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Brent Strickland
6 years ago
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1 !!!"#$%&"#()*+*,-".%*/%0%1*2))%))&%3#)*"3.*453#%3#*678%(#"#53)*!!,-".%*69$#:*;%))53*<* * A"-#(8"3#*A"(B%#* * C%0%158%.*DE*!"(5&D*45>3#E*F%"($%-)* >3.%-*#$%*1%".%-)$8*5@*!"-%*458%1"3.* * * *

2 9&0&158&-* "#$%&#$()*!+!,-#.&!/&0&1!2**&**&3$*!#3.!453$&3$!678&)$#$(53* M-GLAnCE Project Directors Debbie Ferry!"#$%&()*!"+,-%"+.#/0$1/23+"1+ Carol Nowakowski !"+,-%"+.#/0$1/23+"1+ 789:5$;-#+0$$56.1"+$5 Marie Copeland <"55-10$1/$3.6"+-6!"#$%&!)=0 >8?:5$;-#+0$$56.1"+$ Project Contributors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and 2006 Session/Module Developers 0"5$3Q$B"J$B/J L!"+,0$1/23+"1+ *-&H"51-++ G"J-),$5-:2&3.#)#,$$3/ G2"11!255"E N-1-/--()* 7"+,EA3&5-#, L!"+,0$1/23+"1+ =-55.F".+-3 =5-1+$1:2&3.#)#,$$3/ M$8A11-)#,.%%-3CT-11-K L!"+,0$1/23+"1+ *-&&.-F-55E!"#$%&()*!"5.-0$C-3"16 <"55-10$1/$3.6"+-6

3 Grade 8 Session #4 Volume and Surface Area NS)4SZ?SZ\ NS)4SZ?SZ[ NS)4SZ?SZ? 71$B+,-@$32%-T$5%23"/T$5 K-1-5"3.I-6#E3.16-5/]]"5-"$T &"/-^W,-.K,+^LK-1-5"3.I-6 #$1-/"16CE5"%.6/] Y _X]"5-" $T&"/-^W,-.K,+^"16/C,-5-/ ] 9 _XWC.W]5"6.2/^X^"16"CC3E +,-%+$/$3@-C5$&3-%/S Instructional Sequence: a8**5"b.1k/$tx8* H2.36.1K/ `16-5/+"16+,-#$1#-C+$T /25T"#-"5-"L"16T.16+,- /25T"#-"5-"$TC5./%/L#$1-/L /C,-5-/LCE5"%.6/L"16 #E3.16-5/S `16-5/+"16.1K$TD$32%- D$32%-$T:5./%/ )J-+#,"@"5.-+E$T+B$8 6.%-1/.$1"35-C5-/-1+"+.$1/$T +,5--86.%-1/.$1"3/$3.6/.1#326.1K$5+,$K$1"3@.-B/ "161-+/L2/-/2#,+B$ 6.%-1/.$1"35-C5-/-1+"+.$1/+$,-3C/$3@-C5$&3-%/S `16-5/+"16.1K$T)25T"#-A5-" )25T"#-A5-"$T:5./%/ D$32%-$T:E5"%.6/ )25T"#-A5-"$T:E5"%.6/ D$32%-$T0E3.16-5/ )25T"#-A5-"$T0E3.16-5/ D$32%-$T0$1-/ D$32%-$T)C,-5-/ )25T"#-A5-"$T0$1-/ )25T"#-A5-"$T)C,-5-/ NGA10UV?+,N5"6-V)-//.$19VUWC3$5.1KD$32%-"16)25T"#-A5-"8:"5+.#.C"1+:"#J-+ :"K-X4-@./-6YZSY>SZ[

