ࡱ> NPMo nmbjbjVV B<<Y vNNXXXXXX8XT)YXI Z [#[#[#[8&^ jHHHHHHHLFOvHXr48rrH#[#['INNNrX)#[X#[HNrHNN" mH!.#[s&.LXʂ HI0I ^ O O!.OX!.rrNrrrrrHHrrrIrrrrOrrrrrrrrrN W: Circles in the Coordinate Plane Reporting Category Polygons and Circles Topic Writing equations of circles Primary SOL G.12 The student, given the coordinates of the center of a circle and a point on the circle, will write the equation of the circle. Related SOL G.3a, G.3d, G.11 Materials Activity Sheet (attached) Graph paper and compass or dynamic geometry software package A coordinate plane for graphing at the board (or an overhead projector with coordinate plane transparency) Compass and marker for using at the board or with overhead projector Vocabulary circle, radius, diameter, center, coordinates, coordinate plane, equation, reflect, image (earlier grades) tangent circles (G.11), locus (G.12), distance formula (G.3a) Student/Teacher Actions (what students and teachers should be doing to facilitate learning) Using a coordinate plane for graphing on the board, use a compass to graph a circle with center at the origin and radius 5, explaining what you are doing. (You can have students do the same thing using graph paper, compass, and pencil, as they follow along.) Ask individual students to come to the board and mark points on the circle with their coordinates. At this point students will probably identify the points on the axes. List the following ordered pairs on the board: (3, 4), ("4, "4), ("3, 4), ("1, 5), ("3, "4), (3, "4), (2, "4). Ask students which of the points are on the circle. Allow students to graph the points to answer the question. Ask students,  What do all the points that are on the circle have in common? Remind them about the definition of a circle and the distance formula if necessary. Mark the origin as (0, 0) if you havent already. Encourage the class to discover that the distance from the origin to all the points on the circle is (exactly) 5 units. Ask students if the points (2,  EMBED Equation.3 ) and ("2,  EMBED Equation.3  QUOTE  ) lie on the circle. (You can add them to the list.) If necessary, remind them about what they just discovered about points that lie on the circle. Mark any other point on the circle, and label it (x, y). Write out the distance formula. Ask and write the following:  What is the distance from (x, y) to (0, 0)? Plug in (x, y), (0, 0) and 5 into the formula. Point out to students that you are writing (x " 0) rather than (0 " x). Simplify and square both sides. Point to the equation and ask, What is this? (answer: an equation) If necessary, point out the equal sign as a hint. Explain that this is the equation of a circle with center (0, 0) and radius 5. Show how a couple of points on the circle satisfy the equation. Draw a circle on the same coordinate plane with center (0, 0) and radius 6 on the coordinate plane at the board. (Erase the first circle if the graph is too cluttered.) Mark a point on the circle and label it (x, y). Have the class use the distance formula to find the equation of the circle. Draw a circle on the board (not on a coordinate plane). Label the center (0, 0), draw a radius, and label the radius r. Mark a point on the circle, and label it (x, y). Have the class find the equation of a circle with center (0, 0) and radius