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| WK | LSN | TOPIC | SUB-TOPIC | OBJECTIVES | T/L ACTIVITIES | T/L AIDS | REFERENCE | REMARKS |
|---|---|---|---|---|---|---|---|---|
| 1 |
OPENING OF THE SCHOOL AND REVISION OF END OF TERM 2 EXAMINATIONS |
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| 2 | 1 |
Sequences and Series
|
Introduction to sequences and finding terms
|
By the end of the
lesson, the learner
should be able to:
Define sequences and identify sequence patterns Find next terms using established patterns Recognize different types of sequence patterns Apply pattern recognition systematically |
Q/A on number patterns from daily life
Discussions on counting patterns using classroom arrangements Solving pattern completion problems step-by-step Demonstrations using bead or stone arrangements Explaining sequence terminology and pattern continuation |
Chalk and blackboard, stones or beans for patterns, exercise books
|
KLB Mathematics Book Three Pg 207-208
|
|
| 2 | 2 |
Sequences and Series
|
General term of sequences and applications
Arithmetic sequences and nth term |
By the end of the
lesson, the learner
should be able to:
Develop general rules for sequences Express the nth term using algebraic notation Find specific terms using general formulas Apply sequence concepts to practical problems |
Q/A on rule formulation using systematic approach
Discussions on algebraic expression development Solving general term and application problems Demonstrations using position-value relationships Explaining practical relevance using community examples |
Chalk and blackboard, numbered cards made from paper, exercise books
Chalk and blackboard, measuring tape or string, exercise books |
KLB Mathematics Book Three Pg 207-208
|
|
| 2 | 3 |
Sequences and Series
|
Arithmetic sequence applications
Geometric sequences and nth term |
By the end of the
lesson, the learner
should be able to:
Solve complex arithmetic sequence problems Apply arithmetic sequences to real-world problems Handle word problems involving arithmetic sequences Model practical situations using arithmetic progressions |
Q/A on practical applications using local business examples
Discussions on salary progression and savings plans Solving real-world problems using sequence methods Demonstrations using employment and finance scenarios Explaining practical interpretation using meaningful contexts |
Chalk and blackboard, local employment/savings examples, exercise books
Chalk and blackboard, objects for doubling demonstrations, exercise books |
KLB Mathematics Book Three Pg 209-210
|
|
| 2 | 4 |
Sequences and Series
|
Geometric sequence applications
Arithmetic series and sum formula |
By the end of the
lesson, the learner
should be able to:
Solve complex geometric sequence problems Apply geometric sequences to real-world problems Handle population growth and depreciation problems Model exponential patterns using sequences |
Q/A on practical applications using population/growth examples
Discussions on exponential growth in nature and economics Solving real-world problems using geometric methods Demonstrations using population and business scenarios Explaining practical interpretation using meaningful contexts |
Chalk and blackboard, population/growth data examples, exercise books
Chalk and blackboard, counting materials for summation, exercise books |
KLB Mathematics Book Three Pg 211-213
|
|
| 2 | 5 |
Sequences and Series
|
Geometric series and applications
Mixed problems and advanced applications |
By the end of the
lesson, the learner
should be able to:
Define geometric series and understand convergence Derive and apply geometric series formulas Handle finite and infinite geometric series Apply geometric series to practical situations |
Q/A on geometric series concepts using multiplication examples
Discussions on convergence and formula applications Solving geometric series problems including infinite cases Demonstrations using geometric sum patterns Explaining convergence using practical examples |
Chalk and blackboard, convergence demonstration materials, exercise books
Chalk and blackboard, mixed problem collections, exercise books |
KLB Mathematics Book Three Pg 216-219
|
|
| 2 | 6 |
Sequences and Series
Compound Proportion and Rates of Work |
Sequences in nature and technology
Compound Proportions |
By the end of the
lesson, the learner
should be able to:
Identify mathematical patterns in natural phenomena Analyze sequences in biological and technological contexts Apply sequence concepts to environmental problems Appreciate mathematics in the natural and modern world |
Q/A on natural and technological patterns using examples
Discussions on biological sequences and digital applications Solving nature and technology-based problems Demonstrations using natural pattern examples Explaining mathematical beauty using real phenomena |
Chalk and blackboard, natural and technology examples, exercise books
Chalk and blackboard, local business examples, calculators if available, exercise books |
KLB Mathematics Book Three Pg 207-219
|
|