4 Important /-1/-+$+,-/+26-1+/S!R1#-/+26-1+//+"5++$2/-+,-T$5%23"/L%"J-/25-+$5-3"+-+,-C"5+/$T+,-T$5%23"+$+,- +,-.55-K23"5T.K25-/"16#$%C3-WT.K25-/S=,-E#"1-"/.3E2/-+,-"CC3.#"+.$1/$1+,- C5.1+"#$CE$T+,-.5T.K25-"16C,E/.#"33E%-"/25-"166-#$%C$/-+,-T.K25-/+$$&+".1+,- "5-""16C-5.%-+-5S=,-/+26-1+/#"1+,-1#,-#J.T+,-.5%-"/25-6"1/B-5/%"+#,+,- N-$%-+-5O/)J-+#,C"6#$%C2+"+.$1/S Common Misconceptions!)+26-1+/#$1T2/-"5-""16C-5.%-+-5T5-b2-1+3ES=,-E%2/+#$1#-C+2"33E216-5/+"16B,"+.+ %-"1/+$%-"/25-"5-""16C-5.%-+-5$5+,-#$1T2/.$1B.33C-5/./+S!)+26-1+/B.33$T+-1&3.163ET$33$BT$5%23"/B.+,$ /+"16.1KB,"++,-E"5-%-"/25.1KL +,-5-T$5-L+,-EB.331$+"3B"E/2/-+,-#$55-#+T$5%23".1+,-"CC5$C5."+-/.+2"+.$1S!<.+,"5-"T$5%23"/L/+26-1+/B.33+5E+$+"J-/,$5+#2+/&EB5.+.1K> a 21.+/S=,-E"5-5-T-55.1K+$ >/b2"5-21.+/s=,-e6$1$+5-"3.i-+,"+b,"++,-e5-"33eb5$+-./a>21.+/s!<,-1t.16.1k+,-"5-"$t"#.5#3-l.t/+26-1+/"5-k.@-1+,-%-"/25-%-1+$t+,-6."%-+-5l+,-e +5-"+.+"/+,-5"6.2/S!)+26-1+/$T+-16$1$+.1# /B.+,+,-.5"1/B-5/S=,-E6$1$+5-"3.I-+,-.%C$5+"1#-$T.1#326.1K21.+/$5"CC5$C5."+-21.+/T$5+,-.5"1/B-5/SM2/+C2++.1K"12%&-56$B1./R7B.+, +,-%S!)+26-1+/,"@--W+5-%-6.TT.#23+E/2&6.@.6.1K#$%C3-WT.K25-/S=,-EB.33K.@-E$ /+.1KL.1#$55-#+5-/23+/SP$B-@-5L&E-W"%.1.1K+,-.5-55$5/LE$2#"1"6;2/+E$25.1/+52#+.$1+$,-3C +, K5$2CS NGA10UV?+,N5"6-V)-//.$19VUWC3$5.1KD$32%-"16)25T"#-A5-"8:"5+.#.C"1+:"#J-+ :"K-94-@./-6YZSY>SZ[

5 0R!:A4(QNDRG`!U) )+"5+B.+,+B$.6-1+.#"3/,--+/$TC"C-5+,"+"5-?S>.1#,-/&EYY.1#,-/S="C-+,-3$1K/.6-/ $T$1-/,--++$K-+,-5+$T$5%"#E3.16-5SF$5%"#E3.16-5T5$%+,-/-#$16/,--+&E+"C.1K+,- /,$5+/.6-/+$K-+,-5S(%"K.1-+,"+-"#,#E3.16-5,"/"+$C"16&$++$%S HS<,.#,#E3.16-5,"/K5-"+-5/25T"#-"5-"c NGA10UV?+,N5"6-V)-//.$19VUWC3$5.1KD$32%-"16)25T"#-A5-"8:"5+.#.C"1+:"#J-+

6 VOLUME OF CYLINDERS, SPHERES AND CONES Investigation #1: Relationship between the volume of the cylinder and the sphere )+-CdYe 0"5-T233EC$25+,-5.#-T5$%+,-$5.K.1"35.#-#$1+" $+,-#E / T.33-6+$+,-+$CS=,-5-./"5.%"5$216+,-#E ,"+6-T.1-/+,-+$C$T+,- :$25$2+"1E-W#-//5.#-T5$%+,-$5.K.1"35.#-#$1+" $+,-&$++$%$T+,- 3"5K-/+#$1+".1-5B,-5-"33+,-%"+-5."3/"5-/+$5-6S*$1O+K-+5.#-$1E$256-/Jf )+-Cdae :$25+,-5.#-T5$%+,-#E $+,--%C+E$5.K.1"35.#-#$1+".1-5+$C5$#--6 B.+,+,-1-W+/+-CS )+-CdXe =,-5-./"5.%"5$216+,-,-%./C,-5-+,"+6-T.1-/+,-+$C$T+,-,-%./C,-5-SF.33 +,-,-%./C,-5-/,"/&--1T.33-62C+$+,-5.%LC$25+,-5.#-T5$%+,-,-%./C,-5-.1+$+,-#E3.16-5S4-C-"++,./C5$#-//"/-#$16+.%-/.1#-+B$,-%./C,-5-/$T 5.#-"5-1-#-//"5E+$5-C3.#"+-+,-"%$21+$T5.#-+,"+#"1T.33"/C,-5-S )+-Cd9e U/+.%"+-+,-T5"#+.$1$T+,-#E ,"+./T.33-6B.+,5.#-T5$%+,-/C,-5-S The volume of the sphere = of the volume of the cylinder Investigation #2: Relationship between the volume of the cylinder and the cone )+-Cd>e *2%C+,-5.#-T5$%+,-#E3.16-5&"#J.1+$+,-$5.K.1"35.#-#$1+".1-5S )+-Cd\e :$25$5/C$$1+,-5.#-T5$%+,-$5.K.1"35.#-#$1+" $+,-#$1-/.1#-+,- K$"3./+$6-+-5%.1-+,-5-3"+.$1/,.C&-+B--1+,-@$32%-$T+,-#E3.16-5"16+,- #$1-S=,-5-./"5.%"5$216+,-#$1-+,"+6-T.1-/+,-+$C$T+,-#$1-SF.33+,- 5.#-+$+,"+5.%$13EL1$++$+,-@-5E+.C$T+,-"#+2"3#$1-S NGA10UV?+,N5"6-V)-//.$19VUWC3$5.1KD$32%-"16)25T"#-A5-"8:"5+.#.C"1+:"#J-+ :"K-\4-@./-6YZSY>SZ[

