½ price sale.

3 Helping with maths hmewrk Hmewrk is just ne f the many ways in which yu can help yur child t develp cnfidence with mathematics. We aim t ffer a range f different types f maths hmewrk activities eg maths games, investigatins r puzzles and frmal written activities. Hmewrk will usually fllw n frm what has been happening in class and smetimes yur child might be asked t d sme preparatin fr the next tpic t be cvered in schl. There will be times when yur child wrks n their wn, but they will always benefit frm talking t yu abut hw they have tackled their wrk. What yu'll see in yur child's maths bks In Key Stage 2 when children lk at calculatins they will be encuraged t cnsider the mst apprpriate methd f calculatin eg a mental methd, a mental methd with jttings and later a standard written methd. With 7 t 8 year lds the emphasis is n mental wrk rather than n calculatins written dwn in clumns. The aim is fr children t d mathematics in their heads but if the numbers are t large, they may use paper and pencil t avid lsing track. Sme children will sketch pictures and diagrams t help them. Yu may be surprised t see these in yur child's mathematics bk. Fllwing n frm wrk in Key Stage 1, many children in Year 3 children will set calculatins ut like this: = 42-6 = This will cntinue int the later part f Key Stage 2 when children are fcusing n mental methds. Yu will see them keeping track f what they are ding their head like this: = = = = ( ) + (7 + 4) = = 91 Only in the later primary years, when the child s class teacher feels they are ready, will children be taught cnventinal written methds, many f which yu will recgnise. Hwever the rute t reach these methds yu may nt recgnize. We are aiming t develp the children s understanding f the prcess rather than the prcess itself. Teaching children the methds we used at schl t sn can cause irreparable gaps in children s mathematical learning, s please cnsult yur child s class teacher (r this bklet) if yur child s methds are unfamiliar t yu.

4 ADDITION A lt f wrk in Key Stage 1 is dne n adding pairs f single digit numbers tgether mentally s that the children knw their number bnds t 10, 20, etc. Mving n, the children shuld then be able t add pairs f 2 digit numbers mentally reasnably cmfrtably and recrd their mental methd befre being intrduced t vertical written methds. Eg: = (hrizntal) (vertical) In years 3 and 4, children will carry n using hrizntal recrding f additin and subtractin t supprt their mental calculatins. The example belw shws tw ways f adding 76 and 93. The first splits the numbers int tens and nes (units) then adds the tens fllwed by the nes t give 169. The secnd example uses the idea f runding t 100 by taking 7 frm 76 and adding it t the 93 t make it 100 s making the additin easier. Children will als cntinue t use drawings, diagrams and blank number lines t supprt their thinking, as belw. The use f numberlines is strngly encuraged by the Natinal Numeracy Strategy, nt nly fr additin but als fr subtractin. Answer: = 21 Answer: = 7

5 Twards the end f year 3 and int year 4, mst children will be taught written methds, including vertical additin fr thse calculatins that they can t d in their heads. At this stage these will be expanded methds which are ways f recrding that make the prcess f adding the different digits clear t children. These expanded methds build n the mental methds they have been learning and shuld help children t understand what is happening as well as reinfrcing their understanding f place value by calling the digits by their value eg tw hundred add ne hundred rather than Here is an example f adding using an expanded methd. The blue team s scre f 287 pints is increased by 145 pints. What s the new scre? When the number f digits in the numbers is increased r decimals are intrduced the children will practise sme examples using an expanded methd befre returning t the cmpact methd. SUBTRACTION As with additin, the children will need t be able t carry ut simple 2 digit frm tw digit subtractins mentally and recrd their methds befre being intrduced t a vertical written methd e.g r 64-30= = cunting up t find the difference cunting back They shuld als be able t partitin numbers int tens and units e.g. 64 = and a multiple f 10 and a teens number e.g. 64 =

6 They are then intrduced t expanded written methds: 50 1 e.g This is later increased t three digit numbers: This is extended t include exchanges frm hundreds t tens, and frm hundreds t tens t units. e.g e.g When the child s class teacher feels this is cmpletely secure, they will be intrduced t a cmpact methd Which is later increased t three digit numbers When the number f digits in a questin is increased r decimals are intrduced the children will wrk thrugh sme examples using the expanded layut befre returning t a cmpact methd but they will wrk with a methd that is apprpriate fr them.

