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| WK | LSN | TOPIC | SUB-TOPIC | OBJECTIVES | T/L ACTIVITIES | T/L AIDS | REFERENCE | REMARKS |
|---|---|---|---|---|---|---|---|---|
| 2 | 1 |
Differentiation
|
Introduction to Rate of Change
Average Rate of Change |
By the end of the
lesson, the learner
should be able to:
-Understand concept of rate of change in daily life -Distinguish between average and instantaneous rates -Identify examples of changing quantities -Connect rate of change to gradient concepts |
-Discuss speed as rate of change of distance -Examine population growth rates -Analyze temperature change throughout the day -Connect to gradients of lines from coordinate geometry |
Exercise books
-Manila paper -Real-world examples -Graph examples -Calculators -Graph paper |
KLB Secondary Mathematics Form 4, Pages 177-182
|
|
| 2 | 2 |
Differentiation
|
Instantaneous Rate of Change
Gradient of Curves at Points |
By the end of the
lesson, the learner
should be able to:
-Understand concept of instantaneous rate -Recognize instantaneous rate as limit of average rates -Connect to tangent line gradients -Apply to real-world motion problems |
-Demonstrate instantaneous speed using car speedometer -Show limiting process using smaller intervals -Connect to tangent line slopes on curves -Practice with motion and growth examples |
Exercise books
-Manila paper -Tangent demonstrations -Motion examples -Rulers -Curve examples |
KLB Secondary Mathematics Form 4, Pages 177-182
|
|
| 2 | 3 |
Differentiation
|
Introduction to Delta Notation
|
By the end of the
lesson, the learner
should be able to:
-Understand delta (Δ) notation for small changes -Use Δx and Δy for coordinate changes -Apply delta notation to rate calculations -Practice reading and writing delta expressions |
-Introduce delta as symbol for "change in" -Practice writing Δx, Δy, Δt expressions -Use delta notation in rate of change formulas -Apply to coordinate geometry problems |
Exercise books
-Manila paper -Delta notation examples -Symbol practice |
KLB Secondary Mathematics Form 4, Pages 182-184
|
|
| 2 | 4-5 |
Differentiation
|
The Limiting Process
Introduction to Derivatives Derivative of Linear Functions Derivative of y = x^n (Basic Powers) |
By the end of the
lesson, the learner
should be able to:
-Understand concept of limit in differentiation -Apply "as Δx approaches zero" reasoning -Use limiting process to find exact derivatives -Practice systematic limiting calculations -Find derivatives of linear functions y = mx + c -Understand that derivative of linear function is constant -Apply to straight line gradient problems -Verify using limiting process |
-Demonstrate limiting process with numerical examples -Show chord approaching tangent as Δx → 0 -Calculate limits using table of values -Practice systematic limit evaluation -Find derivative of y = 3x + 2 using definition -Show that derivative equals the gradient -Practice with various linear functions -Verify results using first principles |
Exercise books
-Manila paper -Limit tables -Systematic examples -Derivative notation -Function examples Exercise books -Manila paper -Linear function examples -Verification methods -Power rule examples -First principles verification |
KLB Secondary Mathematics Form 4, Pages 182-184
KLB Secondary Mathematics Form 4, Pages 184-188 |
|
| 2 | 6 |
Differentiation
|
Derivative of Constant Functions
|
By the end of the
lesson, the learner
should be able to:
-Understand that derivative of constant is zero -Apply to functions like y = 5, y = -3 -Explain geometric meaning of zero derivative -Combine with other differentiation rules |
-Show that horizontal lines have zero gradient -Find derivatives of constant functions -Explain why rate of change of constant is zero -Apply to mixed functions with constants |
Exercise books
-Manila paper -Constant function graphs -Geometric explanations |
KLB Secondary Mathematics Form 4, Pages 184-188
|
|
| 2 | 7 |
Differentiation
|
Derivative of Coefficient Functions
Derivative of Polynomial Functions |
By the end of the
lesson, the learner
should be able to:
-Find derivatives of functions like y = ax^n -Apply constant multiple rule -Practice with various coefficient values -Combine coefficient and power rules |
-Find derivative of y = 5x³ -Apply rule d/dx(af(x)) = a·f'(x) -Practice with negative coefficients -Combine multiple rules systematically |
