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| WK | LSN | TOPIC | SUB-TOPIC | OBJECTIVES | T/L ACTIVITIES | T/L AIDS | REFERENCE | REMARKS |
|---|---|---|---|---|---|---|---|---|
| 2 | 1 |
Sequences and Series
|
Introduction to sequences and finding terms
General term of sequences and applications |
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
Chalk and blackboard, numbered cards made from paper, exercise books |
KLB Mathematics Book Three Pg 207-208
|
|
| 2 | 2 |
Sequences and Series
|
Arithmetic sequences and nth term
Arithmetic sequence applications |
By the end of the
lesson, the learner
should be able to:
Define arithmetic sequences and common differences Calculate common differences correctly Derive and apply the nth term formula Solve problems using arithmetic sequence concepts |
Q/A on arithmetic patterns using step-by-step examples
Discussions on constant difference patterns and formula derivation Solving arithmetic sequence problems systematically Demonstrations using equal-step progressions Explaining formula structure using algebraic reasoning |
Chalk and blackboard, measuring tape or string, exercise books
Chalk and blackboard, local employment/savings examples, exercise books |
KLB Mathematics Book Three Pg 209-210
|
|
| 2 | 3 |
Sequences and Series
|
Geometric sequences and nth term
Geometric sequence applications |
By the end of the
lesson, the learner
should be able to:
Define geometric sequences and common ratios Calculate common ratios correctly Derive and apply the geometric nth term formula Understand exponential growth patterns |
Q/A on geometric patterns using multiplication examples
Discussions on ratio-based progressions and formula derivation Solving geometric sequence problems systematically Demonstrations using doubling and scaling examples Explaining exponential structure using practical examples |
Chalk and blackboard, objects for doubling demonstrations, exercise books
Chalk and blackboard, population/growth data examples, exercise books |
KLB Mathematics Book Three Pg 211-213
|
|
| 2 | 4 |
Sequences and Series
|
Arithmetic series and sum formula
Geometric series and applications |
By the end of the
lesson, the learner
should be able to:
Define arithmetic series as sums of sequences Derive the sum formula for arithmetic series Apply the arithmetic series formula systematically Calculate sums efficiently using the formula |
Q/A on series concepts using summation examples
Discussions on sequence-to-series relationships and formula derivation Solving arithmetic series problems using step-by-step approach Demonstrations using cumulative sum examples Explaining derivation logic using algebraic reasoning |
Chalk and blackboard, counting materials for summation, exercise books
Chalk and blackboard, convergence demonstration materials, exercise books |
KLB Mathematics Book Three Pg 214-215
|
|
| 2 | 5 |
Sequences and Series
|
Mixed problems and advanced applications
|
By the end of the
lesson, the learner
should be able to:
Combine arithmetic and geometric concepts Solve complex mixed sequence and series problems Apply appropriate methods for different types Model real-world situations using mathematical sequences |
Q/A on problem type identification using systematic analysis
Discussions on method selection and comprehensive applications Solving mixed problems using appropriate techniques Demonstrations using interdisciplinary scenarios Explaining method choice using logical reasoning |
Chalk and blackboard, mixed problem collections, exercise books
|
KLB Mathematics Book Three Pg 207-219
|
|
| 2 | 6 |
Sequences and Series
Vectors (II) |
Sequences in nature and technology
Coordinates in two dimensions |
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, squared paper or grid drawn on ground, exercise books |
KLB Mathematics Book Three Pg 207-219
|
|
| 2 | 7 |
Vectors (II)
|
Coordinates in three dimensions
Column and position vectors in three dimensions |
By the end of the
lesson, the learner
should be able to:
Identify the coordinates of a point in three dimensions Understand the three-dimensional coordinate system Plot points in 3D space systematically Apply 3D coordinates to spatial problems |
Q/A on 3D coordinate understanding using room corner references
Discussions on height, length, and width measurements Solving 3D coordinate problems using systematic approaches Demonstrations using classroom corners and building structures Explaining 3D visualization using physical room examples |
Chalk and blackboard, 3D models made from sticks and clay, exercise books
Chalk and blackboard, movement demonstration space, exercise books |
KLB Mathematics Book Three Pg 222
|
|
| 3 | 1 |
Vectors (II)
|
Position vectors and applications
Column vectors in terms of unit vectors i, j, k |
By the end of the
lesson, the learner
should be able to:
Calculate the position vector Apply position vectors to geometric problems Find distances using position vector methods Solve positioning problems systematically |
Q/A on position vector calculation using origin references
Discussions on position determination using coordinate methods Solving position vector problems using systematic calculation Demonstrations using fixed origin and variable endpoints Explaining position concepts using practical location examples |
Chalk and blackboard, origin marking systems, exercise books
Chalk and blackboard, direction indicators, unit vector reference charts, exercise books |
KLB Mathematics Book Three Pg 224
|
|
| 3 | 2 |
Vectors (II)
|
Vector operations using unit vectors
Magnitude of a vector in three dimensions |
By the end of the
lesson, the learner
should be able to:
Express vectors in terms of unit vectors Perform vector addition using unit vector notation Calculate vector subtraction with i, j, k components Apply scalar multiplication to unit vectors |
Q/A on vector operations using component-wise calculation
Discussions on systematic operation methods Solving vector operation problems using organized approaches Demonstrations using component separation and combination Explaining operation logic using algebraic reasoning |
Chalk and blackboard, component calculation aids, exercise books
Chalk and blackboard, 3D measurement aids, exercise books |
KLB Mathematics Book Three Pg 226-228
|
|
| 3 | 3 |
Vectors (II)
|
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 Find unit vectors from given vectors Apply magnitude concepts to practical problems Use magnitude in vector normalization |
Q/A on magnitude and unit vector relationships
Discussions on normalization and direction finding Solving magnitude and unit vector problems Demonstrations using direction and length separation Explaining practical applications using navigation examples |
Chalk and blackboard, direction finding aids, exercise books
|
KLB Mathematics Book Three Pg 229-230
|
|
| 3 | 4 |
Vectors (II)
|
Parallel vectors
Collinearity |
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 |
KLB Mathematics Book Three Pg 231-232
|
|
| 3 | 5 |
Vectors (II)
|
Advanced collinearity applications
Proportional division of a line |
By the end of the
lesson, the learner
should be able to:
Show that points are collinear Apply collinearity to complex geometric problems Integrate parallel and collinearity concepts Solve advanced alignment problems |
Q/A on advanced collinearity using complex scenarios
Discussions on geometric proof using vector methods Solving challenging collinearity problems Demonstrations using complex geometric constructions Explaining advanced applications using comprehensive examples |
Chalk and blackboard, complex geometric aids, exercise books
Chalk and blackboard, internal division models, exercise books |
KLB Mathematics Book Three Pg 232-234
|
|
| 3 | 6 |
Vectors (II)
|
External division of a line
Combined internal and external division |
By the end of the
lesson, the learner
should be able to:
Divide a line externally in the given ratio Apply the external division formula Distinguish between internal and external division Solve external division problems accurately |
Q/A on external division using systematic formula application
Discussions on external point calculation using vector methods Solving external division problems using careful approaches Demonstrations using external point construction examples Explaining external division using extended line concepts |
Chalk and blackboard, external division models, exercise books
Chalk and blackboard, combined division models, exercise books |
KLB Mathematics Book Three Pg 238-239
|
|
| 3 | 7 |
Vectors (II)
|
Ratio theorem
Advanced ratio theorem applications |
By the end of the
lesson, the learner
should be able to:
Express position vectors Apply the ratio theorem to geometric problems Use ratio theorem in complex calculations Find position vectors using ratio relationships |
Q/A on ratio theorem application using systematic methods
Discussions on position vector calculation using ratio methods Solving ratio theorem problems using organized approaches Demonstrations using ratio-based position finding Explaining theorem applications using logical reasoning |
Chalk and blackboard, ratio theorem aids, exercise books
Chalk and blackboard, advanced ratio models, exercise books |
KLB Mathematics Book Three Pg 240-242
|
|
| 4 | 1 |
Vectors (II)
|
Mid-point
Ratio theorem and midpoint integration |
By the end of the
lesson, the learner
should be able to:
Find the mid-points of the given vectors Apply midpoint formulas in vector contexts Use midpoint concepts in geometric problems Calculate midpoints systematically |
Q/A on midpoint calculation using vector averaging methods
Discussions on midpoint applications using geometric examples Solving midpoint problems using systematic approaches Demonstrations using midpoint construction and calculation Explaining midpoint concepts using practical examples |
Chalk and blackboard, midpoint demonstration aids, exercise books
Chalk and blackboard, complex problem materials, exercise books |
KLB Mathematics Book Three Pg 243
|
|
| 4 | 2 |
Vectors (II)
|
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 ratio theorem to challenging problems Handle complex geometric applications Demonstrate comprehensive ratio mastery |
Q/A on comprehensive ratio understanding using advanced problems
Discussions on complex ratio relationships Solving advanced ratio problems using systematic methods Demonstrations using sophisticated geometric constructions Explaining mastery using challenging applications |
Chalk and blackboard, advanced geometric aids, exercise books
|
KLB Mathematics Book Three Pg 246-248
|
|
| 4 | 3 |
Vectors (II)
Binomial Expansion |
Applications of vectors in geometry
Binomial expansions up to power four |
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, rectangular cutouts from paper, exercise books |
KLB Mathematics Book Three Pg 248-249
|
|
| 4 | 4 |
Binomial Expansion
|
Binomial expansions up to power four (continued)
Pascal's triangle |
By the end of the
lesson, the learner
should be able to:
Expand binomial function up to power four Handle increasingly complex coefficient patterns Apply systematic expansion techniques efficiently Verify expansions using substitution methods |
Q/A on power expansion using multiplication techniques
