ADDITION AND SUBTRACTION

Presen,.,.Arobot is I machine that is mnlr l ed IMJ I computer pl'Of'lfflffle and IKlt1t to help people. hbots perhrm Np1es. wart in fadns.,, . . lllderwattr nl outtr .... enttrtain us. and do l'IIIIIIJ mare tasb. Not al hbots hM the . . . of I person. but the robot shown here Is Ill ....... nlN,t INlilt to Mlp anund the house and also to help elderhJ or sidl people. If Its heicJht 11 Im 50 cm, how lll8IIIJ cm is that? Find the sum. Check your answer by adding up. •' I ob ' a. 1 ! 7 i 8 : • 4: i 2: 1 . •. • ••.•• ( .......... : ••. •. •••• I ··•··•·••:•·•• •· · •: • • •· • ••· • , ..... ;••·• •··•·•;• · •••• • ••'· •• • ••• · I ..... ..... ... ........ .. ;), + 7 :: 4 i; 2 ♦: 1 : 7 \\ 8: : I + 3:9: 1:5 ♦: 4 0: 2: 1 I ······ ··················· ··••· I ; ! : I ········ ······················ ...... ···· ·· · ··: ··· · :· ····\" \"\" :· · · · · · · · · . , • • •••• .,,.,,,., . ...... •·•· I + 7i 4i 2 I ··· ············ ·· .. ··········· ....... , ... ....... ........... , ....... Subtract. Check your answer with addition. •• , .. .... :··• · ·• · ··•:•· \".... . ,, ► ........:..........:......... b. 6 [ 3 ! 5 i 8 .► I -• ·······•• :••····•..•:•-········=········· , ' ••••••• • • ;••• •• • u • o~•• • • • • •• •• i • • •• • • • • • 3 16 ! 5 : + 3 16 \\ 5 2: 1I4:3 ; ••••••• • •: .......... \\ •H •••• • t ·······••:.-·•······•.:·······-·=.········· ,1 + · ·~···1····~····1· ··~···1····~··· .,,I :: : .- I~ ~ :: : • Arobot that has been sent to Mars sends back 459 photos on one day and 765 photos on the next day. How many photos does it send in all? • The same robot has been fitted with 5oo batteries to keep it working on a long space mission. If 324 batteries have died out, how many batteries are still working in the robot?

~ l ) ADDITION ! Addition with Regrouping Example 1:Two robots assemble car parts in a factory. One robot fixes 7125 parts and the other robot fixes 3799 more parts than the first. How many parts does the second robot fix? Parts in all thesecond robot fixes IIP.. 7125 + 3799 =? L _ 2~s~ - ~ -:-~~~7~- _ _ 1_1=2s_____,J--• ....... .. ....,.,,.....?... ,.. ,,,..,. 37·9··9-~·••\" .... _ j1~, Moreparts fixed by Parts the first robot fixes thesecond robot ~HTI If+ ~h H - -1 TTh Th H T 01 .1 Th H T 0 1 1 1i 7 .1 71 ....... 5 7 1 2 '5, 37 2 51 1 3 99 + 9 ·. 9 + , . 3 7 9 7 9 ' 7.. 1 : 2 2 ·4 I 10 +3 7 9 2 41 4 Answer:The second robot fixes 10,924 parts. ..Example2:23512 +28975 = ? :Start with the ones : TryThis! m · Th : H : T [ O : place and move · ..... ' . ': ..' ...... .....-~...... ..:......... : cowards the left. : Solve. a. 8084 + 2946 b. 26341 + 13959 Project Take any 3-digit number. adding up. Reverse it and add. + i 7 6 15 Reverse and add again. ... 1 /3 I3 /2 i+ 2 / 3 / 3 1 ~ou have made a palindrome! A palindro is a word or a number that reads the same both forward or backward.Try it with afew other numbers like 409, 253, and 824.

,t1111111se 2 A ··-.... _.. _.__ ... -··--····· ·---....... -.--...-· :_':.~·..... 1• Add down. Check by adding up. a. o1 7 . 6 ~-- -, I ~ •- • ---···,b. r 6 2 4 8 I!,,' 1 i-- - • - -r· - j 1---------..•l______+ 3 8 6 f- - --.J I I' •' 6 2 4 8 11 0 7 6 ;~ l + I 3 8 6 ,; _J'+ II 1 9 5 6 I'' I j ------ I t-- - j + I_, 9 _5___6. i:' . d. 8176 +7995 .), h. 2754 +3097 c. 35816 + 12307 e. 5946 +9312 f. 27756 +68878 g. 6248 +3986 i. 1591 2 + 56034 j. 39590 +20612 2. Add. Check. a. 2 8 ,b. 3 - 8 4 6 C. 1 3 9 4 2 d. [ 2 6 1 2 5 87 . . . . ·;. 2 6 5 .1 0 ,9 5 .2 -. + 1 5 :9 +3 0 0 0 9 5396 +3 8 7 6 +23 187 l 3, Solve. Project a. Charles Babbage designed the Add consecutive odd numbers. first mechanical computer in 1822. Email was invented 149 years later 1+ 3 =4 =2 x 2 (2 numbers added) by Ray Tomlinson. In which year was email invented? 1+ 3+ 5 = 9 = 3 x 3 (3 numbers added) b. In 1642, Blaise Pascal invented 1+3+5+7 =16 =4 x 4 (4 numbers added) the adding machine. 336 years later, the solar pocket calculator . Continue up to 10 consecutive odd numbers was invented. When was the solar using the pattern. pocket calculator invented? .a.Using aII the digits 1, 2, 4, 6, 8, and 9, create a 3-digit addition question with thegreateot sum possible.