| 2 | 7 |
Compound Proportion and Rates of Work
|
Compound Proportions applications
Proportional Parts Proportional Parts applications |
By the end of the
lesson, the learner
should be able to:
Find the compound proportions Apply compound proportions to complex problems Handle multi-step compound proportion scenarios Solve real-world compound proportion problems |
Q/A on advanced compound proportion using complex scenarios
Discussions on multi-variable relationships using practical contexts Solving challenging compound problems using systematic approaches Demonstrations using construction and farming examples Explaining practical applications using community-based scenarios |
Chalk and blackboard, construction/farming examples, exercise books
Chalk and blackboard, sharing demonstration materials, exercise books Chalk and blackboard, business partnership examples, exercise books |
KLB Mathematics Book Three Pg 290-291
|
|
| 3 | 1 |
Compound Proportion and Rates of Work
|
Rates of Work
Rates of Work and Mixtures |
By the end of the
lesson, the learner
should be able to:
Calculate the rate of work Understand work rate relationships Apply time-work-efficiency concepts Solve basic rate of work problems |
Q/A on work rate calculation using practical examples
Discussions on efficiency and time relationships using work scenarios Solving basic rate of work problems using systematic methods Demonstrations using construction and labor examples Explaining work rate concepts using practical work situations |
Chalk and blackboard, work scenario examples, exercise books
Chalk and blackboard, mixture demonstration materials, exercise books |
KLB Mathematics Book Three Pg 294-295
|
|
| 3 | 2 |
Vectors (II)
|
Coordinates in two dimensions
Coordinates in three dimensions |
By the end of the
lesson, the learner
should be able to:
Identify the coordinates of a point in two dimensions Plot points on coordinate planes accurately Understand position representation using coordinates Apply coordinate concepts to practical situations |
Q/A on coordinate identification using grid references
Discussions on map reading and location finding Solving coordinate plotting problems using systematic methods Demonstrations using classroom grid systems and floor patterns Explaining coordinate applications using local maps and directions |
Chalk and blackboard, squared paper or grid drawn on ground, exercise books
Chalk and blackboard, 3D models made from sticks and clay, exercise books |
KLB Mathematics Book Three Pg 221-222
|
|
| 3 | 3 |
Vectors (II)
|
Column and position vectors in three dimensions
Position vectors and applications |
By the end of the
lesson, the learner
should be able to:
Find a displacement and represent it in column vector Calculate the position vector Express vectors in column form Apply column vector notation systematically |
Q/A on displacement representation using movement examples
Discussions on vector notation using organized column format Solving column vector problems using systematic methods Demonstrations using physical movement and direction examples Explaining vector components using practical displacement |
Chalk and blackboard, movement demonstration space, exercise books
Chalk and blackboard, origin marking systems, exercise books |
KLB Mathematics Book Three Pg 223-224
|
|
| 3 | 4 |
Vectors (II)
|
Column vectors in terms of unit vectors i, j, k
Vector operations using unit vectors |
By the end of the
lesson, the learner
should be able to:
Express vectors in terms of unit vectors Convert between column and unit vector notation Understand the standard basis vector system Apply unit vector representation systematically |
Q/A on unit vector concepts using direction examples
Discussions on component representation using organized methods Solving unit vector problems using systematic conversion Demonstrations using perpendicular direction examples Explaining basis vector concepts using coordinate axes |
Chalk and blackboard, direction indicators, unit vector reference charts, exercise books
Chalk and blackboard, component calculation aids, exercise books |
KLB Mathematics Book Three Pg 226-228
|
|
| 3 | 5 |
Vectors (II)
|
Magnitude of a vector in three dimensions
Magnitude applications and unit vectors |
By the end of the
lesson, the learner
should be able to:
Calculate the magnitude of a vector in three dimensions Apply the 3D magnitude formula systematically Find vector lengths in spatial contexts Solve magnitude problems accurately |
Q/A on 3D magnitude using extended Pythagorean methods
Discussions on spatial distance calculation using 3D techniques Solving 3D magnitude problems using systematic calculation Demonstrations using 3D distance examples Explaining 3D magnitude using practical spatial examples |
Chalk and blackboard, 3D measurement aids, exercise books
Chalk and blackboard, direction finding aids, exercise books |
KLB Mathematics Book Three Pg 229-230
|
|
| 3 | 6 |
Vectors (II)
|
Parallel vectors
Collinearity Advanced collinearity applications |
By the end of the
lesson, the learner
should be able to:
Identify parallel vectors Determine when vectors are parallel Apply parallel vector properties Use scalar multiples in parallel relationships |
Q/A on parallel identification using scalar multiple methods
Discussions on parallel relationships using geometric examples Solving parallel vector problems using systematic testing Demonstrations using parallel line and direction examples Explaining parallel concepts using geometric reasoning |
Chalk and blackboard, parallel line demonstrations, exercise books
Chalk and blackboard, straight-line demonstrations, exercise books Chalk and blackboard, complex geometric aids, exercise books |
KLB Mathematics Book Three Pg 231-232
|
|
| 3 | 7 |
Vectors (II)
|
Proportional division of a line
External division of a line |
By the end of the
lesson, the learner
should be able to:
Divide a line internally in the given ratio Apply the internal division formula Calculate division points using vector methods Understand proportional division concepts |
Q/A on internal division using systematic formula application
Discussions on ratio division using proportional methods Solving internal division problems using organized approaches Demonstrations using internal point construction examples Explaining internal division using geometric visualization |
Chalk and blackboard, internal division models, exercise books
Chalk and blackboard, external division models, exercise books |
KLB Mathematics Book Three Pg 237-238
|
|
| 4 | 1 |
Vectors (II)
|
Combined internal and external division
Ratio theorem |
By the end of the
lesson, the learner
should be able to:
Divide a line internally and externally in the given ratio Apply both division formulas systematically Compare internal and external division results Handle mixed division problems |
Q/A on combined division using comparative methods
Discussions on division type selection using problem analysis Solving combined division problems using systematic approaches Demonstrations using both division types Explaining division relationships using geometric reasoning |
Chalk and blackboard, combined division models, exercise books
Chalk and blackboard, ratio theorem aids, exercise books |
KLB Mathematics Book Three Pg 239
|
|
| 4 | 2 |
Vectors (II)
|
Advanced ratio theorem applications
Mid-point |
By the end of the
lesson, the learner
should be able to:
Find the position vector Apply ratio theorem to complex scenarios Solve multi-step ratio problems Use ratio theorem in geometric proofs |
Q/A on advanced ratio applications using complex problems
Discussions on multi-step ratio calculation Solving challenging ratio problems using systematic methods Demonstrations using comprehensive ratio examples Explaining advanced applications using detailed reasoning |
Chalk and blackboard, advanced ratio models, exercise books
Chalk and blackboard, midpoint demonstration aids, exercise books |
KLB Mathematics Book Three Pg 242
|
|
| 4 | 3 |
Vectors (II)
|
Ratio theorem and midpoint integration
Advanced ratio theorem applications |
By the end of the
lesson, the learner
should be able to:
Use ratio theorem to find the given vectors Apply midpoint and ratio concepts together Solve complex ratio and midpoint problems Integrate division and midpoint methods |
Q/A on integrated problem-solving using combined methods
Discussions on complex scenario analysis using systematic approaches Solving challenging problems using integrated techniques Demonstrations using comprehensive geometric examples Explaining integration using logical problem-solving |
Chalk and blackboard, complex problem materials, exercise books
Chalk and blackboard, advanced geometric aids, exercise books |
KLB Mathematics Book Three Pg 244-245
|
|
| 4 | 4 |
Vectors (II)
|
Applications of vectors in geometry
Rectangle diagonal applications |
By the end of the
lesson, the learner
should be able to:
Use vectors to show the diagonals of a parallelogram Apply vector methods to geometric proofs Demonstrate parallelogram properties using vectors Solve geometric problems using vector techniques |
Q/A on geometric proof using vector methods
Discussions on parallelogram properties using vector analysis Solving geometric problems using systematic vector techniques Demonstrations using vector-based geometric constructions Explaining geometric relationships using vector reasoning |
Chalk and blackboard, parallelogram models, exercise books
Chalk and blackboard, rectangle models, exercise books |
KLB Mathematics Book Three Pg 248-249
|
|
| 4 | 5 |
Vectors (II)
Circles: Chords and Tangents Circles: Chords and Tangents |
Advanced geometric applications
Length of an arc Length of an arc |
By the end of the
lesson, the learner
should be able to:
Use vectors to show geometric properties Apply vectors to complex geometric proofs Solve challenging geometric problems using vectors Integrate all vector concepts in geometric contexts |
Q/A on comprehensive geometric applications using vector methods
Discussions on advanced proof techniques using vectors Solving complex geometric problems using integrated approaches Demonstrations using sophisticated geometric constructions Explaining advanced applications using comprehensive reasoning |