Exercise books
-Manila paper -Coefficient examples -Rule combinations -Polynomial examples -Term-by-term method |
KLB Secondary Mathematics Form 4, Pages 184-188
|
|
| 3 | 1 |
Differentiation
|
Applications to Tangent Lines
Applications to Normal Lines |
By the end of the
lesson, the learner
should be able to:
-Find equations of tangent lines to curves -Use derivatives to find tangent gradients -Apply point-slope form for tangent equations -Solve problems involving tangent lines |
-Find tangent to y = x² at point (2, 4) -Use derivative to get gradient at specific point -Apply y - y₁ = m(x - x₁) formula -Practice with various curves and points |
Exercise books
-Manila paper -Tangent line examples -Point-slope applications -Normal line examples -Perpendicular concepts |
KLB Secondary Mathematics Form 4, Pages 187-189
|
|
| 3 | 2 |
Differentiation
|
Introduction to Stationary Points
|
By the end of the
lesson, the learner
should be able to:
-Define stationary points as points where dy/dx = 0 -Identify different types of stationary points -Understand geometric meaning of zero gradient -Find stationary points by solving dy/dx = 0 |
-Show horizontal tangents at stationary points -Find stationary points of y = x² - 4x + 3 -Identify maximum, minimum, and inflection points -Practice finding where dy/dx = 0 |
Exercise books
-Manila paper -Curve sketches -Stationary point examples |
KLB Secondary Mathematics Form 4, Pages 189-195
|
|
| 3 | 3 |
Differentiation
|
Types of Stationary Points
Finding and Classifying Stationary Points |
By the end of the
lesson, the learner
should be able to:
-Distinguish between maximum and minimum points -Identify points of inflection -Use first derivative test for classification -Apply gradient analysis around stationary points |
-Analyze gradient changes around stationary points -Use sign analysis of dy/dx -Classify stationary points by gradient behavior -Practice with various function types |
Exercise books
-Manila paper -Sign analysis charts -Classification examples -Systematic templates -Complete examples |
KLB Secondary Mathematics Form 4, Pages 189-195
|
|
| 3 | 4-5 |
Differentiation
|
Curve Sketching Using Derivatives
Introduction to Kinematics Applications Acceleration as Second Derivative |
By the end of the
lesson, the learner
should be able to:
-Use derivatives to sketch accurate curves -Identify key features: intercepts, stationary points -Apply systematic curve sketching method -Combine algebraic and graphical analysis -Understand acceleration as derivative of velocity -Apply a = dv/dt = d²s/dt² notation -Find acceleration functions from displacement -Apply to motion analysis problems |
-Sketch y = x³ - 3x² + 2 using derivatives -Find intercepts, stationary points, and behavior -Use systematic curve sketching approach -Verify sketches using derivative information -Find acceleration from velocity functions -Use second derivative notation -Apply to projectile motion problems -Practice with particle motion scenarios |
Exercise books
-Manila paper -Curve sketching templates -Systematic method -Motion examples -Kinematics applications Exercise books -Manila paper -Second derivative examples -Motion analysis |
KLB Secondary Mathematics Form 4, Pages 195-197
KLB Secondary Mathematics Form 4, Pages 197-201 |
|
| 3 | 6 |
Differentiation
|
Motion Problems and Applications
Introduction to Optimization |
By the end of the
lesson, the learner
should be able to:
-Solve complete motion analysis problems -Find displacement, velocity, acceleration relationships -Apply to real-world motion scenarios -Use derivatives for motion optimization |
-Analyze complete motion of falling object -Find when particle changes direction -Calculate maximum height in projectile motion -Apply to vehicle motion problems |
Exercise books
-Manila paper -Complete motion examples -Real scenarios -Optimization examples -Real applications |
KLB Secondary Mathematics Form 4, Pages 197-201
|
|
| 3 | 7 |
Differentiation
|
Geometric Optimization Problems
Business and Economic Applications |
By the end of the
lesson, the learner
should be able to:
-Apply calculus to geometric optimization -Find maximum areas and minimum perimeters -Use derivatives for shape optimization -Apply to construction and design problems |
