2011.04.11 how do i introduce the geometry of the built environment into the curriculum

8/7/2019 2011.04.11 How Do I Introduce the Geometry of the Built Environment Into the Curriculum

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#Mathchat – Monday, 11th

April 2011

@ColinTGraham Hello eMon, 11 Apr 2011 19:30:36 +0000 - tweet id

@perfal RT @ColinTGraMon, 11 Apr 2011 19:30:47 +0000 - tweet id

@ColinTGraham For neconversation whenever you feel rMon, 11 Apr 2011 19:31:37 +0000 - tweet id

@ColinTGraham Today's

environment into the curriculum?"Mon, 11 Apr 2011 19:32:35 +0000 - tweet id

@ColinTGraham Any chMon, 11 Apr 2011 19:34:56 +0000 - tweet id

@reflectivemaths @Colibuilding? #mathchat Mon, 11 Apr 2011 19:35:56 +0000 - tweet id

@ColinTGraham @reflecfundamental, in actually looking foMon, 11 Apr 2011 19:37:02 +0000 - tweet id

@reflectivemaths @Coli

to keep pylons up with strength?Mon, 11 Apr 2011 19:38:37 +0000 - tweet id

@ColinTGraham @reflecthings and see why triangles etcMon, 11 Apr 2011 19:39:22 +0000 - tweet id

@ColinTGraham @reflec

can you measure the height of a tMon, 11 Apr 2011 19:41:28 +0000 - tweet id

How do I introduce the geometry of the b

eryone and welcome to Monday's #mat57525978284556288 - #49

am: Hello everyone and welcome to Mo57526025294331906 - #50

comers, you're welcome to watch, just jady! And don't forget the hashtag --> #

57526235366035456 - #51

topic is: "How do I introduce the geome

#mathchat 57526475380883456 - #52

tters today or is everyone on holiday? #57527069738926080 - #53

TGraham As in using a clinometer and t

57527320084348928 - #54

tivemaths That might be 1 example. I thir examples of how geometry is used #m57527596908417025 - #55

TGraham go on .... #mathchat I guess

57527996701085696 - #56

tivemaths Or finding ways to explore gere used... #mathchat 57528184417165312 - #57

tivemaths Why are houses generally cu

ee using shadows, say? #mathchat 57528713042067456 - #58

ilt environment into the curriculum?

chat

day's #mathchat

mp into theathchat

ry of the built

athchat

rig to calc the height of

k it's morethchat

ore like using triangles

metry by building

oid, for example? How




April 2011

@cherrylkd @reflectivemtriangles in environment? Cross cMon, 11 Apr 2011 19:41:47 +0000 - tweet id

@ColinTGraham @cherrdifferent eras could do with their tMon, 11 Apr 2011 19:43:11 +0000 - tweet id

@dansmath i am here CMon, 11 Apr 2011 19:43:16 +0000 - tweet id

@republicofmath Greatblackpool tower as example of triMon, 11 Apr 2011 19:43:47 +0000 - tweet id

@suburbanlion #mathchwhile walking through each doorwMon, 11 Apr 2011 19:44:26 +0000 - tweet id

@dansmath questions suasked me that once, as exampleMon, 11 Apr 2011 19:45:10 +0000 - tweet id

@ColinTGraham @dansstrengthen geometry/show why thMon, 11 Apr 2011 19:45:28 +0000 - tweet id

@republicofmath @danPhotographing those & discussinMon, 11 Apr 2011 19:45:55 +0000 - tweet id

@ColinTGraham @subuyou'd never leave! #mathchat Mon, 11 Apr 2011 19:46:17 +0000 - tweet id

@republicofmath @danthis? Geom of built environment hMon, 11 Apr 2011 19:47:05 +0000 - tweet id


aths #mathchat Like using blackpool towrricular with victorian history

57528790200500224 - #59

ylkd The historical aspect is important tochnology/materials... #mathchat

57529143960666112 - #60

lin, trying to understand the question. ;-}57529165016072192 - #61

xample @cherrylkd @reflectivemaths #ngles in environment?

57529294599110656 - #62

at Given a particular building, is it possiblay once?57529458160173057 - #63

ch as, "i'm 100 ft from a building, how talf trigonometry ;-) #mathchat

57529645217759232 - #64

ath How can you bring built objects aroings are built that way #mathchat 57529717972156416 - #65

math Built environment has lots of geomin class is one thing. What else? #math

57529833546190848 - #66

banlion Only if each room has two door

57529925896380416 - #67

math Kids often ask about #geometry -elps address that #mathchat 57530124773494784 - #68


er as exanple of

, in terms of what

#mathchat

athchat Using

e to visit every room

l is the bldg?" (my dad

und you into class to

etric shapes.hat

ays, Ryan, otherwise

hen will we ever use




April 2011

@suburbanlion @ColinTrooms w/ odd number of doorwayMon, 11 Apr 2011 19:47:23 +0000 - tweet id

@cherrylkd @dansmathand aqueducts and viaducts. HistMon, 11 Apr 2011 19:47:47 +0000 - tweet id

@ColinTGraham @cherrGreeks didn't use arches, as suchMon, 11 Apr 2011 19:48:41 +0000 - tweet id

@republicofmath Ryan i@suburbanlion #mathchat #didntMon, 11 Apr 2011 19:49:08 +0000 - tweet id

@CutTheKnotMath @CoYou are of course thinking of theMon, 11 Apr 2011 19:49:49 +0000 - tweet id

@dansmath @republicofdiscuss air conditioning. and i havMon, 11 Apr 2011 19:49:56 +0000 - tweet id

@suburbanlion @republiproblem http://bit.ly/c3GVZL #matMon, 11 Apr 2011 19:50:03 +0000 - tweet id

@ColinTGraham To a ceinvolved, as well as the 'traditionaMon, 11 Apr 2011 19:50:22 +0000 - tweet id

@bucharesttutor Sorry pto play with her, then possibly sheMon, 11 Apr 2011 19:50:25 +0000 - tweet id


