Instructinal Plan Representatinal/Drawing Level Name f Math Skill/Cncept: Divisin Prcess and Divisin with Remainders Prerequisite Skills Needed: 1.) Mastery f dividing cncrete bjects int equal grups. 2.) Mastery f dividing cncrete bjects int equal grups and identifying left ver bjects as the remainder. 3.) Mastery f using cncrete bjects t slve divisin prblems withut remainders. 4.) Mastery f using cncrete bjects t slve divisin prblems with remainders. Learning Objectives: 1.) FASTDRAW Strategy (t slve divisin stry prblems by drawing pictures). 2.) Drawing slutins t divisin stry prblems using the FASTDRAW Strategy. Imprtant Ideas fr Implementing This Teaching Plan: 1.) This plan describes hw t teach students a strategy fr slving divisin stry prblems FASTDRAW (Mercer & Mercer, 1998). Students with learning prblems benefit frm systematic instructin f hw t find the imprtant infrmatin in a stry prblem and develp an equatin t slve the prblem. FAST in the FASTDRAW Strategy prvides students explicit steps t d this. DRAW prvides students explicit steps t slve the divisin equatin. 2.) First, teach students the FASTDRAW Strategy. Then teach students t draw the slutin t the stry prblem. 3.) DRAW can be taught t slve divisin equatins withut stry prblems. Instructinal Phase 1: Initial Acquisitin f Skill/Cncept Teacher Directed Instructin I. Teach Skill/Cncept within Authentic Cntext Descriptin: Drawing slutins t divisin prblems shuld cntinue t be taught within the framewrk f stry situatins that resnate with students given their age and interests. II. Build Meaningful Student Cnnectins
Purpse: t assist students t build meaningful cnnectins between what they knw abut slving divisin prblems (with and withut remainders) using cncrete bjects and drawing pictures t slve divisin prblems (with and withut remainders.) Learning Objectives 2: Drawing slutins t divisin equatins using the DRAW Strategy. Materials: Teacher apprpriate cunting bjects and cntainers. visual display f an apprpriate divisin prblem. a visual display that identifies the learning bjective. Descriptin: 1.) L ink t students prir knwledge f slving divisin prblems with cncrete materials The last few days, yu have learned hw t use cncrete materials such as t slve divisin prblems. Yu ve used t represent the ttal, r dividend, in divisin prblems (Hld up the crrespnding cncrete materials) and yu have used t grup, r divide the ttal number f bjects by the divisr (Hld up the crrespnding cntainers used). These cncrete materials have been very helpful fr slving divisin prblems. Let s slve anther divisin prblem tgether using these cncrete materials. (Slve a divisin prblem with yur students using previusly used cncrete materials, highlighting the dividend, divisr, qutient, and remainder (if apprpriate). 2.) I dentify the skill students will learn: Drawing pictures t slve divisin prblems. Tday we are ging t learn hw t draw pictures t slve divisin prblems instead f using these cncrete materials. I will teach yu hw t draw simple pictures that represent the cncrete bjects yu have been using the past few days. The pictures we will draw t slve divisin equatins will be very similar t thse yu learned t draw fr multiplicatin prblems. 3.) P rvide ratinale/meaning fr drawing pictures t slve divisin prblems. Drawing pictures t slve prblems is a lt like using ur cncrete materials. When we use cncrete materials like (cunting bjects) and (cntainers), we can see what it is we are slving. Mving the cncrete bjects arund, like when we grup cunting chips nt plates, als helps us prblem slve because it helps us make the numbers and symbls f a divisin prblem cme alive. Drawing pictures helps in the same way. We can see the pictures we draw and we als can grup pictures much like we did
with ur cncrete materials. Drawing pictures is als faster than using cncrete bjects s it will help yu becme even mre talented at slving divisin prblems. III. Prvide Explicit Teacher Mdeling Purpse: t prvide students a clear mdel f hw t draw slutins t divisin prblems with and withut remainders. Learning Objective 1: FASTDRAW Strategy (t slve divisin stry prblems by drawing pictures). Materials: Teacher A visual display f the FASTDRAW Strategy (Clr-cde the FAST and the DRAW in FASTDRAW. ) *The FASTDRAW strategy cmes frm Mercer & Mercer (1998) a frmat fr visually displaying divisin stry prblems (e.g. chalk-bard, dry-erase bard, chart & chart paper). stry prblems that depict divisin situatins and that clr-cde phrases that represent the dividend and the divisr. a frmat t visually display divisin equatins and drawings. apprpriate writing utensil (e.g. chalk, markers). cue cards/visual displays fr the language dividend, divisr, qutient, & remainder. (Clr-cde the dend in dividend and the sr in divisr t crrespnd with the clr f the crrespnding number phrases.) Descriptin: A. Break dwn the skill f teaching the FASTDRAW Strategy. 1.) Intrduce students t the cncept f a Learning Strategy. 2.) Intrduce students t the FASTDRAW Strategy. 3.) Describe the purpse f the FASTDRAW Strategy. 3.) Teach the purpse fr FAST and the steps FAST. 3a. Find what yu are slving fr. 3b. Ask yurself, what is the imprtant infrmatin (circle it). 3c. Set up the equatin. 3d. Tie dwn the sign. 4.) Teach the purpse f DRAW and the steps DRAW. 4a. Determine the sign. 4b. Read the prblem.