-Find dimensions for maximum area enclosure -Optimize container volumes and surface areas -Apply to architectural design problems -Practice with various geometric constraints |
Exercise books
-Manila paper -Geometric examples -Design applications -Business examples -Economic applications |
KLB Secondary Mathematics Form 4, Pages 201-204
|
|
| 4 | 1 |
Differentiation
Integration |
Advanced Optimization Problems
Introduction to Reverse Differentiation |
By the end of the
lesson, the learner
should be able to:
-Solve complex optimization with multiple constraints -Apply systematic optimization methodology -Use calculus for engineering applications -Practice with advanced real-world problems |
-Solve complex geometric optimization problems -Apply to engineering design scenarios -Use systematic optimization approach -Practice with multi-variable situations |
Exercise books
-Manila paper -Complex examples -Engineering applications Graph papers -Differentiation charts -Exercise books -Function examples |
KLB Secondary Mathematics Form 4, Pages 201-204
|
|
| 4 | 2 |
Integration
|
Basic Integration Rules - Power Functions
Integration of Polynomial Functions Finding Particular Solutions |
By the end of the
lesson, the learner
should be able to:
-Apply power rule for integration: ∫xⁿ dx = xⁿ⁺¹/(n+1) + c -Understand the constant of integration and why it's necessary -Integrate simple power functions where n ≠ -1 -Practice with positive, negative, and fractional powers |
-Derivation of power rule through reverse differentiation -Multiple examples with different values of n -Explanation of arbitrary constant using family of curves -Practice exercises with various power functions -Common mistakes discussion and correction |
Calculators
-Graph papers -Power rule charts -Exercise books -Algebraic worksheets -Polynomial examples Graph papers -Calculators -Curve examples |
KLB Secondary Mathematics Form 4, Pages 223-225
|
|
| 4 | 3 |
Integration
|
Introduction to Definite Integrals
Evaluating Definite Integrals Area Under Curves - Single Functions Areas Below X-axis and Mixed Regions |
By the end of the
lesson, the learner
should be able to:
-Define definite integrals using limit notation -Understand the difference between definite and indefinite integrals -Learn proper notation: ∫ₐᵇ f(x)dx -Understand geometric meaning as area under curve |
-Introduction to definite integral concept and notation -Geometric interpretation using simple curves -Comparison between ∫f(x)dx and ∫ₐᵇf(x)dx -Discussion on limits of integration -Basic examples with simple functions |
Graph papers
-Geometric models -Integration notation charts -Calculators Calculators -Step-by-step worksheets -Exercise books -Evaluation charts -Curve sketching tools -Colored pencils -Area grids -Curve examples -Colored materials |
KLB Secondary Mathematics Form 4, Pages 226-228
|
|
| 4 | 4-5 |
Integration
Vectors (II) |
Area Between Two Curves
Coordinates in two dimensions Coordinates in three dimensions |
By the end of the
lesson, the learner
should be able to:
-Calculate area between two intersecting curves -Find intersection points as integration limits -Apply method: Area = ∫ₐᵇ [f(x) - g(x)]dx -Handle multiple intersection scenarios 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 |
-Method for finding curve intersection points -Working examples: area between y = x² and y = x -Step-by-step process for area between curves -Practice with linear and quadratic function pairs -Advanced examples with multiple intersections 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 |
Graph papers
-Equation solving aids -Calculators -Colored pencils -Exercise books 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 Secondary Mathematics Form 4, Pages 233-235
KLB Mathematics Book Three Pg 222 |
|
| 4 | 6 |
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
|
|
| 4 | 7 |
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
|
|
| 5 | 1 |
Vectors (II)
|
Magnitude of a vector in three dimensions
|
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
|
KLB Mathematics Book Three Pg 229-230
|
|
| 5 | 2 |
Vectors (II)
|
Magnitude applications and unit vectors
Parallel 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
Chalk and blackboard, parallel line demonstrations, exercise books |
KLB Mathematics Book Three Pg 229-230
|
|
| 5 | 3 |
Vectors (II)
|
Collinearity
Advanced collinearity applications |
