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| WK | LSN | TOPIC | SUB-TOPIC | OBJECTIVES | T/L ACTIVITIES | T/L AIDS | REFERENCE | REMARKS |
|---|---|---|---|---|---|---|---|---|
| 1 | 5 |
Vectors (II)
|
Coordinates in two dimensions
|
By the end of the
lesson, the learner
should be able to:
Identify the coordinates of a point in two dimensions Plot points on coordinate planes accurately Understand position representation using coordinates Apply coordinate concepts to practical situations |
Q/A on coordinate identification using grid references
Discussions on map reading and location finding Solving coordinate plotting problems using systematic methods Demonstrations using classroom grid systems and floor patterns Explaining coordinate applications using local maps and directions |
Chalk and blackboard, squared paper or grid drawn on ground, exercise books
|
KLB Mathematics Book Three Pg 221-222
|
|
| 2 | 1 |
Vectors (II)
|
Coordinates in three dimensions
Column and position vectors in three dimensions 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:
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 Chalk and blackboard, direction indicators, unit vector reference charts, exercise books |
KLB Mathematics Book Three Pg 222
|
|
| 2 | 2 |
Vectors (II)
|
Vector operations using unit vectors
Magnitude of a vector in three dimensions Magnitude applications and unit vectors Parallel vectors |
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 Chalk and blackboard, direction finding aids, exercise books Chalk and blackboard, parallel line demonstrations, exercise books |
KLB Mathematics Book Three Pg 226-228
|
|
| 2 | 3 |
Vectors (II)
|
Collinearity
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 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 Chalk and blackboard, internal division models, exercise books |
KLB Mathematics Book Three Pg 232-234
|
|
| 2 | 4 |
Vectors (II)
|
External division of a line
Combined internal and external division Ratio theorem Advanced ratio theorem applications |
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 Chalk and blackboard, ratio theorem aids, exercise books Chalk and blackboard, advanced ratio models, exercise books |
KLB Mathematics Book Three Pg 238-239
|
|
| 2 | 5 |
Vectors (II)
|
Mid-point
Ratio theorem and midpoint integration Advanced ratio theorem applications |
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 Chalk and blackboard, advanced geometric aids, exercise books |
KLB Mathematics Book Three Pg 243
|
|
| 3 | 1 |
Vectors (II)
Binomial Expansion |
Applications of vectors in geometry
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 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 Chalk and blackboard, advanced geometric models, exercise books Chalk and blackboard, rectangular cutouts from paper, exercise books |
KLB Mathematics Book Three Pg 248-249
|
|
| 3 | 2 |
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
|
|
| 3 | 3 |
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
|
|
| 3 | 4 |
Probability
|
Introduction
Experimental Probability Experimental Probability applications Range of Probability Measure |
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 Chalk and blackboard, number line drawings, probability scale charts, exercise books |
KLB Mathematics Book Three Pg 262-264
|
|
| 3 | 5 |
Probability
|
Probability Space
Theoretical Probability Theoretical Probability advanced |
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 Chalk and blackboard, complex probability materials, advanced calculation aids, exercise books |
KLB Mathematics Book Three Pg 266-267
|
|
| 4 | 1 |
Probability
|
Theoretical Probability applications
Combined Events Combined Events OR probability Independent Events |
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 Chalk and blackboard, multiple coins and dice, independence demonstration materials, exercise books |
KLB Mathematics Book Three Pg 268-270
|
|
| 4 | 2 |
Probability
|
Independent Events advanced
Independent Events applications Tree Diagrams Tree Diagrams advanced |
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 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 276-278
|
|
| 4 | 3 |
Compound Proportion and Rates of Work
|
Compound Proportions
Compound Proportions applications Proportional Parts |
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 Chalk and blackboard, sharing demonstration materials, exercise books |
KLB Mathematics Book Three Pg 288-290
|
|
| 4 | 4 |
Compound Proportion and Rates of Work
Graphical Methods |
Proportional Parts applications
Rates of Work Rates of Work and Mixtures Tables of given relations |
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 Chalk and blackboard, mixture demonstration materials, exercise books Chalk and blackboard, ruled paper for tables, exercise books |
KLB Mathematics Book Three Pg 291-293
|
|
| 4 | 5 |
Graphical Methods
|
Graphs of given relations
Tables and graphs integration Introduction to cubic equations |
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 Chalk and blackboard, cubic function examples, exercise books |
KLB Mathematics Book Three Pg 300
|
|
| 5 | 1 |
Graphical Methods
|
Graphical solution of cubic equations
Advanced cubic solutions Introduction to rates of change Average rates of change |
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 Chalk and blackboard, rate calculation examples, exercise books Chalk and blackboard, graph paper, rate examples, exercise books |
KLB Mathematics Book Three Pg 302-304
|
|
| 5 | 2 |
Graphical Methods
|
Advanced average rates
Introduction to instantaneous rates Rate of change at an instant Advanced instantaneous rates Empirical graphs Advanced empirical methods |
By the end of the
lesson, the learner
should be able to:
Calculate the 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 Chalk and blackboard, detailed graph examples, exercise books Chalk and blackboard, advanced rate examples, exercise books Chalk and blackboard, experimental data examples, exercise books Chalk and blackboard, complex data examples, exercise books |
KLB Mathematics Book Three Pg 304-310
|
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