Ganitha Kalika Andlana Teachers Training Mdule 1
Ganitha Kalika Andlana Teacher Training Mdule develped and designed by Akshara Fundatin Akshara Fundatin, April 2015 This cntent is made available by Akshara Fundatin and can be dwnladed fr free frm its website www.akshara.rg.in. Sme rights reserved. This material is CC - BY licensed. Full terms f use and attributin available at www.akshara.rg.in/cc 2
Guideline fr using this mdule: 1. This training mdule is fr the resurce persns identified by DSERT and have been participated in training cnducted by Akshara Fundatin. 2. This shuld be nly used as guideline fr cnducting training fr teachers. But the details f the training shuld be referred frm Teacher handbk. 3. Resurce persns are expected t refer this bk well in advance and prepare fr the training alng with the cntent frm Teacher handbk and frm the cntent prvided during training cnducted by Akshara Fundatin. 4. Since Ganitha Kalika Andlana s apprach is t treat students as a active learner, resurce persns are expected t facilitate the sessin using the TLM and make the participants t perfrm activities using TLMs. Make sure that teachers understand that every student needs t be given pprtunity t use TLMs in the classrm prcess. 5. Please make sure that the apprach f the Ganitha Kalika Andlana is understd by the participants clearly during II sessin n day ne. Since whle prgram is based n Cnstructivism, C-perative learning and CCE it is very imprtant that teachers understands these 3Cs. 6. Please mentin that TLM prvided in the Kit will help teachers in cnducting classes in jyful manner and helps students in cnceptual understanding f the maths cncepts cvered in the text bks f class4 and 5. This is nt a separate prgram and teachers need nt t feel that it will be an extra burden n them. 7. It is recmmended t use the numbers mentined in the examples during activities. 8. Resurce persns are expected t take measures t adhere t the timing mentined in the mdule. 9. Resurce persns are expected t facilitate all the cntent prvided in the mdule withut any negtiatins. 10. Mentin teachers t sick help if needed frm CRPs/RPs during their schl visits. 3
TEACHER TRAINING MODULE DAY 1 Sessin 1: [10:00-10:30] Icebreaker: Make the participants play Fire in the Muntain and then make grups f 5 r 6. The participants sing Fire in the Muntain run run run r Bettadalli benki hachtu di di di. The trainer calls ut a number between 0 and 9. The participants make grups indicating the called number. Eg Trainer calls 9 the participants make grups f 9 members. Fr 0 all have t sit. End this game with 5 r 6 as required. Sessin 2: [10:30 10:45] Apprach f Ganitha Kalika Andlana (GKA): T understand the apprach f Ganitha Kalika Andlana. Material t be used: Teachers manual and ther reading materials. Facilitatr will explain the fllwing briefly based n the infrmatin given during the training and teacher s manual: Abut Akshara Imprtance/need f GKA. 3 C s : Explain Cnstructivism, C-perative Learning and CCE Cntinuus and Cmprehensive Evaluatin emplyed in GKA CRA cycle: Elabrate n Cncrete, Representatinal and Abstract phases f math learning. 5 E mdel f learning: Explain hw 5Es (Engage, Explre, Explain, Elabrate, Evaluate) can be effectively implemented using the TLMs and Cncept cards in the GKA kit. Cperative r Grup Learning: Explain the prcess fr c-perative learning, like: Making Grups Assigning names and chsing leader. Facilitating the grup learning prcess. Mnitring and mtivating the grup. 4
Strategies f Cllabrative r Cperative r Grup Learning: Explain different strategies fr driving the grup activities: Facilitatr driven- Facilitatr gives the prblem. All grups slve it. Any ne member frm each grup explains the slutin. Grup driven - Grup leader frm ne grup ges t the next grup and gives them a prblem and bserves. Each grup leader shares their bservatin with the class. Grup leader driven- Each grup leader gives their grup members a prblem and asks them t explain the slutin t the grup. Grup Member driven- Each grup member gives any ne member a prblem and the rest bserve and share their experience with the grup. Sessin 3: [10:45 11:00] Intrductin t Number system. Thugh the GKA is fr class 4 and 5 the kit cntains the TLM fr class 1 t 5. Knwing t use these