~,,---· SUBTRACTION Subtraction with Regrouping /J. drone isaflying robot that can be controlled remotely. It has many uses, including disaster relief, conservation and tracking of anfmafs, agriculture, and health care among others. Example T: A drone was sent Into a flood-affected area to help peopfe there. ft had to deliver 3421 Foodpackets to be delivered L ---packets of food.So far it has delivered 1732 ---j4f1- - packets. How many more packets need to I1 __ 1732- - _ ,- be delivered? Alreadydelivered Yet to bedef{ :!1> 3421-1732= ? - -- ------ -- - Th H T 0 Th H T 0 Th H T HT0 11 13 1l 13 11 1 11 3 ,,r' 11 z2 ,% / 11 z2 % ~ A' ~ 34z% 3 A' z ,r ~ A' ,r 173 2 1732 173 2 1 73 9 89 689 I1 6 8 Answer. 1,689 more packets need to be delivered. &omple2:21840-18395 =? Check your answer by adding. - Tlh Th H T o : 1 :'. 8 _: 4 ._; 0 7 13 . ___' r y2 ,' ► I 11 . 7 : ,E ' 10 -, : ·a· 3-··r 9-·-;-s··· + ,, z .-1' . g _;~ --: g i 3 / 4 i 4 : 5 ,' '-- ► 2 1 !8 /4 : 1;s :3:9:s Answer: 3,445 c. 2 ; 8 ! 1 i S 9··r6·-\"i 4-·rs··

11btracting with Zeros obotlc cleaners move around a space on their wn, cleaning and mopping floors. ample 1: A powerful robotic cleaner Is built for OOo hours of cleaning. A less powerful robotic First robot hours leaner can work for 1327 hours. How 3000 I1321 m,uch longer can the first robot work? 1 • 3000 - 1327 = 7 Second robot hours SttP 1: Step 2: Step 3: Not enough ones, tens, or hundreds. Regroup hundreds. Regroup tens. Subtract. Regroup thousands. Th H ' T \" O Th : H T '. 0 Th : H : T ! O ......,... •· ..! ........:.,.... . ,. .. ,, : . . . . . \". \" :9: , '9 9 2 <·\"10··;······..··1 ···•··· I:I 2 !' J1j : J6 . 10 3 : .0' ! 0 : 0 2 i .W ; 10 ; ,3' g ; g 'g ····:•\" .. •·;·•··· ·..··:·\"·\"--• .. .......... . . . ..~.J.~.:.~-.! ,o.. I: ' ... 1l3 ;2 :7 1 1 3 ;2 :7 1:6.7l3 Answer:The first robot can work longer by 1,673 hours. Example 2: 4010 - 1867 = ? Th H T 0 ~. . . .. .. . .. ....,..' ... ..' ....,.. ... ··-· . . ·• ...... --·· ... . ·•· . ... ......... ..... .., ... .,,.. , ., Use a shortcut: 9 10 3000 ) ---+ 3 000 - 1) ---+ 2 999 z3 .w y io - 1 3 2 7 -+ - 1 3 2 7 - 1 -+ - 1 3 2 6 A' % g 16 7 3 186 7 *, Use a quicker method. Combine the place values. 214 3 Think of 3000 as 300 tens. Then regroup 300 tens as 299 tens and 10 ones. Answer: 2,143 299 10 Then subtract as usual 3000 - 300 o- 300-8' - 132 7 167 3 ......... . J Try This! a. 6000 - 2938 b. 7010- 5399

