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| WK | LSN | TOPIC | SUB-TOPIC | OBJECTIVES | T/L ACTIVITIES | T/L AIDS | REFERENCE | REMARKS |
|---|---|---|---|---|---|---|---|---|
| 1 | 1 |
Probability
|
Introduction
|
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
|
KLB Mathematics Book Three Pg 262-264
|
|
| 1 | 2 |
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
|
|
| 1 | 3 |
Probability
|
Experimental Probability applications
|
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
|
KLB Mathematics Book Three Pg 262-264
|
|
| 1 | 4 |
Probability
|
Experimental Probability applications
|
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
|
KLB Mathematics Book Three Pg 262-264
|
|
| 1 | 5 |
Probability
|
Range of Probability Measure
|
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
|
KLB Mathematics Book Three Pg 265-266
|
|
| 1 | 6 |
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
|
|
| 1 | 7 |
Probability
|
Theoretical Probability
|
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
|
KLB Mathematics Book Three Pg 266-268
|
|
| 2 | 1 |
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 theoretical probability to complex problems Handle multiple outcome scenarios Solve advanced theoretical problems |
Q/A on advanced theoretical applications using complex scenarios
Discussions on multiple outcome analysis using systematic methods Solving challenging theoretical problems using organized approaches Demonstrations using complex probability setups Explaining advanced theoretical concepts using detailed reasoning |
Chalk and blackboard, complex probability materials, advanced calculation aids, exercise books
|
KLB Mathematics Book Three Pg 268-270
|
|
| 2 | 2 |
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
|
|
| 2 | 3 |
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
|
|
| 2 | 4 |
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
|
|
| 2 | 5 |
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
|
|
| 2 | 6 |
Probability
|
Independent Events
|
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
|
KLB Mathematics Book Three Pg 274-275
|
|
| 2 | 7 |
Probability
|
Independent Events 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
|
KLB Mathematics Book Three Pg 276-278
|
|
| 3 | 1 |
Probability
|
Independent Events applications
|
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
|
KLB Mathematics Book Three Pg 278-280
|
|
| 3 | 2 |
Probability
|
Tree Diagrams
|
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
|
KLB Mathematics Book Three Pg 282
|
|
| 3 | 3 |
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
|
|
| 3 | 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
|
|
| 3 | 5 |
Compound Proportion and Rates of Work
|
Compound Proportions
|
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
|
KLB Mathematics Book Three Pg 288-290
|
|
| 3 | 6 |
Compound Proportion and Rates of Work
|
Compound Proportions applications
|
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
|
KLB Mathematics Book Three Pg 290-291
|
|
| 3 | 7 |
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 | 1 |
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
|
|
| 4 | 2 |
Compound Proportion and Rates of Work
|
Rates of Work
|
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 |
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, work scenario examples, exercise books
|
KLB Mathematics Book Three Pg 294-295
|
|
| 4 | 3 |
Compound Proportion and Rates of Work
|
Rates of Work and Mixtures
|
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
|
KLB Mathematics Book Three Pg 295-296
|
|
| 4 | 4 |
Compound Proportion and Rates of Work
|
Rates of Work and Mixtures
|
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
|
KLB Mathematics Book Three Pg 295-296
|
|
| 4 | 5 |
Graphical Methods
|
Tables of given relations
|
By the end of the
lesson, the learner
should be able to:
Draw tables of given relations Construct organized data tables systematically Prepare data for graphical representation Understand relationship between variables |
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, ruled paper for tables, exercise books
|
KLB Mathematics Book Three Pg 299
|
|
| 4 | 6 |
Graphical Methods
|
Graphs of given relations
|
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
|
KLB Mathematics Book Three Pg 300
|
|
| 4 | 7 |
Graphical Methods
|
Tables and graphs integration
|
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
|
KLB Mathematics Book Three Pg 299-300
|
|
| 5 | 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
|
|
| 5 | 2 |
Graphical Methods
|
Graphical solution of cubic equations
|
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
|
KLB Mathematics Book Three Pg 302-304
|
|
| 5 | 3 |
Graphical Methods
|
Advanced cubic solutions
|
By the end of the
lesson, the learner
should be able to:
Draw graphs of cubic equations Apply graphical methods to complex cubic problems Handle multiple root scenarios Verify solutions using graphical analysis |
Q/A on advanced cubic graphing using complex examples
Discussions on multiple root identification using graph analysis Solving challenging cubic problems using systematic methods Demonstrations using detailed cubic constructions Explaining verification methods using graphical checking |
Chalk and blackboard, advanced graph examples, exercise books
|
KLB Mathematics Book Three Pg 302-304
|
|
| 5 | 4 |
Graphical Methods
|
Advanced cubic solutions
|
By the end of the
lesson, the learner
should be able to:
Draw graphs of cubic equations Apply graphical methods to complex cubic problems Handle multiple root scenarios Verify solutions using graphical analysis |
Q/A on advanced cubic graphing using complex examples
Discussions on multiple root identification using graph analysis Solving challenging cubic problems using systematic methods Demonstrations using detailed cubic constructions Explaining verification methods using graphical checking |
Chalk and blackboard, advanced graph examples, exercise books
|
KLB Mathematics Book Three Pg 302-304
|
|
| 5 | 5 |
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 | 6 |
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
|
|
| 5 | 7 |
Graphical Methods
|
Advanced average rates
|
By the end of the
lesson, the learner
should be able to:
Calculate the average rates of change Handle complex rate scenarios Apply rates to business and scientific problems Integrate rate concepts with other topics |
Q/A on complex rate applications using advanced scenarios