TLM fr teaching number system fr class 1 t class 3 will be prerequisite based n which rest f the cncept is taught. CRP/RP will nly mentin the use f TLM fr the cncept mentined belw withut demnstratin. Material t be used: Cunters, base ten yellw cubes, abacus rings r real life bjects can be used fr this. (Nte: Cunters can be stuck t black bard by dipping it in water.) During this sessin facilitatr will explain/demnstrate the cncepts f number system required fr class 1 t 3 in brief: Existence and Nn Existence: It is imprtant t understand the cncept f existence and nn-existence befre starting t cunt. T teach the cncept f existence shw sme bjects in ne hand t and nne in ther hand t shw nnexistence. Knwledge f bjects: Using cunters prvided in the kit teach participantst srt as per clr. Using mixed bjects ask participantst srt as per shape. Cmparisn: Take tw quantities and ask which is mre? and which is less? If participantsstack the tw sides and cmpare d mentin this is pssible nly when the thickness f the bjects is same. Use ne t ne crrespndence t cmpare. 5
Cnservatin f Quantity: T establish this, use Cllectin f a bject with same attributes, different attributes, Cllectin f different bjects with same attribute and different attributes, Arrangement f bjects Clsely packed r spread ut Oral Number names: Using rhymes r chant intrduce the names f the number. Quantity and ral Number name assciatin: Shw particular quantity f bjects and intrduce the number name. Make sure students recgnize the quantity and say its number name; similarly represents a quantity when the number name is said. Cunting: Frward cunting and Backward cunting Intrduce the cncept f zer by backward cunting and Writing zer. Cmparisn: Intrduce <, > and = sign. Ordering: Intrduce the term ascending and descending and their meaning. Ascending means starting with the smallest number and descending means starting with the biggest number. Numerals: Intrduce t numerals using flashcards and place value strips. Make use child learns recgnitin f quantity and matches it with the crrect numeral and representatin f quantity by identifying the numeral; Writing numerals in square line bk. Using Number beads/line intrduces tw Digit Numbers and place value. Intrduce Number names eleven t nineteen, ten, twenty, thirty, frty, fifty, sixty, seventy, eighty, ninety by cunting till ninety nine. 11:00 11:15 : Tea break Sessin 4 [11.15 12.00]: Three/ Fur/Five Digit Number cncepts This is t address the understanding f 3, 4 and 5 digit number cncepts. Emphasis needs t be given n gruping by ten, place value, face value, rdering and cmparing the numbers. Materials t be used: Cunters, base ten blcks, place value mat, place value strips, Dice, play mney and abacus. Demnstrate regruping a cllectin by tens and left shifting. Mentin t make students t say alud hw many grups f tens and nes are there in a cllectin. 6
Use analgy f- each rm is fr nes and tens and nly 9 members f either nes r tens can be in a rm, if it is mre than 9 it shuld be regruped and shifted t next rm twards left On Place Value Mat using base 10 blcks demnstrate 9 and ne make a 10 (ten yellw cubes is a blue rd). Similarly demnstrate 99 and ne mre makes 100 (ten blue rds makes a green plate). 999 and ne makes 1000 (Ten green plates makes a red cube). Teacher can als use play mney as mentined in the teacher manual. T demnstrate 10000 in similar way use abacus. With each f this activity teachers can intrduce number name hundred, thusand, ten thusand. Ask participants t represent 3 t 4 digit numbers given belw using Base Ten blcks, Play Mney, Place Value strips, abacus. Examples: 503, 9999, 6575, 84356 (use abacus), 07664(use abacus), 85046(use abacus), 35480(use abacus). Make sure participants are aware that students shuld be able t recgnize, Read and Writing 3-5 digit numbers Demnstrate activities related t expansin frm f numbers fr learning f Place Value and Face value f digits with the fllwing examples. Examples: 4007, 8888, 6626, 5046, 3330. Demnstrate activities related t cmparisn f big numbers. Discuss the algrithm t Always start frm the highest place and if the face value f the digit here is same then mve t the next lwer place. Ask participants t cmpare the numbers given belw. Examples: 6447 & 6474, 5470 & 3140, 6586 & 6586, 8461 & 8467 Ordering numbers in ascending and descending frm: Ask participants t pick the smallest frm the set fr ascending and cntinue. Similarly, pick the biggest frm the set fr descending and cntinue. Perfrm the activities using the belw examples. Example: 5994, 8458, 2408, 6620; 482, 29, 715, 5, 8551 Sessin 5: [12.00-1.00] Additin T demnstrate the activities t Teach/Learn additin peratin using GKA TLMs Materials t be used: Cunters, base ten blcks, play mney, place value mat, dice, abacus. 7
