Cross sections of a cube

Season 2 • Episode 16 • Cross sections of a cube

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Cross sections of a cube

Season 2

Episode 16

Time frame 3 periods

Prerequisites :

^{Crosssetionsofa}tetrahedron.Voabularyabouttheube.

Objectives :

•

^{Foldan origamiube by following}instrutions.

•

^{Disover the ross setions of aube.}

•

^{Learn the rules to drawa orss setion ofa ube.}

Materials :

•

Instrutions and paper of the Origamiube.

•

^{Answersheet for the 10possible shapesof the ross setions.}

•

^{Task sheet for the ICT ativity.}

•

^{Examples of orretand inorret} onstrutions.

•

^{Rules for ross setions.}

•

^Exerises

1 – Origami Cube 20 mins

Eah student is given instrutions to buildan origamiube.

2 – Pair work : the possible cross sections of a cube ^{35 mins}

Working inpairs, students have tond 10 possible shape for the setions of aube :

1

^. equilateral triangle;

2

^{. isoseles triangle;}

3

^{. salene triangle;}

4

^{. square;}

5

^{. retangle :}

6

^. parallelogram;

7

^{. isoseles trapezium;}

8

^{. trapezium;}

9

^{. pentagon;}

10

^{. hexagon.}

Season 2 • Episode 16 • Cross sections of a cube

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3 – ICT activity 25 mins

Working inpairs, students go tothe website :

http://www.mhhe.om/math/lt bmat h/ap plet s/h 9/i ndex .htm l

They havetosolveeahofthe 11problems, doasreenapture foreahsolutionandput

all the sreen aptures ona single doument that they willsave and send tothe teaher.

4 – Correct and incorrect constructions 30 mins

Studentsworkinpairs.Theyaregiven apagewithsomerosssetionsofaubeonstru-

ted. Some onstrutions are orret, others are not. They have to deide what are the

orret ones and retify the inorret ones.

5 – How to build a cross section of a cube 15 mins

Using a beamer, the teaher shows the main methodsto draw a ross setion of a ube.

Themost importantrulesareintrodued,alongwiththeproblemofapparentoplanarity

and ollinearityin perspetivedrawing.

6 – Exercises Remaining time

An origami cube

Season 2

Episode 16

Document Instructions

Folda square sheet of paperatthe diagonalsand unfold it.

Put the paper atboth arrows together.

Laythetrianglesatthe topandatthebottomontopofeahother.

The result is a ier triangle, whih is known as the swallow or the

pigeon.

Foldupward on the red lineon the rightand onthe left.

Thenit must look like this.

Foldonthe red lines.

Thenit must look like this.

Foldthe twolittletriangles onthe red lines downward.

Put the lastmade trianglesinthe two pokets onthe rightand on

the left.This isa littlebitddly.

Thenit must look like this.

Turn the whole triangle and repeat the steps 3,4,5,6,7,8,9.

Season 2 • Episode 16 • Cross sections of a cube

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Foldand unfold on the red lines.

Take the folded ube in hand and blow into the hole at the top.

Unfoldthe ube by this.

The ube is ready.

An origami cube

Season 2

Episode 16

Document Cut-out square

Cross sections of a cube

Season 2

Episode 16

Document Answer sheet

Section 1

The cross section is . . . .

Section 2

The cross section is . . . .

Section 3

The cross section is . . . .

Section 4

The cross section is . . . .

Season 2 • Episode 16 • Cross sections of a cube

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Section 5

The cross section is . . . .

Section 6

The cross section is . . . .

Section 7

The cross section is . . . .

Section 8

The cross section is . . . .

Section 9

The cross section is . . . .

Section 10

The cross section is . . . .

Cross sections of a cube

Season II

Episode 4 - Cross sections

Document 16

Forthisativity,youneedtorememberthatany three non-ollinearpointsdene aplane.

We will use this property to build various kinds of ross setions of a ube, with a java

applet.

Log ontothe omputer and use the internetbrowser to load the page.

http://www.mhhe.om/math/lt bmat h/ap plet s/h 9/i ndex .htm l

•

^{Foreahshapeinthe top-leftpull-down,ndthreepointsontheube,not onthesame}

edge, sothat the planedened by these three pointsis the desiredshape.

•

^{CliktheCreatebuttontohekyourhoie.Ifit'snotorret,tryagain.Ifit'sorret,}

doa apture of a sreen and opy itin a word proessor doument.