Graham more specifically, the building c#mathchat

5 7530199180451840 - #69

mathchat Not just me then. Roman arcrical aspect tells us a lot

57530301156573185 - #70

ylkd It's also interesting to compare Rom... #mathchat 57530528483651585 - #71

vents new educational field: topology ofulerdoit

57530643197853696 - #72

linTGraham @cherrylkd The historical areat pyramids #mathchat

57530812991668224 - #73

ath sometimes we measure the L,W,He 'candid geometry' photos. #mathchat 57530843702366208 - #74

cofmath lol, yes, I stole the Seven Bridghchat 57530870889844737 - #75

rtain extent, there is a good deal of engil' maths #mathchat 57530950288027648 - #76

eople, can't join you for the #mathchat awill come n sleep with us ;)

57530965819535360 - #77


n't have more than 2

es copies on buildings

an with Greek, since the

built environment.

pect is important too...

of the classroom and

s of Königsberg

eering-type activity

my toddler wants me




April 2011

@cherrylkd @ColinTGrabeen present now you've made mMon, 11 Apr 2011 19:51:01 +0000 - tweet id

@ColinTGraham @CutTcalendar, the Incas construction oMon, 11 Apr 2011 19:52:05 +0000 - tweet id

@cherrylkd @bucharesttrectangular room probably. HaveMon, 11 Apr 2011 19:52:34 +0000 - tweet id

@ColinTGraham @cherrof buildings was restricted... hamMon, 11 Apr 2011 19:53:05 +0000 - tweet id

@suburbanlion @republisurface level features like length,Mon, 11 Apr 2011 19:53:22 +0000 - tweet id

@dansmath i take groupof string around to make a 10-poiMon, 11 Apr 2011 19:53:44 +0000 - tweet id

@ColinTGraham @subugeometry, though, aren't they? orMon, 11 Apr 2011 19:54:20 +0000 - tweet id

@republicofmath I was o@suburbanlion #mathchat Mon, 11 Apr 2011 19:54:37 +0000 - tweet id

@cherrylkd @CutTheKnbridge is excellent example. #matMon, 11 Apr 2011 19:54:46 +0000 - tweet id

@ColinTGraham @cherr) #mathchat


am #mathchat anglo saxon round house think about it57531117582041088 - #78

eKnotMath And the Aztec sun towers, Sf the Nazca lines. How...? #mathchat 57531384549490689 - #80

utor #mathchat Ah bless. Pop her in a reun

57531505123147776 - #81

ylkd Saxon building was largely based oer-beam roofs develop... #mathchat

57531634488049664 - #82

cofmath my point was that there was morea, volume #mathchat

57531707385053184 - #83

of students outside, arrange 20 of themted star. GCDs. #mathchat

57531801090002944 - #84

banlion Area, length and volume are meare they? What is area? #mathchat 57531948654014464 - #85

nly poking fun, Ryan: I think you have a

57532020733128704 - #86

tMath @ColinTGraham I wasn't but goochat

57532059140366336 - #87

ylkd Think you mean the Forth bridge, ov


s. Geometry's always

tonehenge as a

tangular bed in a

wood, so height/width

re to uncover than just

in a circle, throw a ball

nsuration rather than

ery good point.

one. New Fourth

er the Firth of Forth... ;-




April 2011

Mon, 11 Apr 2011 19:55:28 +0000 - tweet id

@CutTheKnotMath My hdistance from curb to door. PythMon, 11 Apr 2011 19:55:30 +0000 - tweet id

@republicofmath @danseems contrived. #mathchat Mon, 11 Apr 2011 19:55:50 +0000 - tweet id

@republicofmath @Cuttheorem?#mathchat Mon, 11 Apr 2011 19:56:35 +0000 - tweet id

@ColinTGraham @dansthings, bring them back & discussMon, 11 Apr 2011 19:57:04 +0000 - tweet id

@republicofmath @ColiIf no distance then it's topology. #Mon, 11 Apr 2011 19:57:49 +0000 - tweet id

@ColinTGraham @repuand surveying... maybe? #mathchMon, 11 Apr 2011 19:58:59 +0000 - tweet id

@republicofmath @Coli(b) check their understanding of g

Mon, 11 Apr 2011 19:58:59 +0000 - tweet id

@dansmath on Hometimat right angles. didnt use the termMon, 11 Apr 2011 19:59:26 +0000 - tweet id

@CutTheKnotMath Just@republicofmath A page on the u

Mon, 11 Apr 2011 19:59:27 +0000 - tweet id


57532236790104067 - #88

ouse is elevated above ground. City ordh saves backyard #mathchat 57532242217545728 - #89

math Nice activity, but from a built envir

57532328414674944 - #90

heKnotMath A page on the utility of Pyth

57532515098963969 - #91

ath Built environment, to me, suggestswhy they are built that way #mathchat

57532636691836928 - #92

TGraham I think the "metry" in geometrathchat

57532827369095168 - #93

licofmath And the "Geo-" implies earth/ at 57533120039235584 - #94

TGraham I agree. Point is to (a) help theom (van Hiele) #mathchat

57533118923550720 - #95

fixit show they used 6-8-10 triangle topythagorean though. #mathchat

57533234254331905 - #96

oing around telling the joke. But builderility of Pythagoras' theorem? #mathchat

57533236678635520 - #97


ance requires certain

nment perspective it

agoras'

sending Ss out to find

implies measurement.

orld... making maps

m see geom is useful

ut deck support beams

was dead serious.




