17.3 ALGEBRA. Find Unknown Side Lengths. Are You Ready? Lesson Opener Making Connections. Resources. Essential Question

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1 7. ALGEBRA Fid Ukow Side Leths? Essetil Questio How c you fid the ukow leth of side i polyo whe you kow its perimeter? Tes Essetil Kowlede d Skills Geometry d Mesuremet.7.B Determie the perimeter of polyo or missi leth whe ive perimeter d remii side leths i problems MATHEMATICAL PROCESSES..A Apply mthemtics to problems..f Alyze mthemticl reltioships How c you fid the ukow leth of side i polyo whe you kow its perimeter? Lesso Opeer Mki Coectios Ivite studets to tell you wht they kow bout qudrilterls. Wht is qudrilterl? (A qudrilterl is four sided fiure with four striht sides.) Wht re emples of qudrilterls i your clssroom? (Possible Aswer: Top of desk, frot of door, d shpe of the cover of tetbook.) Are You Redy? Access Prior Kowlede Use the Are You Redy? 7. i the Assessmet Guide to ssess studets uderstdi of the prerequisite skills for this lesso. Vocbulry Go to Multimedi eglossry t thikcetrl.com Usi the Diitl Lesso You my wish to reiforce tht qudrilterls hve four sides. Drw emples of differet qudrilterls d hve studets cout the umber of sides ech time. Leri Tsk Wht is the problem the studets re tryi to solve? Coect the story to the problem. Wht problem re you tryi to solve? (Fid the leth of the ukow side of the widshield.) Wht type of polyo is the widshield? ( qudrilterl) How my sides does the widshield hve? (4) Wht re the leths of the left d riht sides of the widshield? (Ech side is feet i leth.) Wht is the leth of the bottom of the widshield? (6 feet i leth) Litercy d Mthemtics Choose oe or more of the followi ctivities. Hve studets red the problem loud with prters. Hve studets bristorm s to wht mthemticl opertios my be used to fid the missi leth. Hve studets review the cocept of perimeter by eplii how they hve foud the perimeter i the pst. For the studet Resources Iterctive Studet Editio provides studets with iterctive leri eviromet! Mth o the Spot Video Tutor itools Virtul Mipultives Sor to Success Mth Olie Itervetio For the techer Diitl Memet Ceter orizes prorm resources by TEKS! etecher Editio Olie Assessmet System Lesso A

2 Ulock the Problem Hve studets red the problem. Ask studets to idetify wht they kow d wht they eed to fid out. Epli how to write equtio for the perimeter. Possible swer: I c use the side leths I kow s four ddeds d the letter, which stds for the ukow side leth, s the fifth dded. I c mke tht sum equl to the perimeter, 7. Epli why you used subtrctio to solve the equtio. Additio d subtrctio re iverse opertios, so I c use subtrctio to udo dditio. How c you check your swer? Possible swer: I c replce 8 for i the equtio d see if the sum of the ddeds is 7. Emple Hve studets complete the eercise. Poit out tht ech side leth is lbeled with the sme vrible becuse their leths re ll equl. Wht does s std for i the equtio? the leth of oe side of the squre Epli why you c use multiplictio to fid the ukow side leths of squre. I c use multiplictio becuse squre hs four sides tht re equl i leth. Could you use dditio to solve the problem? Epli. Yes, I could fid s + s + s + s = 0, sice the sum of the side leths is equl to the perimeter. If studets use dditio to solve, they will eed to use predict d check method i order to fid the leth of ech side.? Nme 7. Fid Ukow Side Leths ALGEBRA Essetil Questio Ulock the Problem How c you fid the ukow