POSTER PROBLEMS LAUNCH POSE A PROBLEM WORKSHOP POST, SHARE, COMMENT STRATEGIC TEACHER-LED DISCUSSION FOCUS PROBLEM: SAME CONCEPT IN A NEW CONTEXT

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1 POSTER PROBLEMS Knowing s Sixth Gre Poster Prolem Geometry This prolem is intene to open stuent s imgintion n to rete isussion on the min topis of the 6thgre geometry stnrs: polygon re, prism volume, oorinte geometry, n nets of prism eges. This lesson pln egins with isussion of geometril nets, llows for the onnetion of geometry n Crtesin oorintes n extens the generliztion of two imensions to three-imensionl retngulr ojets. This lesson lso lys fountion for the omputtion of Crtesin istnes n for when the Pythgoren Theorem n squre roots re introue in lter gres. Lerning Ojetives: Exmine n ientify nets n their properties n relte nets to soli figures. Determine lengths of figures y using oorinte plne. Determine re mesurements of retngles n right tringles (omposing n eomposing). Fining multiple nets for the sme tringulr or retngulr prism. Determine the volume of tringulr prism y ompring it to retngulr prism twie its size. Common Core Stte Stnrs for Mthemtis: 6.G.A.1 4 Mterils: Sissors Tpe Teher Tune Up: Wht is net? The wy this works: one lesson in six phses LAUNCH Tehers set the stge y leing n introutory isussion tht orients stuents to the ontext of the prolem. POSE A PROBLEM Tehers introue mthemtil wy of thinking out the ontext n engge stuents in preliminry pproh tht opens the oor to the workshop phse. WORKSHOP The workshop strts with more hllenging n more openene extension of the prolem. In tems, stuents pln n proue mthemtil posters to ommunite their work. POST, SHARE, COMMENT Tems isply their posters in the lssroom, get to know other tems posters, n tth questions/omments y wy of smll hesive notes (or similr). STRATEGIC TEACHER-LED DISCUSSION Tehers then ompre, ontrst n onnet severl posters. In the proess they highlight progression from more si pproh to more generlizle one. By oing this, tehers emphsize stnrs-ligne mthemtis using stuentgenerte exmples. Dy 1 FLEXIBLE Dy 2 FOCUS PROBLEM: SAME CONCEPT IN A NEW CONTEXT Serving s hek for unerstning, this more fouse prolem gives tehers eviene of stuent unerstning. SERP 2014!!! Knowing s - Sixth Gre Poster Prolem!!!! 1

2 1. LAUNCH Diretions for teher: Show Slie #1 ( vieo lip of Kleenex ox tht is ut prt n flttene). Ask stuents wht they notie out the vieo reoring. The ox ws flttene to eome net n then refole to eome three-imensionl figure one gin. During the isussion, press for preise use of the following onepts: Dimensions Corner (Vertex) Ege Fe POSTER PROBLEMS - KNOWING NETS SLIDE #1 Notie tht sie is not preise mthemtil voulry in this ontext! A squre hs four sies, ut ue hs fes tht meet t eges n verties. Slie #1 Show Slie #2 ( still imge showing the ox s threeimensionl shpe). Hve volunteers ome up to the projete imge n point to orner (vertex), n ege, n fe. Show Slie #3 ( still imge showing the ox s twoimensionl shpe net). Hve volunteers ome up to the projete imge n point to orner (vertex), n ege, n fe. Hve stuents turn to eh other n tlk out these questions: On net, how n the sme ege pper in ifferent prts of the net? How n orner pper on ifferent prts of the net? Enourge lively isussion, ut o not ttempt to settle these questions fully t this stge of the lesson. POSTER PROBLEMS - KNOWING NETS SLIDE #2 Slie #2 POSTER PROBLEMS - KNOWING NETS SLIDE #3 Slie #3 SERP 2014!!! Knowing s - Sixth Gre Poster Prolem!!!! 2

3 2. POSE A PROBLEM Diretions for teher: Show Slie #4. Re the slie to the lss. Mke sure everyone knows wht's eing ske, then istriute Hnout #1. You my hve the stuents work on the hnout with prtners. If stuents struggle or hve no fmilirity with nets, it is oky to llow stuents to use sissors to ut out nets to test. Consier how muh time you woul like to invest t this stge. The purpose of this phse is the help stuents unerstn tht there re ertin properties of nets. Not ll figures of six squre units n fol into ue, ut mny n. Enourge stuents to uil preliminry generliztions out wht shpes re nets n wht shpes re not nets n why. or Not? Emile hs jo s ox esigner. He is looking t possile nets for new ue-shpe ox. Some of these nets will form ue n some will not. Ientify whih of the following nets will mke ue. For those tht will not work, explin why not. For those tht will, try to lel ll orresponing eges. POSTER PROBLEMS - KNOWING NETS SLIDE #4 Slie #4 Answers: ANSWER KEY Stuent Nme: Knowing s 1 or Not? - Hnout Instrutions Emile hs jo s ox esigner. He is looking t possile nets for new ue-shpe ox. Some of these nets will form ue n some will not. Ientify whih of the following nets will mke ue. For those tht will not work, explin why not. For those tht will, try to lel ll orresponing eges. e e or Not? - Hnout #1 SERP 2014!!! Knowing s - Sixth Gre Poster Prolem!!!! 3

