ࡱ> 2415@ ;+bjbj22 0PXX;#XXXXXXXlppppLDlQ htttttttPPPPPPP$RRTlPXtttttPXXttP tXtXtP tP P!/KbXXqPt `SpM,PP0QMRU RUXqPllXXXXRUXqP tt tttttPPllp llpLESSON PLAN (WEEK 14) Total estimated time: 128 minutes Objectives: Arithmetic Series Determine whether a sequence is arithmetic Find a formula for an arithmetic sequence Find the nth term of an arithmetic sequence Find the sum of a finite arithmetic sequence Use an arithmetic sequence to solve an application problem Motivation & Warm up discussion: Begin by considering a real-life example that generates numbers that form an arithmetic sequence Example: [2 minutes] A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third row from the top, and so on, until there are 200 logs in the bottom row. Activity I: [8 minutes] Have the students come up with the total number of rows of logs. Have the students write and interpret the first 10 terms of the sequence of numbers generated from the example Have the students identify the pattern in the sequence of numbers, i.e., come up with the common difference Have the students come up with the formula for the nth term of the sequence and use it to find the number of logs in say the 76th row Have the students compute the number of logs in the first 12 rows Have the students come up with the total number of logs in the pyramid? Formulas that make solving the above problem easier. Formal Definition of an arithmetic sequence Definition: [2 minutes] A sequence is arithmetic if there exists a number d, called the common difference, such that  EMBED Equation.DSMT4  for  EMBED Equation.DSMT4  i.e. If we start with a particular first term, and then add the same number successively, we obtain an arithmetic sequence. Activity II:. Exercises: [6 minutes] Determine whether the sequence is arithmetic. If it is, find the common difference: 2, 5, 9, 14, 20, 25, 23, 21, 19,  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Finding a formula for the nth term of any arithmetic sequence: Teacher Activity: [4 minutes] Denote the common difference by d, and write the first four terms:  EMBED Equation.DSMT4  Activity III: [4 minutes] Have the students state the relation between the coefficient of d and the number of the term, n in each case. Have the students generalize a formula for the nth term of the arithmetic sequence, i.e. come up with the following result: Result 1: The nth term of an arithmetic sequence is given by  EMBED Equation.DSMT4  , for any  EMBED Equation.DSMT4  Activity IV: [4 minutes] Have the students use the formula to find the nth term of the arithmetic sequences identified in Activity II (pay more attention to exercise # 4) Finding a formula for the sum of the first n terms of any arithmetic sequence through an example (Finite Arithmetic Series): Teacher Activity [8 minutes] Consider the sequence of the first 20 even numbers, 2, 4, 6, 8, ,38, 40 (Confirm that the students know why the sequence is arithmetic) The sum of the first 20 terms is denoted by EMBED Equation.DSMT4 . Then  EMBED Equation.DSMT4 = 2 + 4 + 6 + 8 + + 38 + 40 If we reverse the order of the sum, then  EMBED Equation.DSMT4 = 40 + 38 + + 8 + 6 + 4 + 2 If we