leth of side i polyo whe you kow its perimeter? Che hs 7 feet of feci to put roud his rde. He hs lredy used the leths of feci show. How much feci does he hve left for the lst side? Fid the ukow side leth. Write equtio for the perimeter. Thik: If I kew the leth of, I would dd ll the side leths to fid the perimeter. Add the leths of the sides you kow. Thik: Additio d subtrctio re iverse opertios. Write relted equtio. So, Che hs _ 8 feet of feci left. Emple Fid ukow side leths of squre. The squre hs perimeter of 0 iches. Wht is the leth of ech side of the squre? Thik: A squre hs four sides tht re equl i leth. You c multiply to fid the perimeter. Write multiplictio equtio for the perimeter. Use multiplictio fct you kow to solve. So, the leth of ech side of the squre is _ 5 iches. 5 ft ft 7 ft s s s Geometry d Mesuremet.7.B MATHEMATICAL PROCESSES..A,..F 4 ft _ 7 + _ 4 + = = 7 _ 9 + = 7 = 7 9 _ 8 = 7 9 Mth Ide A symbol or letter c std for ukow side leth. 4 s = 0 4 _ 5 = 0 s Module Elish Lue Lerers Leveled Activities Beii: Activity 44 Itermedite: Activity Advced: Activity 58 Advced Hih: Activity 4 ELPS.D,.C.4, 4.C..A.,.G., 4.C..C., 4.C., 4.F.9 4.F.8, 4.G., 4.G.4 thikcetrl.com for the ELL Activity Guide cotii these leveled ctivities. 557 Module 7 ELL Lue Support ELPS.D,.D. Strtey: Defie Iterpersol / Socil Smll Group Studets c defie words by usi them i cotet with their defiitios. Remid studets tht the perimeter of fiure is the distce roud the fiure. Hve studets repet the defiitio usi their ow words or drwis. Drw rectle o the bord with the leth lbeled feet d the width lbeled 4 feet. Put your fier o corer of the rectle, d follow lo the side leths. After ech side leth, hve studets sy the leth of the side loud d write it s dded o the bord. The help studets dd to fid the perimeter. 4 feet

3 Emple Fid ukow side leths of rectle. Lure hs rectulr blket. The perimeter is 8 feet. The width of the blket is 5 feet. Wht is the leth of the blket? Add the leths of the sides you kow. _ 5 + _ 5 = _ 0 Subtrct the leths from the perimeter. 8 _ 0 = _ 8 Divide the differece by. _ 8 = _ 9 So, the leth of the blket is _ 9 feet. Shre d Show Fid the ukow side leths.. Perimeter = 5 cetimeters 9 + _ 6 + _ + = 5 _ 8 + = 5 _ 7 = _ 5 _ 8 l 9 5 ft 5 ft 6 Hit: A rectle hs two pirs of opposite sides tht re equl i leth. Mth Tlk: Possible epltio: sice ll 4 sides of squre re equl i leth, you c divide the perimeter by 4 to fid the leth of oe side. = _ 7 cetimeters l Emple Hve studets look t the picture of the blket. Wht does the letter I std for? the ukow leth Wht equtio c you write for the perimeter? 5 + l l = 8 Epli why you eed to subtrct. you eed to fid the differece betwee the kow d the ukow side leths. Epli why you eed to divide by. both ukow side leths re the sme size, so you eed to divide the differece, 8, by. Go Deeper Ask studets how fidi the ukow side leths of squre is similr to fidi the ukow side leths of rectle. The sk how it is differet. Shre d Show Use the checked eercises for Quick Check. Studets should show their swers for the Quick Check o the MthBord.. Perimeter = 4 meters j. Perimeter = feet r Quick Check 7 m 7 m j j = _ 0 meters 558 r r = _ feet r r Mth Tlk Mthemticl Processes Epli how you c use divisio to fid the leth of side of squre. IF THEN studet misses the checked eercises Differetite Istructio with RtI Tier Lesso 85 Erich Visul / Spcil Idividuls Drw rectle with side leths lbeled d o the bord. Drw the sides lbeled so tht they re twice s lo s sides lbeled. Tell studets tht the perimeter of the rectle is 48. Hve studets fid the ukow side leths. 