r. Optional: If yours is a proofs-based class, you may want to write this derivation as a two-column proof. (The reason for using the distance formula is the Pythagorean Theorem.) Emphasize this equation, and have students write it in their notebook, along with a description. Erase the graph, and graph a circle with radius 5 and center (1, 2). Have students identify a few points on the equation. Mark a point on the circle and label it (x, y). Have the class use the distance formula to find the equation of the circle. Have them square both sides of the equation, but tell them not to expand the expressions (x " 1)2 and (y " 2)2. Explain that this is the equation of a circle with center (1, 2) and radius 5. Show how a couple of points on the circle satisfy the equation. Draw a circle on the board (not on a coordinate plane). Label the center (h, k). Point out that these are the variables that are usually used to identify the center of a circle. Draw a radius, and label the radius r. Mark a point on the circle and label it (x, y). Have the class find the equation of a circle with center (h, k) and radius r. As before, students should not expand the expressions (x " h)2 and (y " k)2, and students should square both sides. Emphasize this equation, and have students write it in their notebook, along with a description. Have students work in pairs to complete the activity sheet. Each student should record his/her own findings. Have students discuss findings with their partners. Discuss findings as a whole group. Assessment Questions Use the distance formula to find the equation of a circle with center ("2, 3) and radius 4. Determine whether the point (6, "8) lies on the circle with equation EMBED Equation.3. Justify your answer. Find the radius and center of the circle with equation EMBED Equation.3. A circle has diameter with endpoints (3, 4) and ("3, "4). Find the equation of the circle. Justify your answer. P(1, 0) and Q(3, "2) are endpoints of a diameter of a circle. What is the radius of the circle? Journal/Writing Prompts Explain how the equation of the circle EMBED Equation.3 is related to the distance formula. Explain how you would find the equation of a circle whose graph is given. Other Have small groups of students design a circle design of their own like the one in Activity Sheet 1. Students should then write directions using a variety of descriptions (including equations) and create a table, as in the Activity. Students should also provide a key (the graph and completed table). Use these student-created activities for assessment purposes. Extensions and Connections (for all students) Have students explore translations and dilations of circles in the coordinate plane and the effect on the equations. Is the graph of a circle a function? Strategies for Differentiation Provide students with circles, paper, or electronic files. Encourage students to use color after their initial pencil work. Review graphing calculator skills and experiment with manipulating variables other than those listed in the lesson. Activity Sheet 1: Circles in the Coordinate Plane Name Date Graph the following circles on the same coordinate plane, using graph paper and a compa 2GHMNXdjkvw|    ! " 0 ; ( ) 4 8 9 : P ý콰죟}v h!h,z h|'.h,z h,z5 hp7hp7 h?