add the corresponding terms of each side of the above equations, we get 2 EMBED Equation.DSMT4  = (2 + 40) + (4 + 38) + (6 + 36) + + (38 + 2) + (40 + 2) = 20(42)  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4 (2 + 40) Activity V: [5 minutes] Have the students write a formula for the sum of the first 20 terms of the above arithmetic sequence, i.e. come up with the following result:  EMBED Equation.DSMT4 =  EMBED Equation.DSMT4 ( first term + last term) Have the students generalize a formula for the sum of the first n terms of an arithmetic sequence, i.e. come up with the following result: Result 2: The sum of the first n terms of an arithmetic sequence is given by  EMBED Equation.DSMT4  Alternative:  EMBED Equation.DSMT4  ( WHY?) Activity VI: [8 minutes] Have the students use the formula to find the sum of the first 15 terms of the arithmetic sequences identified in Activity II Find the sum  EMBED Equation.DSMT4  Activity VII: (Applications) Exercises [8 minutes] Have the students apply the formulas above to the example in Activity I You take a job starting with an hourly rate of $16. You are given a raise of 25 cents per hour every 2 months for 5 years. What will your hourly wage be at the end of 5 years? A student saves $3 dollars on August 1, $5 on August 2, $7 on August 3, and so on. How much will she save in August? Objectives Geometric Series Determine whether a sequence is geometric Find a formula for a geometric sequence Find the nth term of a geometric sequence Find the sum of a finite geometric sequence Use a geometric sequence to solve an application problem Motivation & Warm up discussion: Begin by considering a real-life example which generates numbers that form a geometric sequence Example [2 minutes] One morning (day 1), three people start a chain letter via e-mail. Each of them sends a message to five other people with the instructions that the receiver must forward the message to 5 other people the following morning. Assume this process continues each morning without any repetition of recipients. Activity I: [8 minutes] Have the students calculate the number of new recipients to the message on day 2, day 3, day 4 and day 5. Have the students identify the pattern in the sequence of numbers generated in the first activity i.e. come up with the common ratio Have the students come up with the formula for the nth term of the sequence and use it to calculate the number of new recipients on the 7th day Have the students calculate the total number of people who have received the message in the first 5 days Formulas that make solving the above problem easier Formal Definition of an geometric sequence [2 minutes] Definition: A sequence is geometric if there exists a number r. called the common ratio, such that  EMBED Equation.DSMT4  i.e. If we start with a particular first term, and then multiply the same number successively, we obtain a geometric sequence Activity II: [4 minutes] Exercises: Determine whether the sequence is geometric. If it is, find the common ratio: 3, 6, 10, 15, 1, -2, 4, -8,  EMBED Equation.DSMT4  Finding a formula for the nth term of any geometric sequence: Teacher Activity [4 minutes] Denote the common ratio by r, and write the first few terms:  EMBED Equation.DSMT4  Activity III: [4 minutes] Have the students state the relation between the power of r and the number of the term, n in each case. Have the students generalize a formula for the nth term of the geometric sequence, i.e. come up with the following result: Result 3: The n-th term of a geometric sequence is given by  EMBED Equation.DSMT4  Activity IV: [4 minutes] Have the students use the formula to find the nth term of the geometric sequences identified in Activity II Formula for the sum of the first n terms of any geometric sequence (Finite Geometric Series): Teacher Activity [3 minutes] Write the following result and explain the symbols Result 4: The sum of the first n terms of a geometric sequence is given by  EMBED Equation.DSMT4  Activity V: [10 minutes] Have the students use the formula to find the sum of the first 15 terms of the geometric sequences identified in Activity II Find the sum  EMBED Equation.DSMT4  Activity VI: (Applications) Exercises [10 minutes] Have the students apply the formulas above to the example in Activity I A deposit of $200 is made on the first day of each month in a savings account that pays 8% compounded monthly. What is the balance in the account at the end of 2 years? Activity VII: [4 minutes] Have the students use a calculator to evaluate  EMBED Equation.DSMT4  for  EMBED Equation.DSMT4  Have the students make a conjecture about the value of  EMBED Equation.DSMT4  if  EMBED Equation.DSMT4  Have the students find a formula for the sum of an infinite geometric Teacher Activity [2 minutes] Write the following result and explain the symbols Result 5: When  EMBED Equation.DSMT4 , the sum of the infinite geometric series  EMBED Equation.DSMT4  is given by  EMBED Equation.DSMT4  When  EMBED Equation.DSMT4 , an infinite geometric series does not have a sum. Activity VIII: [14 minutes] Find the sum  EMBED Equation.DSMT4  Find the sum  EMBED Equation.DSMT4  Draw four squares adjacent to each other. The first with side length of 1 unit, the second with side length of , the third with side length , and the fourth with side length 1/8. Calculate the area of each square. Does this form a geometric sequence? Calculate the total area of the four squares using the appropriate formula given above. If the process of adding squares with half the perimeter of the previous square continued indefinitely, what would the total area of all the squares be? :;YB d B D 6 7 C ] g Obeqr}ݺݡ݈jBe@ hQCJUVaJjhQEHUjQ@ hQCJUVaJjhQEHUjsQ@ hQCJUVaJjhQU hQH* hQ6]hQ hQ5\hQ6CJ] hQCJhQ5CJ\3;GY B C d ~~~~~~* & F A`0p @ <1$* & F A`0p @ <1$( D`0p @ <1$;+ U I 7 des;z{ & F  & F  & F  & F & F 789:;UVTUrs >?VWXYfg~ɿ驟鐆wmjhQEHUjQ@ hQCJUVaJjhQEHUjQ@ hQCJUVaJj hQEHUj/a@ hQCJUVaJ hQ6]hQ56\] hQ5\j hQEHUjMe@ hQCJUVaJhQjhQUjhQEHU*>./V?;<T@$a$ & F .Z[ wmj4 hQEHUjhQEHUja@ hQCJUVaJjhQEHUjޗa@ hQCJUVaJjNhQEHUjٗa@ hQCJUVaJjhQEHUjڗa@ hQCJUVaJhQ56\] hQ6] hQ5\hQjhQU*/012<H  #$%&34567CDE\]^ĺrhj.hQEHUja@ hQCJUVaJjW+hQEHUja@ hQCJUVaJ hQ6]j*(hQEHUj*a@ hQCJUVaJj%hQEHUja@ hQCJUVaJ hQ5\j"hQEHUjИa@ hQCJUVaJhQjhQU(7ij,-J`X & F  & F$a$^_iw()*+,JT`XY_g;= %3<VWdp}~   # 0 : ͻjV5hQEHUj Q@ hQCJUVaJ hQH* hQ6]hQ5CJ\hQ6CJ] hQCJj2hQEHUjs@ hQCJUVaJ hQ5\hQjhQU:'Oy_`t* & F A`0p @ <1$* & F A`0p @ <1$t)B} 0 !!!!