Discussions on business and scientific rate applications Solving challenging rate problems using integrated methods Demonstrations using comprehensive rate examples Explaining advanced applications using detailed analysis |
Chalk and blackboard, advanced rate scenarios, exercise books
|
KLB Mathematics Book Three Pg 304-310
|
|
| 6 | 1 |
Graphical Methods
|
Introduction to 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
|
KLB Mathematics Book Three Pg 310-311
|
|
| 6 | 2 |
Graphical Methods
|
Rate of change at an instant
|
By the end of the
lesson, the learner
should be able to:
Calculate the rate of change at an instant Apply instantaneous rate methods systematically Use graphical techniques for instant rates Solve practical instantaneous rate problems |
Q/A on instantaneous rate calculation using graphical methods
Discussions on tangent line slope interpretation Solving instantaneous rate problems using systematic approaches Demonstrations using detailed tangent constructions Explaining practical applications using real scenarios |
Chalk and blackboard, detailed graph examples, exercise books
|
KLB Mathematics Book Three Pg 310-311
|
|
| 6 | 3 |
Graphical Methods
|
Advanced instantaneous rates
|
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
|
KLB Mathematics Book Three Pg 310-315
|
|
| 6 | 4 |
Graphical Methods
|
Advanced instantaneous rates
|
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
|
KLB Mathematics Book Three Pg 310-315
|
|
| 6 | 5 |
Graphical Methods
|
Empirical graphs
|
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
|
KLB Mathematics Book Three Pg 315-316
|
|
| 6 | 6 |
Graphical Methods
Matrices and Transformation |
Advanced empirical methods
Matrices of Transformation |
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
Exercise books -Manila paper -Ruler -Pencils |
KLB Mathematics Book Three Pg 315-321
|
|
| 6 | 7 |
Matrices and Transformation
|
Identifying Common Transformation Matrices
|
By the end of the
lesson, the learner
should be able to:
-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 |
-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 -String |
KLB Secondary Mathematics Form 4, Pages 1-5
|
|
| 7-8 |
ROUND ONE EXAM |
|||||||
| 8 | 5 |
Matrices and Transformation
|
Finding the Matrix of a Transformation
Using the Unit Square Method |
By the end of the
lesson, the learner
should be able to:
-Determine the matrix representing a given transformation -Use coordinate geometry to find transformation matrices -Apply algebraic methods to find matrix elements -Verify transformation matrices using test points |
-Work through algebraic method of finding matrices -Use simultaneous equations to solve for matrix elements -Practice with different types of transformations -Verify results by applying matrix to test objects |
Exercise books
-Manila paper -Ruler -Chalk/markers -String |
KLB Secondary Mathematics Form 4, Pages 6-16
|
|
| 8 | 6 |
Matrices and Transformation
|
Successive Transformations
Matrix Multiplication for Combined 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
|
|
| 8 | 7 |
Matrices and Transformation
|
Single Matrix for Successive Transformations
|
By the end of the
lesson, the learner
should be able to:
-Find single matrix equivalent to successive transformations -Apply commutativity properties in matrix multiplication -Determine order of operations in transformations -Solve complex transformation problems efficiently |
-Demonstrate equivalence of successive and single matrices -Practice finding single equivalent matrices -Compare geometric and algebraic approaches -Solve real-world transformation problems |
Exercise books
-Manila paper -Ruler -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 21-24
|
|
| 9 | 1 |
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
|
|
| 9 | 2 |
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
|
|
|
| 9 | 3 |
Matrices and Transformation
|
Shear Transformations
|
By the end of the
lesson, the learner
should be able to:
-Define shear transformation and its properties -Identify invariant lines in shear transformations -Construct matrices for shear transformations -Apply shear transformations to geometric objects |
-Demonstrate shear using cardboard models -Identify x-axis and y-axis invariant shears -Practice constructing shear matrices -Apply shears to triangles and rectangles |
Exercise books
-Cardboard pieces -Manila paper -Ruler |
KLB Secondary Mathematics Form 4, Pages 28-34
|
|
| 9 | 4 |
Matrices and Transformation
|
Stretch Transformations
|
By the end of the
lesson, the learner
should be able to:
-Define stretch transformation and scale factors -Distinguish between one-way and two-way stretches -Construct matrices for stretch transformations -Apply stretch transformations to solve problems |
-Demonstrate stretch using rubber bands and paper -Practice with x-axis and y-axis invariant stretches -Construct stretch matrices systematically -Compare stretches with enlargements |
Exercise books
-Rubber bands -Manila paper -Ruler |
KLB Secondary Mathematics Form 4, Pages 28-34
|
|
| 9 | 5 |
Matrices and Transformation
|
Stretch Transformations
|
By the end of the
lesson, the learner
should be able to:
-Define stretch transformation and scale factors -Distinguish between one-way and two-way stretches -Construct matrices for stretch transformations -Apply stretch transformations to solve problems |
-Demonstrate stretch using rubber bands and paper -Practice with x-axis and y-axis invariant stretches -Construct stretch matrices systematically -Compare stretches with enlargements |
Exercise books
-Rubber bands -Manila paper -Ruler |
KLB Secondary Mathematics Form 4, Pages 28-34
|
|
| 9 | 6 |
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
|
|
| 9 | 7 |
Matrices and Transformation
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Isometric and Non-isometric Transformations
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By the end of the
lesson, the learner
should be able to:
-Distinguish between isometric and non-isometric transformations -Classify transformations based on shape and size preservation -Identify isometric transformations from matrices -Apply classification to solve problems |
-Compare congruent and non-congruent images using cutouts -Classify transformations systematically -Practice identification from matrices -Discuss real-world applications of each type |
Exercise books
-Paper cutouts -Manila paper -Ruler |
KLB Secondary Mathematics Form 4, Pages 35-38
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