4c. Answer, r draw and check. 4d. Write the answer. B. Explicitly describe and mdel hw t use the FASTDRAW Strategy. 1.) Intrduce students t the cncept f a Learning Strategy. Display strategy language card Pint t cues n card Prmpt student thinking Tday we are ging t learn hw t use smething called a strategy t help us draw pictures that will enable us t slve divisin prblems. (Display and pint t a visual display f the wrd strategy that includes a picture f a tl such as a hammer and a picture f a map, such as a treasure map.) Everybdy say this wrd with me. (Pint t the wrd and encurage students t read it alud with yu.) What pictures d yu see next t the wrd strategy (Elicit the respnse, a hammer and a treasure map. ) Yes, this is a hammer and this is a treasure map (Pint t each picture). Bth the hammer and the map are tls that can help us d smething. A hammer helps us t d what? (Elicit the apprpriate respnse.) Gd. And what des a map help us t d? (Elicit the apprpriate respnse.) Great! The reasn that these tw pictures are next t the wrd strategy is because a strategy (pint t the wrd strategy ) is als a tl that can help us d smething imprtant. What is a strategy like? (Elicit the respnse, a tl/map) Yes, strategies are like tls r maps. Strategies are kind f like tls r maps because they help us find ur way when we are slving math prblems. What can strategies help us t d? (Elicit the respnse, they can help us find ur way when we slve math prblems.) 2.) Intrduce students t the FASTDRAW Strategy. Display FASTDRAW Strategy Clr-cde FAST and DRAW Pint t steps Prmpt student thinking Nw that yu knw what a strategy is and hw it can help us in math, I m ging t teach yu abut a strategy that can help yu d divisin prblems. The name f this strategy is FASTDRAW. (Pint t the visual display f FASTDRAW. ) What is the name f the strategy? (Pint t the visual display and say alud with yur students, FASTDRAW. ) Yes, we are ging t learn abut the strategy FASTDRAW. (Pint t the visual display f FASTDRAW.) The FASTDRAW Strategy can help yu slve divisin
prblems. What kind f math prblems can FASTDRAW help yu t slve? (Elicit the respnse, divisin prblems. ) That s right. The FASTDRAW Strategy will help yu slve divisin prblems. 3.) Teach the purpse fr FAST and the steps FAST. Teach the purpse fr FAST. Cue with finger Prmpt student thinking The FASTDRAW Strategy can be separated r divided int tw parts. The first part is FAST. (Pint t the FAST in FASTDRAW. ) The secnd part is DRAW. (Pint t the DRAW in FASTDRAW. ) Let s learn what FAST means first. (Pint t the FAST in FASTDRAW. ) FAST can help us find the imprtant infrmatin when we have a stry prblem. It als can help us set up an equatin that can then help us slve the stry prblem. What can the FAST in FASTDRAW help us t d? (Pint the FAST in FASTDRAW and elicit the respnse, find the imprtant infrmatin in a stry prblem and set up an equatin t slve the prblem. ) Crrect. The FAST in FASTDRAW can help yu find the imprtant infrmatin in a stry prblem and set up an equatin t slve the prblem (pint t FAST as yu say this). Teach the F step: Find what yu are slving fr. Think alud Cue with finger Circle questin mark Underline questin When we have a stry prblem, the first thing we need t d after we read it is t find what we are slving fr (Pint t the F step). One way t find what we are slving fr is t lk fr a questin. Let me shw yu what I mean. (Shw students a divisin stry prblem and demnstrate first lking fr a questin mark and then reading the questin. Relate t students that the questin tells us what we are slving fr. *Circle the questin mark and underline the sentence as yu find them.) Teach the A step: Ask yurself, What is the imprtant infrmatin. Think alud
Cue with finger Circle imprtant infrmatin Cue extraneus infrmatin Prmpt student thinking Nw that we have fund what we are slving fr by finding the questin mark and the questin, the next thing we d is Ask urselves, What is the imprtant infrmatin? (Pint t A step as yu say this.) What des the A stand fr? (Elicit the respnse, Ask yurself, What is the imprtant infrmatin? ) Right, A stands fr Ask yurself, What is the imprtant infrmatin? We knw that stry prblems have imprtant infrmatin in them that help us slve them. Yu have all slved stry prblems that invlve additin, subtractin, and multiplicatin. What imprtant infrmatin did yu lk fr first when slving thse stry prblems? (Elicit the respnse, number phrases/key wrds ) Great thinking, guys. Yes, we can first lk fr imprtant wrds r phrases, such as wrds r phrases that refer t numbers. A gd way t d that is t read each sentence in the stry prblem and then ask urselves, Is there a number phrase in this sentence? Let s d this tgether nw. (Mdel reading each sentence and asking alud Is there a number phrase in this sentence? Then circle all number phrases. *At this pint, d nt use stry situatins that cntain extraneus infrmatin that includes number phrases. Teaching students hw t determine whether extraneus infrmatin is imprtant r nt shuld cme after students have had plenty f experiences slving stry prblems withut such extraneus infrmatin first.) Teach the S step: Set up the equatin. Think alud Cue step and highlighted infrmatin with finger Cue wrds/phrases that relate t equatin Clr-cde numbers representing dividend and divisr Prmpt student thinking Ok, we have cmpleted the F step and the A step (pint t each step as yu say them) by finding what we are slving fr and asking urselves, What is the imprtant infrmatin? Nw, we can mve t the S step (Pint t the S. ). The S stands fr Set up the equatin. (Pint t the phrase as yu say it.) An equatin represents the prblem that is in this stry. We use the things we learned frm the F step and the A step t set up the equatin. I ll shw hw t d that nw. (First, remind students what they
are slving fr by pinting t and saying alud the underlined questin. Highlight fr students any key wrds that indicate the peratin needed t slve the prblem e.g. in the divisin questin, Hw many CD s des each persn get?, the key wrds wuld be Hw many and each. Discuss with students why this questin and the key wrds indicate the divisin prcess. Secnd, mdel reading the imprtant infrmatin yu circled. Remind students f the language dividend and divisr, and hw t determine which number phrase represents the dividend (e.g. it is the ttal and which number phrase represents the divisr (e.g. the number f grups.). Third, mdel where the dividend and the divisr shuld be written in a divisin equatin. Relate the ratinale fr why they are placed in thse psitins by using the language f the stry (e.g. I have a ttal f and I need t separate them equally int grups. It makes sense that the ttal, r dividend shuld be written first sense I start with the ttal. Then I separate them int the number f grups represented by the divisr. Therefre, it makes sense that I write the divisr secnd. (Write the number and the cntext/phrase as yu set up the equatin.) 14 2 =? ttal CD s children Hw many CD s des each persn get? Teach the T step: Tie dwn the sign. Think alud Cue imprtant infrmatin with finger Great! Nw that I have my equatin set up, I just need t write the symbl r sign that means divisin. That is what the T step reminds me t d. (Pint t the T. ) The T stands fr Tie dwn the sign. Tie dwn the sign means t write the symbl r sign that represents the peratin I will use t slve the equatin. In this case, I tie dwn the sign by writing the divisin symbl/sign next t the dividend and divisr. I will write beside the divisr. This is a gd place t place the divisin symbl because it reminds me that I am dividing r separating the dividend int the number f grups represented by the divisr (Pint t each number as yu refer t it.) 14 2 =? ttal CD s children Hw many CD s des each persn get? Review the steps f FAST and its purpse. Pint t steps
Elicit student respnses Prmpt student thinking Alright, we nw knw what the FAST- F, A, S, & T in the FASTDRAW Strategy means. We als knw what each step in FAST means. Let s review. (Prmpt students t respnd t multiple questins regarding the purpse f FAST and the individual steps. *Prvide visual and auditry cueing as needed. Als prvide crrective feedback and psitive reinfrcement.) 4.) Teach the purpse f DRAW and the steps DRAW. Teach the purpse f DRAW Cue with finger Prmpt student thinking We knw that the FAST in the FASTDRAW Strategy helps us t decide what the imprtant infrmatin in the stry prblem is and it helps us t set up an equatin t slve the prblem. Well, the DRAW in the FASTDRAW Strategy als will help us d smething imprtant. DRAW helps us t slve the equatin we set up. (Pint t DRAW in the wrd FASTDRAW and then t the steps f DRAW. ) What des DRAW in the FASTDRAW Strategy help us t d? (Elicit the respnse, it helps us t slve the equatin. ) That s right. Teach the D step: Discver the sign. Think alud Cue step with finger Circle divisin sign Just like in FAST, each letter in DRAW reminds us f an imprtant step t use. If we fllw these steps, we will be able t slve the equatin. The first step in DRAW is D. (Pint t the D. ) The D stands fr Discver the sign. (Pint t the phrase as yu say it alud.) What des the D stand fr? (Elicit the respnse, Discver the sign. ) Yes, the D stands fr Discver the sign. T discver the sign, I lk at my equatin and find the symbl that tells me what peratin I need t use t slve the equatin. Hmm, where is the sign in the equatin I have written? Oh, here it is. (Pint t the sign.) This sign means t divide. I ll circle it s I can remember what it is I need t d t slve the equatin. (Circle the divisin sign.)