^!z!{!!! & F & F$a$ & F  & F !!!!Èr8OH ?k |@sFH8$谊DlYQY:>W*t6ȐQEx,|secE\wl<@iJ:쳪cjVkT좵k 2.ĕ\Uj7rM 0,d7y`¼Qixyon$Ŵ}_%[ dz׽.o[f㟡E怌!@Ut,RoC#aqb1= ׆qYȒBB;' "OSC%ն\!ݾ$0Dd XJ  C A? "2&HkvV: Y R_f`!HkvV: Y RHxڕRnQ)ɀM#Фu%7:!r:m'4S\5!p l]|骉xe@Cʢ7s|3KQHLSR46w*zu$aգH` jz{ٶ[M|Z<߃LlVO:-t:ݦNĪu^w=XDvk]\aCXWᦋiPWq ,J8DCF> τ` d)a#.OU!?"E^7~/o9kFO 7K(5&Kt$#A+Ezzt"oٳSDd LhJ  C A? "2Pi6}4|(y9,E f`!$i6}4|(y9@ |xڕSkQm6m`nlԋ6 !LZ $Dbn!x(zc>1^MSU}68+30-vl]Θ6jp9n9rflz73W`{;` ζS cY>`aBD5(s%efQxEoQ8 .z1dKSH_3֔'Dd J  C A? "2L!G^/kĭ0C(3 f`! !G^/kĭ0C>  8\ xڭMLA߼ݖִ (RŋIˏ?"%zkVj B1؋1z;1p1Ơ'NdLfwKEMig߼yٙY3!ƀ.5d1,z;``IύиLNC+奶Bej[%ej!LߎJ#Zpm-<ѽ"TZLZo3 @AIz@vq VaFLJBˡwXtj0kQ$,BkȱPbQ9`kbM$3XWyC gm ;j &+uvɟ%ҰT+Ɏf')zT|k&YIbu62E(8vME .",_:W3Uie1ͥga xHpa[V7X5ڠFt'5lVh/yK|WciWCa`4?C)ԍLRQnY9vf'{S)uOh)s=ёB舶mP;zYp,@z.jZmĠ( d1Jz]0 ]qJB F6S>,|"A` fFӌ7 wGP]_:6}HX/`oFѿd82Ni2O@c]Dd |h  !"#$%&'(*+,-./036V789:;<=>@?BACDEFGHJIKLMNOPQSRUTWXwYZ[\^]`_abcedfghijklmnopqrstuxvyz|{~}Root Entry FlS5@QData )jWordDocument0PObjectPool1`~SlS_1079106163F`~S`~SOle CompObjiObjInfo  !"#&)*+,-./012589:;>ABCFIJKNQRSVYZ[^abcfijknqrstuvy|}~ FMathType 5.0 Equation MathType EFEquation.DSMT49q2 DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  a n "-aEquation Native ._1079106210 FSSOle  CompObj i n"-1 ==d, FMathType 5.0 Equation MathType EFEquation.DSMT49q2 DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_ObjInfo Equation Native  _1080378063JFSSOle A  ne"2. FMathType 5.0 Equation MathType EFEquation.DSMT49q#a DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_CompObjiObjInfoEquation Native }_1080380912FSSA   13,  23, 1,  43,  53, ... FMathType 5.0 Equation MathType EFEquation.DSMT49q# DSMT5WinAllBasicCodePagesOle CompObjiObjInfoEquation Native Times New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  a n ==4++3n FMathType 5.0 Equation MathType EFEquation.DSMT49q_1080135215FSSOle $CompObj%iObjInfo'Equation Native (_1079106433FSSOle 3CompObj 4i, DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  a 1 ,a 2 ==a 1 ++d,a 3 ==a 2 ++d==(a 1 ++d)++d==a 1 ++2da 4 ==a 3 ++d==(a 2 ++d)++d==a 1 ++3d FMathType 5.0 Equation MathType EFEquation.DSMT49q2 DSMT5WinAllBasicCodePagesObjInfo!6Equation Native 78_1079106475 $FSSOle <Times New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  a n ==a 1 ++(n"-1)d FMathType 5.0 Equation MathType EFEquation.DSMT49qCompObj#%=iObjInfo&?Equation Native @_1080137690)FSS2 DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  ne"1 FMathType 5.0 Equation MathType EFEquation.DSMT49qOle DCompObj(*EiObjInfo+GEquation Native H, DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  S 20 FMathType 5.0 Equation MathType EFEquation.DSMT49q_1080137689'.FSSOle LCompObj-/MiObjInfo0OEquation Native P_1080137694"E3FSSOle TCompObj24Ui, DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  S 20 FMathType 5.0 Equation MathType EFEquation.DSMT49qObjInfo5WEquation Native X_10801377538FSSOle \, DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  S 20 FMathType 5.0 Equation MathType