Discussions on coefficient identification using pattern analysis Solving expansion problems using systematic approaches Demonstrations using geometric representations Explaining verification methods using numerical substitution |
Chalk and blackboard, squared paper for geometric models, exercise books
Chalk and blackboard, triangular patterns drawn/cut from paper, exercise books |
KLB Mathematics Book Three Pg 256
|
|
| 4 | 5 |
Binomial Expansion
|
Pascal's triangle applications
Pascal's triangle (continued) |
By the end of the
lesson, the learner
should be able to:
Use Pascal's triangle Apply Pascal's triangle to binomial expansions efficiently Use triangle coefficients for various powers Solve expansion problems using triangle methods |
Q/A on triangle application using coefficient identification
Discussions on efficient expansion using triangle methods Solving expansion problems using Pascal's triangle Demonstrations using triangle-guided calculations Explaining efficiency benefits using comparative methods |
Chalk and blackboard, Pascal's triangle reference charts, exercise books
Chalk and blackboard, advanced triangle patterns, exercise books |
KLB Mathematics Book Three Pg 257-258
|
|
| 4 | 6 |
Binomial Expansion
|
Pascal's triangle advanced
Applications to numerical cases |
By the end of the
lesson, the learner
should be able to:
Use Pascal's triangle Apply general binomial theorem concepts Understand combination notation in expansions Use general term formula applications |
Q/A on general formula understanding using pattern analysis
Discussions on combination notation using counting principles Solving general term problems using formula application Demonstrations using systematic formula usage Explaining general principles using algebraic reasoning |
Chalk and blackboard, combination calculation aids, exercise books
Chalk and blackboard, simple calculation aids, exercise books |
KLB Mathematics Book Three Pg 258-259
|
|
| 4 | 7 |
Binomial Expansion
|
Applications to numerical cases (continued)
|
By the end of the
lesson, the learner
should be able to:
Use binomial expansion to solve numerical problems Apply binomial methods to complex calculations Handle decimal approximations using expansions Solve practical numerical problems |
Q/A on advanced numerical applications using complex scenarios
Discussions on decimal approximation using expansion techniques Solving challenging numerical problems using systematic methods Demonstrations using detailed calculation procedures Explaining practical relevance using real-world examples |
Chalk and blackboard, advanced calculation examples, exercise books
|
KLB Mathematics Book Three Pg 259-260
|
|
| 5 | 1 |
Probability
|
Introduction
Experimental Probability |
By the end of the
lesson, the learner
should be able to:
Calculate the experimental probability Understand probability concepts in daily life Distinguish between certain and uncertain events Recognize probability situations |
Q/A on uncertain events from daily life experiences
Discussions on weather prediction and game outcomes Analyzing chance events using coin tossing and dice rolling Demonstrations using simple probability experiments Explaining probability language using familiar examples |
Chalk and blackboard, coins, dice made from cardboard, exercise books
Chalk and blackboard, coins, cardboard dice, tally charts, exercise books |
KLB Mathematics Book Three Pg 262-264
|
|
| 5 | 2 |
Probability
|
Experimental Probability applications
Range of Probability Measure |
By the end of the
lesson, the learner
should be able to:
Calculate the experimental probability Apply experimental methods to various scenarios Handle large sample experiments Analyze experimental probability patterns |
Q/A on advanced experimental techniques using extended trials
Discussions on sample size effects using comparative data Solving complex experimental problems using systematic methods Demonstrations using extended experimental procedures Explaining pattern analysis using accumulated data |
Chalk and blackboard, extended experimental materials, data recording sheets, exercise books
Chalk and blackboard, number line drawings, probability scale charts, exercise books |
KLB Mathematics Book Three Pg 262-264
|
|
| 5 | 3 |
Probability
|
Probability Space
Theoretical Probability |
By the end of the
lesson, the learner
should be able to:
Calculate the probability space for the theoretical probability Define sample space systematically List all possible outcomes Apply sample space concepts |
Q/A on outcome listing using systematic enumeration
Discussions on complete outcome identification Solving sample space problems using organized listing Demonstrations using dice, cards, and spinner examples Explaining probability calculation using outcome counting |
Chalk and blackboard, playing cards (locally made), spinners from cardboard, exercise books
Chalk and blackboard, fair dice and coins, probability calculation aids, exercise books |
KLB Mathematics Book Three Pg 266-267
|
|
| 5 | 4 |
Probability
|
Theoretical Probability advanced
Theoretical Probability applications |
By the end of the
lesson, the learner
should be able to:
Calculate the probability space for the theoretical probability Apply theoretical probability to complex problems Handle multiple outcome scenarios Solve advanced theoretical problems |
Q/A on advanced theoretical applications using complex scenarios
Discussions on multiple outcome analysis using systematic methods Solving challenging theoretical problems using organized approaches Demonstrations using complex probability setups Explaining advanced theoretical concepts using detailed reasoning |
Chalk and blackboard, complex probability materials, advanced calculation aids, exercise books