Teach the R step: Read the prblem. Think alud Cue step with finger Elicit student respnses Prmpt student thinking Nw that I have discvered the sign and I knw what peratin I need t use t slve the equatin, its time t mve t the R step. (Pint t the R. ) The R stands fr Read the prblem. (Pint t the phrase as yu say it alud.) T read this equatin, I start with the dividend (Pint t the dividend). The dividend is. Next I say the peratin. (Pint t the divisin sign and say divided by. ) Last, I say the dividend since that represents the number f grups I will equally divide r separate the dividend int. Let s read the prblem tgether. (Pint t each number and symbl as yu and yur students read the prblem.) Great jb. Reading the prblem alud is a gd strategy t use because it allws yu t nt nly see the equatin, it als lets yu hear it as well. When we read the prblem, what d we start with? (Elicit the respnse, the dividend. ) Gd. And what des the dividend represent? (Elicit the respnse, the ttal. ) Yes, the dividend represents the ttal. What d we read next? (Elicit the respnse, the sign. ) Gd. We read the sign next because that tells us what we need t d with the dividend. The divide sign means we need t d what? (Elicit the respnse, separate the dividend int equal grups. ) Yes, the divide sign tells us t separate ur dividend int equal grups. What d we read last? (Elicit the respnse, the divisr. ) Yes, we read the divisr last. What des the divisr represent? (Elicit the respnse, the number f grups we will separate/divide the dividend int. ) Excellent thinking guys. The divisr tells us the number f grups we will separate r divide the dividend r ttal int. Teach the A step: Answer, r draw and check. Think alud Cue step with finger Elicit student respnses Prmpt student thinking The first tw steps f DRAW, Discver the sign, and Read the prblem get us ready t slve the equatin. The A reminds us it is time t answer r slve the equatin. The A stands fr Answer, r draw and check. What des the A stand fr? (Elicit the respnse, Answer, r draw and check. ) Yes. We answer the equatin by slving it. Fr the last several days, yu have learned hw t slve divisin equatins using cncrete materials like. Tday yu will learn hw t draw pictures that will help yu slve divisin prblems. That is what is meant by the phrase draw and check. (Pint t this
phrase.) I will shw yu hw t d this sn, but fr nw it is imprtant t knw that the A step reminds us t answer the prblem, r draw and check. Teach the W step: Write the answer. Think alud Cue step with finger Elicit student respnses Prmpt student thinking The last step in DRAW is W. (Pint t W. ) It stands fr Write the answer. What des the W stand fr? (Elicit the respnse, write the answer. ) Great, the last thing we d when slving a divisin equatin is t write the answer. If I were t slve the equatin we have written, I wuld write the answer in this psitin. (Pint t the apprpriate space.) Where d I write my answer? (Elicit the apprpriate respnse.) Review the steps f DRAW and its purpse. Alright, we nw knw what the DRAW- D, R, A, & W in the FASTDRAW Strategy means. We als knw what each step in DRAW means. Let s review. (Prmpt students t respnd t multiple questins regarding the purpse f DRAW and the individual steps. *Prvide visual and auditry cueing as needed. Als prvide crrective feedback and psitive reinfrcement.) Review the steps and purpse f FASTDRAW cllectively *Fllw the same prcedure as abve except review the FAST and the DRAW tgether as well as hw the tw parts wrk tgether t help slve divisin stry prblems. Learning Objective 2: Draw slutins t divisin stry prblems using the FASTDRAW Strategy. A. Break dwn the skill f drawing slutins t divisin stry prblems using the FASTDRAW Strategy. 1.) Intrduce stry prblem. 2.) Read the stry prblem alud and then have students read it with yu. 3.) Teach finding the imprtant infrmatin in the stry prblem and setting up an equatin using the steps FAST frm the FASTDRAW Strategy. 3a. Find what yu are slving fr. 3b. Ask yurself, what is the imprtant infrmatin (circle it). 3c. Set up the equatin.