8 d 6 If time permits, studets should repet the ctivity for rectle with perimeter of 40 d side leths d +. 9 d Hve studets write problem of their ow for clssmte. Hve studets eche problems d check ech other s work. COMMON ERRORS Error Studets foret to dd side leth whe fidi perimeter. Emple Studets write the followi equtio to fid the missi side leth = 7. 5 i. i. 7 i. 4 i. Spribord to Leri Tell studets tht i order to be sure they iclude ech side leth whe fidi perimeter, they my wt to mrk or circle the side leths s they use them i their perimeter equtios. Go to Go to thikcetrl.com for dditiol erichmet ctivities i the Erich Activity Guide. Lesso

4 Ulock the Problem Problem 4 wlks studets throuh ech step of writi equtio to fid ukow side leth. Be sure tht studets use the correct iverse opertio whe solvi the equtio. Problem I Problem 5, studets use the leth of oe side of rectle to fid the ukow leth of the other side. Mth o the Spot Video Tutor Throuh the Mth o the Spot Video Tutor, studets will be uided throuh iterctive solvi of this type of H.O.T. problem. Use this video to lso help studets solve the H.O.T. problem i the Iterctive Studet Editio. With these videos d the H.O.T. problems, studets will build skills eeded i the TEXAS ssessmet. Mth o the Spot videos re i the Iterctive Studet Editio d t thikcetrl.com. Nme Ulock the Problem 4. Multi-Step Use Dirms Ltesh wts to mke border with ribbo roud fiure she mde d sketched t the riht. She will use 44 cetimeters of ribbo for the border. Wht is the ukow side leth? A cetimeters C 9 cetimeters B cetimeters D 6 cetimeters c. Write equtio to solve the problem h = Wht do you eed to fid? the leth of the ukow side b. How will you use wht you kow bout perimeter to help you solve the problem? I kow the sum of the leths of ll the sides is the perimeter, so I c dd the sides I kow d the write relted equtio. h 5 d. Complete the seteces. The perimeter is _ 44 cetimeters. The sum of the sides I kow is _ 5 cetimeters. A relted subtrctio equtio is _ 9 = _ 44 _. 5 So, the leth of side h is _ 9 cetimeters. e. Fill i the bubble for the correct swer choice bove. 5. Multi-Step A rectle hs perimeter of 4 iches. The left side is 6 iches lo. Wht is the leth of the top side? iches Module 7 Lesso 559 RtI Tier Lesso 85 Erich 84 Nme Nme Erich 84 LESSON 85 Alebr Fid Ukow Side Leths OBJECTIVE Fid the ukow leth of side of polyo whe you kow its perimeter..7.b Spedi Time t Cmp A ukow side leth is side tht does ot hve its leth lbeled with umber. Isted the side is lbeled with symbol or letter, such s. The perimeter of the trile is 0 meters. 6 m Fid the leth of side. 9 m Thik: There is oly oe ukow side leth. Step Add the kow side leths = 5 Step Subtrct the sum of the kow side leths from the perimeter. 0-5 = 5 Step Add to check your work = 0 Toms hs to mke schedule for dy t p. Use the iformtio below to mke possible schedule tht icludes ech ctivity. Use the umber lie to show whe ech ctivity will hppe.. Brekfst strts t 8:00 A.M. d lsts for 0 miutes.. Luch lsts 45 miutes d eds t :5 P.M.. The dy t p eds fter luch t :5 P.M. 4. Sports lst 60 miutes. 5. Crft clss strts riht fter brekfst d lsts 45 miutes. 6. Fishi lessos lst 0 miutes. So, the ukow side leth,, is 5 meters. The perimeter of the squre is feet. Wht is the leth of ech side of the squre? Thik: A squre hs four sides of equl leth. Step Divide the perimeter by the umber of sides. 