) Exercise,2 B·----___ _____ --------------- ... _________ _ ________ _I~,-- , I I, ... ---- 1. Subtract. Add to check your answer. a. 8 ) O ; O : 0 ,► b. 1 : 4 ; 3 8 : 9 ,► ••• . .• •, • .. • \".\" •. I \" .. .. ·; .. • ...: . ' .. .. ;· •• \" \" . .. ······: · ·•· · .. '' .. ... I - 1 :7 ·6 :2 I+ 1 :7 :6 :2 9 i 7 6 2 :+ I I I I I ,I c. 4865-1673 d. 5632 - 2486 e. 7839 - 4234 g. 68425 - 41395 f. 47653 - 23854 h. 73971 - 12895 2. Subtract. Watch out for the zeros. s..fc. 7 ! 0 / 1 ) 0 a. 6 \\ O : O : O b. 9 l O l O : 1 8.... . . ·•· ···· ·'.···•·····: •....... ,:.,. ...... . ·······:-········=···•·.. ··=..······• - ···,-·..r··2··--1... - 2 [4 :3 :8 - 8 f4 :6 :3 s_J s_j__o_J_o___ e. 9020 - 1896 f. 5002 - 2049 ~8 16 ) 2 g. 7000 - 4213 h. 4600 - 1778 j. 56800 - 25324 i. 18000 - 131 so rare we in now? How long ago were these invented? ~es:_-, Microwave oven-1946 / Ball point pen-1888 · Thermometer-1593 / , -' I\\ • ... •---..._~-...,..~.. ___' _,....,:,I-----~-...---~----rrr-- the data 'Air Distances Between Major aluru to Delhi fly than a plane

robot ls ~howlng Rtyadifferent w.1ysto add 37 .. 22 c•value and 37 + 22 38 + 36 panyone /\\ /\\ aa,.,. 20 2 .;,1 + 8 + 36 37 + 20 = 57 30 + 36 = 66 57 +2= 59 66 + 8 = 74 37 + 22 = 59 38 + 36 = 74 ''· ·---·------~ ............ _.. & Use place value and 37 + 22 C. Count in tens. / \\ / \\lnak up both the numbers. 37 + 22 30 7 20 2 37+ 10 + 10 + 2 30 + 20 = so 7+2=9 47 + 10 + 2 50 + 9 = 59 57 +2=59 37 + 22 = 59 37 + 22 = 59 U. place value to solve. Break up any one number. a. 24 + 12 b. 11 + 58 c. 44 + 24 d. 63 + 19 e. 58 + 18 f. 25 + 48 Mt by counting in tens. b. 37 + 31 c. 62 +26 e. 23 + 48 f. 19 +38 & 33 + 25 c. 34 +36 4. 45 + 34 f. 69 + 42 by breaking up both numbers. 23+42 ~ 55 + 34 53+27 ~ 75 +26 ., -'. .. , ,· ~ • r • • • •_. - - - E'nge! OQQQ Q the pieces in the circle the connecting pieces same number.

] SUBTRACTION STRATEGIES This is how DOST explains different ways to solve 38 - 21 . A. Use place value and 38-21 = ? 72 - 45 I break up the second I number. I\\ I\\ I I 20 1 40 5 I 38- 20 = 18 I I 18 - 1=17 I 38 - 21 = 17 I I I 72 - 40 = 32 : I 32 - 5 = 27 : I I I 72 - 45 = 27 : II : ----------------------~ B. Count for·:1ard from the smaller C. Count forward from the small number to the bigger number number to the bigger number in tens. in steps. 21 to 31 is10 31 to 38 is 7 l1 to 30 is 9 10+7=17 38 - 21 = 17 c. 55-32 d. 91 -25 e. 84-28 f. ard in steps. c. 75-24 d. 38-19 e. 46-27 f. 76-47 j. 61 -58 k. 95-27 I. - -..----,-, - --- -' \\ -·- ' -#....•--· .. - ~- .\"!' .- ... ,.. - - ,- - - - , ~ -

:for a pattern In the differences. Then write the next two. 13, 16, 23, 26, 33, 1s, 16, 21, 25, 26, 31 Make up one of your own using the same idea. Wfdtill you see a pattern. Then complete. a. 1+2+3= _ _ _ _ b. 1+2+3+4+5 = - - - - 2+3+4+5+6 = _ _ __ 2+3+4= ____ 3+4+5= _ _ __ 3+4+5+6+7 = _ _ __ 4+5+6= _ _ __ 4+5+6+7+8 =- - - - What do you notice about the What do you notice about the sum of 5 consecutive numbers? sum of 3 consecutive numbers? c. 1+2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 Give the sum of these numbers. From 11 to 20 = 155 From61 to70= _ _ __ From 21 to 30 = 255 From 71 to 80 = _ _ __ From 31 to 40 = _ _ __ From 81 to 90 = _ _ __ From 41 to 50 = ----==- From 91 to 100= _ _ __ From 51 to60 = - - - - Write a number out of 1, 3, 5, 7, 9, 11, 13, 15, or 17 in each circle so that the sum of the numbers in the circles on each side of the triangle is exactly 30. Each number can be used only once. 'J:ental Maths When you want to subtract 19, • When you want to subtract 29, first subtract 20. Then add 1. first subtract 30. Then add 1. 65-19 - + 1r·6··5·····-····2····0····=····4···5···..\"i- + 65-19 l j--+r..- -···-- -··- -, 87 - 29 1i 87 - 29 ---+ 87 - 30 = 57 i 45 + 1 = 46 1 = 46 I 57 + 1= 58 i. = 58 L .-.. i. .. .. . .... ....... .. ............. J Do these mentally. a. 46 - 19 b. 73 - 19 c. 85-19 d. 37-19 g. 93-29 h. 76-29 f. 57-29