3d. Tie dwn the sign. 4.) Teach drawing slutins using the steps DRAW frm the FASTDRAW strategy. 4a. Determine the sign. 4b. Read the prblem. 4c. Answer, r draw and check. 4d. Write the answer. 5.) Mdel hw t slve the stry prblem by relating the answer t the divisin equatin back t the stry prblem cntext. 6.) Mdel hw t draw slutins t divisin equatins by repeating the steps in#4 and #5 at least tw r three mre times with different divisin equatins. B. Explicitly Describe and Mdel hw t draw slutins t divisin stry prblems using the FASTDRAW Strategy. 1.) Visually display a stry prblem/divisin situatin. (Clr-cde the number phrases that represent the dividend and the divisr.) clr-cde dividend and divisr make visible t all students The lcal music stre was giving away 14 free CD s f the musical grup, the Backstreet Bys as a prmtin. The CD s were given away in packs f three. Hw many packs were given ut? Hw many single CD s were left ver? 2.) Read the stry prblem alud and then have students read it with yu. *Fllw the same prcedure described fr Learning Objectives 2 &3 in the Cncrete Level Instructinal Plan. 3.) Teach finding the imprtant infrmatin in the stry prblem and setting up an equatin using the steps FAST frm the FASTDRAW Strategy. *Fllw the same prcedure as described abve fr teaching the FAST f the FASTDRAW Strategy. 4.) Teach drawing slutins using the steps DRAW frm the FASTDRAW strategy. Fllw the same prcedure as described abve fr teaching the DRAW f the FASTDRAW Strategy. Explicitly describe and mdel hw t draw slutins fr the A step, Answer, r draw and check.
Mdel drawing pictures t represent the dividend and relating the pictures t a cncrete representatin f the dividend. Think alud Pint t bjects and cunt them alud Prmpt student thinking Cue relatinship f bjects and pictures with finger r by drawing a line between them In rder t answer the equatin, we need t slve it. As I mentined earlier, I will shw yu a way t slve divisin equatins withut using cncrete materials. Instead f cncrete materials, I ll shw yu hw t draw pictures t slve a divisin equatin instead. I ll shw yu hw t d this with this equatin. When we used cncrete materials, like, we represented the dividend by cunting ut the apprpriate number f that equaled the ttal, r dividend. I ll d that again. (Cunt ut the apprpriate number f cunting bjects t represent the dividend. Place them in ne single rw.) 14 3 Hw many bjects d I have? (Elicit the respnse, furteen. ) That s right. Why did I cunt ut furteen bjects? (Elicit the respnse, because that is hw many the dividend/ttal is. ) Gd. Nw, I m ging t draw sme simple pictures that represent the same number as des these bjects. (Mdel drawing tallies r dts, which represent the same number f cncrete bjects. *T shw direct ne-t-ne crrespndence, draw each picture directly under each cncrete bject s that the pictures are als arranged in n rw.) 14 3
Hw many tallies/dts did I draw? (Cunt alud with yur students and elicit the apprpriate respnse.) Hw many bjects d I have? (Elicit the apprpriate respnse.) D I have the same number f bjects as pictures? (Elicit the respnse, yes. *If there is cnfusin, prmpt students by recunting the bjects and the pictures and by pinting ut their ne-t-ne crrespndence. Draw a line between each bject and each picture if needed.) Great, I d have the same number f pictures as I d bjects. Mdel separating/dividing the drawings int equal grups determined by the divisr and relate this prcess t gruping cncrete bjects. Think alud Cue bjects and drawings with finger Cunt alud Prmpt student thinking Elicit student respnses Nw that we have ur dividend represented with pictures, it s time t divide the pictures by ur divisr, three. (Pint t the divisr.) We already knw hw t d this with ur cncrete bjects, s let s d that nw. Hw d I divide these bjects? (Elicit the respnse, separate them int grups f three. ) Excellent thinking. We separate them int grups f three because three is ur divisr. (Mdel separating the bjects int grups f three. Use a cntainer r string t represent the grups.) Hw many grups d I have? (Elicit the respnse, fur. ) Hw many bjects d I have left ver? (Elicit the respnse, tw. ) Gd. Why are these tw bjects left ver. (Elicit the respnse, because there aren t enugh t put in each grup. ) Yes. They are left ver because there are nt enugh t put ne mre in each grup. What d we call bjects that are left ver? (Elicit the respnse, remainder. ) Yes, we call the left ver bjects the remainder.
Nw, I want t shw yu hw t divide ur pictures just like we did ur cncrete bjects. I can divide my tallies/dts by cunting three and then drawing a circle arund them. I ll s that nw. (Mdel cunting alud three tallies/dts and then drawing a circle arund them.) The circle means these three tallies/dts are in ne grup. This is the same thing as gruping three bjects n a plate/circling three bjects with string. (Pint t ne grup f three bjects.) I can keep cunting by three s and circle each grup until there are n lnger three tallies/dts left. I ll d that nw. (Cntinue t cunt alud three tallies/dts and circling them until yu have nly tw tallies/dts left.) (Cunt alud the tw remaining tallies/dts.) Hmm, I dn t have three tallies/dts s I knw I cannt grup them with a circle. They must by my remainder. I can t make any mre grups f three s its time t cunt my grups. Hw many grups f three tallies/dts d I have? (Elicit the respnse, fur. ) Yes, I have fur grups. Hw many grups f three bjects did we have? (Elicit the respnse, fur. ) Gd. Nw, hw many tallies/dts are remaining/left ver? (Elicit the respnse, tw. ) Great, there are tw tallies/dts remaining/left ver. Hw many bjects were left ver? (Elicit the respnse, tw. ) Gd. What is ur slutin? (Elicit the respnse, fur grups with tw left ver. ) Mdel checking yur drawings. Think alud Cunt pictures alud Prmpt student thinking Nw that I have finished drawing pictures, I need t check them and be sure I drew them crrectly. I d this by cunting my tallies t be sure they ttal the dividend. (Cunt alud the tallies and cmpare the ttal t the dividend.) I knw I have the crrect number f tallies, s nw I need t