Chalk and blackboard, local game examples, practical scenario materials, exercise books |
KLB Mathematics Book Three Pg 268-270
|
|
| 5 | 5 |
Probability
|
Combined Events
|
By the end of the
lesson, the learner
should be able to:
Find the probability of a combined events Understand compound events and combinations Distinguish between different event types Apply basic combination rules |
Q/A on event combination using practical examples
Discussions on exclusive and inclusive event identification Solving basic combined event problems using visual methods Demonstrations using card drawing and dice rolling combinations Explaining combination principles using Venn diagrams |
Chalk and blackboard, playing cards, multiple dice, Venn diagram drawings, exercise books
|
KLB Mathematics Book Three Pg 272-273
|
|
| 5 | 6 |
Probability
|
Combined Events OR probability
Independent Events |
By the end of the
lesson, the learner
should be able to:
Find the probability of a combined events Apply addition rule for OR events Calculate "A or B" probabilities Handle mutually exclusive events |
Q/A on addition rule application using systematic methods
Discussions on mutually exclusive identification and calculation Solving OR probability problems using organized approaches Demonstrations using card selection and event combination Explaining addition rule logic using Venn diagrams |
Chalk and blackboard, Venn diagram materials, card examples, exercise books
Chalk and blackboard, multiple coins and dice, independence demonstration materials, exercise books |
KLB Mathematics Book Three Pg 272-274
|
|
| 5 | 7 |
Probability
|
Independent Events advanced
Independent Events applications |
By the end of the
lesson, the learner
should be able to:
Find the probability of independent events Distinguish between independent and dependent events Apply conditional probability concepts Handle complex independence scenarios |
Q/A on independence verification using mathematical methods
Discussions on dependence concepts using card drawing examples Solving dependent and independent event problems using systematic approaches Demonstrations using replacement and non-replacement scenarios Explaining conditional probability using practical examples |
Chalk and blackboard, playing cards for replacement scenarios, multiple experimental setups, exercise books
Chalk and blackboard, complex experimental materials, advanced calculation aids, exercise books |
KLB Mathematics Book Three Pg 276-278
|
|
| 6 | 1 |
Probability
|
Tree Diagrams
Tree Diagrams advanced |
By the end of the
lesson, the learner
should be able to:
Draw tree diagrams to show the probability space Construct tree diagrams systematically Represent sequential events using trees Apply tree diagram methods |
Q/A on tree construction using step-by-step methods
Discussions on sequential event representation Solving basic tree diagram problems using systematic drawing Demonstrations using branching examples and visual organization Explaining tree structure using logical branching principles |
Chalk and blackboard, tree diagram templates, branching materials, exercise books
Chalk and blackboard, complex tree examples, detailed calculation aids, exercise books |
KLB Mathematics Book Three Pg 282
|
|
| 6 | 2 |
Compound Proportion and Rates of Work
|
Compound Proportions
Compound Proportions applications |
By the end of the
lesson, the learner
should be able to:
Find the compound proportions Understand compound proportion relationships Apply compound proportion methods systematically Solve problems involving multiple variables |
Q/A on compound relationships using practical examples
Discussions on multiple variable situations using local scenarios Solving compound proportion problems using systematic methods Demonstrations using business and trade examples Explaining compound proportion logic using step-by-step reasoning |
Chalk and blackboard, local business examples, calculators if available, exercise books
Chalk and blackboard, construction/farming examples, exercise books |
KLB Mathematics Book Three Pg 288-290
|
|
| 6 | 3 |
Compound Proportion and Rates of Work
|
Proportional Parts
|
By the end of the
lesson, the learner
should be able to:
Calculate the proportional parts Understand proportional division concepts Apply proportional parts to sharing problems Solve distribution problems using proportional methods |
Q/A on proportional sharing using practical examples
Discussions on fair distribution using ratio concepts Solving proportional parts problems using systematic division Demonstrations using sharing scenarios and inheritance examples Explaining proportional distribution using logical reasoning |
Chalk and blackboard, sharing demonstration materials, exercise books
|
KLB Mathematics Book Three Pg 291-293
|
|
| 6 | 4 |
Compound Proportion and Rates of Work
|
Proportional Parts applications
Rates of Work |
By the end of the
lesson, the learner
should be able to:
Calculate the proportional parts Apply proportional parts to complex sharing scenarios Handle business partnership profit sharing Solve advanced proportional distribution problems |
Q/A on complex proportional sharing using business examples
Discussions on partnership profit distribution using practical scenarios Solving advanced proportional problems using systematic methods Demonstrations using business partnership and investment examples Explaining practical applications using meaningful contexts |
Chalk and blackboard, business partnership examples, exercise books
Chalk and blackboard, work scenario examples, exercise books |
KLB Mathematics Book Three Pg 291-293
|
|
| 6 | 5 |
Compound Proportion and Rates of Work
Graphical Methods |
Rates of Work and Mixtures