^h,zh~h,z6h'~ghlh,zaJhNhNh2@h,zaJ h~aJh@h,z5aJ hP{qaJhP{qhP{qaJhP{qhNaJ h@h,z h,zaJhNhN5aJh,z, Hk " < y ) 4 : = `vgd! & Fegd!!gd~gdp7 & F gdDgdN#gdNgdk <JV^z1234 02468FHJNPRXtvxzߘyyr h!h@mh8h,z6h!h,z6h'9jnh!h,zUjh!h,zUj=h{R h8CJOJPJQJUV_Hjh{ $xxgdQp`gd,zgd,zgdNgd~+++++++,@@@@@@@AA6A8AAAAAAABBjBlBpBBBBBBHCXCZCCCCCCCCCCDD4D5D6D@DȽȽͽͰ͙ͨͨӐhHh,z5aJhHh,zaJh#h,z6 hn@Bh,zh2h,zH* hAh,z hQ^JhQ hh,z h,zH*h,zU h,zaJ hQp`aJh%EhQp`5>*CJ\hQp`5CJ\hQp`5>*CJ\4ss or a dynamic geometry or graphing software package, and complete the table. Circle c1 has center (0, 0) and radius 2. Circle c2 has center (0, 0), and ("3, 4) is one point on the circle. Circle c3 has center ("3, 0), and ("3, 2) is one point on the circle. Circle c4 has center (3, 0) and is congruent to c3. (1, 0) and ("1, 0) are two points on a diameter of the circle c5. (Hint: What is the center of the circle?) Circle c6 has center (0, 3) and is tangent to c2 and c5. Reflect circle c6 across the x-axis. The image is circle c7. Complete the table below. center = (h, k)radius = rList four points on the circle.Equation of the Circlec1c2c3c4c5c6c7 Activity Sheet 2: Circles in the Coordinate Plane Name Date Graph the following equations, using a graphing calculator or graphing software. Then, answer the questions. Graph the equations EMBED Equation.3 and EMBED Equation.3on the same graph. What is the difference between the two graphs? How does this relate to the difference between the two equations? Be specific, and use vocabulary from this class. Graph the equations EMBED Equation.3 and EMBED Equation.3 on the same graph. What is the difference between the two graphs? How does this relate to the difference between the two equations? Be specific, and use vocabulary from this class. Graph the equations EMBED Equation.3 and EMBED Equation.3 on the same graph. What is the difference between the two graphs? How does this relate to the difference between the two equations? Be specific, and use vocabulary from this class. Graph the equations EMBED Equation.3 and EMBED Equation.3 on the same graph. What is the difference between the two graphs? How does this relate to the difference between the two equations? Be specific, and use vocabulary from this class.     Mathematics Enhanced Scope and Sequence Geometry Virginia Department of Education 2011  PAGE 3 @DDDODPDoDpDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDEEE'EWEXEoEEü h3h,zhgh%Eh2zA5>*CJ\h2zA5>*CJ\h2zA5CJ\h,z h%dh,z h,zaJhHh,zH*aJhHh,zaJ hHh,z ha5aJhHh,z5aJhQp`h,z56aJ2QDqDDDDDD=kdT"$$Ifl@r $? R t0644 la yt,z $$Ifa$gd,zDDDDDDD=kd8#$$Ifl@r $? R t0644 la yt,z $$Ifa$gd,zDDDDDDD=kd$$$Ifl@r $? R t0644 la yt,z $$Ifa$gd,zDDDDDDD=kd%$$Ifl@r $? R t0644 la yt,z $$Ifa$gd,zDDDDDDD=kd%$$Ifl@r $? R t0644 la yt,z $$Ifa$gd,zDDDDDDD=kd&$$Ifl@r $? R t0644 la yt,z $$Ifa$gd,zDDDDDDD=kd'$$Ifl@r $? R t0644 la yt,z $$Ifa$gd,zDDDDDD=83gd,zgd,zkd($$Ifl@r $? R t0644 la yt,z $$Ifa$gd,zDEoEeFfFgFhFiFjFaGbGcGdGeGfG]H^H_H`HaHbH[I]IgdQp`  h^hgdQp`h^hgdQp` & FQ h^hgdQ>gd2zA $xxgd2zAEEEEEEEEEEEEE?F@FdFeFiF~FFFFFFFFFFFFF;GhHQh <B*EHU^JaJmHnHphu8j =hHQh <B*EHU^JaJmHnHphu]I^I`IaIcIdIfIgIIIIIIIIIIIIIIIIIIIIIIgdD&VIIIIIIIIIIIIIIIIIIIIIIIIIIIII$a$gd gd IIIIJllllllll l l l l llllllllllll$a$gd gd  llllllll l!l"l#l$l%l&l'l(l)l*l+l,l-l.l/l0l1l2lgd`6$a$gd`6$a$gd`6gd 