check t see if I have my dividend drawn crrectly. The dividend is represented by the tallies in each circle r grup. I can check this by cunting the number f tallies in each grup and be sure they equal the divisr. (Cunt alud the tallies in each grup and cmpare the ttal in each grup t the divisr.) Last, I check my remainder by being sure there are fewer tallies left ver than there are in each grup. (Cunt alud the remaining tallies and cmpare the ttal t the divisr/the number f tallies in each grup.) 5.) Mdel finding the slutin t the stry prblem by relating the slutin t the divisin equatin t the stry prblem cntext. Think alud Prmpt student thinking Cue imprtant infrmatin with finger Nw that we have drawn ur slutin and checked ur wrk, we have ne mre thing left t d. Wh knws what we need t d nw that we have slved the divisin equatin, furteen divided by three? (Elicit the respnse, answer/slve the stry prblem. ) That s right, we need t use ur slutin t answer the stry prblem. What is it we needed t slve fr? (Elicit the respnse, Hw many packs f three CD s were given ut? and Hw many single CD s were left ver? ) Great thinking! S, hw many packs f CD s were given ut? (Pint t the apprpriate questin in the stry prblem and elicit the respnse, fur. ) And hw d yu knw this? (Elicit the respnse, because we circled fur grups f tallies. ) Yes, and what did each tally represent? (Elicit the respnse, ne CD. ) That s right, each tally represented ne CD. Each circle represented ne pack f three CD s. (Pint t ne circle and cunt the three tallies alud.) Because we have fur circled grups f three tallies, we knw fur packs f CD s were given ut. Were any single CD s left ver? (Pint t the apprpriate questin in the stry prblem and elicit the respnse, tw. ) Yes, there are tw single CD s left. I knw this because I have tw tallies left ver. (Pint t the tw left ver tallies.) Excellent jb guys! 6.) Mdel hw t draw slutins t divisin equatins by repeating the steps in #4 at least tw r three mre times with different divisin equatins. It is recmmended that yu use cncrete materials as a cmparisn t drawings fr ne mre example and then fade the use f cncrete bjects fr cmparisn. IV. Scaffld Instructin *This teaching plan prvides a descriptin f hw t scaffld instructin fr using DRAW t slve divisin equatins withut and with remainders. The same basic prcess can be used fr scafflding instructin fr ther skills/cncepts explicitly mdeled during Explicit Teacher Mdeling. First, break the skill/cncept int learnable parts (e.g. use thse parts taught during Explicit Teacher Mdeling) and then fade yur directin in three phases:
1.) High level f teacher supprt; 2.) Medium level f teacher supprt; 3.) Lw level f teacher supprt. Scafflding Instructin shuld ccur fr each skill/cncept taught during Explicit Teacher Mdeling befre prviding student practice. Purpse: t prvide students the pprtunity t build their understanding f hw t draw slutins t divisin stry prblems and equatins, with and withut remainders, and t prvide yu the pprtunity t evaluate yur students level f understanding after yur initial mdeling f these skills. Learning Objective 2: Drawing slutins t divisin stry prblems using the FASTDRAW Strategy Slving divisin equatins using DRAW. Materials: Teacher apprpriate divisin equatins represented visually n chalkbard, dry-erase bard, chart/chart paper, verhead prjectr. chalk, markers fr writing and drawing Students - paper with apprpriate divisin equatins t practice drawing slutins t during 3rd phase f Scafflding Instructin Lw Level f Scafflding Instructin. pencils fr drawing and writing answers. Descriptin: 1.) Scaffld Using a High Level f Teacher Directin/Supprt a. Chse ne r tw places in the prblem-slving sequence t invite student respnses. Have these chices in mind befre yu begin scafflding instructin. (Examples f chices are shwn in red.) *Clr-cde the dividend and the divisr in each equatin during this phase f instructinal scafflding. Review steps f DRAW I have an equatin here. Hmm, I knw there is a strategy that can help me draw pictures t slve this equatin. What is the name f the strategy? Oh, yes, it is called the DRAW. (Pint t DRAW in the FASTDRAW Strategy r display DRAW and its steps separately.) What is the name f the strategy that can help me draw pictures t slve this equatin? (Elicit the respnse, DRAW. ) I knw each letter in DRAW stands fr a step in slving an equatin. The D stands fr Discver the sign. (Pint t the apprpriate phrase as yu say it.) What des the D stand fr? (Elicit the respnse, Discver the sign. ) Yes, D stands fr Discver the sign. (*Repeat this prcess fr each step f DRAW.)
Mdel the D step, Discver the sign. Nw that I knw I can use the DRAW Strategy t help me slve this equatin, I can begin by cmpleting the first step, D. What des D stand fr? (Pint t the D step and elicit the respnse, Discver the sign. ) Yes, I first need t discver the sign. I d this by finding the symbl that tells me what math peratin t use. (Pint t the divisin sign.) Hmm, this sign has a line in the middle and a dt n the tp and a dt n the bttm. It als lks like a sideways face. I see a lng nse with tw eyes. (Pint t the relevant features f the divisin sign.) What can I d t help me remember what math peratin I need t use? (Elicit the respnse, circle it. ) Yes, I can circle it t help me remember what math peratin t use. (Circle the divisin sign.) Mdel the R step, Read the prblem. I ve discvered the sign, and knw I need t divide. The next step is R. What des R stand fr? (Pint t the R step and elicit the respnse, Read the prblem. ) Yes, I need t read the prblem. When I read a divisin prblem, I knw I need t read the dividend r ttal first. Usually, the dividend will be the number that has the higher value because it represents the ttal. In this equatin, the dividend must be because it has the higher value. (Pint t the dividend and say it alud.) I knw that I have t divide because the sign I discvered is a divisin sign. (Pint t the divisin sign.) Last, I find the divisr. This number must be my divisr because it is the remaining number. It als represents a lwer value. The divisr usually is a number that has a lwer value than the dividend. Nw that I knw all the parts f this equatin, I ll read it. (Read the equatin alud.) Nw, read the prblem with me. (Encurage students t read the prblem alud with yu as yu pint t each part f the equatin.) Mdel the A step, Answer, r draw and check. Draw pictures t represent the dividend. - Nw that I knw what the prblem is and what math peratin I need t use, I need t cmplete A step. What is the A step? (Elicit the respnse, Answer, r draw and check. ) Yes, I need t answer the equatin. I knw I can draw pictures t slve a divisin equatin. Hmm, I remember using cncrete materials t d this. When I did this, I first represented the dividend by cunting ut that number f bjects. I can d the same thing by drawing pictures instead f using cncrete bjects. What kind f pictures can I draw? (Elicit the respnse, tallies r dts. ) Yes, I can represent the dividend by drawing tallies r dts. I m ging t draw tallies. My dividend is s I need t draw tallies. (Draw the apprpriate number f tallies.) Draw circles arund pictures t represent dividing them int equal grups based n the divisr. Nw I have t divide r separate these tallies int grups. I knw the
