MESSAGE TO TEACHERS: NOTE TO EDUCATORS:


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1 MESSAGE TO TEACHERS: NOTE TO EDUCATORS:
2 Attached herewith, please fid suggested lesso plas for term 1 of MATHEMATICS Grade 12. Please ote that these lesso plas are to be used oly as a guide ad teachers are ecouraged to develop their ow learer activities to supplemet ad/or substitute some of the activities give here (depedig o the school eviromet, umber ad type of learers i your class, the resources available to your learers, etc). Lesso plaig is a ecessary exercise for each ad every idividual teacher however it helps whe teachers sometimes pla together as a group. This iteractio ot oly help teachers to uderstad how to apply the Learig Outcomes (LOs) ad Assessmet Stadards (ASs) but also build up the cofidece of the of teachers i hadlig the cotet usig ew teachig strategies. The Learig Outcomes for the other subjects with which oe ca itegrate have ot bee idetified. The other subjects with which possible itegratio ca be made have bee listed. The Lesso pla could therefore chage if the other subject/s, their LOs ad Ass could be clearly stated. Do ot forget to build i the tasks for the Programme of Assessmet ito your Lesso Plas. Stregthe your efforts by supportig each other i clusters ad share ideas. Good Luck with your edeavors to improve Teachig, Learig ad Assessmet.
3 LESSON PLAN: 1 Lesso Pla: NUMBER PATTERNS Number of Activities 3 Duratio: 4h30 Week 13 Date Cotext: Mathematical : Sequeces ad series Lik with previous lesso: Grade Number patters KNOWLEDGE (K): Arithmetic ad geometric sequeces SKILLS (S): Calculate ad iterpret VALUES (V): Appreciatio, respect ACTIVITY 1 ACTIVITY 2 ACTIVITY 3 Activity Cotet Arithmetic ad geometric sequeces Sigma otatio Sum of series LO,s ad AS s LO 1 AS a, b, c. LO 1 AS a, b, c. LO 1 AS a, b, c. Learers give worksheets to clearly idetify ad solve problems ivolvig umber patters, Educator gives worksheet so that learers Correctly iterpret sigma otatio ad covert fluetly betwee Σ otatio ad expaded icludig: icludig but ot limited to otatio. arithmetic ad geometric 1 = ; sequeces ad series. i=1 They should make liks clearly ( + 1) liks betwee patters doe i i = grade so that for example, 2 i= 1 ; learers uderstad that a arithmetic sequece is a liear a + ( i 1) d = [2 2 patter ad a geometric sequece i= 1 is a expoetial patter. Calculate the term value ad the umber of terms i a sequece of ay patter. Prove ad correctly select the formula for ad calculate the sum of series, i= 1 i= 1 a. r a. r i 1 i 1 a( r 1) = ; r 1 r 1 a = 1 r a + ( 1) d] for 1 < r < 1 Teachig Methods Questio ad aswer Questio ad aswer Discussio, questio ad aswer Educator, idividual, peer Class work, home work, test Expaded Opportuities: Differet examples ad remedial work Use of differet equatios
4 Teacher reflectio LESSON PLAN:2 Lesso Pla: FUNCTIONS, INVERSES AND LOGARITHMS Number of Activities 3 Duratio: 4h30 Week 45 Date Cotext: Mathematical : FUNCTIONS, INVERSES AND LOGARITHMS Lik with previous lesso: Fuctios, sequeces ad series KNOWLEDGE (K): Logarithms, fuctios, iverse relatios SKILLS (S): Ivestigate, discover, demostrate, calculate, problem solvig, drawig VALUES (V):Appreciatio ACTIVITY 1 ACTIVITY 2 ACTIVITY 3 Activity Cotet Logarithms Types of fuctios Graphs of iverse relatios LO,s ad AS s LO1.AS LO2 AS12.1,2,3 LO2 AS12.1,2,3 Learers give worksheets to demostrate a uderstadig of the defiitio of a logarithm ad ay laws eeded to solve reallife problems (Defiitio of a logarithm uderstad that the logarithmic fuctio is the iverse of the expoetial fuctio. Learers eed to covert fluetly betwee logarithmic form ad expoetial form. Note: Solvig logarithm equatios ad iequalities must be see i the cotext of fuctios. Learers demostrate the ability to work with various types of fuctios ad relatios icludig the iverses listed i the followig Assessmet Stadard. Demostrate kowledge of the formal defiitio of a fuctio. Give the relatioship betwee x ad y i  a set of graphs  tables  words  algebraic formulae Determie whether the give iformatio represets a fuctio. Learers draw graphs of the iverse relatios, of fuctios, i particular the iverse of: y = ax + q ; y = ax 2 ; y = a x ; a > 0: Teachig Methods questio ad aswer Questio ad aswer Discussio, questio ad aswer Educator, idividual, peer Class work, home work, test Expaded Opportuities: Differet examples ad remedial work Use of differet equatios