Intrductin t additin Using Cunters demnstrate the fllwing- Additin is jining: Take tw grups f cunters and jin. Nw cunt and find the sum; Nw intrduce the signs and tell children that jin is represented by + and make/sum by =. Cmmutative prperty: Shw that 3 + 4 and 4 +3 are the same. Identity prperty: Shw that 4 + 0 is 4.When we add nthing t a quantity the quantity remains unchanged. Representatin using square line bk. Additin table: Fr each number say 7, ask them t write all cmbinatin that make that number using cunters. Additin f 3-5 digit numbers: Using Base ten blcks, Play mney r abacus demnstrate activities fr Teach/Learning 3-5 digit number additin Initially demnstrate additin f tw 3-5 digit numbers withut carry. Shw hw this can be dne using square line bk. Examples: 234+123 =?, 555 + 202=?, 4003+506=? 10430+9030=? Mentin t always start frm the units place. Nw chse numbers that generate a carry and shw hw regruping is dne. Examples: 9999+1=?, 555 + 606=?, 4003+909=?, 10430+9070=? 777+7777=? 1:00 1:45 : Lunch break Sessin 6 [1.45-2.30] Subtractin T demnstrate the activities t learn subtractin peratin using GKA TLMs Materials t be used: Cunters, base ten blcks, play mney, place value mat, dice, abacus. Intrductin t subtractin: Using Cunters demnstrate the fllwing: 8
Subtractin is remving a quantity frm anther: Take cunters. Nw remve a few. What remains is the difference. Nw intrduce the signs and tell children that take away r minus is represented by and get/difference by =. Ask participants if they can take away 8 frm 5. Let them cme t a cnclusin that nly a smaller number can be taken away frm a bigger number. Shw that 3-0 = 3. When we remve nthing frm a quantity it is unchanged. Shw that fr every additin fact there are tw subtractin facts. Eg. 5+4 = 9 gives 9-5 = 4 and 9-4 = 5. Subtractin n Place value mat. Using Base ten blcks subtract a smaller number frm bigger number. Place the minuend n the mat. Remve subtrahend and place belw it. Write the difference. Repeat with different cmbinatins. Subtractin f tw digit number Using base ten blcks r Play mney Subtract a number frm anther. Chse numbers that d nt need a brrw. Always start frm the units place. Nw chse numbers that need brrwing and shw hw regruping is dne. When the child remves if there is less than what he needs naturally there cmes a need t brrw. Explain we can d this nly if there is smething in the higher place. Shw hw a blue rd can be exchanged fr ten yellw nes. Add these t the already existing and remve frm this. Similarly explain the use f play mney and abacus fr brrwing. Ask participants t perfrm the fllwing prblems using TLMs Subtractin f 3,4 and 5 digit numbers Using Base ten blcks, Play mney r abacus Subtract withut brrw. Examples: 4044-4003, 25684-10403, Subtract with brrw. Examples: 10002-9999, 10000-1, 37051-34809, 4638-3929 Sessin 7 [2:30-3.30]: Multiplicatin T demnstrate the activities t Teach/Learn multiplicatin using GKA TLMs 9
Materials t be used: Cunters, base ten blcks, play mney and abacus. Intrductin t Multiplicatin Using Cunters and number line demnstrate the fllwing: Using number line demnstrate skip cunting. Using cunters start with additin f any tw numbers. Fr example add 3 with 3. T this add 3 and cntinue. Ask what is different. Establish that we are adding the same number multiple times. This is called multiplicatin. Multiplicatin is repeated additin. Nw using number line shw repeated additin. Arrange varius repeated additins as a rectangle and shw that multiplicatin is always a rectangle with ne number as rws and the ther as clumns. Intrduce X sign fr multiplicatin. D the multiplicatins table. Explain hw t write this n square line bk. Shw that when we multiply anything by 0 we are multiplying with