4 . Look at the pattern to complete the towers. . . · · · , • • flj ....... .. .. . . . . . . a. b. .: The nurn top is the the two nu below· . .••••••• Ill! •• s. Explore a shortcut to add consecutive numbers. 1+2+3+4+5+6=? 7 Project +~+ Complete this famous series of numbers call the Fibonacci Series. 7 1, 1,2,3,5,8, 13, _ _ _ _ 7 Use this idea in an addition trick. 3 +4 = 7, 2 + 5 = 7, Write any two numbers. 1+6 =7 Say 7 and 4 there are 3 pairs ofnumbers I up to 7 each. the sum. Add them: 7 + 4 +8 Add the previous two numbers: 4 + 11 IAdd the previous two numbers: 11 + 15 Add the previous two numbers: 15 + 26 when you have six circled numbers. numbers. What do yo

ON AND SUBTRACTION OF MONEY ng and subtracting money, take care to place the points one below the then add or subtract like you add or subtract any other numbers. to put the point In the same place (two digits from the right) in the ...,..•And the total money due in this bill. If a?500 note and a ~200 note were the shopkeeper, then what was the amount received as change? -r-~ -~......,,,.. ..,. !Wlterbottle Bill ;\"! .,, v-t -:• .ill .'!' ~ ,.i.4i.so·. · --···,1s.oo~ , •-,-···-· -........_,,........... _, · • 1 '9 i L - \"\" ._,., !. School'bag . .. . . -:- .. . . . . ,214~50. . . . . . . Pend,box·. . . . .T. -......~·2a.'so. . . . . . .--- \"''·•....................i......................... .. ............... Money given 99 6 )6 )6 10 7/a!a .fl0 Total t , 520.50 Bill amount -520.50 Balance due f179.50 .......,179.50 was received as change. -,,,,at-r.~Lr ;findthetotal moneydue in each bill. Find the amount received aschange in ach case. .. Pa,d: ~~ -~ '1 l'::'1~ 1,• ' 9 _J ~ i'91 1 •-\"\"'• ~ ••lilJi'J~ '\"\"\"\" Bill Bill - ..--.,.n••-•-•.,..•o....•••.,.••••••••••-•..••••••••••••••.,. -••••••--••..•••.......,........~..••••..... -•••-•u•\"•••..•--••--- .,• Shirt ! f 220.00 ...umbrella ......Lf245.S0···-····· Pant I f350.S0 · ..~~t:...Raincoat........Lf1.60.S0______ boots..I· ,,so.so_._______ --.--······-·······--······· .················................. 1 Tie I f 165.00 •---•-••••-•l•O-••-•-•••••••: ••••••••••••••-•-• ••- •••••••••••• Total dfferent ways to make f100. Use more high-value notes. ber of notes and coins ···················· ............... ··············· ······································· ······················•····· 0 i f20 fl0 fS ..........;.. '............ ...., .................. ','.... ..U...s..e...f.S.. ..a..n..d....f..1..0........................................ ,·······=··············· ···············............... ··U···s··e···f··1··0···a··n···d···f·2··0···· ······ ··············. ·········· ....,...:......4........................ ....' ..2........ ..U...s.e....f.2..0...,..f..1..0..,..a...n..d...f..S.............................. 0, and f10

•'· o,,3. \"rpltl ''\"\"l\" 11, r<'•'' Ufo o,w pJt tll ul,H d,,y, tlw b.,nk rt'tt'IVl'd t'i0,928 ttntl gr1vc out t 45,021, Haw mN<' mont'y w,H n•t t•lvrd by tlw b.mk th,rn glv<.•n out 7 b. M, l\\h,\"' h\"\\ ,Q,23, In thr b,rnk. 1ll' w.rnt s to l~ave only f 2,500 there and take re~\\. How much mo,wy c,rn hr t,,kc oul? c. Th~ Meht,,s bought fridge W M, vi\\lued at i\\ nrw f, ldq<' ;rnd g.wr In their old fridge In exchange.Their 2,300.Thry h,Hi to p,1y the dealer t 16,756. What was the t th~lr new frldgr? d. The Mathew family went on a holiday to Coimbatore. On the fi rst day they spe day they spe , i.24S. Over the next two d,,ys they spent t2.457 and on the last 't980. How much money did they spend In all? Had '25,000 Gave out \" 10,000 Received \" 8750 How much money Is In the machine now7 It coin, they will both have ~.... h wlll have twice the num I ,