divisr tells me hw many tallies belng in each grup. (Pint t the divisr and say alud hw many tallies shuld be in each grup.) I can put the tallies int grups by drawing circles arund them. Hw many tallies d are in each grup? (Elicit the apprpriate respnse.) Yes, I need t circle tallies at a time. I ll d that nw. (Circle the tallies until yu have tallies left ver. ) I have tallies left ver. That is nt enugh t put in a grup s I knw this is my remainder. Mdel checking yur drawings. Nw that I have finished drawing pictures, I need t check them and be sure I drew them crrectly. I d this by cunting my tallies t be sure they ttal the dividend. (Cunt alud the tallies and cmpare the ttal t the dividend.) I knw I have the crrect number f tallies, s nw I need t check t see if I have my dividend drawn crrectly. The dividend is represented by the tallies in each circle r grup. I can check this by cunting the number f tallies in each grup and be sure they equal the divisr. (Cunt alud the tallies in each grup and cmpare the ttal in each grup t the divisr.) Last, I check my remainder by being sure there are fewer tallies left ver than there are in each grup. (Cunt alud the remaining tallies and cmpare the ttal t the divisr/the number f tallies in each grup.) Mdel hw t find the answer t the equatin. Nw, t answer the equatin, I cunt the number f grups. (Cunt alud the grups.) Hw many grups d I have? (Elicit the apprpriate respnse.) Yes. And hw many tallies d I have left ver? (Elicit the apprpriate respnse.) Mdel the W step, Write the answer. I have fund my answer by drawing pictures and I have checked my drawings t be sure they are accurate. Nw I can finish slving the prblem by cmpleting the W step. What is the W step? (Elicit the respnse, Write the answer. ) Great, after I have fund my answer by drawing, I write the answer. I knw the answer t a divisin equatin shuld be written here. (Pint t the apprpriate space.) What is my answer? (Elicit the apprpriate respnse.) Yes, my answer is. I knw this because I have grups (Pint t each circled grup f tallies and cunt them alud.) and I have tallies left ver (Pint t the remaining tallies and cunt them alud.) I ll write the answer here. (Pint t the apprpriate space and write the answer.) b. Maintain a high level f teacher directin/supprt fr anther example if students demnstrate misunderstanding/nn-understanding; mve t a medium level f teacher directin/supprt if students respnd apprpriately t the selected questins/prmpts. 2.) Scaffld Using a Medium Level f Teacher Directin/Supprt a. Chse several mre places in the prblem-slving sequence t invite student respnses. Have these chices in mind befre yu begin scafflding instructin. (Examples f chices are shwn in red.)
Review steps f DRAW I have anther equatin. What is the name f the strategy that can help me draw pictures t slve this equatin? (Elicit the respnse, DRAW. ) I knw each letter in DRAW stands fr a step in slving an equatin. The D stands fr Discver the sign. (Pint t the apprpriate phrase as yu say it.) What des the D stand fr? (Elicit the respnse, Discver the sign. ) Yes, D stands fr Discver the sign. (*Repeat this prcess fr each step f DRAW.) Mdel the D step, Discver the sign. Nw that I knw I can use the DRAW Strategy t help me slve this equatin, I can begin by cmpleting the first step, D. What des D stand fr? (Pint t the D step and elicit the respnse, Discver the sign. ) Yes, I first need t discver the sign. Hw d I d this? (Elicit the respnse, by finding the symbl that tells what math peratin t use. ) Gd. (Pint t the divisin sign.) What is the sign? (Elicit the respnse, divisin. ) Gd. Hw d yu knw it is a divisin sign? (Elicit the respnse, it has a line in the middle and a dt n the tp and a dt n the bttm/it als lks like a sideways face. I see a lng nse with tw eyes. (Pint t the relevant features f the divisin sign.) Excellent thinking! What can I d t help me remember what math peratin I need t use? (Elicit the respnse, circle it. ) Yes, I can circle it t help me remember what math peratin t use. (Circle the divisin sign.) Mdel the R step, Read the prblem. I ve discvered the sign, and knw I need t divide. The next step is R. What des R stand fr? (Pint t the R step and elicit the respnse, Read the prblem. ) Yes, I need t read the prblem. When I read a divisin prblem, I knw I need t read the dividend r ttal first. Usually, the dividend will be the number that has the higher value because it represents the ttal. What is the dividend in this prblem? (Elicit the apprpriate respnse.) Yes. (Pint t the dividend and say it alud.) I knw that I have t divide because the sign I discvered is a divisin sign. (Pint t the divisin sign.) Last, I find the divisr. This number must be my divisr because it is the remaining number. It als represents a lwer value. The divisr usually is a number that has a lwer value than the dividend. Nw that I knw all the parts f this equatin, I ll read it. (Read the equatin alud.) Nw, read the prblem with me. (Encurage students t read the prblem alud with yu as yu pint t each part f the equatin.) Mdel the A step, Answer, r draw and check. Draw pictures t represent the dividend. - Nw that I knw what the prblem is and what math peratin I need t use, I need t cmplete A step. What is the A
step? (Elicit the respnse, Answer, r draw and check. ) Yes, I need t answer the equatin. I knw I can draw pictures t slve a divisin equatin. What kind f pictures can I draw? (Elicit the respnse, tallies r dts. ) Yes, I can represent the dividend by drawing tallies r dts. I m ging t draw tallies. My dividend is s I need t draw tallies. (Draw the apprpriate number f tallies.) Draw circles arund pictures t represent dividing them int equal grups based n the divisr. Nw I have t divide r separate these tallies int grups. What number tells me hw many tallies belng in each grup. (Elicit the respnse, the divisr. ) Gd. (Pint t the divisr and say alud hw many tallies shuld be in each grup.) I can put the tallies int grups by drawing circles arund them. Hw many tallies d are in each grup? (Elicit the apprpriate respnse.) Yes, I need t circle tallies at a time. I ll d that nw. (Circle the tallies until yu have tallies left ver. ) I have tallies left ver. Can I circle these tallies? (Elicit the respnse, n. ) Why? (Elicit the respnse, because there are nt enugh/they are fewer than the divisr. ) That s right, there are fewer tallies left than are represented by the divisr. Mdel checking yur drawings. Nw that I have finished drawing pictures, I need t check them and be sure I drew them crrectly. Hw d I check the dividend? (Elicit the respnse, cunt the ttal number f tallies t be sure they ttal the dividend. ) Yes. (Cunt alud the tallies and cmpare the ttal t the dividend.) I knw I have the crrect number f tallies, s nw I need t check t see if I have my dividend drawn crrectly. The dividend is represented by the tallies in each circle r grup. I can check this by cunting the number f tallies in each grup and be sure