7 )+-Cd[e :$25+,-5.#-.1+,-#$1-&"#J.1+$+,--%C+E#E3.16-5S )+-Cd?e U/+.%"+-+,-T5"#+.$1$T+,-#E ,"+./T.33-6B.+,5.#-T5$%+,-#$1-S The volume of the cone = of the volume of the cylinder )+-Cdhe :$25"33+,-5.#-&"#J.1+$+,-$5.K.1"35.#-#$1+".1-5+$C"#J"B"ES NGA10UV?+,N5"6-V)-//.$19VUWC3$5.1KD$32%-"16)25T"#-A5-"8:"5+.#.C"1+:"#J-+ :"K-[4-@./-6YZSY>SZ[

8 DERIVING THE FORMULA FOR SPHERES D$32%-$T+,-/C,-5-ejjjjjjjjjjjjjjjjjjjjjjjj ).1#-+,-,-.K,+$T+,-/C,-5-B"/-b2"3+$+B.#-.+/5"6.2/L+,-1a5%"E&-/2&/ T$5,S 4-B5.+-+,-T$5%23"T$5+,-/C,-5-S D$32%-$T+,-/C,-5-i 3 2!5 a, ).1#-,ia5 i 3 2!5 a ]a5^ 0$1/.6-5"/C,-5-B,$/-5"6.2/./-b2"3+$+,-5"6.2/$T+,-&"/-$T"#E3.16-5"16B,$/-,-.K,+./-b2"3+$+B.#-.+/5"6.2/S,ia5 5 5 =,-T$5%23""&$@-#"1+,-1&-/.%C3.T.-6e Di 3 2!5 a ]a5^ Di 3 4!5 X NGA10UV?+,N5"6-V)-//.$19VUWC3$5.1KD$32%-"16)25T"#-A5-"8:"5+.#.C"1+:"#J-+ :"K-?4-@./-6YZSY>SZ[

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10 Q2%&-5$TG"E-5/.1 +,-k:e5"%.6l$t02&-/ Y a X 9 > \ [? h YZ D$32%-$T+,- k:e5"%.6l$t02&-/ D$32%-$T+,- 0$55-/C$16.1K02&.# :5./%B.+,+,-)"%- H"/-"16P-.K,+ 1 NGA10UV?+,N5"6-V)-//.$19VUWC3$5.1KD$32%-"16)25T"#-A5-"8:"5+.#.C"1+:"#J-+ :"K-YZ4-@./-6YZSY>SZ[ 4A=(R D$32%-$Tk:E5"%.6l D$32%-$T02&.#:5./%

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SPAREPARTSCATALOG: CONNECTORS SPARE CONNECTORS KTM ART.-NR.: 3CM EN

SPAREPARTSCATALOG: CONNECTORS ART.-NR.: 3CM3208201EN CONTENT SPARE CONNECTORS AA-AN SPARE CONNECTORS AO-BC SPARE CONNECTORS BD-BQ SPARE CONNECTORS BR-CD 3 4 5 6 SPARE CONNECTORS CE-CR SPARE CONNECTORS