5 Teacher reflectio LESSON PLAN: 3 Lesso Pla: Fuctios ad iverses Number of Activities 2 Duratio: 4h30 Week 6 Date Cotext: Mathematical : Fuctios ad iverses Lik with previous lesso: Logarithms, iverses KNOWLEDGE (K): Iverse Fuctios SKILLS (S):Drawig, determie, iterpretatio VALUES (V): Appreciatio, Respect ACTIVITY 1 ACTIVITY 2 Activity Cotet Iverse Fuctios Characteristics of graphs LO,s ad AS s LO2 AS12.1,2,3 LO2 AS12.1,2,3 Determie which iverses are fuctios ad how the domai of the Origial fuctio eeds to be restricted so that the iverse is also a fuctio. Use ad iterpret fuctioal otatio. I the teachig process learers must uderstad how f (x) has bee trasformed to geerate f ( x), f (x), f ( x + a), f ( x) + a, f (ax), af (x) ad x = f (y) Idetify characteristics as listed below ad hece use applicable characteristics to sketch graphs of the iverses of the fuctios listed above: (a) domai ad rage; (b) itercepts with the axes; (c) turig poits, miima ad maxima; (d) asymptotes; (e) shape ad symmetry; (f) Average gradiet (average rate of chage); itervals o which the fuctio icreases/decreases. Teachig Methods questio ad aswer Questio ad aswer Educator, idividual, peer Expaded Opportuities: Differet examples ad remedial work Differet examples ad remedial work Teacher reflectio
6 LESSON PLAN: 4 Lesso Pla: Aalytical Geometry Number of Activities 3 Duratio: 4h30 Week 7 Date Cotext: Mathematical : Ivestigatio of space Lik with previous lesso: Distace formula betwee 2 poits, Radius perpedicular to the taget at poit of cotact, completig the square. KNOWLEDGE (K): Eq of the circle cetre at the origi ad ot at the origi. Fid the cetre & radius of a circle by completig the square. Determie the equatio of a circle. Calculate the equatio of a taget of a circle. SKILLS (S): Derive, calculatio, applicatio VALUES (V): Appreciatio ad sharig ideas. ACTIVITY 1 ACTIVITY 2 ACTIVITY 3 Activity Cotet Equatio of a circle Fidig the cetre ad the radius of the circle Equatio of the taget LO,s ad AS s (a) (a) (b) Learers are remided of the distace formula betwee 2 poits o a Cartesia plae i the form of a class exercise. The teacher presets a chart with oe circle at the origi ad the other oe ot at the origi. Learers are the asked to fid the distace P i both cases. Learers will first get the coordiates of poits P ad O. OP 2 = r 2 = (x0) 2 + (y0) 2 ad (xa) 2 + (yb) 2 = r 2 The teacher further explais to learers the differece betwee the 2 circles. Examples from the textbook to fid the equatio of a circle are doe o the chalkboard. Class work is give to learers so as to fid the equatio of circle. I both cases, learers will be asked to work i groups. The teacher will be movig aroud guidig them where ecessary. More exercises are give as homework. Learers will be give the equatio e.g. x 2 +y 2 + 6x 8y 11 =0 the asked to group them accordig to the commo factors. They are the asked to complete the square for both x ad y with guidace of the teacher. Gettig to (x+3) 2 + (y4) 2 = 36. They will be asked to determie the cetre ad the radius of the circle. The teacher will be helpig the groups comparig with the geeral equatio i.e. (xa) 2 + (yb) 2 = r 2. Where the cetre is (a;b) ad radius r From this, learers will idetify the cetre after completio of the square i.e. (3; 4) ad r= 6. Learers will be give more exercises i class to do ad will be give more time to discuss ad teach each other i groups. Learers are asked the relatio betwee the radius ad the taget of a at the poit of cotact. The teacher explais to learers how to get the gradiet of the taget from AB perpedicular to PO where M AB *M PO = 1 Example to be doe o the chalkboard. Give a sketch learers will get the gradiet of OP which will be guided to get to the gradiet of the taget AB. M OP = 3/2 ad M AB = 2/3. Learers i groups will get the equatio of the straight lie AB usig the equatio of a circle. Learers will do differet exercises i groups with the help of the teacher.
