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| WK | LSN | TOPIC | SUB-TOPIC | OBJECTIVES | T/L ACTIVITIES | T/L AIDS | REFERENCE | REMARKS |
|---|---|---|---|---|---|---|---|---|
| 1 |
OPENER EXAM |
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| 2 | 1-2 |
Matrices and Transformation
|
Matrices of Transformation
Identifying Common Transformation Matrices Finding the Matrix of a Transformation Using the Unit Square Method |
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 -Identify matrices for reflection, rotation, enlargement -Describe transformations represented by given matrices -Apply identity matrix and understand its effect -Distinguish between different types of 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 -Use unit square drawn on paper to identify transformations -Practice with specific matrices like (0 1; 1 0), (-1 0; 0 1) -Draw objects and images under various transformations -Q&A on transformation properties |
Exercise books
-Manila paper -Ruler -Pencils Exercise books -Manila paper -Ruler -String -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 1-5
|
|
| 2 | 3 |
Matrices and Transformation
|
Successive Transformations
Matrix Multiplication for Combined Transformations Single Matrix for Successive Transformations |
By the end of the
lesson, the learner
should be able to:
-Understand the concept of successive transformations -Apply transformations in correct order -Recognize that order matters in matrix multiplication -Perform multiple transformations step by step |
-Demonstrate successive transformations with paper cutouts -Practice applying transformations in sequence -Compare results when order is changed -Work through step-by-step examples |
Exercise books
-Manila paper -Ruler -Coloured pencils -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 16-24
|
|
| 2 | 4 |
Matrices and Transformation
|
Inverse of a Transformation
Properties of Inverse Transformations |
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 |
KLB Secondary Mathematics Form 4, Pages 24-26
|
|
| 2 | 5 |
Matrices and Transformation
|
Area Scale Factor and Determinant
|
By the end of the
lesson, the learner
should be able to:
-Establish relationship between area scale factor and determinant -Calculate area scale factors for transformations -Apply determinant to find area changes -Solve problems involving area transformations |
-Measure areas of objects and images using grid paper -Calculate determinants and compare with area ratios -Practice with various transformation types -Verify the relationship: ASF = |
det A
|
|
|
| 2 | 6 |
Matrices and Transformation
|
Shear Transformations
Stretch 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 -Rubber bands |
KLB Secondary Mathematics Form 4, Pages 28-34
|
|
| 2 | 7 |
Matrices and Transformation
|
Combined Shear and Stretch Problems
|
By the end of the
lesson, the learner
should be able to:
-Apply shear and stretch transformations in combination -Solve complex transformation problems -Identify transformation types from matrices -Calculate areas under shear and stretch transformations |
-Work through complex transformation sequences -Practice identifying transformation types -Calculate area changes under different transformations -Solve real-world applications |
Exercise books
-Manila paper -Ruler -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 28-34
|
|
| 3 | 1-2 |
Matrices and Transformation
Probability |
Isometric and Non-isometric Transformations
Introduction Experimental Probability |
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 Calculate the experimental probability Conduct probability experiments systematically Record and analyze experimental data Compare experimental results with expectations |
-Compare congruent and non-congruent images using cutouts -Classify transformations systematically -Practice identification from matrices -Discuss real-world applications of each type 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 |
Exercise books
-Paper cutouts -Manila paper -Ruler Chalk and blackboard, coins, dice made from cardboard, exercise books Chalk and blackboard, coins, cardboard dice, tally charts, exercise books |
KLB Secondary Mathematics Form 4, Pages 35-38
KLB Mathematics Book Three Pg 262-264 |
|
| 3 | 3 |
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
|
|
| 3 | 4 |
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
|
|
| 3 | 5 |
Probability
|
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 Apply mathematical reasoning to find probabilities Use equally likely outcome assumptions Calculate theoretical probabilities systematically |
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 |
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 266-268
|
|
| 3 | 6 |
Probability
|
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 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
|
KLB Mathematics Book Three Pg 268-270
|
|
| 3 | 7 |
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
|
|
| 4 | 1-2 |
Probability
|
Combined Events OR probability
Independent Events Independent Events advanced |
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 Find the probability of independent events Distinguish between independent and dependent events Apply conditional probability concepts Handle complex independence scenarios |
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 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, Venn diagram materials, card examples, exercise books
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 272-274
KLB Mathematics Book Three Pg 276-278 |
|
| 4 | 3 |
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
|
|
| 4 | 4 |
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
|
|
| 4 | 5 |
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
|
|
| 4 | 6 |
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
|
|
| 4 | 7 |
Compound Proportion and Rates of Work
|
Proportional Parts applications
|
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
|
KLB Mathematics Book Three Pg 291-293
|
|
| 5 | 1-2 |
Compound Proportion and Rates of Work
Graphical Methods |
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 rate of work Understand work rate relationships Apply time-work-efficiency concepts Solve basic rate of work problems Draw tables of given relations Construct organized data tables systematically Prepare data for graphical representation Understand relationship between variables |
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 Q/A on table construction using systematic data organization Discussions on variable relationships using practical examples Solving table preparation problems using organized methods Demonstrations using data collection and tabulation Explaining systematic data arrangement using logical procedures |
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 294-295
KLB Mathematics Book Three Pg 299 |
|
| 5 | 3 |
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
|
|
| 5 | 4 |
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
|
|
| 5 | 5 |
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
|
|
| 5 | 6 |
Graphical Methods
|
Introduction to 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
|
KLB Mathematics Book Three Pg 304-306
|
|
| 5 | 7 |
Graphical Methods
|
Average rates of change
|
By the end of the
lesson, the learner
should be able to:
Calculate the average rates of change Apply average rate methods to various functions Use graphical methods for rate calculation Solve practical rate problems |
Q/A on average rate calculation using graphical methods
Discussions on rate applications using real-world scenarios Solving average rate problems using systematic approaches Demonstrations using graph-based rate calculation Explaining practical applications using meaningful contexts |
Chalk and blackboard, graph paper, rate examples, exercise books
|
KLB Mathematics Book Three Pg 304-306
|
|
| 6 | 1-2 |
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 Apply instantaneous rate methods systematically Use graphical techniques for instant rates Solve practical instantaneous rate problems |
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 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, 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 |
|
| 6 | 3 |
Graphical Methods
|
Advanced instantaneous rates
Empirical graphs Advanced empirical methods |
By the end of the
lesson, the learner
should be able to:
Calculate the rate of change at an instant 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 Chalk and blackboard, complex data examples, exercise books |
KLB Mathematics Book Three Pg 310-315
|
|
| 7-9 |
ENDTERM EXAM AND CLOSING |
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