,110BLEM SOLVING • teps of Problem Solving 41,e steps of problem solving help you think In an organised way and decide how to solve aword problem. Scientists need 250 samples of rock from deep under the sea. Ifarobot brings 125 samples on one trip and 90 samples on 11,e second trip, how many will it need to bring on the last trip to finish the job? SteP 1: Read the problem and understand the question. We need to find out how many samples the robot has to bring on the last trip to complete the job. Step 2: Rnd the important fnformation in the problem. • 250 samples were needed. • So far, the robot has brought 125 samples and 90 samples on the first and second trips, respectively. Step 3: Decide what to do. Wemust first find out how many samples were brought in all on the first two trips and then subtract that from the number of samples required by the scientists. This is a two-step problem. Step 4: Solve the problem and answer the question. • 125 + 90 = 215 samples already brought • 250 - 215 = 35 samples left to be brought Answer:The robot will need to bring 35 samples on the last trip. Step 5: Check your answer. • Is the calculation correct? Yes, I have checked the addition by adding in reverse: 125 + 90 = 215 is correct · because 90 + 125 = 215. ✓ I have also checked the subtraction with addition: 250 - 215 = 35 is correct because 35+ 215 = 250. Have you answered the question correctly using the correct units? Yes, the answer gives the number of samples that the robot will bring on its last trip. Does your answer make sense? Yes, the answer of 35 samples makes sense as it is a smaller figure than the number of samples required in all.

I• ' Read - R -- j -- - - l :··E~~-;~·~·~;;i~k-~f·~-;~·~~~-~~;····:.. fi I.I1 -Find- - --·of .··_-~_J_.__. _.._. ·-· ·- · ·· · ·-- -, =· to remember the steps .•.:::••• R - F- O - S - C? ~ ••• J' ·-· .........- __ ., : .I. O.~ci<:1e _-- ·-- ...... ... - -· ·.....{ My sentence is Rita Finds · ;. .. s~lve ...L .. -· ~ - ·-·/ -· ----· --- .. . -· --· .. ·I . Dogs So Cute. What is yours? : r: . i_ Chee~_!___ C __J __ _ •. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ••: '' Solve keeping the steps of problem solving in mind. Use addition, subtraction, or multiplication. Some may be two-step problems. 1. Mrs Mathews ordered 275 id/is for the school party. She ordered 125 less samosa id/ls. How many samosas did she order? 2. You have f750. You want to buy a sweater for t455 and a jacket for f570. How m1 more money do you need? 3. Amber threw a ball to a distance of 25 m. Ankita threw it three times as far. How Ankita throw the ball? 4. A laptop has enough charge for 75 minutes of usage. It is charged for another 9 minutes of use. It is then used for 112 minutes. How many minutes of charge is s available on the laptop? 5. Rashid practised 8 maths questions every day for 5 days. In those same days, Ro practised 12 fewer questions than Rashid. How many questions did Rohan practi I ··········································~ ' ~~r:ii~~1;1.1;,4.it~~-~' ~.-!• .................................• ~ 125 - 25 99 + 1 350-2 W/ti'IJ~lt '~ ~Qi ~\"1~t~~~ ~fJ>~IWV 11 QJI? c::otnp&.\\te.. codin9 lan9\"a9e, 100 is 1100100, ht.-y is 100 yea..s lon9. 0th day of this yea.. is a _ _ Is 1 followed by a 100 ze..os. 20x 5 60+

PROBLEM SOLVING USING BAR MODELS In the steps of problem solving, in step 3you have to decide how to solve the problem. Sometimes drawing a simple bar model can help you during this step. Addition Models , Example 1: At the Inventions Competition, there were 125 entries from secondary school, 98 entries from middle school, and 75 entries from primary school. How many entries were there in all? The bar model shows 125 us that we need to 1 • Entries in all 98 add to find how many + 75 t ···· ·····1··2···5········ ·· ·····c:·····?·····9··8····· •·······i·········7···5··· ······ l . I entries in all. 298 Secondary Middle Primary 125 +98 + 75 =? School School School ~ Answer: There were 298 entries in all. Example 2: Class IV students went to the Science Quiz. There were 26 boys in the class. There were 7 more girls than boys in the class. How many girls were in Class IV? 1Llt Girls in all 26+ 7=? 26 +7 Boys More girls than boys 33 The bar model shows us that we need to add the number of boys to the number of girls more than the boys, to find the total number of girls. Answer:There were 33 girls in Class IV. Example 3: Anushka has to download some songs from the internet. So far she has downloaded 24 songs. There are still 19 songs left to be downloaded. How many songs does Anushka have to download in all? Hit Songs 24 Try This! I· · · 24········ ? .- ··· ·19 I + 19 Solve with the help ofa bar model. Downloaded Left to be 43 Akila has 543 stamps and her downloaded uncle gave her his collection d 264 stamps. How many stamps Answer: Anushka has to download 43 songs in all. does she have now?