they equal the divisr. (Cunt alud the tallies in each grup and cmpare the ttal in each grup t the divisr.) Last, I check my remainder by being sure there are fewer tallies left ver than there are in each grup. (Cunt alud the remaining tallies and cmpare the ttal t the divisr/the number f tallies in each grup.) Mdel hw t find the answer t the equatin. Nw, t answer the equatin, I cunt the number f grups. (Cunt alud the grups.) Hw many grups d I have? (Elicit the apprpriate respnse.) Yes. And hw many tallies d I have left ver? (Elicit the apprpriate respnse.) What d we call the left ver tallies? (Elicit the respnse, remainder. ) Yes, they represent the remainder. Mdel the W step, Write the answer. I have fund my answer by drawing pictures and I have checked my drawings t be sure they are accurate. Nw I can finish slving the prblem by cmpleting the W step. What is the W step? (Elicit the respnse, Write the answer. ) Great, after I have fund my answer by drawing, I write the answer. Where t I write the answer? (Elicit the apprpriate respnse.) Great thinking! I knw the answer t a divisin
equatin shuld be written here. (Pint t the apprpriate space.) What is my answer? (Elicit the apprpriate respnse.) Yes, my answer is. I knw this because I have grups (Pint t each circled grup f tallies and cunt them alud.) and I have tallies left ver (Pint t the remaining tallies and cunt them alud.) I ll write the answer here. (Pint t the apprpriate space and write the answer.) b. Maintain a medium level f teacher directin/supprt fr anther example if students demnstrate misunderstanding/nn-understanding; mve t a lw level f teacher directin/supprt if students respnd apprpriately t the selected questins/prmpts. 3.) Scaffld Using a Lw Level f Teacher Directin/Supprt a. When students demnstrate increased cmpetence, d nt mdel the prcess. Ask students questins and encurage them t prvide all respnses. (Examples f chices are shwn in red.) Direct students t replicate the prcess at their desks as yu wrk tgether. Review steps f DRAW I have anther equatin. What is the name f the strategy that can help me draw pictures t slve this equatin? (Elicit the respnse, DRAW. ) What des each letter in DRAW stand? (Elicit the respnse, the steps fr slving an equatin. ) Yes. What des the D stand fr? (Elicit the respnse, Discver the sign. ) Yes, D stands fr Discver the sign. (*Repeat this prcess fr each step f DRAW.) Mdel the D step, Discver the sign. Nw that I knw I can use the DRAW Strategy t help me slve this equatin, I can begin by cmpleting the first step, D. What des D stand fr? (Pint t the D step and elicit the respnse, Discver the sign. ) Yes, I first need t discver the sign. Hw d I d this? (Elicit the respnse, by finding the symbl that tells what math peratin t use. ) Gd. (Pint t the divisin sign.) What is the sign? (Elicit the respnse, divisin. ) Gd. Hw d yu knw it is a divisin sign? (Elicit the respnse, it has a line in the middle and a dt n the tp and a dt n the bttm/it als lks like a sideways face. I see a lng nse with tw eyes. (Pint t the relevant features f the divisin sign.) Excellent thinking! What can I d t help me remember what math peratin I need t use? (Elicit the respnse, circle it. ) Yes, I can circle it t help me remember what math peratin t use. (Circle the divisin sign.) Mdel the R step, Read the prblem. I ve discvered the sign, and knw I need t divide. What is the next step? (Elicit the respnse, R. ) What des R stand fr? (Pint t the R step and elicit the
respnse, Read the prblem. ) Yes, I need t read the prblem. When I read a divisin prblem, what d I read first? (Elicit the respnse, the dividend. ) Yes, I knw I need t read the dividend r ttal first. What des the dividend represent? (Elicit the respnse, the ttal. ) Gd. The dividend represents the ttal. What is the dividend in this prblem? (Elicit the apprpriate respnse.) Yes. (Pint t the dividend and say it alud.) Hw d yu knw this is the dividend? (Elicit the respnse, because it has the highest value/it is mre. ) What d I read next? (Elicit the respnse, the divisin sign. ) Yes, need t read the sign because it tells me what math peratin t use t slve the prblem. (Pint t the divisin sign.) What d I read last? (Elicit the respnse, the divisr. ) Right, I read the divisr last. What is the divisr? (Elicit the apprpriate respnse.) Hw d yu knw this is the divisr? (Elicit the respnse, because it is less than the dividend. ) Right, this number must be my divisr because it is less than the dividend and because it is the remaining number. Nw that we knw all the parts f this equatin, we ll read it. (Encurage students t read the prblem alud with yu as yu pint t each part f the equatin.) Mdel the A step, Answer, r draw and check. Draw pictures t represent the dividend. - Nw that we knw what the prblem is and what math peratin I need t use. What is the next step? (Elicit the respnse, the A step.) What is the A step? (Elicit the respnse, Answer, r draw and check. ) Yes, I need t answer the equatin. I knw I can draw pictures t slve a divisin equatin. What kind f pictures can I draw? (Elicit the respnse, tallies r dts. ) What d we draw first? (Elicit the respnse, tallies. ) Why d we draw tallies? (Elicit the respnse, because that is the dividend/ttal. ) Yes, we represent the dividend first by drawing tallies r dts. I m ging t draw tallies and yu draw them n yur paper (Draw the apprpriate number f tallies.) Draw circles arund pictures t represent dividing them int equal grups based n the divisr. Hw d we divide r separate these tallies int grups? (Elicit the respnse, circle them. ) What number tells me hw many tallies belng in each grup. (Elicit the respnse, the divisr. ) Gd. (Pint t the divisr and say alud hw many tallies shuld be in each grup.) We can put the tallies int grups by drawing circles arund them. Hw many tallies d are in each grup? (Elicit the apprpriate respnse.) Yes, we need t circle tallies at a time. Let s d that nw. (I ll circle tallies here and yu d the same n yur paper.) D we have any tallies left ver? (Elicit the apprpriate respnse.) Yes, we have tallies left ver. Can we circle these tallies? (Elicit the respnse, n. ) Why? (Elicit the respnse, because there are nt enugh/they are fewer than the divisr. ) That s right, there are fewer tallies left
