BLUEPRINTS. Getting Ready. The Activity. Overview. Introducing

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Mildred Malone
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BLUEPRINTS GEOMETRY LOGIC Satial visualization Tansfomational eomety Gettin Reay What You ll Nee Cuisenaie Ros, 1 set e ai 1-centimete i ae, ae 99 Tansaent tae an/o lue sticks 3" x 5" cas onto which

1 BLUEPRINTS GEOMETRY LOGIC Satial visualization Tansfomational eomety Gettin Reay What You ll Nee Cuisenaie Ros, 1 set e ai 1-centimete i ae, ae 99 Tansaent tae an/o lue sticks 3" x 5" cas onto which 1-centimete i ae has been lue, 2 e ai Lae books o foles to act as baies Ovehea Cuisenaie Ros an/o 1-centimete i ae tansaency (otional) Oveview Chilen buil stuctues with Cuisenaie Ros an aw the iffeent twoimensional views of each font, back, left, iht, to, an bottom. Then they evese the ocess by usin one anothe s awins to buil matchin stuctues. In this activity, chilen have the ootunity to: aw a thee-imensional fiue in two imensions inteet two-imensional awins to ceate a thee-imensional fiue The Activity Make sue that the ats of the os in the stuctue that touch ae multiles of one squae centimete. Intoucin Show chilen this Cuisenaie Ro stuctue attache to a 3" x 5" ca. Hel chilen ientify the six ossible views (font, back, left, iht, to, an bottom). Point out that each view of you stuctue can be awn on i ae. On the i, aw the two views of the stuctue shown below in colos that match the os. Dislay the two views an ask chilen to etemine which two of the six ossible views ae shown. Veify that View A is the font of the stuctue an View B is the left. View A font iht View B ETA/Cuisenaie

2 On Thei Own How can you use awins of a Cuisenaie stuctue to buil it? Wok with a atne. Each of you shoul secetly buil a stuctue with u to 6 Cuisenaie Ros. Follow these ules when builin you stuctue: The os shoul be tae o lue toethe so that the stuctue is in 1 iece. Each o must touch at least 1 othe o. Whee the os ae joine, they must touch alon 1 o moe whole squae centimetes (cm 2 ). 2 cm y 2 4 cm cm 2 { y { 1.5 cm 2 Okay Not okay Attach you stuctue to a ca covee with 1-centimete i ae. Make sue that the os on the bottom of you stuctue lie within the i lines. Decie which sie of you stuctue is the font. Daw an colo all 6 views of you stuctue on i ae. Label each view as font, back, to, bottom, iht, an left. Exchane awins with you atne. Use you atne s awins to ty to buil an exact coy of you atne s hien stuctue. Comae an iscuss the stuctue you built fom you atne s awins. The Bie Pictue Thinkin an Shain Invite chilen to islay thei stuctues an elate awins. Have them exlain how thei own awins show iffeent views of thei stuctues. Use omts such as these to omote class iscussion: What was ha about builin stuctues? about awin stuctues? How i you solve these oblems? What ae some oo ways to e-ceate stuctues fom awins? When you e-ceate stuctues, which views wee moe helful than othes? Why? Was the stuctue you built fom the awins iffeent fom the oiinal? Why? What nees to be chane to make them match? ETA/Cuisenaie

3 Di you stuctue match you atne s awins but not you atne s stuctue? Why? What miht you o iffeently if you buil an aw stuctues aain? Teache Talk Whee s the Mathematics? The skills use in Blueints ae imotant in ou thee-imensional wol whee objects ae commonly ecoe in two imensions in iaams, floo lans, an mas. Such skills, howeve, ae often not easy fo chilen to evelo. Many ootunities to wok thouh oblems of visualization an inteetation ae necessay if chilen ae to ain a useful level of oficiency. Most chilen will fin the awin hase easie than the builin hase. This is because while awin, they can efe to an maniulate thei stuctue as often as necessay to confim an evise thei wok. Some chilen may have touble holin stuctues in a way that allows them to see a sinle view lainly. Suest that they lace the stuctue on a flat suface an then ben own until they ae eye level with the stuctue so that they see only the squae o ectanula faces of os neaest to the eye. The view fom the bottom may be the haest to aw because the ca obstucts the view. Hee ae the six views of the stuctue iven in the Intoucin activity: Font Left Back Riht To Bottom When statin to constuct fom awins, most chilen will fist ientify the os use in the hien stuctue by matchin o colos with the colos on the awins. Many will then stuy the stuctue fom the bottom u, eteminin which os ae use in the base an how they ae attache befoe consiein othe views an how they influence ue layes of the ETA/Cuisenaie

4 Extenin the Activity 1. Have chilen buil an aw views of Cuisenaie Ro stuctues usin any numbe of os they choose. 2. Have chilen eeat the activity with a new stuctue, this time without usin colos in thei awins. stuctue. Anothe aoach chilen may take is to stuy the imensions of the stuctue in its tallest, wiest, an lonest views. Chilen who o this ealize that any stuctue they make cannot ossibly match the oiinal if it excees these imensions. Howeve chilen aoach the oblem of builin fom awins, successful stateies must be base on ceatin o confiuations sueste by one o moe views an checkin the accuacy of those confiuations by makin sue they ae consistent with all the othe views. Takin that job on all at once may be vey ifficult fo some chilen. Those who oanize thei wok by wokin fom the bottom u o by focusin on how os ae attache two at a time may make smoothe oess. Chilen ae accustome to lookin at eal-wol objects, such as houses, fom thei sies. This may exlain why many chilen will fin sie views (font, back, left, iht) easy to inteet. They may also notice that the outlines of oosite views of stuctues often mio one anothe, makin the aeaance of a sie easie to fiue out once they ae sue how its oosite sie looks. Without coloe awins, this activity woul be vey ifficult fo many chilen. Usin colo ives some ae ootunities fo inteetation. Some chilen will econize that a sinle squae of colo can only be inteete as the en of a o o at of a o face that is blocke fom view by anothe o. Othe chilen will exan on this iea an ealize that wheneve a colo aeas in a lenth shote than the lenth of the coesonin o, (fo examle, seein only thee squae centimetes of ule) then at of that o is blocke by anothe o. Lookin at othe views can confim this. When a colo aeas in a lenth eate than the lenth of the coesonin o, then chilen may see that moe than one o of that colo must have been use in the stuctue. If you want to make the activity easie, you can have chilen use fewe os, have the the whole class wok with exactly the same os, o tell chilen that os use in stuctues must all be of iffeent colos. ETA/Cuisenaie

5 1-CENTIMETER GRID PAPER ETA/Cuisenaie

EE 168 Handout #32 Introduction to Digital Image Processing March 7, 2012 HOMEWORK 7 SOLUTIONS

EE 168 Handout #32 Introduction to Digital Image Processing March 7, 2012 HOMEWORK 7 SOLUTIONS EE 168 Handout #32 Intoduction to Diital Imae Pocessin Mach 7, 2012 HOMEWORK 7 SOLUTIONS Polem 1: Colo Wheels We can epesent an N x N colo imae y a thee-dimensional aay such that the fist two dimensions