nthing i.e we are nt multiplying. S it is 0. Demnstrate multiplicatin activity as repeated additin as given in teachers manual. Ask participants t perfrm multiplicatins with fllwing examples using base ten blcks/play mney. Example: 465x8, 3082x4 Intrduce the area methd. Remind that we can nly use rds and yellw cubes even fr a 3 digit numbers. Ask participants t perfrm multiplicatin f the fllwing numbers using area methd. Examples: 12x12, 103x11, 15x13 Shw hw t represent this in square line bk. Shw hw t cnnect this with lng multiplicatin methd by taking any f the belw examples. Examples: 107x8, 300x10, 8x20 3:30-3:45 - Tea break Sessin 8 : [3.45-4.00] Factrs and multiples. T demnstrate the activities t Teach/Learn factrs and multiples using GKA TLMs Materials t be used: Cunters 10
Factrs and Multiples Frm rectangles using cunter by adding rws t shw multiples Fr a given number make different rectangles the rw and clumns indicate the factrs ex: 24 (2x12, 1x24, 6x4, 8x3) Sessin 9 [3:45-5:15] Measurements T demnstrate the activities t Teach/Learn varius frms f measurement like mney, time, length, weight and vlume using GKA TLMs Materials t be used: Play mney, clck, measurement tape, weighing balance Nte: Please make sure students use and experiment with varius measurement f the bjects fund in daily life Explain/demnstrate the cncept f mney and mney handling Intrduce Nnstandard measure as in Barter system Intrduce mney as a standard measure in terms f currency Shw/demnstrate varius denminatins f mney (1,2,5,10,50,100,500,100) given in the kit. Shw varius ways f exchanging mney Demnstrate hw t make an amunt using varius denminatins. Make sure participants als d this activity. Demnstrate additin and subtractin using play mney. Time Explain Time is a measurement f duratin. Intrduce Nn-standard/ Standard measure f time. Intrduce basic structure f Clck (arms and numbers). Explain Reading f hurs, Reading half hurs, Reading quarter past and quarter t. Explain the clck marking and its relatin t multiple f 5 Explain reading f minutes, elapsed Time, 24 hur clck, duratin, cnversin f time frm 12 hur clck reading t 24 hur clck reading. Demnstrate reading f Calendar Length 11
Explain Length as a measurement between tw pints Explain varius vernacular nn-standard measurements like Flwers elbw length fr mla and full arm fr maaru, Hand span, Ft length. Intrduce standard units f measurements. Demnstrate the use f measuring Tape fr measuring the bjects. Perfrm additin and subtractin using measurement. Explain the cnversin f units like Cm t meter, meter t kilmeter etc. Weight Explain Weight as a measurement. Intrduce vernacular nn-standard measurement f weight Demnstrate standard measure using weighing balance. Yu can use base ten yellw cubes fr 1 gram and blue rds fr 10gms, water fr ther measure. Perfrm additin and subtractin using weight. Explain the cnversin f units like milligrams t grams and gram t kilgram etc. Vlume Explain Vlume as a measurement Intrduce vernacular nn-standard measurement f vlume Demnstrate standard measurement f vlume using the pans f weighing balance. Perfrm additin and subtractin using vlume. Explain the cnversin f units like milliliter t liter. Sessin 1 : [10.30-11.30] Divisin. DAY 2 T demnstrate the activities t Teach/Learn divisin using GKA TLMs 12
Materials t be used: Cunters, base ten blcks, play mney and abacus. Intrductin t Divisin: Ask a student t distribute 12 cunters t 3 participantsne by ne. Frm this activity establish that divisin is equal distributin. Similar t demnstratin f repeated additin as multiplicatin demnstrate that divisin is repeated subtractin. Shw hw multiplicatin and divisin are cnnected. Intrduce sign. Shw that every multiplicatin fact leads t tw divisin facts. E.g 6 x 4 = 24 gives 24 6 = 4 and 24 4 = 6. Explain that yu cannt give smething t nbdy and explain that divisin by 0 is nt pssible. Divide 13 by 3. Shw that 1 remains. Intrduce the wrds qutient, Dividend, Divisr and remainder. Demnstrate the divisin f a 2 digit, 3 digit and 4 digit number by ne digit using base ten blcks and play mney. Yu can use the fllwing examples. Example: 30/6, 693/3, 455/5, 144/4, 714/7, 9009/9, 600/6, 12/12 Demnstrate the divisin f a 2 digit, 3 digit and 4 digit number by ne digit with remainder using belw examples. Example: 147/4, 2034/7, 3008/9, Shw hw t cnnect this with lng divisin methd. Sessin 2 [11:45 1:00] Fractins 11:30-11:45 - Tea break T demnstrate the activities t Teach/Learn fractins using GKA TLMs Materials t be used: Fractin shapes and fractin strips Discuss Divisin and ask participantst divide 12 bjects (cunters) equally t 3 children. Write as. Nw ask them t divide 16 equally t 4 children. Write Using fractin shapes intrduce fractin as a part f whle. Nw take different whle and shw,,, etc Using fractin strips demnstrate reading, writing and value f a given fractin. 13