April 2011

@republicofmath @ColiMon, 11 Apr 2011 19:59:54 +0000 - tweet id

@ColinTGraham @dansthough? If not, could provide interMon, 11 Apr 2011 20:00:45 +0000 - tweet id

@cherrylkd @ColinTGrathey bring back to discuss ?Mon, 11 Apr 2011 20:01:12 +0000 - tweet id

@republicofmath @danMon, 11 Apr 2011 20:01:16 +0000 - tweet id

@dansmath @republicofbrings numericals to a visual geoMon, 11 Apr 2011 20:01:29 +0000 - tweet id

@ColinTGraham @repu

actually separate measuring fromMon, 11 Apr 2011 20:02:03 +0000 - tweet id

@ColinTGraham @cherrrectangles, squares, quadrilateralMon, 11 Apr 2011 20:03:14 +0000 - tweet id

@dansmath this chat is tgeometry to solve blood spatter cMon, 11 Apr 2011 20:03:19 +0000 - tweet id

@suburbanlion @ColinTbut mensuration seems to be a laMon, 11 Apr 2011 20:03:22 +0000 - tweet id

@republicofmath @cheroctagonal .... Why so many trianglMon, 11 Apr 2011 20:03:25 +0000 - tweet id


TGraham I thought the "Geo" was for "57533352902787073 - #98

ath Did they explain why the trianglessting 'hook' for lesson #mathchat 57533563884679168 - #99

am @dansmath #mathchat What sort o

57533678829576192 - #100

math Pythagorean Builders - we do it rig57533694625320962 - #101

ath yes totally contrived; never seen aetry state though. #mathchat

57533749587492864 - #102

licofmath My point about measurement i

geometry... (DUH!) #mathchat 57533891451424769 - #103

ylkd @dansmath I would, say, ask them, other shapes... #mathchat

57534191771975682 - #104

tally interrupting my watching Dexter, inimes. #mathchat 57534209299980289 - #105

Graham yes, there's more to geometry tge part of present curriculum#mathchat

57534224147824640 - #106

rylkd Are objects round, pointy, circular,es? Properties of figures ... #mathchat 57534235740872704 - #107


eorge" ! #mathchat

ere designed that way,

things would you hope

ht (angled)#mathchat

0-pt star in the wild.

s that some curricula

o find circles, triangles,

which he uses

an just measurement,

quare, diamond,




April 2011

@ColinTGraham @cherretc try to reason why those shapeMon, 11 Apr 2011 20:04:06 +0000 - tweet id

@republicofmath @Colifigure why curriculum is as it is? #Mon, 11 Apr 2011 20:04:20 +0000 - tweet id

@ColinTGraham @dansDead! #mathchat Mon, 11 Apr 2011 20:04:45 +0000 - tweet id

@ColinTGraham @subuGEOmetry... #mathchat Mon, 11 Apr 2011 20:05:39 +0000 - tweet id

@republicofmath Are yowatching Dexter: uses geometry tMon, 11 Apr 2011 20:05:42 +0000 - tweet id

@republicofmath I oncetell me angles can't be measuredMon, 11 Apr 2011 20:07:11 +0000 - tweet id

@ColinTGraham Antoniowhen teaching geometry. #mathcMon, 11 Apr 2011 20:07:34 +0000 - tweet id

@ColinTGraham @repuEuclidean sense, but I don't expeMon, 11 Apr 2011 20:08:38 +0000 - tweet id

@ColinTGraham Gary (important, often overlooked, modMon, 11 Apr 2011 20:10:16 +0000 - tweet id

@JohnAllenPaulos StudKong is impossible, etc. #mathch


ylkd @dansmath then by comparing circs were used for that purpose #mathchat 57534406369357825 - #108

TGraham I know - it seems odd, but themathchat 57534468008841216 - #109

ath Well I have one eye on the last eve

57534573369757697 - #110

banlion Agreed, it tends to be more geo

57534796502536192 - #111

pulling our collective legs? @dansmathsolve blood spatter crimes. #mathchat

57534812675776513 - #112

had a bunch (correct collective noun?) oon Earth cause it's round #mathchat 57535183590653953 - #113

Gutierrez's site http://bit.ly/ig70ao showat

57535280810438657 - #114

licofmath Well, they may have been partt they were being that deep! #mathchat

57535548402839552 - #115

republicofmath) mentioned van Hiele el of learning #mathchat

57535958911942656 - #116

nts rarely exposed to geometric scalingt


lar objects, triangular,

e you are. Who can

r episode of Waking the

ETRY, rather than

chat interrupting

geography teachers

the richness available

ially correct in a

rlier. Theirs is an

arguments. Why King




April 2011

Mon, 11 Apr 2011 20:10:32 +0000 - tweet id

@republicofmath @Colito measure angles on a sphere, uMon, 11 Apr 2011 20:10:37 +0000 - tweet id

@_R_Srikanth RT @Joharguments. Why King Kong is imMon, 11 Apr 2011 20:11:19 +0000 - tweet id

@republicofmath Problemuch different van Hiele level. LaMon, 11 Apr 2011 20:11:46 +0000 - tweet id

@ColinTGraham There iand the Wikipedia entry is good toMon, 11 Apr 2011 20:12:21 +0000 - tweet id

@dansmath i often mentiwe all make polyhedra from cardbMon, 11 Apr 2011 20:12:35 +0000 - tweet id

@republicofmath @Joh#mathchat Mon, 11 Apr 2011 20:12:50 +0000 - tweet id

@ColinTGraham @repuworld instead of measuring it! #m

Mon, 11 Apr 2011 20:13:08 +0000 - tweet id

@suburbanlion Last timeVan Hiele level 1.5. How do we hMon, 11 Apr 2011 20:14:21 +0000 - tweet id

@republicofmath @dansight of others, who can ask ques

Mon, 11 Apr 2011 20:14:30 +0000 - tweet id


57536025559437312 - #117

TGraham I've had pre-service elementasing tangent planes #mathchat 57536047889911808 - #118

AllenPaulos: Students rarely exposed tossible, etc. #mathchat 57536224180703232 - #119

in teacher discussing geometry is if stguage misunderstood #mathchat

57536338840403968 - #120

a good mind map on the Van Hieles' mo: http://bit.ly/gOj2Qw #mathchat 57536482700836866 - #121

on soccer(foot)balls & the <5,6,6> patteroard and scotch tape. #mathchat 57536543824429056 - #122

AllenPaulos - and thinking about volume

57536607028387840 - #123

licofmath Probably because Geographethchat

57536682148364289 - #124

on #mathchat, @ColinTGraham suggeslp them move up to 2?

