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| WK | LSN | TOPIC | SUB-TOPIC | OBJECTIVES | T/L ACTIVITIES | T/L AIDS | REFERENCE | REMARKS |
|---|---|---|---|---|---|---|---|---|
| 2 | 1 |
Formulae and Variations
|
Introduction to formulae
|
By the end of the
lesson, the learner
should be able to:
Define formulae and identify formula components Recognize formulae in everyday contexts Understand the relationship between variables Appreciate the importance of formulae in mathematics |
Q/A on familiar formulae from daily life
Discussions on cooking recipes as formulae Analyzing distance-time relationships using walking examples Demonstrations using perimeter and area calculations Explaining formula notation using simple examples |
Chalk and blackboard, measuring tape or string, exercise books
|
KLB Mathematics Book Three Pg 191-193
|
|
| 2 | 2 |
Formulae and Variations
|
Subject of a formula - basic cases
Subject of a formula - intermediate cases Subject of a formula - advanced cases |
By the end of the
lesson, the learner
should be able to:
Make simple variables the subject of formulae Apply inverse operations to rearrange formulae Understand the concept of subject change Solve basic subject transformation problems |
Q/A on inverse operations using number examples
Discussions on formula rearrangement using balance method Solving basic subject change problems using step-by-step approach Demonstrations using see-saw balance analogy Explaining inverse operations using practical examples |
Chalk and blackboard, simple balance (stones and stick), exercise books
Chalk and blackboard, fraction strips made from paper, exercise books Chalk and blackboard, squared paper patterns, exercise books |
KLB Mathematics Book Three Pg 191-193
|
|
| 2 | 3 |
Formulae and Variations
Sequences and Series |
Applications of formula manipulation
Introduction to variation Direct variation - introduction Introduction to sequences and finding terms |
By the end of the
lesson, the learner
should be able to:
Apply formula rearrangement to practical problems Solve real-world problems using formula manipulation Calculate unknown quantities in various contexts Interpret results in meaningful situations |
Q/A on practical applications using local examples
Discussions on real-world formula use in farming/building Solving application problems using formula rearrangement Demonstrations using construction and farming scenarios Explaining practical interpretation using community examples |
Chalk and blackboard, local measurement tools, exercise books
Chalk and blackboard, local price lists from markets, exercise books Chalk and blackboard, beans or stones for counting, exercise books Chalk and blackboard, stones or beans for patterns, exercise books |
KLB Mathematics Book Three Pg 191-193
|
|
| 2 | 4 |
Sequences and Series
|
General term of sequences and applications
Arithmetic sequences and nth term Arithmetic sequence applications |
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 Chalk and blackboard, local employment/savings examples, exercise books |
KLB Mathematics Book Three Pg 207-208
|
|
| 2 | 5 |
Sequences and Series
|
Geometric sequences and nth term
Geometric sequence applications Arithmetic series and sum formula |
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 Chalk and blackboard, counting materials for summation, exercise books |
KLB Mathematics Book Three Pg 211-213
|
|
| 3 | 1 |
Sequences and Series
Vectors (II) |
Geometric series and applications
Mixed problems and advanced applications Sequences in nature and technology Coordinates in two dimensions |
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 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 216-219
|
|
| 3 | 2 |
Vectors (II)
|
Coordinates in three dimensions
Column and position vectors in three dimensions Position vectors and applications |
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 Chalk and blackboard, origin marking systems, exercise books |
KLB Mathematics Book Three Pg 222
|
|
| 3 | 3 |
Vectors (II)
|
Column vectors in terms of unit vectors i, j, k
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 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 Chalk and blackboard, 3D measurement aids, exercise books |
KLB Mathematics Book Three Pg 226-228
|
|
| 3 | 4 |
Vectors (II)
|
Magnitude applications and unit vectors
Parallel vectors Collinearity |
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 Chalk and blackboard, straight-line demonstrations, exercise books |
KLB Mathematics Book Three Pg 229-230
|
|
| 3 | 5 |
Vectors (II)
|
Advanced collinearity applications
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:
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 Chalk and blackboard, external division models, exercise books Chalk and blackboard, combined division models, exercise books |
KLB Mathematics Book Three Pg 232-234
|
|
| 4 | 1 |
Vectors (II)
|
Ratio theorem
Advanced ratio theorem applications Mid-point |
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 Chalk and blackboard, midpoint demonstration aids, exercise books |
KLB Mathematics Book Three Pg 240-242
|
|
| 4 | 2 |
Vectors (II)
|
Ratio theorem and midpoint integration
Advanced ratio theorem applications Applications of vectors in geometry |
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 Chalk and blackboard, parallelogram models, exercise books |
KLB Mathematics Book Three Pg 244-245
|
|
| 4 | 3 |
Vectors (II)
Binomial Expansion |
Rectangle diagonal applications
Advanced geometric applications 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 rectangle Apply vector methods to rectangle properties Prove rectangle theorems using vectors Compare parallelogram and rectangle diagonal properties |