Intrduce Numeratr and Denminatr. Using cunters shw Fractin as part f a cllectin Using Number line shw fractins with whle as 100, then with whle as 60, 12 and s n. Cmpare fractins using fractin shapes and fractin strips. Shw rdering f fractins using fractin strip when numeratr is same and denminatr is same. Shw equivalent fractins using fractins shapes and fractin strips. Shw hw t find a fractin part f a cllectin the OF peratr. Eg. OF 20, f 12. Sessin 3 [1:45-2:45] : Decimals 1:00 1:45: Lunch break T demnstrate the activities t Teach/Learn decimal using GKA TLMs Materials t be used: Play mney, decimal grid and decimal place value strip. After discussing fractins, intrduce a fractin with 10 as denminatr and 100 as denminatr. Using the decimal grid explain dividng whle int 10 strips and divinding this further int 10 giving 100 squares. Nw shw equivalents e.g 3/10 = 30 /100. Using Play mney shw when 1000 is exchanged we get ten 100 s, 100 is exchanged fr ten 10 s, 10 fr ten 1 s. When we want t exchange 1 rupee we get ten 10 paise and when 1 ten paise is exchanged we get ten 1 paise. Cnnect it with the decimal number system. Nw write the place value. Thusands when divided by 10 gives 100 which further divided by 10 gives 10 which further divided by 10 gives 1 which further divided by 10 give 1/10 and then 1/100. Nw represent varius decimal numbers using Play mney. Intrduce the Decimal pint as the separatr between the whle and part. Cmparisn and rdering f decimals. Additin, Subtractin f decimals. Sessin 4: [2:45-4:00] Gemetry 3D Shapes T demnstrate the activities t Teach/Learn f shapes, angle, area and perimeter using GKA TLMs 14
Materials t be used: 3-D and 2-D shapes, nets, prtractr and ge-bard with rubber band. Intrduce 3 D shapes with their names based n face, edge vertex and als based n rlling and sliding prperties. Cmpare real life bjects that resemble these shapes Use 2 D nets t make 3 D shapes Angles Explain angle as a means f measurement. Explain capturing angles and measuring angle using prtractr. Demnstrate different types f angles by making angles n prtractr. Area and Perimeter Shw frmatin f different 2 D shapes using Ge-brad Intrduce the cncept f perimeter as a walk r mvement alng the utline f a shape. Demnstrate measurement f perimeter in units using ge-bard. Shw that perimeter maybe same even if the shape is different. Shw the perimeter f a square n ge-bard and derive its frmula. Shw the perimeter f rectangle n ge-bard and derive its frmula Intrduce area cncept as the space within a shape and area as unit squares that fill the shape. Demnstrate that area maybe same but shape maybe different Shw that shapes having same perimeter may have different area and vice versa Using ge-bard, shw the area f a square and derive its frmula. Using ge-bard, shw the area f a square and derive its frmula. 4:00-4:15 - Tea Break Sessin 5: [4:15-4:45] Data Handling and Pattern T demnstrate the activities t Teach/Learn data handling and pattern using GKA TLMs Materials t be used: square cunter, abacus rings and shapes. Demnstrate data cllectin and handling as fllws: 15
Cllectin f data using different clred square cunters r abacus rings Tabulate data f clrs cllected using tally. Tabulate using Srting and Cunting Represent the cllected square cunters in the frm f hrizntal and vertical bar graph using square cunters Analyze the Data using Bar graph. Patterns Demnstrate different patterns using shapes based n clr and rientatin Shw different patterns f Number Squares hw many cunters make a square. Eg 4, 9, 16, 25, 36 Triangular numbers. Hw many cunters make a triangle 3, 6, 10, Symmetry Sessin 6: [4:45-5:00] Feedback 16