Chalk and blackboard, advanced geometric models, exercise books
Geometrical set, calculators |
KLB Mathematics Book Three Pg 248-250
|
|
| 4 | 6 |
Circles: Chords and Tangents
|
Chords
Parallel chords |
By the end of the
lesson, the learner
should be able to:
Calculate the length of a chord Apply chord properties and theorems Understand chord-radius relationships |
Q/A on chord definition and properties
Discussions on chord calculation methods Solving basic chord problems Demonstrations of geometric constructions Explaining chord theorems |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 126-128
|
|
| 4 | 7 |
Circles: Chords and Tangents
|
Equal chords
Intersecting chords |
By the end of the
lesson, the learner
should be able to:
Find the length of equal chords Apply equal chord theorems Solve equal chord problems |
Q/A on equal chord properties
Discussions on chord equality conditions Solving equal chord problems Demonstrations of proof techniques Explaining theoretical foundations |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 131-132
|
|
| 5 | 1 |
Circles: Chords and Tangents
|
Intersecting chords
Chord properties |
By the end of the
lesson, the learner
should be able to:
Calculate the length of intersecting chords Solve complex intersection problems Apply advanced chord theorems |
Q/A on advanced intersection scenarios
Discussions on complex chord relationships Solving challenging intersection problems Demonstrations of advanced techniques Explaining sophisticated applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 135-139
|
|
| 5 | 2 |
Circles: Chords and Tangents
|
Tangent to a circle
|
By the end of the
lesson, the learner
should be able to:
Construct a tangent to a circle Understand tangent properties Apply tangent construction methods |
Q/A on tangent definition and properties
Discussions on tangent construction Solving basic tangent problems Demonstrations of construction techniques Explaining tangent characteristics |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 139-140
|
|
| 5 | 3 |
Circles: Chords and Tangents
|
Properties of tangents to a circle from an external point
Tangent properties Tangents to two circles |
By the end of the
lesson, the learner
should be able to:
State the properties of tangents to a circle from an external point Apply external tangent properties Solve external tangent problems |
Q/A on external tangent concepts
Discussions on tangent properties Solving external tangent problems Demonstrations of property applications Explaining theoretical foundations |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 142-144
|
|
| 5 | 4 |
Circles: Chords and Tangents
|
Tangents to two circles
Contact of circles |
By the end of the
lesson, the learner
should be able to:
Calculate the tangents of transverse common tangents Find transverse tangent properties Compare direct and transverse tangents |
Q/A on transverse tangent concepts
Discussions on tangent type differences Solving transverse tangent problems Demonstrations of comparison methods Explaining tangent classifications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 150-151
|
|
| 5 | 5 |
Circles: Chords and Tangents
|
Contact of circles
Circle contact |
By the end of the
lesson, the learner
should be able to:
Calculate the radii of contact circles Understand external contact properties Compare internal and external contact |
Q/A on external contact concepts
Discussions on contact type differences Solving external contact problems Demonstrations of contact analysis Explaining contact applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 153-154
|
|
| 5 | 6 |
Circles: Chords and Tangents
|
Angle in alternate segment
|
By the end of the
lesson, the learner
should be able to:
Calculate the angles in alternate segments Apply alternate segment theorem Understand segment angle properties |
Q/A on alternate segment concepts
Discussions on segment angle relationships Solving basic segment problems Demonstrations of theorem application Explaining geometric proofs |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 157-160
|
|
| 5 | 7 |
Circles: Chords and Tangents
|
Circumscribed circle
Escribed circles |
By the end of the
lesson, the learner
should be able to:
Construct circumscribed circles Find circumscribed circle properties Apply circumscription concepts |
Q/A on circumscription concepts
Discussions on circumscribed circle construction Solving circumscription problems Demonstrations of construction techniques Explaining circumscription applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 165
|
|
| 6 | 1 |
Circles: Chords and Tangents
|
Centroid
Orthocenter |
By the end of the
lesson, the learner
should be able to:
Construct centroid Find centroid properties Apply centroid concepts |
Q/A on centroid definition and properties
Discussions on centroid construction Solving centroid problems Demonstrations of construction techniques Explaining centroid applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 166