57536986067632128 - #125

math Rapid learning occurs if 1 studentions about it. #mathchat

57537025313738753 - #126


ry teachers tell me how

geometric scaling

dents are operating at

delhttp://bit.ly/eXUYc3

at each vertex; then

versus surface area.

s prefer to draw the

ted that most Ss were

as polyhedron out of




April 2011

@ColinTGraham @dansangle too... eg some pentagons tMon, 11 Apr 2011 20:14:30 +0000 - tweet id

@ColinTGraham @subuthought level 1.5 #mathchat Mon, 11 Apr 2011 20:15:35 +0000 - tweet id

@republicofmath @subsight of others, & has to answersMon, 11 Apr 2011 20:16:17 +0000 - tweet id

@ColinTGraham @subumuch more play, exploration andMon, 11 Apr 2011 20:16:55 +0000 - tweet id

@ColinTGraham Most ofseems related to language of teacMon, 11 Apr 2011 20:18:37 +0000 - tweet id

@republicofmath @Colisimilar) ?Mon, 11 Apr 2011 20:18:46 +0000 - tweet id

@suburbanlion @republifigures?#mathchat Mon, 11 Apr 2011 20:18:53 +0000 - tweet id

@reflectivemaths @Coliwith those problems. Even I couldMon, 11 Apr 2011 20:19:06 +0000 - tweet id

@ColinTGraham @repuso...#mathchat Mon, 11 Apr 2011 20:19:14 +0000 - tweet id

@MrHonner I have enjoyyear. A great way to play, interact,


ath exploring tiling (tessellation) is a grssellate, but not all #mathchat

57537024139333632 - #127

banlion That was on leaving high school

57537296743940096 - #128

rbanlion Have found that student who hs about it, rises in VH level #mathchat

57537475224141825 - #129

banlion I think increasing van Hiele levelisualization work earlier on #mathchat

57537633185828865 - #130

the problems or issues related to spaceher being 'too high' #mathchat 57538061441048576 - #131

TGraham Is this a Mega-Marathon-Mon

57538097876963328 - #132

cofmath like playing "I Spy" but with geo

57538129296490496 - #133

TGraham #mathchat Think my studentsdo with a "Would use this for..."

57538184019578880 - #134

licofmath Yep, we're on for another 40

57538218593239040 - #135

d incorporating paper folding into geom, experiment. #mathchat


at way of discovering

, 1st year undergrad, I

s geom object out of

s has to be done by

and shape I see in 14yo

ay #mathchat (or

etric

would really struggle

inutes or

try discussions this




April 2011

Mon, 11 Apr 2011 20:19:15 +0000 - tweet id

@ColinTGraham @MrHopaper-engineering! #mathchat Mon, 11 Apr 2011 20:20:02 +0000 - tweet id

@dansmath ok here's a chexagons vs squares: #mathchat Mon, 11 Apr 2011 20:20:26 +0000 - tweet id

@republicofmath @subresult of Qs from others. StrikingMon, 11 Apr 2011 20:20:40 +0000 - tweet id

@republicofmath I needminutes or so... #mathchat Mon, 11 Apr 2011 20:21:14 +0000 - tweet id

@ColinTGraham @reflecbring in an understanding of mateMon, 11 Apr 2011 20:21:29 +0000 - tweet id

@republicofmath Beautifshopping cart! hexagons vs squarMon, 11 Apr 2011 20:22:02 +0000 - tweet id

@reflectivemaths @Coliwording seems clunky. 'Shifting fr

Mon, 11 Apr 2011 20:22:18 +0000 - tweet id

@ColinTGraham @reflecinteresting questions about 'desigMon, 11 Apr 2011 20:22:23 +0000 - tweet id

@MrHonner @ColinTGratransformations this year. A nice c

Mon, 11 Apr 2011 20:22:24 +0000 - tweet id


57538220572942336 - #136

nner Oh, well, try holding me back from

57538418598617088 - #137

andid geometry shot, a richly tessellatedhttp://yfrog.com/h0e58xbj 57538519916224513 - #138

rbanlion Yes. Student with figure has to lg: icosahedron #mathchat

57538577126522880 - #139

an energy drink! @ColinTGraham Yep,

57538719166627841 - #140

tivemaths Questions such as "Why arerials used for building too. #mathchat 57538781598859264 - #141

ul! @dansmath here's candid geom shotes: #mathchat http://yfrog.com/h0e58xbj 57538923043368960 - #142

TGraham #mathchat I like the mind mam simple identification to..virtual model

57538989468557312 - #143

tivemaths Comparing a house with a tenfor purpose' too. #mathchat

57539009982906368 - #144

ham I've used folding with concurrency,hange-up activity! #mathchat

57539014554697728 - #145


rigami, tangrams and

shopping cart!

ook more deeply as a

e're on for another 40

ouses cuboid?" need to

, richly tessellated

but some of the..'

t, though, raises

olid geometry, and




April 2011

@reflectivemaths @Colithen is: Why are bricks cuboidal?Mon, 11 Apr 2011 20:23:14 +0000 - tweet id

@MrHonner Plus, I definithinking. #mathchat Mon, 11 Apr 2011 20:23:26 +0000 - tweet id

@ColinTGraham For me,things is one of the best ways of eMon, 11 Apr 2011 20:24:07 +0000 - tweet id

@ColinTGraham @reflecare/were difficult to build... #mathMon, 11 Apr 2011 20:24:55 +0000 - tweet id

@monsoon0 Thanks #mMon, 11 Apr 2011 20:25:32 +0000 - tweet id

@dansmath don't forget tthree corners, they might find theMon, 11 Apr 2011 20:25:44 +0000 - tweet id

@reflectivemaths @ColiI'd love to use lego: what task/chaMon, 11 Apr 2011 20:26:01 +0000 - tweet id

@MrHonner I just concluGeogebra to fit curves to them, likMon, 11 Apr 2011 20:26:09 +0000 - tweet id

@MrHonner A nice way tMon, 11 Apr 2011 20:26:24 +0000 - tweet id

@ColinTGraham Also @arguments ties in with, say, buildiMon, 11 Apr 2011 20:26:42 +0000 - tweet id