Subtract· °'EhXasam43p/neo7t·e••TobhoneoMktesaotcodhecehlrsewcaks. of Cla check.ing t he h rnework notebooks So far she has mathskedo17 notebooks. How manys'ls\\~•',Two- chec 1Exam Il . c _notebooks does she have to check? rest v, 43 - -- - - - t Notebooks to be checked I d I shows us that tt The bar mo fi~d the difference I J11 - 43 i we need to tebooks to find how many no Already Yet to be are yet to be checked. checked checked 1 ' Answer: 26 notebooks are yet to be checked. . nd She has an order for 162 candles. Sheh~ special ny candles has Serena already~ Example 2: Serena makes ca ies. made some, but still has 49 left to make. How ma An Ill.. 162-49= 7 162 Try This! Ex Candles to be made l th· I 16 2 Solve with the help of abar 49 t r _ _, _62_ _ _ 113 _ model. 11 t 49- - I ? Of a 1,000 piece jigsaw p~ .J Amrita has fitted 807 pieces. Left to be Already How many more pieces are · made made needed to complete the pld Answer: Serena has already made 113 candles. Comparison Model Example: Anandita weighs 48 kg. Her younger sister Priya weighs 36 kg. How much less does Priya weigh than Anandita? . . . . . . . . . . . . . . . . . . . ··••111111 n• The first bar shows Anandita's weight. The second bar is a :· When we compai shorter bar because 36 < 48. The difference in the length of f quantities, we ~ the two bars shows the d1·u11erence • we1.g ht of the two sisters. :····· .. -~tw··o····b.a.:rs.:·\"1 in Anand/ta [ 48 kg ] 48 .:.·· i - 36 Priya J___3_6_k_g_---...1] 7 II . 12 j I Answer: Priya weighs 12 kg less than Anandita. -

Two-Step Problems Example 1:There were 1SO people at the party. 62 were men, 58 were women, and the rest were children. How many children were at the party? I'~ People-in all -- ] 62 The first model tells us to add to f 150 find how many men and women were there in all. I62 62 +58 =? Men 58 ? + 58 In the second model, we use the Children information from the first model Women 120 and subtract to find how many 120 children were at the party. People in all ? 150 150 Children - 120 150-120 =? 120 30 Men and women in all Answer: There were 30 children at the party. Example 2: There were 654 apple trees in an orchard. There were 112 more pear trees than apple trees in the orchard. How many trees in all were there in the orchard? m• I·.. . . .Thohwe fimrsatnmyopdeealrtterellsesuswteoreadthdetroePear trees in all 654 ~ind _ +112 in a11. 1 _ . . ·······I 654 i 112 . 766 654 + 112 = ? Apple trees More pear trees than apple trees 766 Trees in all 766 The second model tells us to add to find how many trees were there in all. 1 1- 766 ' 654 ··1 + 6 5 4 766+654=? 14 2 0 Pear trees Apple trees Answer:There were 1,420 trees in the orchard. Try This! Solve with the help of bar models. Anewly launched website was visited by 9,875 people on its first day and 6,532 p the second day. How many more people visited the website on the first day than second day?

.. Exercise 2 G··-----.-.-.----·········-···-·-·--·--------··---·-·',-:'·__ Solve these addition and subtraction problems r· ....... ··- ... with the help of bar models. 1 1. Alarge bookstore needs to keep 1,500 copies of the dictionary in stock. It presently has 987 copies In stock. How many more copies does it need to reach the number of dictionaries it needs to have? 2. Abuilding set came with 325 pieces. Kriti added some more pieces from her previous set to the new set and she now has 402 pieces in all. How many pieces did she add to it? 3. Aparking lot can hold many cars. Presently 2,090 cars are parked in it. There is space for 1,632 more cars. How many cars can the parking lot hold? 4. Acarpet factory manufactured 16,453 carpets in one year. It manufactured 1,243 more than that in the following year.How many carpets did it manufacture in both the years together? S. Aconstruction site needs 8,976 bricks to complete a wall. The masons have used 3,098 bricks and have 2,813 bricks in stock. How many more bricks have to be bought to complete the wall? 6. Students of Class IV collected 2,197 used ~ storybooks in one week and 1,123 books in the second week. Of these, 974 books were __,\\.................- ,..............................._..... __,,,,_,........... ............. donated to the school library and the rest were sent to avillage school. How many books were sent to the village school? Journal :Explain why ItIs Important to write the numbers correctly according to place value whlleadding and subtracting.