EFEquation.DSMT49qCompObj79]iObjInfo:_Equation Native `_10801379366@=FSS, DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  S 20 FMathType 5.0 Equation MathType EFEquation.DSMT49qOle dCompObj<>eiObjInfo?gEquation Native h, DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A   202 FMathType 5.0 Equation MathType EFEquation.DSMT49q_1080138026BFSSOle lCompObjACmiObjInfoDoEquation Native p_1080138121;YGFSSOle wCompObjFHxi,~ DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A   (number of terms in the sequence) 2 FMathType 5.0 Equation MathType EFEquation.DSMT49q,4 DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  S n == n2(a 1 ++a ObjInfoIzEquation Native {P_1080138239^LFSSOle n ) FMathType 5.0 Equation MathType EFEquation.DSMT49q,F DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_CompObjKMiObjInfoNEquation Native b_1081326109wQFSSA  S n == n2[2a 1 ++(n"-1)d]. FMathType 5.0 Equation MathType EFEquation.DSMT49q# DSMT5WinAllBasicCodePagesOle CompObjPRiObjInfoSEquation Native 4Times New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  p(2n++5) n==1300 " FMathType 5.0 Equation MathType EFEquation.DSMT49q_1079107084chVFSSOle CompObjUWiObjInfoXEquation Native _1080668575O[FSSOle CompObjZ\i2 DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A   a n++1 a n ==r,  or  a n++1 ==a n r,  for any ne"1. FMathType 5.0 Equation MathType EFEquation.DSMT49q DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  3.   1ObjInfo]Equation Native _1080319249`FSSOle ,  12,  14,  18, ...4.   a n ==2 23() n"-1 FMathType 5.0 Equation MathType EFEquation.DSMT49qCompObj_aiObjInfobEquation Native _1079107083eFSSx DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  a 1 ,a 2 ==a 1 r,a 3 ==a 2 r==(a 1 r)r==a 1 r 2 a 4 ==a 3 r==(a 1 r 2 )r==a 1 r 3 FMathType 5.0 Equation MathType EFEquation.DSMT49q2e DSMT5WinAllBasicCodePagesOle CompObjdfiObjInfogEquation Native Times New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  a n ==a 1 r n"-1 ,  for any ne"1. FMathType 5.0 Equation MathTy_1079107128jFSSOle CompObjikiObjInfolpe EFEquation.DSMT49q2 DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  S n == a 1 (r n "-1)r"-1,  for aEquation Native _1081326344oFSSOle CompObjnpiny r`"1. FMathType 5.0 Equation MathType EFEquation.DSMT49q#? DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_ObjInfoqEquation Native [_1080669989tFSSOle A  p8 25() n==130 "  n"-1 FMathType 5.0 Equation MathType EFEquation.DSMT49q DSMT5WinAllBasicCodePagesCompObjsuiObjInfovEquation Native _1080670011r|yFSSTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  r n FMathType 5.0 Equation MathType EFEquation.DSMT49q DSMT5WinAllBasicCodePagesOle CompObjxziObjInfo{Equation Native Times New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  r== 12 and n==1, 2, 5, 10, 50, and 100. FMathType 5.0 Equation MathTy_1080670117~F@S@SOle CompObj}iObjInfope EFEquation.DSMT49q DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  r n  as n!"Equation Native _1080670344F@S@SOle CompObji FMathType 5.0 Equation MathType EFEquation.DSMT49q DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  |r|<<1ObjInfoEquation Native _1079107295T,F@S@SOle CompObjiObjInfoEquation Native _1079107337F@S@S    !