4 3. WORKSHOP Diretions for teher: As wrm-up to the workshop phse of this lesson, hve stuents fous upon of the one of Emile s oxes shown in Slie #5. As you sk the following questions, write them on the or. Then write the nswers with units s stuents give them. (Hving the questions n nswers for the simple ue visile will help stuents s they mke their posters.) Wht is the length of n ege? [1 unit] Wht is the re of one fe? [1 squre unit] Wht is the totl re of ll the surfes (surfe re)? [6 squre units] Wht is the volume of the ue? [1 ui unit] Is this the only net for the ue? [no] POSTER PROBLEMS - KNOWING NETS SLIDE #5 Slie #5 Sy to your stuents: During the workshop phse of this lesson, you re going to reeive hnout with net tht is more interesting thn Emile s oxes. The hllenge for your group is to figure out s muh s you n out the figure n mke poster showing wht you wht etermine. Be sure to isply wht you isovere n show how you isovere it. Distriute Hnout #2 two opies to eh group. Stuent Nme: Knowing s 12 Workshop - Hnout Workshop - Hnout #2 SERP 2014!!! Knowing s - Sixth Gre Poster Prolem!!!! 4

5 4. POST, SHARE, COMMENT Diretions for teher: Hve stuents post their posters roun the lssroom. Enourge stuents to trvel roun to view the posters rete y other groups. Stuents shoul e enourge to leve questions for other groups y tthing smll hesive notes. During this time, tehers shoul e reviewing ll the posters n onsiering whih to highlight uring Phse 5. Smple Posters: Poster A - These stuents use the oorinte plne to etermine sie lengths. Poster B - These stuents lulte the re of the retngles with the net n then move one of the right tringles to new position so they oul onsier the two tringles s one retngle. They then totle the res to etermine the surfe re. A Poster C - These stuents lele eges with letters n then ut out n fole the net to see if the letter lels orrespone. B Poster D - These stuents knew how to etermine the volume of the retngulr prism n notie tht two of the tringulr prisms they were working with oul e joine to rete retngulr prism. So they lulte the volume of the retngulr prism n then hlve tht to get the volume of the tringulr prism. Poster E - Here, the stuents rotte one of the right tringles to new position on the net n then ut it n fole to test. D C E SERP 2014!!! Knowing s - Sixth Gre Poster Prolem!!!! 5

6 5. STRATEGIC TEACHER-LED DISCUSSION Diretions for teher: As you egin the isussion, estlish tht the figure on the hnout is inee net of tringulr prism. Then hve vrious groups present their posters. Unlike in other Poster Prolems, we hven t efine levels stuents might rise through. Inste, help stuents onnet the vrious onepts tht pper in this tivity. To tht en, hve groups show posters with exmples of the vrious onepts elow. Hve stuents explin their thinking n onnet onepts from vrious posters. Also point out posters on whih stuents hve lrey onnete these ies. Conept 1: You n use oorinte plne (or even just gri) to lote n esrie verties, to etermine ege lengths, n to ompose n eompose shpes. Conept 2: Are n e etermine for eh iniviul fe using the net. The tringles n e oule to mke retngles (re = l x w) n then hlve to eome tringles gin. Logilly, then, the re of the tringle equls ½ (l x w). Cution: height of tringles re not lwys etermine y one of the sie lengths! Conept 3: The surfe re of the finl prism is the totl re of ll the fes. A net helps mke this ler. Conept 4: You n use the net to visulize n ount eges. Some eges get fole n other eges get ut. Stuents n ount the numer of eges y hnging the net into soli or y thinking through how to ount ut ege if it joins with nother ege. Some stuents might lel or olor-oe orresponing eges. etermine tht the volume of this tringulr prism is hlf of the retngulr prism. Conept 6: The ext sme tringulr prism n e me with nets tht re shpe ifferently thn the exmple given. Aitionl Questions n Explortions: Wht rithmeti o you o to fin istnes on gri? [ sutrtion ] Wht hs to e true for tht to work? [ the two ples hve to e on the sme line ] Wht woul you o to fin istne if they re not on the sme line? [ Stuents proly on t know the Pythgoren Theorem ut they n tell things out the istne, e.g., it hs to e more thn the horizontl istne ut less thn the sum of horizontl n vertil ] Wht s goo wy to lel eges so you n see whih go together? How n you preit whih go together without foling? Wht s relile wy to ount the eges of soli if you hve the net? [ perimeter ivie y two plus the insie fol lines ] Wht s the mximum numer of ples single vertex n pper on net? [ vries, ut for our nets it s proly 3 ] Some nets on t fol up into solis. Wht re some wys you n immeitely tell net is? Conept 5: You n fin the volume of this tringulr prism y joining two tringulr prisms together to rete retngulr prism. In Gre 6, stuents lern tht the volume of retngulr prism is foun y multiplying length x with x height. Stuents n then use logi to SERP 2014!!! Knowing s - Sixth Gre Poster Prolem!!!! 6

7 6. FOCUS PROBLEM: SAME CONCEPT IN A NEW CONTEXT Diretions for teher: Distriute Hnout #3. You n present this tsk in rnge of wys, from homework ssignment for iniviuls to nother group tsk. Here the hllenge is to rw net tht orrespons to piture of retngulr prism. There numer of orret wys to rw the net ssoite with the soli piture on the hnout. Fous stuents ttention on reting n urte representtion of the imensions n eges. Stuents n go on to o etermine surfe re n volume. Stuent Nme: Knowing s 13 Drw - Hnout Instrutions Drw net for the figure piture here. Write own s muh s you n out the figure Drw - Hnout #3 SERP 2014!!! Knowing s - Sixth Gre Poster Prolem!!!! 7