TGraham Presumably, because bricks#mathchat 57539225272336385 - #146

ely believe working with your hands enh

57539272902844416 - #147

using paper and Lego bricks and gettinxploring geometry #mathchat 57539443871072256 - #148

tivemaths Spherical houses would use lhat

57539648867667968 - #149

thchat I hadn't heard of the Van Hiele m57539801506775040 - #150

o have them cut out different-shaped triaadd to a constant! #mathchat

57539853985918977 - #151

TGraham Are you a primary or secondallenge do you set?57539922902528000 - #152

ed a great project where students takee this: http://goo.gl/8dmNF #mathchat 57539959262945281 - #153

start seeing the math all around us. #m57540021200224256 - #154

ohnAllenPaulos's earlier statement abog cathedrals vs houses #mathchat

57540096441847808 - #155


re cuboidal. Obs Q

ances creative, active

the Ss to build/make

ss materials, but

odel before.

ngles & tear off the

ry teacher?#mathchat

hotos and use

athchat

t exposure to scaling




April 2011

@baevmilena RT @Colinrichness available when teachingMon, 11 Apr 2011 20:27:20 +0000 - tweet id

@ColinTGraham @refleca Yr8/9 class in my 1st teaching pMon, 11 Apr 2011 20:27:38 +0000 - tweet id

@ColinTGraham @reflecbricks and ask them to build the tMon, 11 Apr 2011 20:28:40 +0000 - tweet id

@reflectivemaths @Colifurniture doesn't fit! #mathchat Mon, 11 Apr 2011 20:29:06 +0000 - tweet id

@ColinTGraham @reflecand I go past and flick them over..Mon, 11 Apr 2011 20:29:28 +0000 - tweet id

@republicofmath Here'sMon, 11 Apr 2011 20:29:31 +0000 - tweet id

@republicofmath Her's shttp://twitpic.com/4jqokq#mathchMon, 11 Apr 2011 20:30:15 +0000 - tweet id

@dmarain @ColinTGrahfixed # of ice cream sticks is instrMon, 11 Apr 2011 20:30:37 +0000 - tweet id

@ColinTGraham @reflecstart building a base to support...Mon, 11 Apr 2011 20:30:54 +0000 - tweet id

@ColinTGraham 20ish Rbe? Also, what can you say they'vMon, 11 Apr 2011 20:31:43 +0000 - tweet id


TGraham: Antonio Gutierrez's site http:// geometry. #mathchat 57540256420986880 - #156

tivemaths Secondary trained... but thereractice school... #mathchat 57540332459536384 - #157

tivemaths I give groups/pairs the same nllest tower... #mathchat

57540592263114753 - #158

TGraham Spherical houses would caus

57540700711043072 - #159

tivemaths They, of course, stack them o. oops, unstable try again #mathchat 57540790343315456 - #160

a pic of part of my office wall http://twitpi57540803211436032 - #161

ome students sitting at tables:t 57540989908291584 - #162

m Having teams of Ss build strongest stctive. #mathchat

57541081880997889 - #163

tivemaths They go back, use the same necomes column... #mathchat

57541153574240256 - #164

T @reflectivemaths: And how many brice learned by doing that task? #mathchat 57541356054249472 - #165


bit.ly/ig70ao shows the

was a 5-year gap with

umber and size of

mean that my

e on top of the other

.com/4jqoga#mathchat

ructure possible with

umber of bricks and

s (approx) would that




April 2011

@baevmilena RT @Colinhttp://bit.ly/eXUYc3 and the WikipMon, 11 Apr 2011 20:32:24 +0000 - tweet id

@ColinTGraham @dmarthey have to devise the criteria forMon, 11 Apr 2011 20:32:56 +0000 - tweet id

@CutTheKnotMath Whethe best ways of exploring geomeMon, 11 Apr 2011 20:33:00 +0000 - tweet id

@NISSSAMSI @republictracking#mathchat, so am intrigueMon, 11 Apr 2011 20:34:10 +0000 - tweet id

@ColinTGraham @CutTpaper-folding stuff! I am happy witMon, 11 Apr 2011 20:34:11 +0000 - tweet id

@republicofmath @Cutexplanations for observed facts. #Mon, 11 Apr 2011 20:34:23 +0000 - tweet id

@dansmath two of my alpic:http://yfrog.com/hsnrekvj #matMon, 11 Apr 2011 20:34:36 +0000 - tweet id

@reflectivemaths @Colion top of the other no problem! #Mon, 11 Apr 2011 20:35:02 +0000 - tweet id

@ColinTGraham @CutTUsing geometry to explore algebrMon, 11 Apr 2011 20:35:16 +0000 - tweet id


TGraham: There is a good mind map ondia entry is good too: http://bit.ly/gOj2Q

5 7541528259805184 - #166

ain having students build anything -est ismeasurement too #mathchat

57541662796296192 - #167

does proving come in? @ColinTGrahary #mathchat

57541683012829184 - #168

fmath Just looked at your photos and hd by these random shots.57541973933957120 - #169

eKnotMath Ok, that is out of context, beh conjecture/play #mathchat 57541977784336384 - #170

heKnotMath Proving - early, I hope, starmathchat 57542028594135040 - #171

ebra students using geometry to factor thchat 57542084755865600 - #172

TGraham I'd've thought that 20 bricks cathchat

57542193128292352 - #173

eKnotMath Proof, in the sense of deducic proofs visually? ASAP #mathchat

57542250456031232 - #174


the Van Hieles' model#mathchat

instructive, especially if

Lego bricks is one of

ven't been

cause you removed the

ing with a need for

rinomials!

uld be just built up one

tive reasoning, not early.