$'()*+.12345789:;<>?@ABD FMathType 5.0 Equation MathType EFEquation.DSMT49q2 DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  |r|<<1Ole CompObjiObjInfo Equation Native  a FMathType 5.0 Equation MathType EFEquation.DSMT49q2E DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  a 1 ++a 2 r++a 3 r 2 ++... FMathType 5.0 Equation MathType EFEquation.DSMT49q2 DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E__1079107514F@S@SOle CompObjiObjInfoEquation Native 5_1079107512F@S@SOle CompObjiA  S " == a 1 r"-1. FMathType 5.0 Equation MathType EFEquation.DSMT49q2 DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_ObjInfoEquation Native _1081326570F@S@SOle "APAPAE%B_AC_A %!AHA_D_E_E_A  |r|e"1 FMathType 5.0 Equation MathType EFEquation.DSMT49q#; DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_CompObj#iObjInfo%Equation Native &W_1081326569mF@S@SAPAPAE%B_AC_A %!AHA_D_E_E_A  p4 12() n==1" "  n"-1 FMathType 5.0 Equation MathType EFEquation.DSMT49qOle ,CompObj-iObjInfo/Equation Native 0R#6 DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  p3 "-23() n==0" "  nOh+'0 J  C A? "2xE39X[o^bTf`!LE39X[o^b ` @|xڝSkQmV6Ih5MAM F"MzCm $ј[PoDпB A㼷PCEcg77;C "x}JTY^}YCwaϟ$SKCF@ #AڊN"|:xڰk ]6+nygFNQ=|Ҫ-D4/Yg]ڭ]-_ iӆ.z2k3hz723y; ?W,{&}1aG1VMXi7GZn~w)τ܇I>,);A-B7j/@YPJ}I%79ͨzY ;Sͳvn]CKUxj DM*' l- 2XEk2s*'7IRphX&ԂZ- $ȨH2}H !ŷ 4Be&lw|nq_|S=#8?LS~Dd hhJ   C A? "2|fy^S)Mf`!|fy^S)M@@||xڕRNP#)ƨDRGPZQ^wuWKܘpeH]XwN{;=)BWAC=̶m᪗ i]eڞ 6/&~1U]ث@I]Ua r>{&}1aG1VMXi7GZn~w)τ܇I>,);A-B7j/@YPJ}I%79ͨzY ;Sͳvn]CKUxj DM*' l- 2XEk2s*'7IRphX&ԂZ- $ȨH2}H !ŷ 4Be&lw|nq_|S=#8?LS~Dd hhJ   C A? " 2|fy^S)M4f`!|fy^S)M@@||xڕRNP#)ƨDRGPZQ^wuWKܘpeH]XwN{;=)BWAC=̶m᪗ i]eڞ 6/&~1U]ث@I]Ua r>{&}1aG1VMXi7GZn~w)τ܇I>,);A-B7j/@YPJ}I%79ͨzY ;Sͳvn]CKUxj DM*' l- 2XEk2s*'7IRphX&ԂZ- $ȨH2}H !ŷ 4Be&lw|nq_|S=#8?LS~Dd hhJ   C A? " 2|fy^S)Mf`!|fy^S)M@@||xڕRNP#)ƨDRGPZQ^wuWKܘpeH]XwN{;=)BWAC=̶m᪗ i]eڞ 6/&~1U]ث@I]Ua r>{&}1aG1VMXi7GZn~w)τ܇I>,);A-B7j/@YPJ}I%79ͨzY ;Sͳvn]CKUxj DM*' l- 2XEk2s*'7IRphX&ԂZ- $ȨH2}H !ŷ 4Be&lw|nq_|S=#8?LS~Dd hhJ   C A? " 2|fy^S)Mx f`!|fy^S)M@@||xڕRNP#)ƨDRGPZQ^wuWKܘpeH]XwN{;=)BWAC=̶m᪗ i]eڞ 6/&~1U]ث@I]Ua r>{&}1aG1VMXi7GZn~w)τ܇I>,);A-B7j/@YPJ}I%79ͨzY ;Sͳvn]CKUxj DM*' l- 2XEk2s*'7IRphX&ԂZ- $ȨH2}H !ŷ 4Be&lw|nq_|S=#8?LS~Dd hlJ   C A ? " 2r4hվy#f`!r4hվy@|xڥRMKQhQDjP* 7~P- I%h3L5Gaj"_-Uȴ)Λ7Z2o޹{3Hi2"]0/gE7ü V6yhiL9dX|/|dwTYAʚBBB{Za$' /<p}/Y~d J۵ZZŬRgŒ I7Dd hhJ  C A? " 2|fy^S)M%f`!|fy^S)M@@||xڕRNP#)ƨDRGPZQ^wuWKܘpeH]XwN{;=)BWAC=̶m᪗ i]eڞ 6/&~1U]ث@I]Ua r>{&}1aG1VMXi7GZn~w)τ܇I>,);A-B7j/@YPJ}I%79ͨzY ;Sͳvn]CKUxj DM*' l- 2XEk2s*'7IRphX&ԂZ- $ȨH2}H !ŷ 4Be&lw|nq_|S=#8?LS~-Dd p lJ  C A ? "2ڄ'cL2Gwkn(f`!cڄ'cL2GwS!1xڥSn@]'ФP"BtS(nh%bڎJ.Q"pH|W (23 \Yy̾219Ȣpb{z[K^5+k.&,epj`T*@79\GP ]wʁ(m GrUu1'O~Kdz(umG<=SM:8@tN_;@خRp,݁SANB,0?2jU*Qqt=[v{ʲ ۹iu`O_خ9{^v 7wL7¥7ml.B9Xnߙ[Yuev\)7lBTl4_yUсZCt`LZb>qO1`I.Š7,I?Xd(ߢRa#kF7l&o}Д WARIweϣf8=47SɅU> H7|V6Yr0g =o8L/ [q8RjQY~5ĿW׸۬Cw\3㢦t,]|utcccUVX)Kר LkͪQmцBjU3ZBJ=t+r]Qዙu:+g]e,-p@#,JOJ9g_&C2`9k"C/@1)mS^!ūnؔ2#I81R.*-I#^(YwBV:hw+'[+!v #JsVq. ADd LJ  C A ? "2h6oSY2f`!wh6oSB@ ExڭTkAfv͚*@lRiJЃiI,5_$ Kգ<EW)a=fwCZT7ov pc ys\q˲l2;bGx?m$y%wGIGVk>*5ضWoKy^ x#X(FxUooWZ_[; 1d/Oc\b!ZC ]0|nc`Ko$2>G[.GAU8 /'q}=꞊24P(oy&8F^"W#9cMg_prx:WG_tlch[):h}$0:Hl!L)VRҒ(OW9mCo ݧ~Mȓ>"$g ̓f]Q]쩑NdΦr@ f08 12`:_8WIp<z|6콪Z0Ui5R` eGlywpvQ8j>/Xb:{vP-2 [^#́0ZJšܷi{t' M cZ!H]F8G_+`no7jU6E?cNؚ{}!