Tables of given relations |
By the end of the
lesson, the learner
should be able to:
Calculate the rate of work Apply work rates to complex scenarios Handle mixture problems and combinations Solve advanced rate and mixture problems |
Q/A on advanced work rates using complex scenarios
Discussions on mixture problems using practical examples Solving challenging rate and mixture problems using systematic approaches Demonstrations using cooking, construction, and manufacturing examples Explaining mixture concepts using practical applications |
Chalk and blackboard, mixture demonstration materials, exercise books
Chalk and blackboard, ruled paper for tables, exercise books |
KLB Mathematics Book Three Pg 295-296
|
|
| 6 | 6 |
Graphical Methods
|
Graphs of given relations
Tables and graphs integration |
By the end of the
lesson, the learner
should be able to:
Draw graphs of given relations Plot points accurately on coordinate systems Connect points to show relationships Interpret graphs from given data |
Q/A on graph plotting using coordinate methods
Discussions on point plotting and curve drawing Solving graph construction problems using systematic plotting Demonstrations using coordinate systems and curve sketching Explaining graph interpretation using visual analysis |
Chalk and blackboard, graph paper or grids, rulers, exercise books
Chalk and blackboard, graph paper, data examples, exercise books |
KLB Mathematics Book Three Pg 300
|
|
| 6 | 7 |
Graphical Methods
|
Introduction to cubic equations
Graphical solution of cubic equations |
By the end of the
lesson, the learner
should be able to:
Draw tables of cubic functions Understand cubic equation characteristics Prepare cubic function data systematically Recognize cubic curve patterns |
Q/A on cubic function evaluation using systematic calculation
Discussions on cubic equation properties using mathematical analysis Solving cubic table preparation using organized methods Demonstrations using cubic function examples Explaining cubic characteristics using pattern recognition |
Chalk and blackboard, cubic function examples, exercise books
Chalk and blackboard, graph paper, cubic equation examples, exercise books |
KLB Mathematics Book Three Pg 301
|
|
| 7 | 1 |
Graphical Methods
|
Advanced cubic solutions
|
By the end of the
lesson, the learner
should be able to:
Draw graphs of cubic equations Apply graphical methods to complex cubic problems Handle multiple root scenarios Verify solutions using graphical analysis |
Q/A on advanced cubic graphing using complex examples
Discussions on multiple root identification using graph analysis Solving challenging cubic problems using systematic methods Demonstrations using detailed cubic constructions Explaining verification methods using graphical checking |
Chalk and blackboard, advanced graph examples, exercise books
|
KLB Mathematics Book Three Pg 302-304
|
|
| 7 | 2 |
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
|
|
| 7 | 3 |
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
|
|
| 7 | 4 |
Graphical Methods
|
Rate of change at an instant
Advanced instantaneous rates |
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 |
KLB Mathematics Book Three Pg 310-311
|
|
| 7 | 5 |
Graphical Methods
|
Empirical graphs
Advanced empirical methods |
By the end of the
lesson, the learner
should be able to:
Draw the empirical graphs Understand empirical data representation Plot experimental data systematically Analyze empirical relationships |
Q/A on empirical data plotting using experimental examples
Discussions on real data representation using practical scenarios Solving empirical graphing problems using systematic methods Demonstrations using experimental data examples Explaining empirical analysis using practical interpretations |
Chalk and blackboard, experimental data examples, exercise books
Chalk and blackboard, complex data examples, exercise books |
KLB Mathematics Book Three Pg 315-316
|
|
| 7 | 6 |
Matrices and Transformation
|
Matrices of Transformation
Identifying Common Transformation Matrices Finding the Matrix of a Transformation |
By the end of the
lesson, the learner
should be able to:
-Define transformation and identify types -Recognize that matrices can represent transformations -Apply 2×2 matrices to position vectors -Relate matrix operations to geometric transformations |
-Review transformation concepts from Form 2 -Demonstrate matrix multiplication using position vectors -Plot objects and images on coordinate plane -Practice identifying transformations from images |
Exercise books
-Manila paper -Ruler -Pencils -String -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 1-5
|
|
| 7 | 7 |
Matrices and Transformation
|
Using the Unit Square Method
Successive Transformations Matrix Multiplication for Combined Transformations Single Matrix for Successive Transformations |
By the end of the
lesson, the learner
should be able to:
-Use unit square to find transformation matrices -Read matrix elements directly from unit square images -Apply unit square method to various transformations -Compare unit square method with algebraic method |
-Demonstrate unit square method systematically -Practice reading transformation matrices from diagrams -Apply method to reflections, rotations, enlargements -Compare efficiency of different methods |
Exercise books
-Manila paper -Ruler -String -Coloured pencils -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 6-16
|
|
| 8 |
Mid term |
|||||||
| 9 | 1 |
Matrices and Transformation
|
Inverse of a Transformation
Properties of Inverse Transformations Area Scale Factor and Determinant |
By the end of the
lesson, the learner
should be able to:
-Define inverse transformation conceptually -Find inverse matrices using algebraic methods -Apply inverse transformations to return objects to original position -Verify inverse relationships using matrix multiplication |
-Demonstrate inverse transformations geometrically -Practice finding inverse matrices algebraically -Verify that A × A⁻¹ = I -Apply inverse transformations to solve problems |
Exercise books
-Manila paper -Ruler -Chalk/markers det A |
KLB Secondary Mathematics Form 4, Pages 24-26
|
|
| 9 | 2 |
Matrices and Transformation
|
Shear Transformations
|
By the end of the
lesson, the learner
should be able to:
-Define shear transformation and its properties -Identify invariant lines in shear transformations -Construct matrices for shear transformations -Apply shear transformations to geometric objects |
-Demonstrate shear using cardboard models -Identify x-axis and y-axis invariant shears -Practice constructing shear matrices -Apply shears to triangles and rectangles |
Exercise books
-Cardboard pieces -Manila paper -Ruler |
KLB Secondary Mathematics Form 4, Pages 28-34
|
|
| 9 | 3 |
Matrices and Transformation
|
Stretch Transformations
Combined Shear and Stretch Problems |
By the end of the
lesson, the learner
should be able to:
-Define stretch transformation and scale factors -Distinguish between one-way and two-way stretches -Construct matrices for stretch transformations -Apply stretch transformations to solve problems |
-Demonstrate stretch using rubber bands and paper -Practice with x-axis and y-axis invariant stretches -Construct stretch matrices systematically -Compare stretches with enlargements |
Exercise books
-Rubber bands -Manila paper -Ruler -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 28-34
|
|
| 9 | 4 |
Matrices and Transformation
Statistics II |
Isometric and Non-isometric Transformations
Introduction to Advanced Statistics |
By the end of the
lesson, the learner
should be able to:
-Distinguish between isometric and non-isometric transformations -Classify transformations based on shape and size preservation -Identify isometric transformations from matrices -Apply classification to solve problems |
-Compare congruent and non-congruent images using cutouts -Classify transformations systematically -Practice identification from matrices -Discuss real-world applications of each type |
Exercise books
-Paper cutouts -Manila paper -Ruler -Real data examples -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 35-38
|
|
| 9 | 5 |
Statistics II
|
Working Mean Concept
Mean Using Working Mean - Simple Data |
By the end of the
lesson, the learner
should be able to:
-Define working mean (assumed mean) -Explain why working mean simplifies calculations -Identify appropriate working mean values -Apply working mean to reduce calculation errors |
-Demonstrate calculation difficulties with large numbers -Show how working mean simplifies arithmetic -Practice selecting suitable working means -Compare results with and without working mean |
Exercise books
-Manila paper -Sample datasets -Chalk/markers -Student data |
KLB Secondary Mathematics Form 4, Pages 39-42
|
|
| 9 | 6 |
Statistics II
|
Mean Using Working Mean - Frequency Tables
Mean for Grouped Data Using Working Mean |
By the end of the
lesson, the learner
should be able to:
-Calculate mean using working mean for frequency data -Apply working mean to discrete frequency distributions -Use the formula with frequencies correctly -Solve real-world problems with frequency data |
-Demonstrate with family size data from local community -Practice calculating fx and fd systematically -Work through examples step-by-step -Students practice with their own collected data |
Exercise books
-Manila paper -Community data -Chalk/markers -Real datasets |
KLB Secondary Mathematics Form 4, Pages 42-48
|
|
| 9 | 7 |
Statistics II
|
Advanced Working Mean Techniques
|
By the end of the
lesson, the learner
should be able to:
-Apply coding techniques with working mean -Divide by class width to simplify further -Use transformation methods efficiently -Solve complex grouped data problems |
-Demonstrate coding method on chalkboard -Show how dividing by class width helps -Practice reverse calculations to get original mean -Work with economic data from Kenya |
Exercise books
-Manila paper -Economic data -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 42-48
|
|
| 10 | 1 |
Statistics II
|
Introduction to Quartiles, Deciles, Percentiles
Calculating Quartiles for Ungrouped Data |
By the end of the
lesson, the learner
should be able to:
-Define quartiles, deciles, and percentiles -Understand how they divide data into parts -Explain the relationship between these measures -Identify their importance in data analysis |
-Use physical demonstration with student heights -Arrange 20 students by height to show quartiles -Explain percentile ranks in exam results -Discuss applications in grading systems |
Exercise books
-Manila paper -Student height data -Measuring tape -Test score data -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 49-52
|
|
| 10 | 2 |
Statistics II
|
Quartiles for Grouped Data
Deciles and Percentiles Calculations |
By the end of the
lesson, the learner
should be able to:
-Calculate quartiles using interpolation formula -Identify quartile classes correctly -Apply the formula: Q = L + [(n/4 - CF)/f] × h -Solve problems with continuous grouped data |
-Work through detailed examples on chalkboard -Practice identifying quartile positions -Use cumulative frequency systematically -Apply to real examination grade data |
Exercise books
-Manila paper -Grade data -Chalk/markers -Performance data |
KLB Secondary Mathematics Form 4, Pages 49-52
|
|
| 10 | 3 |
Statistics II
|