2l3l4l5l6l7l8l9l:l;ll?l@lAlBlClDlElFlGlHlIlJlKlLlMlNlgd`6NlOlPlQlRlSlTlUlVlWlXlYlZl[l\l]l^l_l`lalblcldlelflglhlgd,zgd`6$a$gd`6gd`6hliljlklllmlnlolplqlrlsltlulvlwlxlylzl{l|l}l~llllllllgd,zllllllllllllllllllllllllll hgd,z ^`gd,z$a$gd,zgd,zllllllllllllllllllllllllllll$a$gd,z<gd,zgd,zlllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllmmmmmmmmm m m m m mmm$a$gdpgdpmmmmmmmmmmmmmmmmm m!m"m#m$m%m&m'm(m)m*m+mgdp+m,m-m.m/m0m1m2m3m4m5m6m7m8m9m:m;mm?m@mAmBmCmDmEmFmGm$a$gdpgdpGmHmImJmKmLmMmNmOmPmQmRmSmTmUmVmWmXmYmZm[m\m]m^m_m`mambmcmgdpcmdmemfmgmhmimjmkmlmmmnm  h^hgdQp`$a$gdpgdp @P&P1h:pp/ =!"#$%@ Dp=Dd Tb  c $A? ?3"`?2{ |nOFicD`![{ |nOFi XJ)x]?KA̝r n-$XT*ˀ)Rm  pZIqX+:l xۤpaf~}}-7"QEDFЖ\#J́g=Kd~X1:˳b]B_b_hf:K6%Ǟ SGѻQB{nՃ.𨏇ψ;WI6 C4^DQ =Rk8[ #V<*TCA̻]w dbv@NC~' WKFq1Dd Tb  c $A? ?3"`?2{X49Gʷ) W`!OX49Gʷ)  XJxcdd``~ @c112BYL%bpu3X?E?|Dd ,  3 A#"  12?@ABCDFGHIJKLpORTSUVWYXZ[\^]_a`bdcefgihjlkmn qrstuvwxyz{|}~Root EntryQ F`G.LQData E@WordDocumentPBObjectPoolWS -L`G.L_1383457722JF -L-LOle CompObjfObjInfo  !$(+/269=@DGKNRUY[\]^_`acdefgijkmnopqs FMicrosoft Equation 3.0 DS Equation Equation.39q.|q  22  FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native 6_1379855318 F-L-LOle CompObj fObjInfo Equation Native  6_1383383914 &F-L-LOle  y  21  FMicrosoft Equation 3.0 DS Equation Equation.39qoowL x"1()CompObj fObjInfo OlePres000$Equation Native  2 +y+4() 2 =169 FMicrosoft Equation 3.0 DS Equation Equation.39qooЏL x"1()_1383383588F-L-LOle CompObjfObjInfoOlePres000$Equation Native _13833860592F-L-LOle  2 +y+4() 2 =169 FMicrosoft Equation 3.0 DS Equation Equation.39qoo| x"1()CompObjfObjInfoOlePres000$Equation Native  2 +y+4() 2 =169 FMicrosoft Equation 3.0 DS Equation Equation.39qo9|q x 2 +y_1383386014"F-L-LOle "CompObj!$#fObjInfo%OlePres000#%&$Equation Native 'U_1383386017 ,(F-L-LOle ) 2 =1 FMicrosoft Equation 3.0 DS Equation Equation.39qo9Huܞ x 2 +y 2 =4CompObj'**fObjInfo,OlePres000)+-$Equation Native .U_1383386034.F-L-LOle 0CompObj-01fObjInfo3 FMicrosoft Equation 3.0 DS Equation Equation.39qo9(v x 2 +y 2 =1OlePres000/14$Equation Native 5U_13833860908D4F-L-LOle 7CompObj368fObjInfo:OlePres00057;$Equation Native <e FMicrosoft Equation 3.0 DS Equation Equation.39qoI (x"2) 2 +y 2 =1 FMicrosoft Equation 3.0 DS Eq_1383386083:F-L-LOle >CompObj9<?fObjInfoAuation Equation.39qo9(.T x 2 +y 2 =1 FMicrosoft Equation 3.0 DS Equation Equation.39qOlePres000;=B$Equation Native CU_1383386109@F-L-LOle ECompObj?BFfObjInfoHOlePres000ACI$Equation Native JeoIܞ x 2 +(y"2) 2 =1 FMicrosoft Equation 3.0 DS Equation Equation.39q_1383386119>FF-L-LOle LCompObjEHMfObjInfoOOlePres000GIP$Equation Native QU_1383386123LF-L-LOle So9(v x 2 +y 2 =1 FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjKNTfObjInfoVOlePres000MOW$Equation Native XuoY+H (x"2) 2 +(y"2) 2 =1Oh+'0 , L X d p|Lesson Title jsl47365 Normal.dotmChrista H Southall5Microsoft Office Word@ p:val="006F6865"/>√21b&Hؘ0{-E#rOnHؘ0{-E#rOPNG  IHDR<ʮsRGB pHYs+IDAT8OnP'07cbwL]6_&DWӅ?N&Nt& Op=pFP{&9_Bܽro`(v-F1t߳Jα&tZjb\ȄanL_ÜzHR1 t:ũ`&q, GJ(^R歵<;'/9 W8>;oP' r+(FagyMy K(8 {4VM ҌWnU N][*Q*SśHag̻tVij`p'Q3M)~f0;GF naՁa9>b@HDxюvNR$mq]Jt%~(ҍ^ $?INdwm:Y]6w \ K$r>0V^Idok9gq#&QW׮~:lr,]h`>67'/ Wx߻`V3f<-WP^ӳ{[{5#8Nw gƍɼqK,EYihxp*.ժLVGTHwu*xS];g=X_Kjt;?⒚?ت9Cx-1a}R}jht3cӓ@Be5ByR`'b+גyzUߧaDd hb  c $A? ?3"`?2Q]}zUri~`!Q]}zUri~ @|xSKA~3ꪫnB0pЩC%1[g˛l^{7︿a}t+`^SjtR^y.l1SV[/[7XB(irV*.5VvGԃ0N^EET[g$Bw\{+bL:N" mTb+*9 j}̎Bpv@X[b_ٜ0 V\vQ `lx7d;IL095g snϝ%N벃~ >}ǃCRkP)]UCJJw2 gF2J3 ^᭚8vT#?