޹71~$5>լ冴bp>Ef9w w̬nEJciuެ!OV2RB&9^:+IG4A- PRVdb \G3#QJ`.ņ!,'`k-"QO4ԏL <Ÿ!Nv2& ^T_07ap5wnqapa޽谡>'*;k^J@.;U|&Pϫ4W:s?@lX*(Dd xJ  C A? "2ٳv|2Tfn9f`!^ٳv|2T  ,xڵUOA3QT"[g -hЀ|AV)1R&5I$Q$x"xࡉ1MEfggK+0ۙ}{oo~o3M@5`MN 1-BKa䠉PyE(`ly_aT0nǷ( Ʋ"qFX ³uMfV-ZUem[ 읃cƱy`X6oʽ>季T+qg~ԸG!1@`})HiLdෘuMt]<܂1,Gc%R#(ԯ*Gm[scY=cq;Xyz%Xo+U*^UUrUY8QXVZ펎؆Z6)%o'`O%o:Z,.uoym;Nmw_VHy-7˕3^[Zן7/ګKwӿ|& ox0rwThb'Iñ xL^7=5O2'x ;' QR4.4 uNJ =Q<^'b~u_.(. ~(/_"XB PNx0׎cb 0G3g=hhk6 ?AHfc0,j6ѸqA&8SAx v35ʍV>ىW"8El oe${rѰ!Xْ  [g-Dd $ J  C A? "2H=FυcU̔9*$=f`!=FυcU̔9*  (xڵMhAlb$G&6"L=TIv@Ӕ"ozbC"lqrZU]{,43^>|8n?"ĭ{y`VZy,Gqxh~%_0/P#~G s[Wt( Ɔa>-b$H?Gtl:ӑ5qfP;wmU% DcU[[1d[Bon}nʌRԠRuhH1)Ur :)ĒHVMzexL MOVeS3`I*N7HJpݦQv(¹J~hx\ߎVXmҞX,za9cm?*<Ʀӳ+Nn)8%r9%ݗKutE~[𰘓|l&0R88`-8SsreFԦ8yj ^5\h I3C0$"j\:.iX>yaCSXJої'1uz @XpBݚj$` G>럷,j_LZ'޹>8ު_YXt"UFe؜nDd |J  C A? "2,."5!QL/ |Af`!,."5!QL/ `(80rxڭTkQy&eVnIEzboɪ[ $E I<"xEBzŃ qMRbؙ7o0o2 C-d~_XI6>_p[eo|a~[f(#]Bx`jTKzr}ٺaF"x5#?yٺkW OB$+j [-bR&ߛ?ɻ YZ*Vkz a1UW9EJ)/ꀌB"* l4J4&Iش rU`&|ǓkCŕ=tLE2["I]pv bND2^p G"ۉ Dd T J  C A? "2.qTJsaXp1 Df`!qTJsaXp1  dxڭUMhA~3[$5IZ즠SXh1]uf#H B "FiKK͊g r:o'k2ng`lKm?1\[1L0TE;W#cPi{֨) I+Jzqʥ/06jF\X1Sw&V:krrsO#um&NZcޝ \4I=kYԢu-89kh?KF `&ːAimr&&f%0)&vzÄCR(u|m؍bA_AqO ˷$L&-nzctRWY^PX9-)LW%#O M~ 8mDd LJ  C A? "2hA0 Hf`!hA0 ( (+xڵUkA~ofHVؤ/$6m)h-Ru@s -""쥧C^ T{E{;I̷߼7` y DBQVmt6yłwuTA'T92ًtF(/&&*]LLF>Q/%[d=jen:N~`UMj'30 \&ؗ * Y=j[['0jYpY&Kج"D\Z*үfl苀T36DZW{t 8tiH=Ihc'uz9WbFn -kޤ]o3Ċ&WFiw_fkL3Zw},,]m%]DMOERY']Ng33é|H9c!i<M376 m<ݟKA;zUr|2:Y:`Ŭ#Vy8I7BC+X1 @u*~(9YH2PP@)j埵 \mv??Ώ|]0 K QDϏ^6t'wn nsϏʮ;duNjy3 '6fWΟ 32Dd ,J  C A? "2~ dw|U?0ZLf`!~ dw|U?0xڝRJA=3I<`"f#F`B$ ~@L7X7l5`3(he} g; A69c^`0ja>Ϭ-)@l&(~ ?"[+M+it,NE~`nEnof~ŷU̗RXw;53Solj'F9O؟m>oՌMBؗ/܋NK3ٸ:,GLa)XreYF+b7\_b ޱV>[EL00cÀ*VCz' JR:)TMg^NSCrލqpNUniZЛnmn-* )f{`r.{Ѡx~n|vDd @J  C A? "2Yl;, C8=5QRf`!-l;, C8=x xڕS1o@9! rB[!Pڕ Z!0M#`H*F׀A![+$A CHLY0dd@d&$̻]AB={& #S8u.XIdqe1+,u휁e2Gc{+Qe4l[>!EqDhbzޒ*N |>L6;xKL"C֙pDÌ3:+.f鸃::~!Z䈦d$Kk{bɀ+tJdN>f%j@\V}Xxnw ;Oj^}慨Okj{Zeyj68o_;Z݌ Q=*F9Y 0j܋.EcƯ8N=m@ "Aev^rJ]&;\B.ܛw֔ו ~dI>V>ZpU[S/vDd X@J  C A? "2*:P~ӭ{HUf`!:P~ӭ{  xڕR=oA}g'tvP!$ GV|HN$q)JgJ• *RٖRdu3n4o"vA9 "1UC,&yq18Zc+6xӀ!Yq{ʪJD2Zǔ:]+)'0ݚL8afm !޷g<*1Fڔ-)ȌIfx9oO$9*ڻF Z.&c@?3%~!L,fR2_koݺQM$8uD2_R n =O$C%3]lb%tdeWQ6@7'~(ٍR(c_~GV*38q$xiPrF6}(tCNrO>9ccS%V:͖S')\SzGM7}Dd X@J  C A? "2*:X˝m4nXf`!:X˝m4n  xڕROQ- nPjM#`"&qpv[7- H`Áhbc EF]I9hp[Mn6= _u~MV5 k15z T hSH? dםqtAm|jYg GbA8q(NɝKb*[ g9UoeBL_L n}z'bR5Y0!xڥS;oAf&ll qc(N`:Cљ(P7P'uTH{đ v۹nfg @ԊP#1L|ͤ!_J4g!(g^im?h R(ǵShQ*PQ"kGޒ kͶ3n;nmw0s%p/!)LĖb;]ɲ_mWe&WED3Lihp #+e2ض.6EbM>>- 1ЉkO-\.&!NCQ(N[kr20ٱZk>(v:C&>qFܦCdbQzwmq=;.ߨ[)-x%7*YKEKDZXFނ7bD}^c)Z!NR/*ayGAoVlM6sClcuT=TtӨML_;jVAAi9aﴕ)hAIDd 8lJ  C A? "2$"xC]f`!$"xCv MxڵTAkA~of7k IHmi@I1mT0o[]j &(!$Că/b|Ʀjud|73S#P b`!;B^} Yˑ8P%~M ӮzPqZā(ߘ!ˢ~˅5CUXSBON';K (@RkX-m7=R uPDW456[H?7/9xo@Mj4pN9$st>?q8#,ǜ'ر^'j/OGo\cj>Aޜ,Xvײ okkUi*Wݩ٬+k5!o_T #f9bJ*!^4;kU:7sbDd X@J   C A? "2+BFn!ygɊiw>af`!BFn!ygɊiw  xڕRkQF#֔ڜk?h{0HUrl%4`fO@/=Sr-\ !7{!m@@rlȏHL&ms[8bzd`+v[_θܢFn;e=!%CI\_u|#"jiƷvcnbmf&$1FFrmz)`p$3- N}QC{~_S1b䟹9tb1sB-ۮZnVONwwjmzqVWD4P(-,$Rkc+1LYfqb /e7^K0{ a嬼'?AkAܞ%gHjsG |MoGT+cu撋'Kf˩˓.zטDd `J ! C A? " 2* .f.?df`!