April 2011

@republicofmath @NISdistribution. #mathchat Mon, 11 Apr 2011 20:35:34 +0000 - tweet id

@ColinTGraham @reflecdon't tell them I'm going to do thatMon, 11 Apr 2011 20:35:52 +0000 - tweet id

@republicofmath van Hinot a question of age or grade, buMon, 11 Apr 2011 20:37:02 +0000 - tweet id

@dmarain Triangle is theNot so for quads where sides&anMon, 11 Apr 2011 20:37:12 +0000 - tweet id

@CutTheKnotMath I amstarting with a need for explanatioMon, 11 Apr 2011 20:38:42 +0000 - tweet id

@republicofmath @dma#mathchat Mon, 11 Apr 2011 20:38:46 +0000 - tweet id

@ColinTGraham @CutThttp://bit.ly/cryBab eg sum of n odMon, 11 Apr 2011 20:38:50 +0000 - tweet id

@ColinTGraham @dmarfour legs isn't necessarily so... #mMon, 11 Apr 2011 20:39:37 +0000 - tweet id

@MrHonner @dmarain Tcardboard together in a frame. #Mon, 11 Apr 2011 20:39:49 +0000 - tweet id

@LesLinks RT @Deboratime I watch this: http://bit.ly/dV98


SAMSI Maybe random, but not uniforml

5 7542325978677248 - #175

tivemaths Not if the teacher comes rounthough... #mathchat

57542400947654657 - #176

le levels deal explicitly with proving. It'st VH level. #mathchat 57542694716710912 - #177

simplest geom fig that retains shape if siles must be fixed #mathchat

57542740069711872 - #178

trying think of that @republicofmath Prons for observed facts. #mathchat 57543116055515136 - #179

rain. Right - triangles are rigid. Why so o

57543130915930112 - #180

eKnotMath Some examples of 'visual prnumbers is n squared, etc. #mathchat

57543148984999936 - #181

ain A table with three legs is always stabathchat 57543344993218560 - #182

his is fun to show by taping three, and thathchat

57543397333925889 - #183

hMersino: Who Will Change Everything?u2 #edchat #gtchat #gifted #ntchat #mat


so. Opportunistic

and pushes it over! I

higher up in levels. So

de-lengths are fixed.

ing - early, I hope,

ten seen in buildings.

oofs' on my Lego page

le, whereas one with

en four, long pieces of

Get goosebumps everychatelemchat




April 2011

Mon, 11 Apr 2011 20:39:58 +0000 - tweet id

@republicofmath @CutGood grade 5-7 question. #mathcMon, 11 Apr 2011 20:40:18 +0000 - tweet id

@ColinTGraham I havehttp://bit.ly/fQrRfe hyperbolic paraMon, 11 Apr 2011 20:42:29 +0000 - tweet id

@reflectivemaths @Colimilking stools are 'always three leMon, 11 Apr 2011 20:42:32 +0000 - tweet id

@dmarain Property I meNow what are all the reasons for tMon, 11 Apr 2011 20:42:36 +0000 - tweet id

@LesLinks Cat's face isMon, 11 Apr 2011 20:42:55 +0000 - tweet id

@CutTheKnotMath Veryexamples of 'visual proofs' on myMon, 11 Apr 2011 20:42:55 +0000 - tweet id

@ColinTGraham @LesLiintroduce the geometry of built enMon, 11 Apr 2011 20:44:23 +0000 - tweet id

@reflectivemaths @dmaand 'squash them' they will naturaMon, 11 Apr 2011 20:44:23 +0000 - tweet id

@republicofmath There'environment#mathchat @LesLinkMon, 11 Apr 2011 20:44:50 +0000 - tweet id


5 7543435510480896 - #184

heKnotMath. E.g. why do polyominoes hhat 57543518498983937 - #185

one a couple of lessons using drinking sboloid-style #mathchat 57544068544204800 - #186

TGraham @dmarain I've heard that saiged' #mathchat

57544078954479616 - #187

tioned helps Ss to see why tri's are usedhe honeycomb shape! #mathchat 57544096557965312 - #188

pentagon... Hi folks Leslinks in Ireland57544176069378048 - #189

good, though, it's more algemetry @ColiLego page http://bit.ly/cryBab #mathchat 57544174647513088 - #190

nks Hi Les, we still have 15 minutes or sironment into the curric?" #mathchat

57544545981837312 - #191

rain As for honeycombs, apparently, if ylly become honeycomb like #mathchat 57544545675644929 - #192

another whole realm in geometry of nats57544657290276864 - #193


ave even perimeter?

traws to create curves...

as a reason for why

for simple trusses.

ipping in...#mathchat

nTGraham Some

left on "How do I

u take a lot of circles

ural




April 2011

@MrHonner @republicofgeometry of the lunch table changMon, 11 Apr 2011 20:44:50 +0000 - tweet id

@baevmilena I find disseformulas. #mathchat Mon, 11 Apr 2011 20:44:58 +0000 - tweet id

@CutTheKnotMath Goopolyominoes have even perimeterMon, 11 Apr 2011 20:44:58 +0000 - tweet id

@vizlearning Get out you(perimeter) Activity pdf: http://bit.lMon, 11 Apr 2011 20:45:02 +0000 - tweet id

@reflectivemaths @ColiLEGO!#mathchat Mon, 11 Apr 2011 20:45:14 +0000 - tweet id

@ColinTGraham @reflecsmallest quantity of material to enMon, 11 Apr 2011 20:45:16 +0000 - tweet id

@LesLinks Alot of geomMon, 11 Apr 2011 20:45:57 +0000 - tweet id

@ColinTGraham @reflectimes! Lego digital designer is greMon, 11 Apr 2011 20:46:25 +0000 - tweet id

@republicofmath @CutMon, 11 Apr 2011 20:46:31 +0000 - tweet id

@LesLinks RT @republienvironment #mathchat @LesLinMon, 11 Apr 2011 20:46:45 +0000 - tweet id


ath's pictures put me in mind of a studees the group dynamic. #mathchat 5 7544656971513856 - #194

tions useful figuring out properties. Wor

57544693034135552 - #195

Should not you collect such Qs? @rep? Good grade 5-7 question #mathchat 57544692950253568 - #196

r bikes...the MathStart Book of Day? "R/emu8Ia #math #mathchat #NCTM11

57544709719076864 - #197

TGraham Oh come on! You're not even

57544759857786881 - #198

tivemaths @dmarain And the circle comlose an area...(?) #mathchat

57544767516585984 - #199

try in nature too... Aahh thanks @Colin57544938337996802 - #200

tivemaths Oh, I've done all those with reat for visualization work... #mathchat 57545055531048960 - #201

heKnotMath Yes!!! #mathchat 57545080927559680 - #202

ofmath: Theres another whole realm ins Ya..;-D.. good topic Ilike.. #mathchat

57545140780273664 - #203


nt essay about how the

ks cool with area

blicofmath E.g. why do

cing Around"

using real

s down to using the

Graham #mathchat

l Lego many, many

eometry of natural




April 2011

@ColinTGraham @baev#mathchat Mon, 11 Apr 2011 20:47:34 +0000 - tweet id

@Turkeydoodles See, IThanks for telling me about van HMon, 11 Apr 2011 20:47:36 +0000 - tweet id