7 Teachig Methods Discussio, questio ad aswer Questio ad aswer Discussio, questio ad aswer Educator, idividual, peer Class work, home work, test Expaded Opportuities: Differet examples ad remedial work. Use of differet equatios
8 LESSON PLAN: 5 Lesso Pla: FINANCIAL MATHEMATICS Number of Activities 3 Duratio: 4h30 Week89 Date Cotext: Fiacial Lik with previous lesso: Number patters KNOWLEDGE (K): Calculatig the period of ivestmet, uderstadig differet types of loas, SKILLS (S): Ivestigate, Calculate VALUES (V): Team member, fiacial disciplie ACTIVITY 1 ACTIVITY 2 ACTIVITY 3 Activity Cotet Periods of ivestmet Auities Bod repaymet LO,s ad AS s LO 1 AS12.1.4,5 LO 1 AS12.1.4,5 LO 1 AS12.1.4,5 Educators hads out worksheet ad assess the learers work (ability to use calculators) to calculate the value of i the formula : A = P (1 ± i) Facilitates ad use a checklist to see if learers are able to calculate the value of usig a calculator ad later discuss the differet periods of ivestmets. Discussioteacher explais the auity cocept ad how the geometric series is used for the calculatio of auities, givig examples. Apply kowledge of geometric series to solve auity, with or without the use of the formulae: x[ (1 + i) 1] F = I ad P = x [(1 (1 + i) ] i Timelies are a useful strategy to solve problems i Fiacial Mathematics. Discussioteacher explais bod repaymet problems ad how the geometric series is used for the calculatio of bod repaymets, givig examples. Apply kowledge of geometric series to bod repaymet problems, with or without the use of the formulae: x[ (1 + i) 1] F = I ad P = x [(1 (1 + i) ] i Timelies are a useful strategy to solve problems i Fiacial Mathematics.
9 Teachig Methods Expaded Opportuities: Discussio, questio ad aswer Questio ad aswer Discussio, questio ad aswer Class work, home work, test Educator, idividual, peer Differet examples ad remedial work Learers are asked to go to the differet Bakig Istitutios to ivestigate differet types of ivestmet ad which oe gives better returs. Teacher brigs to class differet pamphlets from differet Bakig Istitutios ad let the learers ivestigate which bak will give a better retur.
10 LESSON PLAN: 6 Lesso Pla: Fiacial Matters Number of Activities 2 Duratio: 4h30 Week10 Date Cotext: Fiacial Lik with previous lesso: umber patters, logarithms KNOWLEDGE (K): Calculatig the period of ivestmet, uderstadig differet types of loas, SKILLS (S): Ivestigate, Calculate VALUES (V): Team member, fiacial disciplie ACTIVITY 1 ACTIVITY 2 Activity Cotet Sikig value Aalysis of ivestmet ad loas LO,s ad AS s LO 1 AS12.1.4,5 LO 1 AS12.1.4,5 Teacher explais the sikig fud cocept ad how it ca be calculated ad apply kowledge of geometric series to sikig fud problems, with or without the use of the formulae: x[ (1 + i) 1] F = i ad P = x [(1 (1 + i) ] i Timelies are a useful strategy to solve problems i Fiacial Mathematics. Critically aalyse ivestmet ad loa optios ad make iformed decisios as to the best optio(s) (icludig pyramid ad microleders schemes). Teachig Methods Questio ad aswer Questio ad aswer Discussio, questio ad aswer Educator, idividual, peer Class work, home work, test Expaded Opportuities: Differet examples ad remedial work Learers are asked to go to the differet Bakig Istitutios to ivestigate differet types of ivestmet ad which oe gives better returs. Teacher brigs to class differet pamphlets from differet Bakig Istitutios ad let the learers ivestigate which bak will give a better retur.
11
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