Introduction to Cumulative Frequency
Drawing Cumulative Frequency Curves (Ogives) |
By the end of the
lesson, the learner
should be able to:
-Construct cumulative frequency tables -Understand "less than" cumulative frequencies -Plot cumulative frequency against class boundaries -Identify the characteristic S-shape of ogives |
-Create cumulative frequency table with class data -Plot points on manila paper grid -Join points to form smooth curve -Discuss properties of ogive curves |
Exercise books
-Manila paper -Ruler -Class data -Pencils |
KLB Secondary Mathematics Form 4, Pages 52-60
|
|
| 10 | 4 |
Statistics II
|
Reading Values from Ogives
Applications of Ogives |
By the end of the
lesson, the learner
should be able to:
-Read median from cumulative frequency curve -Find quartiles using ogive -Estimate any percentile from the curve -Interpret readings in real-world context |
-Demonstrate reading techniques on large ogive -Practice finding median position (n/2) -Read quartile positions systematically -Students practice reading their own curves |
Exercise books
-Manila paper -Completed ogives -Ruler -Real problem datasets |
KLB Secondary Mathematics Form 4, Pages 52-60
|
|
| 10 | 5 |
Statistics II
|
Introduction to Measures of Dispersion
|
By the end of the
lesson, the learner
should be able to:
-Define dispersion and its importance -Understand limitations of central tendency alone -Compare datasets with same mean but different spread -Identify different measures of dispersion |
-Compare test scores of two classes with same mean -Show how different spreads affect interpretation -Discuss variability in real-world data -Introduce range as simplest measure |
Exercise books
-Manila paper -Comparative datasets -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 60-65
|
|
| 10 | 6 |
Statistics II
|
Range and Interquartile Range
Mean Absolute Deviation |
By the end of the
lesson, the learner
should be able to:
-Calculate range for different datasets -Find interquartile range (Q3 - Q1) -Calculate quartile deviation (semi-interquartile range) -Compare advantages and limitations of each measure |
-Calculate range for student heights in class -Find IQR for the same data -Discuss effect of outliers on range -Compare IQR stability with range |
Exercise books
-Manila paper -Student data -Measuring tape -Test score data -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 60-65
|
|
| 10 | 7 |
Statistics II
|
Introduction to Variance
Variance Using Alternative Formula |
By the end of the
lesson, the learner
should be able to:
-Define variance as mean of squared deviations -Calculate variance using definition formula -Understand why deviations are squared -Compare variance with other dispersion measures |
-Work through variance calculation step by step -Explain squaring deviations eliminates negatives -Calculate variance for simple datasets -Compare with mean absolute deviation |
Exercise books
-Manila paper -Simple datasets -Chalk/markers -Frequency data |
KLB Secondary Mathematics Form 4, Pages 65-70
|
|
| 11 | 1 |
Statistics II
|
Standard Deviation Calculations
Standard Deviation for Grouped Data |
By the end of the
lesson, the learner
should be able to:
-Calculate standard deviation as square root of variance -Apply standard deviation to ungrouped data -Use standard deviation to compare datasets -Interpret standard deviation in practical contexts |
-Calculate SD for student exam scores -Compare SD values for different subjects -Interpret what high/low SD means -Use SD to identify consistent performance |
Exercise books
-Manila paper -Exam score data -Chalk/markers -Agricultural data |
KLB Secondary Mathematics Form 4, Pages 65-70
|
|
| 11 | 2 |
Statistics II
Loci |
Advanced Standard Deviation Techniques
Introduction to Loci |
By the end of the
lesson, the learner
should be able to:
-Apply transformation properties of standard deviation -Use coding with class width division -Solve problems with multiple transformations -Verify results using different methods |
-Demonstrate coding transformations -Show how SD changes with data transformations -Practice reverse calculations -Verify using alternative methods |
Exercise books
-Manila paper -Transformation examples -Chalk/markers -String |
KLB Secondary Mathematics Form 4, Pages 65-70
|
|
| 11 | 3 |
Loci
|
Basic Locus Concepts and Laws
Perpendicular Bisector Locus |
By the end of the
lesson, the learner
should be able to:
-Understand that loci follow specific laws or conditions -Identify the laws governing different types of movement -Distinguish between 2D and 3D loci -Apply locus concepts to simple problems |
-Physical demonstrations with moving objects -Students track movement of classroom door -Identify laws governing pendulum movement -Practice stating locus laws clearly |
Exercise books
-Manila paper -String -Real objects -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 73-75
|
|
| 11 | 4 |
Loci
|
Properties and Applications of Perpendicular Bisector
|
By the end of the
lesson, the learner
should be able to:
-Understand perpendicular bisector in 3D space -Apply perpendicular bisector to find circumcenters -Solve practical problems using perpendicular bisector -Use perpendicular bisector in triangle constructions |
-Find circumcenter of triangle using perpendicular bisectors -Solve water pipe problems (equidistant from two points) -Apply to real-world location problems -Practice with various triangle types |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 11 | 5 |
Loci
|
Locus of Points at Fixed Distance from a Point
Locus of Points at Fixed Distance from a Line |
By the end of the
lesson, the learner
should be able to:
-Define circle as locus of points at fixed distance from center -Construct circles with given radius using compass -Understand sphere as 3D locus from fixed point -Solve problems involving circular loci |
-Construct circles of different radii -Demonstrate with string of fixed length -Discuss radar coverage, radio signal range -Students create circles with various measurements |
Exercise books
-Manila paper -Compass -String -Ruler -Set square |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 11 | 6 |
Loci
|
Angle Bisector Locus
Properties and Applications of Angle Bisector |
By the end of the
lesson, the learner
should be able to:
-Define angle bisector locus -Construct angle bisectors using compass and ruler -Prove equidistance property of angle bisector -Apply angle bisector to find incenters |
-Construct angle bisectors for various angles -Verify equidistance from angle arms -Find incenter of triangle using angle bisectors -Practice with acute, obtuse, and right angles |
Exercise books
-Manila paper -Compass -Protractor -Ruler |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 11 | 7 |
Loci
|
Constant Angle Locus
Advanced Constant Angle Constructions |
By the end of the
lesson, the learner
should be able to:
-Understand constant angle locus concept -Construct constant angle loci using arc method -Apply circle theorems to constant angle problems -Solve problems involving angles in semicircles |
-Demonstrate constant angle using protractor -Construct arc passing through two points -Use angles in semicircle property -Practice with different angle measures |
Exercise books
-Manila paper -Compass -Protractor |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 12 | 1 |
Loci
|
Introduction to Intersecting Loci
Intersecting Circles and Lines |
By the end of the
lesson, the learner
should be able to:
-Understand concept of intersecting loci -Identify points satisfying multiple conditions -Find intersection points of two loci -Apply intersecting loci to solve practical problems |
-Demonstrate intersection of two circles -Find points equidistant from two points AND at fixed distance from third point -Solve simple two-condition problems -Practice identifying intersection points |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 83-89
|
|
| 12 | 2 |
Loci
|
Triangle Centers Using Intersecting Loci
|
By the end of the
lesson, the learner
should be able to:
-Find circumcenter using perpendicular bisector intersections -Locate incenter using angle bisector intersections -Determine centroid and orthocenter -Apply triangle centers to solve problems |
-Construct all four triangle centers -Compare properties of different triangle centers -Use triangle centers in geometric proofs -Solve problems involving triangle center properties |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 83-89
|
|
| 12 | 3 |
Loci
|
Complex Intersecting Loci Problems
Introduction to Loci of Inequalities |
By the end of the
lesson, the learner
should be able to:
-Solve problems with three or more conditions -Find regions satisfying multiple constraints -Apply intersecting loci to optimization problems -Use systematic approach to complex problems |
-Solve treasure hunt type problems -Find optimal locations for facilities -Apply to surveying and engineering problems -Practice systematic problem-solving approach |
Exercise books
-Manila paper -Compass -Real-world scenarios -Ruler -Colored pencils |
KLB Secondary Mathematics Form 4, Pages 83-89
|
|
| 12 | 4 |
Loci
|
Distance Inequality Loci
Combined Inequality Loci |
By the end of the
lesson, the learner
should be able to:
-Represent distance inequalities graphically -Solve problems with "less than" and "greater than" distances -Find regions satisfying distance constraints -Apply to safety zone problems |
-Shade regions inside and outside circles -Solve exclusion zone problems -Apply to communication range problems -Practice with multiple distance constraints |
Exercise books
-Manila paper -Compass -Colored pencils -Ruler |
KLB Secondary Mathematics Form 4, Pages 89-92
|
|
| 12 | 5 |
Loci
|
Advanced Inequality Applications
Introduction to Loci Involving Chords |
By the end of the
lesson, the learner
should be able to:
-Apply inequality loci to linear programming introduction -Solve real-world optimization problems -Find maximum and minimum values in regions -Use graphical methods for decision making |
-Solve simple linear programming problems -Find optimal points in feasible regions -Apply to business and farming scenarios -Practice identifying corner points |
Exercise books
-Manila paper -Ruler -Real problem data -Compass |
KLB Secondary Mathematics Form 4, Pages 89-92
|
|
| 12 | 6 |
Loci
|
Chord-Based Constructions
Advanced Chord Problems |
By the end of the
lesson, the learner
should be able to:
-Construct circles through three points using chords -Find loci of chord midpoints -Solve problems with intersecting chords -Apply chord properties to geometric constructions |
-Construct circles using three non-collinear points -Find locus of midpoints of parallel chords -Solve chord intersection problems -Practice with chord-tangent relationships |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 92-94
|
|
| 12 | 7 |
Loci
|
Integration of All Loci Types
|
By the end of the
lesson, the learner
should be able to:
-Combine different types of loci in single problems -Solve comprehensive loci challenges -Apply multiple loci concepts simultaneously -Use loci in geometric investigations |
-Solve multi-step loci problems -Combine circle, line, and angle loci -Apply to real-world complex scenarios -Practice systematic problem-solving |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 73-94
|
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