}Muޅ=L^w#]o: Ԅu jA!ڍ%z\=e2ng};&ѱ?UvjDd $hb  c $A? ?3"`?2S'}z=/,`!S'}z=/r@HD |VxuQJA};wJF8l`!" ll EVϙP fv "r| 4H)xkj>S\Bs(1r7" [Y3~{l~۬G6=uAJ2"{3w?>MS^v@g1̻Οtqڂ5]g4:*T'VFgmBGP߇yX0\g_hAlPrHwSfhϻQ\qC&fLz[y|Dd hb   c $A ? ?3"`? 2|Ɗ7C壼(D5`!|Ɗ7C壼(D` @|hxuJBAƿ9^]UE[( Aa-M FR`sݪG}e/Ph+9C%̽9g~͌B+iqiFxA`Fj1el^t.p|=epnX_A!1qp9B>sݮߴ >9|&jRk8V W~/ﯯb}~.H 4j`ތ"ZN _\i FU63?рgDd hb   c $A ? ?3"`? 2~ɱ&͊h9U8`!~ɱ&͊h9r@ |SxuQJ@vF 9(47B@T⽅E uoo||Gz*gIPK6ٙGv@XXO)~21Eq۶ZJb W {U06\'w&+' S}N ^n^Dq~w^yNEIieB> 6wVuW~"*oSf.Anݺ6/;WuG,Mt"bt6gt{>Q~"J 3}A!ٍ9z]Z]6iFc&I{,ۆw]Dd hb  c $A? ?3"`? 2ezzia L0:`!ezzia L0 @|xuRMKBA=3HZ -U ?d$(E 6upDئ]haBh6VB{餉̙9wνg@$#@3"G;)J yޭ,jx1Yn,E8@\HkhќvJ}uRv@~–pJj|B᫹M-|7öMô李pF%xy|5xϚJ,|>{5.c:ߋ0;_Λc#2GOW΄/|IU|\қCja8iꍇ |?7ugގHetʡS Gws0B=R.YRGK?x{c䁥Dd ,p  s >A?Picture 9"bڃ`Cɝ&P=nڃ`Cɝ&PNG  IHDR{GsRGB@}0PLTEO&ICIDATӍ @6`-V?h.&'hENlE97W>$)ΝŜ1y<^"~]IENDB`Dd ,r  s @A?Picture 33"bf:h2]?nf:h2]PNG  IHDRrpysRGB@}0PLTEO&I?IDATӅ ?YDdQpHX":'+@` BTitle$,&d P33 m$B*CJ,OJPJQJaJ,ph33ZaZ B Title Char-B*CJ,OJPJQJ_H aJ,mH ph33sH tH <Or< BBullet 1  & F(PJaJRR B Bullet 1 Char CJOJPJQJ_H mH sH tH JOJ B Numbered Para  & F)<PJaJHH pNumbered Para Char CJPJ_H nn B Table Grid7:V0PJ4@4 BHeader 6CJaJJOJ B Header Char6OJQJ_H mH sH tH 4 @4 BFooter  %CJJJ B Footer CharOJQJ_H aJmH sH tH ZZ !Bvocabulary Char#6CJOJQJ_H aJmH sH tH DOD B vocabulary!h<^h6aJL1"L B SOL Bullet" p ^ `TOT *BHanging Indent# p@ <^@ `XOqRX B Bullet 1 Bold$$ & F) ^5aJBORB BBullet 2% & F) $ ^6Ua6 B Hyperlink >*B*ph2)@q2 B Page NumberCJHH )B Balloon Text(CJOJQJ^JaJ^^ (,zBalloon Text Char$CJOJQJ^J_H aJmH sH tH ^^ #{Hanging Indent Char CJOJQJ_H aJmH sH tH FVF :FollowedHyperlink >*B*phPK![Content_Types].xmlj0Eжr(΢Iw},-j4 wP-t#bΙ{UTU^hd}㨫)*1P' ^W0)T9<l#$yi};~@(Hu* Dנz/0ǰ $ X3aZ,D0j~3߶b~i>3\`?/[G\!-Rk.sԻ..a濭?PK!֧6 _rels/.relsj0 }Q%v/C/}(h"O = C?hv=Ʌ%[xp{۵_Pѣ<1H0ORBdJE4b$q_6LR7`0̞O,En7Lib/SeеPK!kytheme/theme/themeManager.xml M @}w7c(EbˮCAǠҟ7՛K Y, e.|,H,lxɴIsQ}#Ր ֵ+!,^$j=GW)E+& 8PK!Ptheme/theme/theme1.xmlYOo6w toc'vuر-MniP@I}úama[إ4:lЯGRX^6؊>$ !)O^rC$y@/yH*񄴽)޵߻UDb`}"qۋJחX^)I`nEp)liV[]1M<OP6r=zgbIguSebORD۫qu gZo~ٺlAplxpT0+[}`jzAV2Fi@qv֬5\|ʜ̭NleXdsjcs7f W+Ն7`g ȘJj|h(KD- dXiJ؇(x$( :;˹! I_TS 1?E??ZBΪmU/?~xY'y5g&΋/ɋ>GMGeD3Vq%'#q$8K)fw9:ĵ x}rxwr:\TZaG*y8IjbRc|XŻǿI u3KGnD1NIBs RuK>V.EL+M2#'fi ~V vl{u8zH *:(W☕ ~JTe\O*tHGHY}KNP*ݾ˦TѼ9/#A7qZ$*c?qUnwN%Oi4 =3ڗP 1Pm \\9Mؓ2aD];Yt\[x]}Wr|]g- eW )6-rCSj id DЇAΜIqbJ#x꺃 6k#ASh&ʌt(Q%p%m&]caSl=X\P1Mh9MVdDAaVB[݈fJíP|8 քAV^f Hn- "d>znNJ ة>b&2vKyϼD:,AGm\nziÙ.uχYC6OMf3or$5NHT[XF64T,ќM0E)`#5XY`פ;%1U٥m;R>QD DcpU'&LE/pm%]8firS4d 7y\`JnίI R3U~7+׸#m qBiDi*L69mY&iHE=(K&N!V.KeLDĕ{D vEꦚdeNƟe(MN9ߜR6&3(a/DUz<{ˊYȳV)9Z[4^n5!J?Q3eBoCM m<.vpIYfZY_p[=al-Y}Nc͙ŋ4vfavl'SA8|*u{-ߟ0%M07%<ҍPK! ѐ'theme/theme/_rels/themeManager.xml.relsM 0wooӺ&݈Э5 6?$Q ,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-![Content_Types].xmlPK-!֧6 +_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!Ptheme/theme/theme1.xmlPK-! ѐ' theme/theme/_rels/themeManager.xml.relsPK]   !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~l";>       !"#$%&'()*+,-. /!0"1#2$3%4&5'6(7)8*9+:,;-<.=/>0?1@2A3B4C 5D7E8F6 :9G<H? @ AD=IBJFQEUITJKRCKGP+WXYZ[\]^ _ ` a b cdefghijklmnoOLprstuv w!x"y#z${%|&}'~()*HSLNM.V,-qMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~/0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTU V W X Y Z[\]^_`abcdefghijkl m!n"o#p$q%r&s't(u)v*w+x,y-z.