By the end of the
lesson, the learner
should be able to:
Show that points are collinear Apply vector methods to prove collinearity Test for collinear points using vector techniques Solve collinearity problems systematically |
Q/A on collinearity testing using vector proportion methods
Discussions on point alignment using vector analysis Solving collinearity problems using systematic verification Demonstrations using straight-line point examples Explaining collinearity using geometric alignment concepts |
Chalk and blackboard, straight-line demonstrations, exercise books
Chalk and blackboard, complex geometric aids, exercise books |
KLB Mathematics Book Three Pg 232-234
|
|
| 5 | 4-5 |
Vectors (II)
|
Proportional division of a line
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 internally in the given ratio Apply the internal division formula Calculate division points using vector methods Understand proportional division concepts 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 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 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, internal division models, exercise books
Chalk and blackboard, external division models, exercise books Chalk and blackboard, combined division models, exercise books |
KLB Mathematics Book Three Pg 237-238
KLB Mathematics Book Three Pg 238-239 |
|
| 5 | 6 |
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
|
|
| 5 | 7 |
Vectors (II)
|
Mid-point
|
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
|
KLB Mathematics Book Three Pg 243
|
|
| 6 | 1 |
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
|
|
| 6 | 2 |
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
|
|
| 6 | 3 |
Vectors (II)
|
Advanced geometric applications
|
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
|
KLB Mathematics Book Three Pg 248-250
|
|
| 6 | 4-5 |
Binomial Expansion
|
Binomial expansions up to power four
Binomial expansions up to power four (continued) Pascal's triangle Pascal's triangle applications |
By the end of the
lesson, the learner
should be able to:
Expand binomial function up to power four Apply systematic multiplication methods Recognize coefficient patterns in expansions Use multiplication to expand binomial expressions Use Pascal's triangle Construct Pascal's triangle systematically Apply triangle coefficients for binomial expansions Recognize number patterns in the triangle |
Q/A on algebraic multiplication using familiar expressions
Discussions on systematic expansion using step-by-step methods Solving basic binomial multiplication problems Demonstrations using area models and rectangular arrangements Explaining pattern recognition using organized layouts Q/A on triangle construction using addition patterns Discussions on coefficient relationships using triangle analysis Solving triangle construction and application problems Demonstrations using visual triangle building Explaining pattern connections using systematic observation |
Chalk and blackboard, rectangular cutouts from paper, exercise books
Chalk and blackboard, squared paper for geometric models, exercise books Chalk and blackboard, triangular patterns drawn/cut from paper, exercise books Chalk and blackboard, Pascal's triangle reference charts, exercise books |
KLB Mathematics Book Three Pg 256
KLB Mathematics Book Three Pg 256-257 |
|
| 6 | 6 |
Binomial Expansion
|
Pascal's triangle (continued)
|
By the end of the
lesson, the learner
should be able to:
Use Pascal's triangle Apply triangle to complex expansion problems Handle higher powers using Pascal's triangle Integrate triangle concepts with algebraic expansion |
Q/A on advanced triangle applications using complex examples
Discussions on higher power expansion using triangle methods Solving challenging problems using Pascal's triangle Demonstrations using detailed triangle constructions Explaining integration using comprehensive examples |
Chalk and blackboard, advanced triangle patterns, exercise books
|
KLB Mathematics Book Three Pg 258-259
|
|
| 6 | 7 |
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
|
|
| 7 |
Mid-term Exam |
|||||||
| 7 | 6 |
Binomial Expansion
Probability |
Applications to numerical cases (continued)
Introduction |
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
Chalk and blackboard, coins, dice made from cardboard, exercise books |