Q/A on rectangle properties using vector analysis
Discussions on diagonal relationships using vector methods Solving rectangle problems using systematic approaches Demonstrations using rectangle constructions and vector proofs Explaining rectangle properties using vector reasoning |
Chalk and blackboard, rectangle models, exercise books
Chalk and blackboard, advanced geometric models, exercise books Chalk and blackboard, rectangular cutouts from paper, exercise books |
KLB Mathematics Book Three Pg 248-250
|
|
| 4 | 4 |
Binomial Expansion
|
Binomial expansions up to power four (continued)
Pascal's triangle Pascal's triangle applications Pascal's triangle (continued) |
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 Chalk and blackboard, Pascal's triangle reference charts, exercise books Chalk and blackboard, advanced triangle patterns, exercise books |
KLB Mathematics Book Three Pg 256
|
|
| 4 | 5 |
Binomial Expansion
|
Pascal's triangle advanced
Applications to numerical cases Applications to numerical cases (continued) |
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 Chalk and blackboard, advanced calculation examples, exercise books |
KLB Mathematics Book Three Pg 258-259
|
|
| 5 | 1 |
Probability
|
Introduction
Experimental Probability Experimental Probability applications |
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 Chalk and blackboard, extended experimental materials, data recording sheets, exercise books |
KLB Mathematics Book Three Pg 262-264
|
|
| 5 | 2 |
Probability
|
Range of Probability Measure
Probability Space Theoretical Probability Theoretical Probability advanced |
By the end of the
lesson, the learner
should be able to:
Calculate the range of probability measure Express probabilities on scale from 0 to 1 Convert between fractions, decimals, and percentages Interpret probability values correctly |
Q/A on probability scale using number line representations
Discussions on probability conversion between forms Solving probability scale problems using systematic methods Demonstrations using probability line and scale examples Explaining scale interpretation using practical scenarios |
Chalk and blackboard, number line drawings, probability scale charts, exercise books
Chalk and blackboard, playing cards (locally made), spinners from cardboard, exercise books Chalk and blackboard, fair dice and coins, probability calculation aids, exercise books Chalk and blackboard, complex probability materials, advanced calculation aids, exercise books |
KLB Mathematics Book Three Pg 265-266
|
|
| 5 | 3 |
Probability
|
Theoretical Probability applications
Combined Events Combined Events OR probability |
By the end of the
lesson, the learner
should be able to:
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 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, local game examples, practical scenario materials, exercise books
Chalk and blackboard, playing cards, multiple dice, Venn diagram drawings, exercise books Chalk and blackboard, Venn diagram materials, card examples, exercise books |
KLB Mathematics Book Three Pg 268-270
|
|
| 5 | 4 |
Probability
|
Independent Events
Independent Events advanced Independent Events applications |
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 Chalk and blackboard, complex experimental materials, advanced calculation aids, exercise books |
KLB Mathematics Book Three Pg 274-275
|
|
| 5 | 5 |
Probability
Compound Proportion and Rates of Work |
Tree Diagrams
Tree Diagrams advanced Compound Proportions |
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 Chalk and blackboard, local business examples, calculators if available, exercise books |
KLB Mathematics Book Three Pg 282
|
|
| 6 | 1 |
Compound Proportion and Rates of Work
|
Compound Proportions applications
Proportional Parts Proportional Parts applications Rates of Work |
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 Chalk and blackboard, work scenario examples, exercise books |
KLB Mathematics Book Three Pg 290-291
|
|
| 6 | 2 |
Compound Proportion and Rates of Work
Graphical Methods Graphical Methods |
Rates of Work and Mixtures
Tables of given relations Graphs 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 Chalk and blackboard, graph paper or grids, rulers, exercise books |
KLB Mathematics Book Three Pg 295-296
|
|
| 6 | 3 |
Graphical Methods
|
Tables and graphs integration
Introduction to cubic equations Graphical solution of 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 Chalk and blackboard, graph paper, cubic equation examples, exercise books |
KLB Mathematics Book Three Pg 299-300
|
|
| 6 | 4 |
Graphical Methods
|
Advanced cubic solutions
Introduction to rates of change Average rates of change Advanced average rates |
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
Chalk and blackboard, rate calculation examples, exercise books Chalk and blackboard, graph paper, rate examples, exercise books Chalk and blackboard, advanced rate scenarios, exercise books |
KLB Mathematics Book Three Pg 302-304
|
|
| 6 | 5 |
Graphical Methods
|
Introduction to instantaneous rates
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 Understand instantaneous rate concepts Distinguish between average and instantaneous rates Apply instant rate methods |
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, tangent line examples, exercise books
Chalk and blackboard, detailed graph examples, exercise books Chalk and blackboard, advanced rate examples, exercise books |
KLB Mathematics Book Three Pg 310-311
|
|
| 7-8 |
ELEVATOR JOINT EXAMS |
|||||||
| 9 | 1 |
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
|
|
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