|
|
| 6 | 2 |
Circles: Chords and Tangents
Graphical Methods Graphical Methods |
Circle and triangle relationships
Tables of given relations Graphs of given relations |
By the end of the
lesson, the learner
should be able to:
Solve comprehensive circle-triangle problems Integrate all circle and triangle concepts Apply advanced geometric relationships |
Q/A on comprehensive geometric understanding
Discussions on integrated relationships Solving complex geometric problems Demonstrations of advanced applications Explaining sophisticated geometric principles |
Geometrical set, calculators
Chalk and blackboard, ruled paper for tables, exercise books Chalk and blackboard, graph paper or grids, rulers, exercise books |
KLB Mathematics Book Three Pg 164-167
|
|
| 6 | 3 |
Graphical Methods
|
Tables and graphs integration
Introduction to cubic equations |
By the end of the
lesson, the learner
should be able to:
Draw tables and graphs of given relations Integrate table construction with graph plotting Analyze relationships using both methods Compare tabular and graphical representations |
Q/A on integrated table-graph construction using comprehensive methods
Discussions on data flow from tables to graphs Solving integrated problems using systematic approaches Demonstrations using complete data analysis procedures Explaining relationship analysis using combined methods |
Chalk and blackboard, graph paper, data examples, exercise books
Chalk and blackboard, cubic function examples, exercise books |
KLB Mathematics Book Three Pg 299-300
|
|
| 6 | 4 |
Graphical Methods
|
Graphical solution of cubic equations
Advanced cubic solutions |
By the end of the
lesson, the learner
should be able to:
Draw graphs of cubic equations Plot cubic curves accurately Use graphs to solve cubic equations Find roots using graphical methods |
Q/A on cubic curve plotting using systematic point plotting
Discussions on curve characteristics and root finding Solving cubic graphing problems using careful plotting Demonstrations using cubic curve construction Explaining root identification using graph analysis |
Chalk and blackboard, graph paper, cubic equation examples, exercise books
Chalk and blackboard, advanced graph examples, exercise books |
KLB Mathematics Book Three Pg 302-304
|
|
| 6 | 5 |
Graphical Methods
|
Introduction to rates of change
Average rates of change |
By the end of the
lesson, the learner
should be able to:
Calculate the average rates of change Understand rate of change concepts Apply rate calculations to practical problems Interpret rate meanings in context |
Q/A on rate calculation using slope methods
Discussions on rate interpretation using practical examples Solving basic rate problems using systematic calculation Demonstrations using speed-time and distance examples Explaining rate concepts using practical analogies |
Chalk and blackboard, rate calculation examples, exercise books
Chalk and blackboard, graph paper, rate examples, exercise books |
KLB Mathematics Book Three Pg 304-306
|
|
| 6 | 6 |
Graphical Methods
|
Advanced average rates
Introduction to instantaneous rates |
By the end of the
lesson, the learner
should be able to:
Calculate the average rates of change Handle complex rate scenarios Apply rates to business and scientific problems Integrate rate concepts with other topics |
Q/A on complex rate applications using advanced scenarios
Discussions on business and scientific rate applications Solving challenging rate problems using integrated methods Demonstrations using comprehensive rate examples Explaining advanced applications using detailed analysis |
Chalk and blackboard, advanced rate scenarios, exercise books
Chalk and blackboard, tangent line examples, exercise books |
KLB Mathematics Book Three Pg 304-310
|
|
| 6 | 7 |
Graphical Methods
|
Rate of change at an instant
Advanced instantaneous rates Empirical graphs Advanced empirical methods |
By the end of the
lesson, the learner
should be able to:
Calculate the rate of change at an instant Apply instantaneous rate methods systematically Use graphical techniques for instant rates Solve practical instantaneous rate problems |
Q/A on instantaneous rate calculation using graphical methods
Discussions on tangent line slope interpretation Solving instantaneous rate problems using systematic approaches Demonstrations using detailed tangent constructions Explaining practical applications using real scenarios |
Chalk and blackboard, detailed graph examples, exercise books
Chalk and blackboard, advanced rate examples, exercise books Chalk and blackboard, experimental data examples, exercise books Chalk and blackboard, complex data examples, exercise books |
KLB Mathematics Book Three Pg 310-311
|
|
| 7 |
FORM 3 KIRINYAGA WEST JOINT EXAMINATIONS |
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| 8 |
FORM 3 KIRINYAGA WEST JOINT EXAMINATIONS |
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| 9 |
FORM 3 KIRINYAGA WEST JOINT EXAMINATIONS AND CLOSING OF THE SCHOOL |
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