@LesLinks RT @republipassed on cuttheknot to folk.. ;-DMon, 11 Apr 2011 20:47:57 +0000 - tweet id

@dmarain @ColinTGrahthen bring one in to demo! #mathMon, 11 Apr 2011 20:47:59 +0000 - tweet id

@nwhyluckysgirl @dmb#mathchat Mon, 11 Apr 2011 20:48:02 +0000 - tweet id

@republicofmath Didn'tMon, 11 Apr 2011 20:48:08 +0000 - tweet id

@CutTheKnotMath I meMon, 11 Apr 2011 20:48:23 +0000 - tweet id

@reflectivemaths @Coliwasteful if cut out of sheets of woMon, 11 Apr 2011 20:48:30 +0000 - tweet id

@ColinTGraham Yes, I tJames May try to build a real LegMon, 11 Apr 2011 20:49:23 +0000 - tweet id

@republicofmath @CutMon, 11 Apr 2011 20:50:19 +0000 - tweet id


ilena I assume you mean dissections o

57545345269370880 - #204

on't even have to to show up for #mathciele levels! #hsmath 57545353838338048 - #205

ofmath: @CutTheKnotMath Yes!!! Yay..mathchat

57545441293762560 - #206

m Have Ss guess how carpenter insurehat

57545452505137152 - #207

ates05 A nice resource courtesy of @ms

57545465226465281 - #208

ames May try to build a real Lego house57545490002219008 - #209

nt collect for sharing @republicofmath57545551696232448 - #210

TGraham @dmarain Not sure. Circles ad: likely cross section of tree #mathchat 57545583065436160 - #211

ink there's a video on YouTube RT @rehouse #mathchat

57545805585846272 - #212

heKnotMath Sure, for sharing #mathcha57546040076800003 - #213


solids and not frogs! ;-)

hat and I learn things.

I have frequently

edges are parallel,

atcary:http://bit.ly/ge4Elf

#mathchat

es!!! #mathchat

re good, but very

publicofmath: Didn't




April 2011

@ColinTGraham @refleccubes can be packed less wastefMon, 11 Apr 2011 20:51:10 +0000 - tweet id

@dmarain Many studentto floor as it collapses. This is a gMon, 11 Apr 2011 20:51:19 +0000 - tweet id

@ColinTGraham Leads tstudents joke! Polygons can be diMon, 11 Apr 2011 20:52:36 +0000 - tweet id

@CutTheKnotMath Wheand now square? #mathchat Mon, 11 Apr 2011 20:53:06 +0000 - tweet id

@maxmathforum #math#wcydwthttp://twitpic.com/4jqwpc Mon, 11 Apr 2011 20:53:47 +0000 - tweet id

@LesLinks Slightly off togarden..http://bigpicture.posterouMon, 11 Apr 2011 20:54:12 +0000 - tweet id

@ColinTGraham @CutTdissection... #mathchat Mon, 11 Apr 2011 20:54:31 +0000 - tweet id

@republicofmath Max, eat#NCTM #NCSM #wcydwt http:// Mon, 11 Apr 2011 20:55:03 +0000 - tweet id

@MrHonner @CutTheKnmonday-mathematical-coffee-tablMon, 11 Apr 2011 20:55:25 +0000 - tweet id

@ColinTGraham @CutTdissection, isn't it? #mathchat


tivemaths @dmarain Yes, this then turnlly than spheres. Tetrapak? #mathchat

5 7546251981434880 - #214

struggle to relate properties to why ironiod app! #mathchat

57546290438995968 - #215

o sum of internal angles RT @baevmilenssected and rearranged. Cool proofs. #57546612850950144 - #216

e did I see this hinged table of 4 parts o

57546740013858816 - #217

hat view out my window at #NCTM #NC 57546913247006720 - #218

ic.might enjoy looking at this unusual.com/the-garden-of-cosmic-speculation

57547018284974081 - #219

eKnotMath I know the one you mean...

57547097989332992 - #220

xcellent! @maxmathforum #mathchat vitwitpic.com/4jqwpc 57547231892488192 - #221

otMath Here:http://blog.makezine.com/a.html #mathchat

57547323559002113 - #222

eKnotMath I think it's based on http://bit


into a packing problem,

ng board stays parallel

a That's how myathchat

7 legs, now triangle

SM

mathchat

elated to a hinged

w out my window

chive/2011/04/math-

.ly/ftbHVh type of




April 2011

Mon, 11 Apr 2011 20:55:28 +0000 - tweet id

@ColinTGraham OK, anMon, 11 Apr 2011 20:56:39 +0000 - tweet id

@republicofmath This hMon, 11 Apr 2011 20:57:23 +0000 - tweet id

@CutTheKnotMath Yes.based on http://bit.ly/ftbHVh typeMon, 11 Apr 2011 20:57:24 +0000 - tweet id

@MrHonner @maxmathfMon, 11 Apr 2011 20:57:39 +0000 - tweet id

@ColinTGraham @MrHoMon, 11 Apr 2011 20:58:09 +0000 - tweet id

@dmarain Challenge to

and angles of both and write dowMon, 11 Apr 2011 20:58:20 +0000 - tweet id

@CutTheKnotMath @MrMon, 11 Apr 2011 20:58:45 +0000 - tweet id

@ColinTGraham @dmarworking at higher Van Hiele levelsMon, 11 Apr 2011 20:59:42 +0000 - tweet id

@dansmath "Geometry -Mon, 11 Apr 2011 20:59:47 +0000 - tweet id

@dmarain Thank you ColMon, 11 Apr 2011 21:00:04 +0000 - tweet id

@MrHonner @CutTheKnproject for me. #mathchat


5 7547336720719872 - #223

final thoughts for the last 5 minutes? #57547634205917185 - #224

s been a most interesting #mathchat. T57547818537201665 - #225

It also had legs - project for kids @Colinf dissection, isn't it? #mathchat

57547820944732160 - #226

rum Is that the shell method, or the disk57547882827481088 - #227

nner's link shows the table itself... @Cut57548010099449856 - #228

s: Construct an example to show that S

observations. #mathchat 57548057411198976 - #229

Honner Yes. Thank you. That's it http://b57548163023773696 - #230

ain Challenges involving SSA would req, though, if not explored 1st #mathchat 57548401872613376 - #231

it never gets old. Just ask Euclid." #mat57548422982545408 - #232

in. Stream of consciousness is fun! #ma57548493341995008 - #233

otMath @ColinTGraham That may very


athchat

anks everyone!