KLB Mathematics Book Three Pg 259-260
|
|
| 7 | 7 |
Probability
|
Experimental Probability
|
By the end of the
lesson, the learner
should be able to:
Calculate the experimental probability Conduct probability experiments systematically Record and analyze experimental data Compare experimental results with expectations |
Q/A on frequency counting using repeated experiments
Discussions on trial repetition and result recording Solving experimental probability problems using data collection Demonstrations using coin toss and dice roll experiments Explaining frequency ratio calculations using practical examples |
Chalk and blackboard, coins, cardboard dice, tally charts, exercise books
|
KLB Mathematics Book Three Pg 262-264
|
|
| 8-9 |
Half-Term |
|||||||
| 9 | 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
|
|
| 9 | 3 |
Probability
|
Probability Space
|
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
|
KLB Mathematics Book Three Pg 266-267
|
|
| 9 | 4-5 |
Probability
|
Theoretical Probability
Theoretical Probability advanced Theoretical Probability applications Combined Events |
By the end of the
lesson, the learner
should be able to:
Calculate the probability space for the theoretical probability Apply mathematical reasoning to find probabilities Use equally likely outcome assumptions Calculate theoretical probabilities systematically Calculate the probability space for the theoretical probability Apply theoretical concepts to real situations Solve practical probability problems Interpret results in meaningful contexts |
Q/A on theoretical calculation using mathematical principles
Discussions on equally likely assumptions and calculations Solving theoretical problems using systematic approaches Demonstrations using fair dice and unbiased coin examples Explaining mathematical probability using logical reasoning Q/A on practical probability using local examples Discussions on real-world applications using community scenarios Solving application problems using theoretical methods Demonstrations using local games and practical situations Explaining practical interpretation using meaningful contexts |
Chalk and blackboard, fair dice and coins, probability calculation aids, exercise books
Chalk and blackboard, complex probability materials, advanced calculation aids, exercise books Chalk and blackboard, local game examples, practical scenario materials, exercise books Chalk and blackboard, playing cards, multiple dice, Venn diagram drawings, exercise books |
KLB Mathematics Book Three Pg 266-268
KLB Mathematics Book Three Pg 268-270 |
|
| 9 | 6 |
Probability
|
Combined Events OR probability
|
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
|
KLB Mathematics Book Three Pg 272-274
|
|
| 9 | 7 |
Probability
|
Independent Events
Independent Events advanced |
By the end of the
lesson, the learner
should be able to:
Find the probability of independent events Apply multiplication rule for independent events Calculate "A and B" probabilities Understand independence concepts |
Q/A on multiplication rule using independent event examples
Discussions on independence identification and verification Solving AND probability problems using systematic calculation Demonstrations using multiple coin tosses and dice combinations Explaining multiplication rule using logical reasoning |
Chalk and blackboard, multiple coins and dice, independence demonstration materials, exercise books
Chalk and blackboard, playing cards for replacement scenarios, multiple experimental setups, exercise books |
KLB Mathematics Book Three Pg 274-275
|
|
| 10 | 1 |
Probability
|
Independent Events applications
Tree Diagrams |
By the end of the
lesson, the learner
should be able to:
Find the probability of independent events Apply independence to practical problems Solve complex multi-event scenarios Integrate independence with other concepts |
Q/A on complex event analysis using systematic problem-solving
Discussions on rule selection and application strategies Solving advanced combined problems using integrated approaches Demonstrations using complex experimental scenarios Explaining strategic problem-solving using logical analysis |
Chalk and blackboard, complex experimental materials, advanced calculation aids, exercise books
Chalk and blackboard, tree diagram templates, branching materials, exercise books |
KLB Mathematics Book Three Pg 278-280