7 The price f a cmputer is reduced frm 767 t 619. By hw much is it reduced? This shws the same calculatin in its cmpact frm and is the methd yu may recgnise. It is reduced by 148. MULTIPLICATION Children shuld be reasnably cmfrtable with multiplying single digit numbers by single digit numbers (they might nt have instant recall f all multiplicatin facts but shuld be able t wrk ut facts reasnably quickly). If children knw the 2 times table, which is nly duble the 1 times, then the 4 times is easy because yu just duble the 2 times. Then yu can duble the 4 times t get the 8 times. The 3 times dubles t the 6 times and 12 times, the ten times can be halved t give 5 times and s n. This uses the knwledge children are develping thrugh additin and subtractin and makes imprtant cnnectins fr them. This chart shws hw this wrks fr the 2x, 4x and 8x tables. x times times times The early wrk children d intrduces them t the ideas f multiplicatin and divisin. They are cunting in different patterns, helping t see hw multiplicatin is repeated additin and divisin is repeated subtractin, shwn hw divisin is the ppsite f multiplicatin and taught t understand place value (that in 234 the 2 is 200, the 3 is 30 and the 4 is 4 nes (units)). This knwledge and understanding, with much f the wrk being dne in their heads, pens up a whle wrld f facts fr them and they dn t all have t be memrised. That can make dealing with numbers feel a lt easier. The children are taught t be able t use single digit multiplicatin facts e.g. 3x4 t calculate single digit x multiple f 10 e.g. 30 x 4 and partitin numbers int tens and units eg 34 = 30 and 4.

8 Partitining e.g. 12 x 4 (10x4) + (2x4) = = 48 43x = 215 (40x5) (3x5) Grid layut same methd slightly different layut 17x3 x =51 add mentally This is extended t numbers where the answer ges ver x6 x = 228 add mentally Later mve n t a 2 digit number by a multiple f 10 42x30 x =1260 add mentally This is then extended t 2 digit by 2 digit 34x27 x ) add these ) mentally if pssible 918

9 Finally children are intrduced t a cmpact methd by relating it t the grid layut same calculatin different layut 38 x x x 6 x ( 6 x 8) 28 ( 7 x 4) 180 (6 x 30) 210 (7 x 30) (20 x 4) 600 (20 x 30) x 6 38 x x27 34 x (7x34) 680 (20x34) 918 DIVISION Befre undertaking written divisin, children shuld be able t divide numbers by 10 and 100 mentally, understanding hw the digits mve. They shuld be able t halve numbers and be beginning t understand relatinship between x and. ie that they are inverse peratins and that divisin facts can be derived frm multiplicatin nes. 10 2=5 5x2=10 They will have experience f sharing 12 3 = 4 and f gruping (repeated subtractin) 12 3 = hw many 3 s make 12? They shuld be able t wrk ut examples such as 12 3 by rephrasing as hw many 3 s make 12? then cunting up in multiples f 3 t 12. 3, 6, 9, 12. 4x3=12 The idea f repeated subtractin eg hw many 3s make 12 is carried thrugh t the written methd chunking. Chunking invlves taking away chunks f the same size until yu run ut. It uses the fact that divisin is repeated subtractin f the same size grup.

10 Fr example, 20 4=5 invlves subtracting 4s frm 20 until it s been used up. Yu can d this 5 times. The children start with simple calculatins linked t their mental wrk and as the size f the numbers increases, the chunking written methd is mre efficient than cunting up. e.g hw many 5 s make 73? x x = 14 r3 Children are encuraged t think abut chunks they knw first giving a bank f knwn r derived facts t wrk frm. e.g. 10x5=50 This enables children t remve larger chunks s 20x5=100 etc. Once the children have mastered this, divisin ntatin is intrduced but the prcess is retained. Children then extend t 3 digit numbers subtracting chucks 7 ) x x x 7 4 Answer 36 r4. This is cmpacted by remving larger chunks e.g. 10x7 = 70 20x7 = ) x7 = x x7 4 Answer 36 r4.

11 By the end f Key Stage 2, this is extended t 3 digit divided by 2 digit: e.g. 36 ) x x x36 0 Answer 27. Mre cmplex divisin will invlve dividing 3 digit numbers by a 1 digit number and 3 digit numbers by a 2 digit number. With divisin, as with all calculatin, it s imprtant t think abut what the actual prblem is asking when yu cme t give an answer. As they mve int years 5 and 6 children will still be encuraged t chse the mst suitable methd f calculatin, mentally if pssible. Where this is nt pssible they will be using expanded r cmpact methds and a calculatr fr mre cmplex and invlved wrk. Children need t feel cnfident with numbers and t enjy playing with them and using them. If yu have any questins n any f the issues raised in these ntes, please d nt hesitate t cntact yur child s teacher at schl. Further infrmatin can be fund n the fllwing websites: fllw the link fr parents, then curriculum then numeracy which includes games and puzzles fr children t play the schls sectin f the bbc website has a whle range f fun activities fr children t d n the cmputer. Fllw the numeracy link t find activities t help children learn tables, recgnize shapes, d simple calculatins and even revise fr their KS2 SATs. This dcument was riginally prduced by Bringtn C f E Primary Schl and we wuld like t thank Peter Allen, wh was the Head Teacher at that time, fr sharing it.