{/|0}1~23456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~l"  AAuuux "&+@DEGXInm%/01)QDDDDDDDDD]IIIl2lNlhllllllm+mGmcmnm&'()*+,-.234789:;<=>?@ABC1EGSgijtu%'v|xtl"::#:::::::::::iprx!%0  82$nOT 7dr b$bW 6b$~W.D5Ry6Ĉb$K3É+b$ Vt3g `sJb$Kl>l!b$DP;E=iy6b$({Bf)÷2$*kͱB.7b$Q`~QyMH۝t@4b$Ñјu0:F6b$8YؖHԢ([rb$y:46H!.b$fV RbBo b$Ώ햮 lQ& 2$D-f:W5/ W$2$b-/0T~U{J2$<(wX@I.υ6"2$tn?`y"yYK2$ +Z eObm2$z&:R2$ a$',dOe2$ZŊ n,J2$HE~N<K2$l~S&P_2$W`Af{Gf2$u#)LPR2$6 ICMY2$k$ꣲ6ESS2$S@nk\( f2$JO+R8>PV%K2$aclx;j2$v\ifzy@R}(Zۆ5b$Ugb$$>'˵ CU]@rDb$jGG5 ]Buw.b$IG.s2)3b$=5tKK9(J;b$3ǫyY@dm?b$R`gteRb$p1*ۅ{KEg%Ub$vF~Q評6AFAt>b$[]& b$sXmÉ] "$B0jb$LQ9 ʃ 3x2"$MͳvXT(7Vo"$9KMݰb$VVDMZﮮ"b$ ܤ|٣%b$DmE P1 $b$^$M;r"b$g&!Yyo$b$j]_6Q?R9hb$jIk$0TZL5Z;hb$U[aľx**]ob$&6`ww(|\8pb$,*n]0}-jmb$^zMaVT|uDqhb$dvfn +c-b$ckmJt p"$@k!Fx瞀hi{="$B4s$` e"$C0R11"$dz'f"$䀯R:l /^["$~"rx)oތ04"$z6H vLue"$'0R)*3w'<"$z")8*U>"$|KBĽ26rƋT<"$뿥}J =TOgT"$.Ú>tHa"$ :3a> -)qmN-"$VT{{Ekx/"$C;>ag'."$EFЙQO i8"$ -행/8!eqtL@"$wc R#QG"$H3R3nOw,b$NYXNdEb$'Pu2$@z@ab$kfpD)1m;9b$&)F4`@b$.KkTVwGljb$MW&$"]b$B f! `b$ՒdĊz i b$ *_;C?b$.uz&a=v`l"db$Rl'E<<b$c?&?$wekb$5PʲY`>b$оJ䣁 b$L#3ӥh(b$q|LWTb$Meeisb$Df6N+o'V2$ 4oc`Kb$FPiN ޡb$|az9Mb$\d|WMb$EF &Ce7b$Ztn_5~@Q b$ C &;]}jN b$6—RvY)$Ab$ ȧ2IX3b$lJ: QE7T`4b$ȬE`Y{~h b$9TD*4+LI4b$@T[LU$5 b$c`RBK_b$+r)trab$pH u Wo?b$C[dY/ b$tfMEm I8LR~ub$ f9sq:H5b$yǃ<ub$ z@sgG "$VPv`$ [I&b$Td2zk %CASbb$ngȕ@V b$£.jQԎ;Ȳ b$ g_%?ofBb$ VX*h* bb$CWUb3 (2$[)/QbgXb$5pVʉwb$;냧 #B`#b$l?zeY$kb$~e<.6:Ib$y=`fc U\Y25b$ʂ;^{Eb$b0W[x0zFb$HLv|E >"$#3vrI"$x0K,8ڣb$%9Wa$s b$|g;OH5Z+|9:x56t1 2 V X Y Y \ \ e !!!!!!!!!!!!!!!!!! ! ! ! ! ! ! ! ! ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! !!!!!"!"!#!#!$!$!%!%!&!&!'!'!(!(!)!)!*!*!+!+!,!,!-!-!.!.!/!/!0!0!1!1!2!2!3!3!4!4!5!5!6!6!7!7!8!8!9!9!:!:!;!;!!>!?!?!@!@!A!A!B!B!C!C!D!D!E!E!F!F!G!G!H!H!I!I!J!J!K!K!L!L!M!M!N!N!O!O!P!P!Q!Q!R!R!S!S!T!T!U!U!V!V!W!W!X!X!Y!Y!Z!Z![![!\!\!]!]!^!^!_!_!`!`!a!a!b!b!c!c!d!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""j"m"1HSj,-   / 0 -.PQ(vMMNO=>|9:x56t1 2 V X Y Y [ \ \ ^ _ a b d e !!!!!!!!!!!!!!!!!! ! ! ! ! ! ! ! ! ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !j"m"8 BR0(¹| j$%p z1Z F ZdE#~4@vME^~Ek0*U!>hxr.7'`F-),)+( lg.U37Q9zn:[::?: "^ ;m>FB qZA\GB+nDE)"GʜԅyHPhy,ELEj_L " M\0M*Zv~xO xZxREs VZ,[W_[(*X_E/`D\"a’la&?1c " cb|de Vpc_hVH(!z)m8rI/im=mx~#DoV@`vEo+>rHORsE7SuEj6ixDd ^`56^Jo(.^`^J.pLp^p`L^J.@ @ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PLP^P`L^J.h}}^}`^J.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH.^`^J.^`^J.pL^p`L^J.@ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PL^P`L^J.^`^Jo(hH.'^`56CJOJQJ^JaJo(hH!$ $ ^$ `CJOJQJ^JaJo(hHo @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH. ^`56^Jo(. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.h^`^Jo(hH.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH. 8^8`CJ^Jo(.^`^J. L^ `L^J. ^ `^J.x^x`^J.HL^H`L^J.^`^J.^`^J.L^`L^J.h^`^Jo(hH.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH. 8^8`CJ^Jo(.^`^J. L^ `L^J. ^ `^J.x^x`^J.HL^H`L^J.^`^J.^`^J.L^`L^J. 8^8`CJ^Jo(.^`^J. L^ `L^J. ^ `^J.x^x`^J.HL^H`L^J.^`^J.^`^J.L^`L^J.h^`^Jo(hH.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH.^`^Jo(.^`^J.pLp^p`L^J.@ @ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PLP^P`L^J.h^`^Jo(hH.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH.^`^Jo(.^`^J.pLp^p`L^J.@ @ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PLP^P`L^J.^`^Jo(.^`^J.pLp^p`L^J.@ @ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PLP^P`L^J.h}}^}`^J.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH.^`^J.^`^J.pLp^p`L^J.@ @ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PLP^P`L^J.hF^`5CJOJQJaJo(G CJOJ%PJ%QJ%sH tH aJ_H 5hH ^`OJQJo(o p^p`OJ QJ o( @ ^@ `OJQJo( ^`OJQJo(o ^`OJ QJ o( ^`OJQJo( ^`OJQJo(o P^P`OJ QJ o(8^8`^J)^`^J. L^ `L^J. ^ `^J.x^x`^J.HL^H`L^J.^`^J.^`^J.L^`L^J.v^v`^J.F^F`^J.L^`L^J. ^ `^J. ^ `^J.L^`L^J.V^V`^J.&^&`^J.L^`L^J.8^8`56CJ^Jo(.h^`56CJ^Jo(hH. L^ `L^J. ^ `^J.x^x`^J.HL^H`L^J.^`^J.^`^J.L^`L^J. ^`56^Jo(. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.}^}`^J)M^M`^J. L^ `L^J. ^ `^J.^`^J.L^`L^J.]^]`^J.-^-`^J.L^`L^J.8^8`^J)^`^J. L^ `L^J. ^ `^J.x^x`^J.HL^H`L^J.^`^J.^`^J.L^`L^J.     !"#$%&'()*+,-./01234567^`56^Jo(. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.^`OJQJo(hH'^`56CJOJQJ^JaJo(hH!$ $ ^$ `CJOJQJ^JaJo(hHo @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.^`^Jo(.^`^J.pLp^p`L^J.@ @ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PLP^P`L^J. 8^8`CJ^Jo(.^`^J. L^ `L^J. ^ `^J.x^x`^J.HL^H`L^J.^`^J.^`^J.L^`L^J.@ ^@ `^Jo()^`^J.L^`L^J.^`^J.^`^J.PL^P`L^J. ^ `^J.^`^J.!L^!`L^J.h^`^Jo(hH.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH. 8^8`CJ^Jo(.^`^J. L^ `L^J. ^ `^J.x^x`^J.HL^H`L^J.^`^J.^`^J.L^`L^J.}^}`^J)M^M`^J. L^ `L^J. ^ `^J.^`^J.L^`L^J.]^]`^J.-^-`^J.L^`L^J.8}}^}`^J.8 ^`hH.8 L^`LhH.8 pp^p`hH.8 @ @ ^@ `hH.8 L^`LhH.8 ^`hH.8 ^`hH.8 L^`LhH. ^`56^Jo(. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.^`^Jo(.^`^J.pLp^p`L^J.@ @ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PLP^P`L^J. 8^8`CJ^Jo(.^`^J. L^ `L^J. ^ `^J.x^x`^J.HL^H`L^J.^`^J.^`^J.L^`L^J.h}}^}`^J.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH.h^`^Jo(hH.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH.h^`^Jo(hH.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH. 8^8`CJ^Jo(.^`^J. L^ `L^J. ^ `^J.x^x`^J.HL^H`L^J.^`^J.^`^J.L^`L^J.^`^Jo(.^`^J.pLp^p`L^J.@ @ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PLP^P`L^J.^`^Jo(.^`^J.pLp^p`L^J.@ @ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PLP^P`L^J.^`^Jo(.^`^J.pLp^p`L^J.@ @ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PLP^P`L^J.}^}`^J)M^M`^J. L^ `L^J. ^ `^J.^`^J.L^`L^J.]^]`^J.-^-`^J.L^`L^J.^`^Jo(.^`^J.pLp^p`L^J.@ @ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PLP^P`L^J. Ik@R4D'@C@WL՜.+,0 hp  (Virginia IT Infrastructure Partnership:I   Lesson Title Title30BPYOQWCQ==2U-Ls&.LItem VhPropertieslUCompObjry   F'Microsoft Office Word 97-2003 Document MSWordDocWord.Document.89q^`56^Jo(. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.h^`^Jo(hH.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH. ^`56^Jo(. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.}^}`^Jo(.M^M`^J. L^ `L^J. ^ `^J.^`^J.L^`L^J.]^]`^J.-^-`^J.L^`L^J.^`^Jo(.^`^J.pLp^p`L^J.@ @ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PLP^P`L^J.h^`^Jo(hH.h ^`hH.h pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH.^`^Jo(.^`^J.pLp^p`L^J.@ @ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PLP^P`L^J. ^`56^Jo(. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH. 8^8`CJ^Jo(.^`^J. L^ `L^J. ^ `^J.x^x`^J.HL^H`L^J.^`^J.^`^J.L^`L^J. 8^8`CJ^Jo(.