pROBLEM SOLVING SKILLS Extra Information 50,ne problems may have information that you do not need to use to solve it. Read the problem given below carefully and use only the facts you need. Example: Sarita supplies costumes for school programmes. L_. She buys 67 m of green cloth, 23 m of red cloth, 81 m of blue cloth, and 66 m of white cloth. Sarita used the green, red, and blue cloth for 98 costumes. How much material did she use in all? 111• To find out how much material Sarita used in all, we do not need the number of costumes. Since she used only the red, blue, and green cloth, we do not need the length of the white cloth. We only need to use the lengths of green, red, and blue cloth. 67 +23 +81 = 171 m Answer: Sarita used 171 m of material in all. Solve. Use only the information you need. 1. In aword game, Ananya scored 231 points, Abhishek scored 147 points, and Apoorva scored 204 points. How many more points did Ananya score than Apoorva? 6Eji rJ 2. The painters of 25 buildings have to complete the work in 30 days. They need 423 cans of white paint and 678 cans of B red paint. How many cans of paint do they need in all? 3. For awedding that was to be attended by 750 people, the decorators used 795 red roses and 670 white lilies. How many flowers did they use for the decoration? 4. Class 4 had 300 tickets to sell for the school fete. They sold 67 tickets in one week and twice that number in the next week. How many tickets did they sell in both weeks? 5. Anuj had a fS00 note. He first spent f 142 on an ice cream for himself and his friends. Later he bought apacket of chips for f20. How much change did he get when he bought the lee cream?

PROBLEM SOLVING STRATEGIES Simpler Numbers Sometimes when the numbers in a word problem are large or the words are confusing, we are not sure how to solve it. It helps to think of the problem again u..._ smaller numbers. -, Example: What number should be added to 45,386 so that the sum is 93,942? ,.., Observe: 45,386 is smaller than 93,942. Think: Take 4 instead of 45,386 and 9 instead of 93,942. What should be added to 4 so that the sum is 9? You know that the answer is s. You have to subtract 4 from 9 to get 5. Solve the actual sum. 9 \\. 3 ) 9 , 4 ( 2 - - : . : Answer: 48,556 should be added to . 45,386 to get 93,942. 4 [- 5 ; 3 \\ 8 ) 6 - - - 4 \\-. s i- s \\ s \\-. 6 . ~ 2 I ·----------- -- - - - - - - - - - - - - - - - ' - ~ , ---- ---~I Use the simpler number strategy if you need to. ····················-········-- ,_,_.-..9.. the number that is 9,284 more than 18,394. { Find the number which\\ ~ is 2 more than 5. The ~ lhe number that is 8,392 less than 15,896. :·-...a..n.s..w...e.r..i.s.·7-..!..:S·.··o···a··d..,d_.,.,I': ......,....JfflillerJs 3,698 than 21,065? -lsAaM2 iegthan 50,693? subb• led from 64,932 sothatthl: diffe.ence is 13 sum m9,146 and 2,9341ssubbaded tmm ~~.., to 23,192 to get47,938?

Counting in tens • Count forward • Regrouping ° Consecutive I Information • Bar models • Difference a Number patterns f I • I : I t Solve the following questions. 1298 b. 6 o 1 o c. 3 8 0 0 d. 6 0 1 0 5 - 29352 +7538 +4 386 - 1674 Bill Balance=? Ice cream j f 52.00 Paid =~: i ::m:ii . ·Tot~·i. .. .. .-. .·r·. ·· ···. · ···. . . . . . Solve. If there is extra information, use only the information you need. a. Aschool shop had 100 sets of uniforms for sale. Of these, 27 sets were sold in the morning and 35 more sets than that were sold in the evening. How many sets were sold in the evening? b. Alarge stadium can hold 10,000 people. One day there were 5,050 people of which 2,976 were women. How many were men? • Solve using bar models. a. There are 42 adventure books in a library. There are 12 more puzzle books than adventure books in the library. How many puzzle books are there in the library? b. Azookeeper has to feed 52 animals in all. [ ~[ID~· ---------', So far, he has fed 23 animals. How many more animals does he have to feed? : Write the following numbers using 1 Tick (✓) the correct answer. : Roman numerals. find the number that is 1260 less than 7296. : a. 19= - - b. 2 4 - - - ................·-·············-·........... ·······•..........................-...............................,.........l : c. 37=-- {a. 8556 b. 6036 c. 8000 d. 12987 l • ••• .. ••••-• •••••• ••••••.. ••••••••o•u ••••••••••• •••• •••-• ••• ••• •• ••--• • ••• .. •••• ••• ••••••• •••• •.. ••• .. •• • ••• • •• ••••• • •••)