Graham I think it's

method? #mathchat

heKnotMath#mathchat

A fails. Measure sides

it.ly/hhrQKD#mathchat

ire that students are

chat

hchat

ell be a summer




April 2011

Mon, 11 Apr 2011 21:01:07 +0000 - tweet id

@ColinTGraham I'm justor engineering or surveying or...inMon, 11 Apr 2011 21:01:13 +0000 - tweet id

@LesLinks Thanks 4 lettiunusual, &great geometric structuMon, 11 Apr 2011 21:01:52 +0000 - tweet id

@ColinTGraham @MrHothen!http://bit.ly/dNRkkV #mathchMon, 11 Apr 2011 21:02:21 +0000 - tweet id

@CutTheKnotMath @Leyear#mathchat Mon, 11 Apr 2011 21:02:51 +0000 - tweet id

@republicofmath @colinMon, 11 Apr 2011 21:02:57 +0000 - tweet id

@MrHonner @ColinTGraset.#mathchat Mon, 11 Apr 2011 21:03:18 +0000 - tweet id

@ColinTGraham OK, thanext#mathchat is on "introducing/iMon, 11 Apr 2011 21:03:48 +0000 - tweet id

@LesLinks RT @CutTheday a year= Ya I know.. real pity...Mon, 11 Apr 2011 21:04:06 +0000 - tweet id

@reflectivemaths #mathlinked to Design TechMon, 11 Apr 2011 21:04:06 +0000 - tweet id


5 7548758522662912 - #234

wondering at what stage we end up teacstead of mathematics! ;-) #mathchat 57548781285150720 - #235

ng me sit in 4 a little while.. do check outre things..;-D #mathchat 57548945605402624 - #236

nner It's worth investing in Frederickson't

57549065507979264 - #237

sLinks A beautiful garden. Shame it is o

57549190980583424 - #238

?TGraham "Along with" ? #mathchat 57549216683266048 - #239

ham Thanks for the link! Maybe I'll desig

57549305476681728 - #240

nk you everyone for another fast-and-furncreasing investigative work"57549433948221440 - #241

KnotMath: @LesLinks A beautiful gardeshould bemore.. #mathchat

57549509445693440 - #242

hat In our redesign of the yr7 SoW, we

57549506882961408 - #243


hing design technology

that garden link.. most

s book,

en for 1 day a

n a whole

ious! The

. Shame it is open for 1

re having a term that's




April 2011

@MariaDroujkova JoinET http://mathfuture.wikispaces.cMon, 11 Apr 2011 21:05:06 +0000 - tweet id

@ColinTGraham @oldakmathematics... I will post a poll onMon, 11 Apr 2011 21:05:19 +0000 - tweet id

@ColinTGraham Have acontributions! Archive online in anMon, 11 Apr 2011 21:06:06 +0000 - tweet id

@dmarain Giving Ss twoconclusions is lower-level Van HiMon, 11 Apr 2011 21:06:49 +0000 - tweet id

@idevbooks RT @Mariain math ed 8pm ET http://mathfutMon, 11 Apr 2011 21:08:53 +0000 - tweet id

@CutTheKnotMath Boothe Math http://bit.ly/htzavv #mathMon, 11 Apr 2011 21:11:27 +0000 - tweet id

@CoachGinsburg My neConquerhttp://bit.ly/hA1RB7#edcMon, 11 Apr 2011 21:23:11 +0000 - tweet id

@ColinTGraham "Develohttp://bit.ly/fS7U9D free workshopMon, 11 Apr 2011 21:25:21 +0000 - tweet id

@ColinTGraham Pleasea #philosophy session on #matheMon, 11 Apr 2011 21:32:28 +0000 - tweet id

@cherrylkd @ColinTGrastay a short time but learnt lots of


nprmathguy Keith Devlin: using video gm/KeithDevlin #mathchat #edchat

5 7549761376563201 - #244

is interested in having a philosophical dithat later #mathchat

57549814359003136 - #245

good night, afternoon, day... whatever, ahour or so #mathchat

57550011256422401 - #246

SSA triangles, having them measure allle but still powerful! #mathchat

57550190772621313 - #247

roujkova: Join @nprmathguy Keith Devre.wikispaces.com/KeithDevlin #mathch

57550713378705408 - #248

review: Shai Simonson's Rediscovering#mathed #mathchat #homeschooling

57551356101271552 - #249

post: Fractions: Divide andat #mathchat #elemchat #midleved

57554312150261760 - #250

ping mathematical thinking through prob! #mathchat #ukedchat #MathsJam 57554855438450689 - #251

register interest, voting ends 25th April:hatics #mathchat #sschat#math

57556646003617792 - #252

am #mathchat Thanks for good learninexciting lesson ideas thank you


mes in math ed 8pm

scussion related to

nd thanks for your

arts and drawing

lin: using video gamest#edchat

Mathematics: You Do

lems, puzzles & games"

tp://twtpoll.com/r/z5t4nl

session. Could only



Mon, 11 Apr 2011 21:32:38 +0000 - tweet id

@ColinTGraham @cherrarchive goes online and to hear aMon, 11 Apr 2011 21:33:27 +0000 - tweet id

57556688932306944 - #253

ylkd You're welcome. Follow @mathchatout future topics too... #mathchat

57556893564026880 - #254

so you know when the

2011.04.11 how do i introduce the geometry of the built environment into the curriculum

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