^`^J. L^ `L^J. ^ `^J.x^x`^J.HL^H`L^J.^`^J.^`^J.L^`L^J.^`^J.^`^J.pL^p`L^J.@ ^@ `^J.^`^J.L^`L^J.^`^J.^`^J.PL^P`L^J.jlg.)"G)+R0(j6ixORs*X_nD7SuxRQ9y,EL@vM^~n:Zd^ ;37/im ~xO"amx/`\GBvEo c7'la1cj_L?:,[W#Do#!>1Zlg. pc_h_[kyH M d d d d q q q q q (q 0q 8q @q Hq Pq Xq `q hq pq xq q q q q q q q q q Ȱq аq ذq q q qs V q q q qz)mp m>>r::|de0M-) q q (q 0q 8q @q Hq PqqZA  JJLJJhJJJJJJJJJJJJJJJJJJБ@JJJJJJPbJJJJJJJJJJ|WW8Num1|<                 p '|z      <        p        z        p        z        z        p        p                NE        p<                <          '|z      ~        *        p        ]                <        .&                p        p                 h                 <        p        <                 p        <        U        D                                   Ơ(                J̡        z        z        J:r                2X        Ơ(                                                                               d                 J̡                 D                                   bH                                  _:^|6"Y[_j~/^:;@HLT >v??Q\z]an,z -@iX]a{}IHM1Yss(a)HJ`Wa<LEc[r["u| O6KbggYv    @ <] ` Hc -6 ? k X| S    .  0 A N j  $ 5K c {j   [2 u8 (N +Z cb mc @p @CE  2ALUA ~#T=I#SyZZy [RLU[e{q@hY%]Csb 8JU-X1mkp3$a4Pbsm699AZ{o$u' hu1 !3}MlQQVlI|dikz5o v& 045Rljr#1@T!c vC|Y 3QGT^} ) < T@ R \ !!!!!%!+!.!V!d!*"""o""F"G"Od"Mr""#fG#uU#dk#Eo#y#x $+$,$S$[X$x$ %%^%!%'%-%/%O0%F%~%p&s&u&4' '+;'H>'SI'O'Ml'q''%(.(f(z())$u)ey)rC*J*\*~* ++E+ O+aP+Y+[+o+8,@,d$,X1,s,- - -,-}5-G-K-T-b-Sp-..|'.K._.b.f.z. /./E8/HC/W/x/0000{0>0G0I0P0AP0R0c0l0x 12191@1nI1Z11 2242E2[2_3o3$3<3dF3[3qf3t3{34:4!4.34Ez4U555*5Q5 t5w5.}56,6+<6;E6P6b6*7<7A7k7m7mq7z78!8&808I58A8iF8V89?#9'90929689r9p:-:{E:6]:r_:^;0;:;I;Z;<<<3<6<7<D<d<~<=Q!=6>@>Q>S>??)?\.?t?y?{?H@@@0$@&@J3@oE@5a@g@g@A A AGALAgA2zAB%B?BTBnBqB C!CLCxCbDGDQD,D?DrYD3cDm~DW EE|EEE2mE}EPF"F'Fm-FDWFeeF+GG0GgoG~GTHH H'HL.H0H9H=HYH_HZI%I 2I4IJIf^I^IbIdInIJ %J*JFJ`JxJt|JO K*]9]=]?E]H]K]n]2^_^C^cD^L^Q^R^o^__0#_"3_<`_`_(8`O`Qp`W}`aa%aE%a+a6;a,Hafaxab0=bgDbwbIxbcKdMd_=e7Beme}e-~e+Wf g2g6g9gA=g'~g~gh+h2hN3h:hQh'i,iMiUijjT3jGjGjASj\jcjIgjOij$kp,kx,k51kKJkrTkmwk{ l,lllQlXlkl;~lmmw8m%FmBGmHfmofm nL,nGn]njno9o/ o1o2o*~oc(pKp.q3qNaqP{q#rP|j|Vp|N}%}7}zK},a}t}~,~4~A~C~)\~i~k~v~R|~_,\2:JSi#} P([(5j<tD'/0_hisPyThuioOUFoL  #>)3 CTMa./\^f2V $C), 3|LLP\aniR]i}~a6C"m*/2CTVYXnY(0./Ud6 m3Cd(o*nTqy{Qeg--q268 H{Q5=C(WelR!-F2N7$<vR_bp;##J&8>@T2%):G&K(Smr[^+.p7I NHctmG*9KbhN]0bkqv|;#O)`6c9ZC[].bf +!-u/C*uOm\p|T J""+a,2?_\tt<M>Yxr#YP^Ib\u<9>ps| 's;>NdfykE !GZl1 ~&Z),|9PZ_Dk #'9AOk(op"*2M4=Xw[5,KM[^q{ ,/3gG+`dk#s,TVetK&.<j@mPIQ`p#'@/:~]atFzX~u}H*2fj<$LLg8KW0c.msp S68;X/p-b+2<<XWdBHJ0gp{'A2gL7boxzD7Aogup}!+-.29{A~\gpY`br9~Bw{5SQTZt~p#U1_ekVW(NooC-&66m_3bky\$.<S`Kfx>BU a\\Vji ?:Feq< =-;TdyzS&:5b<EYJWgkly3+3::G4\Hn<(:Bfv|% % q`}H.;p  Z""rWeny\ EcKewr=kk0n*0@N\y f"z(1Vykvnp 6>O^g`hN29K+ C/3FiI~J`?a`RQ 7c\n:rxq ?Lk] $'9 EMQ\3a)@VMY}kxxf#-!.2g*!.AOH{ (#%4AvAFphjlqZyQ)2,OQWi+l x}$e&(;E?jd w-AS] c607@KpN;KfG<^~/F<\_g0z r 8 iahQn#!BNP\cc;iY [ @OOO  l"X@XX @XXX,@XX<@X X"X$X&XP@X@XBX@X@Unknown G* Times New Roman5Symbol3. * Arial7.{ @Calibri;SimSun[SO7K@Cambria5. *aTahomaO1 CourierCourier New?= * Courier New;WingdingsA BCambria Math"hS3FG{F::!4dI I  2qX V k2d! xx Lesson Titlejsl47365Christa H Southall8                           ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7