4 = Step Multiply to check your work. 4 = So, the leth of ech side,, is feet. Fid the ukow side leths.. Perimeter = 8 cetimeters. Perimeter = 0 yrds 6 b 5 b = 4 cetimeters = 5 yrds 7. Nture wlk lsts 45 miutes d eds before sports. Possible swers re ive. Check studets work. dy dy strts brekfst crfts ture wlk fishi sports luch eds 8:0 A.M. 9:5 A.M. 0:00 A.M. 0:0 A.M. :0 A.M. 8. How lo is dy t p? Write the elpsed time. 55 miutes, or 4 hours 5 miutes 9. Stretch Your Thiki Use the schedule d your umber lie. C fishi hppe before the ture wlk? Epli. Yes. The schedule tells me tht the ture wlk comes before sports. This mes tht fishi could come fter crfts d before the ture wlk. So, there is eouh time for fishi before the ture wlk. 559 Module 7 Geometry d Mesuremet 69 Erich E84

5 Dily Assessmet Tsk Fill i the bubble completely to show your swer. 6. A wildlife sctury puts fece roud sectio of their ld. The fece is 9 kilometers lo. Wht is the leth of the ukow side? A 5 kilometers C kilometers B 7 kilometers D 4 kilometers Mthemticl Processes km 4 km 4 km 4 km Dily Assessmet Tsk C studets fid the ukow leth of side i polyo whe they kow its perimeter? IF THEN 7. Cir buys piece of ribbo to sew roud the edes of squre blket. She uses 6 iches of ribbo. How lo is ech side of the blket? NO Sor to Success Mth Wrm-Up 47. A 8 iches C 4 iches B 9 iches D iches 8. Multi-Step Key puts fece roud his 5-sided rde. He strts with 5 feet of feci. After he is doe, he hs 5 feet of feci left over. How lo is ech side of his rde? A 7 feet C 6 feet B 5 feet D feet YES Erich 84 Homework d Prctice Lesso 7. TEXAS Test Prep Coch Test Prep Coch helps techers to idetify commo errors tht studets c mke. 560 TEXAS Test Prep 9. Elei wts to put fece roud her squre rde. The rde hs perimeter of 8 meters. How lo will ech side of the fece be? A B C D 8 meters 7 meters 4 meters 6 meters I the Test Prep eercise, if studets selected: A, C, or D They do ot kow how to write multiplictio equtio to fid side leths.? Essetil Questio Write Mth How c you fid the ukow leth of side i polyo whe you kow its perimeter? Possible swer: I c dd the side leths I kow d subtrct the sum from the perimeter to fid the ukow side leth. Differetited Ceters Kit Literture Jmes Frmes Studets red bout usi perimeter to fid how much wood is eeded to mke picture frmes. Activities Perimeter Prde Studets complete ore Activity Crd 0 by fidi the perimeter of ptter blocks. Activities Roll To 00! Studets complete ore Activity Crd by fidi the sum of three umbers. Lesso

6 5 Homework d Prctice 7. ALGEBRA Fid the ukow side leths.. Perimeter = 8 cetimeters m 6 6 m Problem Solvi Nme Fid Ukow Side Leths m feet m = _ 8 cetimeters = _ 9 feet Use the dirm for 4.. Mitch eeds to replce the fece i his bckyrd. The dirm shows the leths of the borders of the fece. The leth of the fece is 6 meters. Wht is the ukow side leth? Epli how you will solve the problem. The write equtio to solve the problem. 