AYear On APlanet ... ............ , -..... ..·. : This worksheet '•,.. The Earth takes 365 days to go around the Sun. ~ connects maths t··\\ The other planets are also orbiting around the Sun. . and science. ..:~ We can calculate the time taken by them to do so I. ♦.•• •• in terms of earth-days. I e e I• f •. f •II e f f • Some of the information inthe table is missing.Use the clues given below to fill in the information.Then answer the questions. I IJPlanet : lNumber of earth-days I: to go around l1 10759 I 60190 I lj :I ll I, 365 687 the Sun lI r-••-. U•••-•••••••• ••••••· Oo• ·•·•• • ..... •••••••••h•••••••••to-.oo• \"•••••••••• • ••• • •• •l••oOo oo.. , o..... ,,ooo, ......... , O•·•-••••••••••• ••• •• ••• • OOOOO.. • • •••••••--••- ._ 0 ' CLUES 1. Venus takes 140 earth-days less than Earth to go around the Sun. ! 2. Jupiter takes 3,646 earth-days more than Mars to go around the Sun. I 3. Uranus's journey around the Sun takes 19,928 earth-days more than Saturn. i \\ 4. Mercury and Neptune together have atotal of 60,278 earth-days in their journey ! around the Sun. l · i ! _,...i'\\,, . ..........._ • ••- -..... ,' . . . ....... \" . ....... ... . .. .. . . . ........ ' . .... . ....... . _. , •• • ' ......... . . ' ..... .. ...... ' . .... ....... .. . . ...... . .. . . . . ' .. ,.,_ , ... , ...... . ................ ,.._, •••••••••••••• ' .... . .... .. .... . ... . . ••1<••· ........... Answer these questions. 1. If an astronaut spends one year each on Jupiter, Uranus, and Mars, how many days would he be away for? 2. What can you say about the relationship between th'e planets' distance from the Sun and the time taken to go around it? 3. How much less time does Jupiter take to go around the Sun as compared to Saturn? 4. How much longer does Neptune take to go around the Sun as compared to Earth?

Background: Robots are programmed using [North] computer language called coding in order for them Up to follow instructions. Robots often need to be able ('- to move about a space in order to perform their functions. For that they need to be programmed ~ \\' with directions-north, south, east, and west. ~ Left (- ( ...\\ ) .. ·, r.:==l ·-- ( · ::_J Right ~ Materials: Pencil for shading '· . \\. ,) - I ,; \"- ~ .1 .T Preparation: Students may work independently after Ji ; ·- ✓ understanding the chart alongside. Down Procedure: DOST the robot needs to be programmed to go from [ South ] the orange square to the green square using a particular path. Fill in the squares on the grid following the programme given as sequence of letters. a. Go south b. Move 9 spaces a. Go west b. Move 5 spaces d. Move 7 spaces d. Move 5 spaces c. Turn east c. Turn north f. Move 4 spaces e. Turn west I• I DOST is now moving about in a home. The grey portions show obstacles in its path. Write a programme giving it directions for the shortest path from the orange square to the green square. Cupboard ------- -..,,' Ext . ..... It Fridge , , ens1on \"',' t-- t-- ,' Ifyou invent a \\ Bed ,' robot, make a list of \\ !: at least five things that Counter ~ you would program it ,' Wall \\ -Desk shelves >-- \\ to do to help people ,' ' ,' everywhere. , ,, ' ... .... ... _______ , , It

tA_ ,, - #- - 'V --· . ~ ' --~ ':) 23 + 25 = ? 102 + 98 :: ? P/.i~s1r.g con~eortive number= 2'1 r···· .. ,..,-·· ... ✓-, - ____ _ Double of 24 = ~8 t·\" 98 + 100 = 198 23 + 25 = 48 198 + 2 = 200 __ _.,,,... ../ ;/ 102 + 98 = 200 Practice b. 34+36= - -- -----c. 49+51 :: a. 21-4-23 = - - e. 102+ 64 = - - - f. 202 + 53 ::: -~ d. 101 +38= __ _ --- Use B - .. - -- - A- a. Sum of place values of the digit 6 a. 81 more than 19 is in 63,826 is _ _ _ __ b. 649 rounded to the nearest 100 is b. 3,00,000 + 5 = c. 69,399 Is one less than C. 6,000-50 = d. 72,642 - 70,000 = d. 42+44 = e. Double of 90 is : f. 96,000 + 4,000 = e. 89+ 101 = g. 1,16,000 Is one more than f. 125 + 75 = g. - 1000= 587 h. 714 rounded to the nearestten ~ h. 59 + = 100 29+ =SO i. Half of 1SO is _ _ _ __. j . Roman numeral for 29 is 5,800 + 8,964 - 5,000 =