|
|
| 10 | 2 |
Probability
|
Tree Diagrams advanced
|
By the end of the
lesson, the learner
should be able to:
Use tree diagrams to find probability Apply trees to multi-stage problems Handle complex sequential events Calculate final probabilities using trees |
Q/A on complex tree application using multi-stage examples
Discussions on replacement scenario handling Solving complex tree problems using systematic calculation Demonstrations using detailed tree constructions Explaining systematic probability calculation using tree methods |
Chalk and blackboard, complex tree examples, detailed calculation aids, exercise books
|
KLB Mathematics Book Three Pg 283-285
|
|
| 10 | 3 |
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
|
|
| 10 | 4-5 |
Compound Proportion and Rates of Work
|
Proportional Parts
Proportional Parts applications Rates of Work |
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 Calculate the rate of work Understand work rate relationships Apply time-work-efficiency concepts Solve basic rate of work problems |
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 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, sharing demonstration materials, exercise books
Chalk and blackboard, business partnership examples, exercise books Chalk and blackboard, work scenario examples, exercise books |
KLB Mathematics Book Three Pg 291-293
KLB Mathematics Book Three Pg 294-295 |
|
| 10 | 6 |
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
|
|
| 10 | 7 |
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
|
|
| 11 | 1 |
Graphical Methods
|
Introduction to 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
|
KLB Mathematics Book Three Pg 301
|
|
| 11 | 2 |
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
|
|
| 11 | 3 |
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
|
|
| 11 | 4-5 |
Graphical Methods
|
Advanced average rates
Introduction to instantaneous rates Rate of change at an instant |
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 Calculate the rate of change at an instant Understand instantaneous rate concepts Distinguish between average and instantaneous rates Apply instant rate methods |
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 Q/A on instantaneous rate concepts using limiting methods Discussions on instant vs average rate differences Solving basic instantaneous rate problems Demonstrations using tangent line concepts Explaining instantaneous rate using practical examples |
Chalk and blackboard, advanced rate scenarios, exercise books
Chalk and blackboard, tangent line examples, exercise books Chalk and blackboard, detailed graph examples, exercise books |
KLB Mathematics Book Three Pg 304-310
KLB Mathematics Book Three Pg 310-311 |
|
| 11 | 6 |
Graphical Methods
|
Advanced instantaneous rates
Empirical graphs |
By the end of the
lesson, the learner
should be able to:
Calculate the rate of change at an instant Handle complex instantaneous rate scenarios Apply instant rates to advanced problems Integrate instantaneous concepts with applications |
Q/A on advanced instantaneous applications using complex examples
Discussions on sophisticated rate problems using detailed analysis Solving challenging instantaneous problems using systematic methods Demonstrations using comprehensive rate constructions Explaining advanced applications using detailed reasoning |
Chalk and blackboard, advanced rate examples, exercise books
Chalk and blackboard, experimental data examples, exercise books |
KLB Mathematics Book Three Pg 310-315
|
|
| 11 | 7 |
Graphical Methods
|
Advanced empirical methods
|
By the end of the
lesson, the learner
should be able to:
Draw the empirical graphs Apply empirical methods to complex data Handle large datasets and trends Interpret empirical results meaningfully |
Q/A on advanced empirical techniques using complex datasets
Discussions on trend analysis using systematic methods Solving challenging empirical problems using organized approaches Demonstrations using comprehensive data analysis Explaining advanced interpretations using detailed reasoning |
Chalk and blackboard, complex data examples, exercise books
|
KLB Mathematics Book Three Pg 315-321
|
|
| 12 |
End-Term Exam |
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| 13 |
Marking and Closing |
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