than are represented by the divisr. What d we call the left ver tallies? (Elicit the respnse, remainder. ) Yes, they represent the remainder. Mdel checking yur drawings. Nw that I have finished drawing pictures, what d I need t d? (Elicit the respnse, check the drawings. ) Yes, we need t check them and be sure we drew them crrectly. Hw d we check the dividend? (Elicit the respnse, cunt the ttal number f tallies t be sure they ttal the dividend. ) Yes. Let s cunt them. Yu cunt yurs and I ll cunt mine. Hw many tallies shuld yu have? (Elicit the apprpriate respnse.) We knw we have the crrect number f tallies. What d we check next? (Elicit the respnse, t see if we have the dividend drawn crrectly. ) Yes. Hw d we knw if the dividend is drawn crrectly? (Elicit the respnse, make sure the number f tallies we circled is the same as the divisr. ) Excellent thinking! I can check this by cunting the number f tallies in each grup and be sure they equal the divisr. What is the divisr? (Elicit the apprpriate respnse.) Yu cunt yurs and I ll cunt mine. What d we check last? (Elicit the respnse, the remainder. ) Yes, we have t check the remainder. Hw d we d this? (Elicit the respnse, cunt them t see that they are less than the divisr/less than the number f tallies in each grup. ) Right. Cunt yur remaining tallies and I ll cunt mine. Are there enugh t make anther grup f? (Elicit the respnse, n. ) Mdel hw t find the answer t the equatin. Nw, t answer the equatin, I cunt the number f grups. (Cunt alud the grups.) Hw many grups d I have? (Elicit the apprpriate respnse.) Yes. And hw many tallies d I have left ver? (Elicit the apprpriate respnse.) Mdel the W step, Write the answer. I have fund my answer by drawing pictures and I have checked my drawings t be sure they are accurate. What d I d next? (Elicit the respnse, the W step. ) Yes. What is the W step? (Elicit the respnse, Write the answer. ) Great, after I have fund my answer by drawing, I write the answer. Where t I write the answer? (Elicit the apprpriate respnse.) Great thinking! I knw the answer t a divisin equatin shuld be written here. (Pint t the apprpriate space.) What is my answer? (Elicit the apprpriate respnse.) Yes, my answer is. Hw d yu knw this? (Elicit the respnse, because there are grups and there are tallies left ver. ) Great. I ll write the answer and yu write yurs n yur paper. b. When yu are cnfident students understand, ask individual students t direct the prblem slving prcess r have the class direct yu: Students ask questins and yu and the students respnd/perfrm the skill.
Instructinal Phase 2: Facilitate Acquisitin t Mastery Student Practice *The student practice strategies described belw can be used fr bth drawing slutins frm divisin stry prblem cntexts and frm divisin equatins withut stry prblem cntexts. A detailed descriptin fr prviding practice fr drawing slutins t divisin equatins at the receptive/recgnitin and expressive levels is prvided. 1. Receptive/Recgnitin Level Purpse: t prvide students multiple pprtunities t practice matching apprpriate drawings t given divisin equatins and written slutins. Learning Objective 2: Drawing slutins t divisin stry prblems using the FASTDRAW Strategy Slving divisin equatins using DRAW. Instructinal Game/Structured Cperative Learning Grups Materials: Teacher verhead prjectr marker fr writing large cards with a variety f apprpriate divisin number sentences written n them in large enugh writing t be seen frm all areas f the classrm. a bx r suitable cntainer t place the cards in Cards with the individual rles written n them fr describing each rle. (i.e. grup writer, grup checker, grup drawer, grup reprter, grup scre-keeper) Students - paper fr drawing slutins paper fr keeping scre pencils and markers fr keeping scre and drawing slutins Descriptin: Activity: Class is divided int grups f apprximately five students. Each grup member is assigned ne f the fllwing rles: grup writer, grup checker, grup drawer, grup reprter, grup scre-keeper. The teacher leads game frm verhead prjectr. A bx is placed at the frnt f the classrm cntaining large cards with divisin number sentences written n them (e.g. 10 4 = 2 r2.). Grups are assigned a number that
reflects the rder that a student frm that grup will cme t the frnt f the classrm t pull a card frm the bx. Students in each grup are assigned numbers that reflect the rder they will pull a card frm the bx when it is their grup s turn. The respective student hlds the card up s all grups can see it and then reads the divisin number sentence. Each grup writer cpies the number sentence n a piece f paper. The checker fr each grup verifies the number sentence is written crrectly. The student returns t his/her grup and each grup draws the slutin t the divisin number sentence. The grup drawer makes the final drawing fr their grup. An apprpriate time frame is prvided fr grups t draw their slutins. Meanwhile the teacher draws three different examples f slutins, nly ne f which is accurate, n the verhead with the prjectr turned ff. The teacher numbers each example, 1, 2, 3. At the apprpriate time, the teacher signals grups t stp drawing and then reveals the three chices. Grups have a shrt perid f time t make their chice fr which f the three examples is crrect. At the end f the time perid, the teacher instructs the grup writer t write the number f the chice their grup has made. The grup reprter then says the grup s chice while hlding up the number they wrte when asked fr it by the teacher. After all grups have made their selectins, the teacher reveals the crrect drawing. Grups get 1 pint fr making the crrect selectin. After the teacher reveals the crrect drawing, then she/he asks each grup t hld up their drawing. If the grup s drawing is crrect, then that grup gets an additinal pint. The grup recrder keeps a recrd f their grup s scre n a sheet f paper by making a tally fr each pint their grup earns. Teacher prvides feedback including psitive reinfrcement and crrective feedback as apprpriate. Fr each example, the teacher talks alud why the drawing represents the number sentence, emphasizing the dividend, the divisr, and the qutient with remainder. Instructinal Game/Structured Cperative Learning Grups Steps: 1.) Prvide explicit directins fr the instructinal game/cperative grup activity including what yu will d, what students will d, and reinfrce any behaviral expectatins fr the game. 2.) Arrange students in cperative grups. Grups shuld include students f varying skill levels. 3.) Assign rles t individual grup members and explain them (e.g. grup writer, grup checker, grup drawer, etc.). 4.) Distribute materials. 5.) Have students number themselves fr the rder in which they will pull a card frm the bx. 6.) Number grups fr the rder in which a representative f their grup will pull a card frm the bx. 7.) Review/mdel apprpriate cperative grup behavirs and expectatins. 8.) Mdel ne example f skill(s) (i.e. drawing slutins and making an apprpriate chice frm three examples f drawings) within the cntext f the game. 9.) Prvide pprtunity fr students t ask questins. 10.) Play ne practice rund s students can apply what yu have mdeled. Prvide specific feedback/answer any additinal questins as needed. 11.) Teacher mnitrs and prvides specific crrective feedback & psitive. 12.) Play game.