* .f.?X (+xڵUkA~3HVI_X*V`چZ0% !ꢁ BOM/9xݓK vv71m-5:d2/{;09 Pqr,FaZg1 vP. @qxqЮ⬹ K/O:*t#Db2azC\z]kߐ۟0LN/gEB.̗g8e9`Xjjn2S6D,yЍL>NK;z<}O/Om>a=O,<K݁STNEH8≀5NZ^$.!!@QUQAxj*5`Cybhdy=% XkXu<ؑa܉TU8/r `͞O |{wGV ]&֌@IDfECK>¹{G&Dd LJ " C A? "!2LeRn|MV |=#gf`!LeRn|MV |=#p (+xڵT͋RQ?ާͼ1ԙ"aF>F!RGj ERYգ?5̝DV&(g߲h]S"USQvPy36u߹9`@, 6 7g̰u4)n9ԵϠuY3.mv /sƚЅ Dq #}oǂVmdM6ل`h}瞾~>ӣ+/*UOB{.V>02aIzϿ͵m]˿i0C[4j Q#!]i.*{;'FFJs@> Heading 2$@& 5CJ\DAD Default Paragraph FontVi@V  Table Normal :V 44 la (k@(No List TOT _MultiChoice1$7$8$H$^`CJROR Choices% & F(1$7$8$H$^`(CJ;#P;GYBCdUI  7des;z{> . / V  ? ; < T @7ij,-J`X'Oy_`t)B}0!^z{xyWXSop01MdVWXrPi !I!!H""9#:#=#000 0 0 0 0 0000000 0 0 0 0 0 000000 0 0 0 0  0  0  0  0 0 0 0 0 0 0  0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 0 0  0 0 0 0 0 0 0 0  0Y  0Y 0 0 0 0J 0J 0J0J0J0J0J0J0J0J0J0J0J0J0J0J0J0J0J0J0J0J0J0J0 0 0 0 0 0000000 0 0 0 0000000000 0 000000000 0 000000000000000 0 0000 0M 0M0M0M0M 0M 0M 0M0M0M0M0M0M0M0M0M0M 0M 0M 0M 0 0 000^ k$L');+"$%' t!&;+ !#&;+79> V X f ~       / 1  #%35D\^(*}^vxSkm,.,.4LN  ? W Y i !!!-!E!G!;#::::::::::::::::::::::::::::::::::/23:;E8:;B> Y ^ a f   ! " $ % &    0 4 $'(-67B]_}^y{Snpxyz/19:</02MO     ? Z \ ^ _ d i !! !$!%!(!-!H!I!M!N!R!=# pr   af =#3333333333333333=#pvazpvazRichRichRichRichRichRichpvazabramson0@Q8\do RkBQ} tNPCBEx6 HHA:j!RkBtg"tw$3 J*H0DkW2VlIRkB2Lz8@9M-+-3aRkB,KNaw|0 NfRkBfjt\?e86G{nb5CJOJQJ^JaJ.h ^`OJQJo(hhh^h`o(.h pp^p`OJQJo(h @ @ ^@ `OJQJo(h ^`OJQJo(oh ^`OJQJo(h ^`OJQJo(h ^`OJQJo(oh PP^P`OJQJo( hh^h`OJQJo(^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L.hh^h`o(.^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L.hh^h`o(.^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L.hh^h`o(.^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L.hh^h`o(.^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L.hh^h`o(.^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L.h^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hH hh^h`OJQJo( ^`OJQJo(o pp^p`OJQJo( @ @ ^@ `OJQJo( ^`OJQJo(o ^`OJQJo( ^`OJQJo( ^`OJQJo(o PP^P`OJQJo( hh^h`OJQJo( ^`OJQJo(o pp^p`OJQJo( @ @ ^@ `OJQJo( ^`OJQJo(o ^`OJQJo( ^`OJQJo( ^`OJQJo(o PP^P`OJQJo( hh^h`OJQJo(^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L.hh^h`o(.^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L. hh^h`OJQJo( ^`OJQJo(o pp^p`OJQJo( @ @ ^@ `OJQJo( ^`OJQJo(o ^`OJQJo( ^`OJQJo( ^`OJQJo(o PP^P`OJQJo( hh^h`OJQJo(^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L.hh^h`o(.^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L. hh^h`OJQJo(^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L.hh^h`o(.^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L.h^`OJQJo(hHhhh^h`o(.hpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHV86G{w$,KNa*:j!-3ado NflIDkW2fjtQ}9M2L6 H0tg"PC6 H@V 00V 0V0.а P Qw@P $Of       sx        $z        sL        ƕ*        Xvp        5Q                 sx        sx        sx        r        sx        sx        Xvp        sx        $z         `       Qh~6@;#@@UnknownGz Times New Roman5Symbol3& z ArialOz Times New Roman TUR;Wingdings?5 z Courier New"1hddudB?B?!24d)#)# 3QH(?h~6LESSON PLAN (WEEK 14)pvazabramsonX