•

^{Youhave20minutestondthe 10possiblerosssetionsinthemenu.Atthe end,you}

should have a word proessor with 10 images. Save it under your name and send it to

Mr Védrine :

mikael.vedrinefree.fr

Cross sections of a cube

Season 2

Episode 16

Document ICT task sheet

Forthisativity,youneedtorememberthatany three non-ollinearpointsdene aplane.

We will use this property to build various kinds of ross setions of a ube, with a java

applet.

Log ontothe omputer and use the internetbrowser to load the page.

http://www.mhhe.om/math/lt bmat h/ap plet s/h 9/i ndex .htm l

•

^{Foreahshapeinthe top-leftpull-down,ndthreepointsontheube,not onthesame}

edge, sothat the planedened by these three pointsis the desiredshape.

•

^{CliktheCreatebuttontohekyourhoie.Ifit'snotorret,tryagain.Ifit'sorret,}

doa apture of a sreen and opy itin a word proessor doument.

•

^{Youhave20minutestondthe 10possiblerosssetionsinthemenu.Atthe end,you}

should have a word proessor with 10 images. Save it under your name and send it to

Mr Védrine :

Correct or incorrect

Season 2

Episode 16

Document Answer sheet

Below are reprodued 30 ross setions of a ube. Some them are orret, others aren't.

Find out the inorret ones and, ineahase, explain why is itinorret. You may name

some pointstodoso.Toget abonuspoint,retifythe inorretsetiontomekitorret.

^{Corret / Inorret}

^{Corret / Inorret}

^{Corret / Inorret}

... ... ...

... ... ...

... ... ...

^{Corret / Inorret}

^{Corret / Inorret}

^{Corret / Inorret}

... ... ...

... ... ...

Season 2 • Episode 16 • Cross sections of a cube

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^{Corret /Inorret}

^{Corret / Inorret}

^{Corret / Inorret}

... ... ...

... ... ...

... ... ...

^{Corret /Inorret}

^{Corret / Inorret}

^{Corret / Inorret}

... ... ...

... ... ...

... ... ...

^{Corret /Inorret}

^{Corret / Inorret}

^{Corret / Inorret}

... ... ...

... ... ...

Season 2 • Episode 16 • Cross sections of a cube

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^{Corret /Inorret}

^{Corret /Inorret}

^{Corret /Inorret}

... ... ...

... ... ...

... ... ...

^{Corret /Inorret}

^{Corret /Inorret}

^{Corret / Inorret}

... ... ...

... ... ...

... ... ...

^{Corret /Inorret}

^{Corret /Inorret}

^{Corret / Inorret}

... ... ...

... ... ...

Season 2 • Episode 16 • Cross sections of a cube

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^{Corret /Inorret}

^{Corret / Inorret}

^{Corret /Inorret}

... ... ...

... ... ...

... ... ...

^{Corret /Inorret}

^{Corret / Inorret}

^{Corret / Inorret}

... ... ...

... ... ...

Cross sections of a cube

Season 2

Episode 16

Document Exercises

In eah of the situationsbelow, draw the ross setion of the ube by the plane dened

by the three points.

Season 2 • Episode 16 • Cross sections of a cube

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Cross sections of a cube

Season 2

Episode 16

Document Rules

Rule 1 : Youan join twopointsof the setion if they are onthe same fae.

Rule 2 : When a line of the setion plane is in a fae, and a third point is on a fae

withanedgeinommon,youan drawtheintersetionof thelinewiththeommon

edge.

Rule 3 : When alineof the setionplaneisinafae,youan builditsintersetionwith

an edge of the fae.

Rule 4 : When a lineofthe setion planeis ina faeand apointof the setionplane is

ona parallelfae,youan draw the paralleltothe linepassing through that point.

Cross sections of a cube

Season 2

Episode 16

Document Rules

Rule 1 : Youan join twopointsof the setion if they are onthe same fae.

Rule 2 : When a line of the setion plane is in a fae, and a third point is on a fae

withanedgeinommon,youan drawtheintersetionof thelinewiththeommon

edge.

Rule 3 : When alineof the setionplaneisinafae,youan builditsintersetionwith

an edge of the fae.

Rule 4 : When a lineofthe setion planeis ina faeand apointof the setionplane is