9 meters; possible epltio: I dd the leths of the sides. The I write relted subtrctio setece to solve = 6; = 6 4; = 9 m. Perimeter = 40 feet Geometry d Mesuremet.7.B MATHEMATICAL PROCESSES..A,..F feet 4 m 5 m 7 m 5 m 4. Wht if Mitch ches the shpe of his fece to rectle? How much feci will Mitch eed? Epli. 6 meters; possible epltio: I kow the leth of oe side is m d other side is 9 m. If the fiure is rectle, the two sides re 9 m d two sides re m = 6 m Module 7 Lesso 56 Lesso Check Fill i the bubble completely to show your swer. 5. Ni hs mirror i the shpe of heo. He puts frme roud it tht hs perimeter of 4 iches. How lo is ech side? A 7 iches C 8 iches B 6 iches D 9 iches 7. A frmer is putti ew fece roud sectio of his rch. The fece is 5 kilometers lo. Wht is the leth of the ukow side? A 6 kilometers B 9 kilometers C 7 kilometers D 5 kilometers 8. Multi-Step Gled puts border of wllpper roud her bedroom wll. The room is rectle with side leths of meters d 4 meters. If she hs 0 meters of wllpper, how much wllpper is left over? A meters C 7 meters B 6 meters D 4 meters 56 5 km 9 km TEXAS Test Prep 6. Ze hs squre picture frme with perimeter of 8 iches. Which equtio c she use to fid the leth of ech side? A 4 s = 8 B 4 + s = 8 C D 8 4 = s = s 8 km 7 km 9. Multi-Step Jore sews trim roud the ede of tblecloth with 8 sides. He hs feet of trim. If ech side of the tblecloth is feet lo, how much trim will Jore hve left? A 0 feet C 4 feet B 8 feet D 6 feet Homework d Prctice Use the Homework d Prctice pes to provide studets with more prctice o the cocepts d skills of this lesso Module 7

7 Module 7 Assessmet Vocbulry Vocbulry Choose the best term from the bo.. Formtive Assessmet Use the Module Assessmet to ssess studets leri d proress i the module. The formtive ssessmet provides the opportuity to djust techi methods for idividul or whole clss istructio. Vocbulry re perimeter. The distce roud fiure is the perimeter (p. 545) Cocepts Cocepts d d Skills Skills Fid the perimeter of the fiure. Ech uit is cetimeter.. 6 cetimeters _ 4 cetimeters _ Fid the ukow side leths. 4. q TEKS.7.B Perimeter = cetimeters 5. Perimeter = feet 0 ft 4 k 6 cetimeters =_ 4 feet k=_ Use cetimeter ruler to fid the perimeter. q TEKS.7.B k ft 0 6. q TEKS.7.B. 5 6 cetimeters _ Module 7 56 _MTXESE0687_M7A.idd 56 0/0/5 7:4PM Dt-Drive Decisio Mki Bsed o the results of the Module 7 Assessmet, use the followi resources to strethe idividul or whole clss istructio. Itervee With RtI* Tier Lessos Sor to Success Mth My cout uits icorrectly B My foret to dd side leth before subtrcti B My foret to dd side leth or my dd icorrectly Item Lesso TEKS*, 7..7.B 4, Commo Error *TEKS Tes Essetil Kowlede d Skills; RtI Respose to Itervetio Module 7 Assessmet 56 Module 7 Assessmet Nme

8 Module 7 Assessmet Fill i the bubble for the correct swer choice. 7. Jcob built toolbo with perimeter of 70 iches. Wht is the leth of side m? q TEKS.7.B A B C D 50 iches 0 iches 5 iches 0 iches 8. Adriee is decorti squre picture frme. She lued iches of ribbo roud the ede of the frme. Wht is the leth of ech side of the picture frme? q TEKS.7.B A 4 iches C 8 iches B 8 iches D 6 iches 9. Wht is the perimeter of the fiure? Ech uit is cetimeter. q TEKS.7.B A 0 cetimeters C cetimeters B 8 cetimeters D 9 cetimeters TEXAS Test Prep m 0 i. 0 i. m 0. Jeff is mki poster for cr wsh for the Cmpout Club. Wht is the perimeter of the poster? q TEKS.7.B A 8 feet C 6 feet B feet D 4 feet ft ft ft ft Depth of Kowlede DOK Level Items, 6, 8 4 5, 7. A rectle hs side leths of 8 iches d 0 iches. Wht is the perimeter of the rectle? q TEKS.7.B 564 A 8 iches C iches B 8 iches D 6 iches Dt-Drive Decisio Mki Item Lesso TEKS* Commo Error Itervee With RtI* Tier Lessos Sor to Success Mth B My subtrct oly oe side leth from the perimeter B My multiply or divide icorrectly B My cout uits icorrectly , 7..7.B My dd oly two side leths *TEKS Tes Essetil Kowlede d Skills; RtI Respose to Itervetio 564 Module 7 Assessmet