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| WK | LSN | TOPIC | SUB-TOPIC | OBJECTIVES | T/L ACTIVITIES | T/L AIDS | REFERENCE | REMARKS |
|---|---|---|---|---|---|---|---|---|
| 2 | 1 |
Matrices
|
Matrix representation and order of matrix
|
By the end of the
lesson, the learner
should be able to:
Represent matrix State the order of a matrix |
Discussions
Solving Demonstrating Explaining |
Chart showing tabular data
|
KLB Mathematics
Book Three Pg 168-170 |
|
| 2 | 2 |
Matrices
|
Addition of matrix
Subtraction of matrices Combined addition and subtraction of matrices |
By the end of the
lesson, the learner
should be able to:
Add matrices |
Discussions
Solving Demonstrating Explaining |
Chart showing tabular data
|
KLB Mathematics
Book Three Pg 170 |
|
| 2 | 3 |
Matrices
|
Matrix multiplication
Identity matrix |
By the end of the
lesson, the learner
should be able to:
Multiply matrices |
Discussions
Solving Demonstrating Explaining |
Chart showing tabular data
|
KLB Mathematics
Book Three Pg 174-175 |
|
| 2 | 4 |
Matrices
|
Determinant of a 2
Inverse of a 2 Inverse of a 2 |
By the end of the
lesson, the learner
should be able to:
Find the determinant of a 2 |
Discussions
Solving Demonstrating Explaining |
Calculator
Calculators |
KLB Mathematics
Book Three Pg 183 |
|
| 2 | 5 |
Matrices
|
Solutions of simultaneous equations by matrix method
Problem solving |
By the end of the
lesson, the learner
should be able to:
Solve simultaneous equations by matrix method |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 188-190 |
|
| 2 | 6 |
Formulae and variations
|
Formulae
Direct variation Inverse variation |
By the end of the
lesson, the learner
should be able to:
Make subject of the given formula |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 191-193 |
|
| 2 | 7 |
Formulae and variations
|
Partial variation
Joint variation Joint variation |
By the end of the
lesson, the learner
should be able to:
Solve problems involving partial variations |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 201-203 |
|
| 3 | 1 |
Sequences and series
|
Sequences
Arithmetic sequences Geometric sequence |
By the end of the
lesson, the learner
should be able to:
Find the next terms |
Discussions
Solving Demonstrating Explaining |
|
KLB Mathematics
Book Three Pg 207-208 |
|
| 3 | 2 |
Sequences and series
|
Arithmetic series
Geometric series |
By the end of the
lesson, the learner
should be able to:
Find the nth term of a given arithmetic series |
Discussions
Solving Demonstrating Explaining |
|
KLB Mathematics
Book Three Pg 214-215 |
|
| 3 | 3 |
Sequences and series
Vectors II Vectors II |
Geometric series
Coordinates in two dimensions Coordinates in three dimensions |
By the end of the
lesson, the learner
should be able to:
Find the nth term of a given geometric series |
Discussions
Solving Demonstrating Explaining |
Wire mesh in 3 dimensions
|
KLB Mathematics
Book Three Pg 216-219 |
|
| 3 | 4 |
Vectors II
|
Column vectors
Position vector Unit vectors |
By the end of the
lesson, the learner
should be able to:
Find a displacement and represent it in column vector |
Discussions
Solving Demonstrating Explaining |
Wire mesh in 3 dimensions
|
KLB Mathematics
Book Three Pg 223-224 |
|
| 3 | 5 |
Vectors II
|
Unit vectors
Magnitude of a vector in three dimensions Parallel vectors |
By the end of the
lesson, the learner
should be able to:
Express vectors in terms of unit vectors |
Discussions
Solving Demonstrating Explaining |
calculators
Geoboard |
KLB Mathematics
Book Three Pg 226-228 |
|
| 3 | 6 |
Vectors II
|
Collinear points
Proportion division of a line |
By the end of the
lesson, the learner
should be able to:
Show that points are collinear |
Discussions
Solving Demonstrating Explaining |
Geoboard
Geoboard, calculators |
KLB Mathematics
Book Three Pg 232 |
|
| 3 | 7 |
Vectors II
|
Proportion division of a line
Ratio theorem |
By the end of the
lesson, the learner
should be able to:
Divide a line externally in the given ratio |
Discussions
Solving Demonstrating Explaining |
Geoboard, calculators
|
KLB Mathematics
Book Three Pg 238 |
|
| 4 | 1 |
Vectors II
|
Ratio theorem
Mid-point Ratio theorem |
By the end of the
lesson, the learner
should be able to:
Find the position vector |
Discussions
Solving Demonstrating Explaining |
Geoboard, calculators
|
KLB Mathematics
Book Three Pg 242 |
|
| 4 | 2 |
Vectors II
|
Ratio theorem
Applications of vectors Applications of vectors |
By the end of the
lesson, the learner
should be able to:
Use ratio theorem to find the given vectors |
Discussions
Solving Demonstrating Explaining |
Geoboard, calculators
|
KLB Mathematics
Book Three Pg 246-248 |
|
| 4 | 3 |
Binomial expansion
|
Binomial Expansion up to power four
Pascal Pascal |
By the end of the
lesson, the learner
should be able to:
Expand binomial function up to power four |
Discussions
Solving Demonstrating Explaining |
calculators
|
KLB Mathematics
Book Three Pg 256 |
|
| 4 | 4 |
Binomial expansion
|
Pascal
Applications to numerical cases Applications to numerical cases |
By the end of the
lesson, the learner
should be able to:
Use Pascal |
Discussions
Solving Demonstrating Explaining |
calculators
Calculators |
KLB Mathematics
Book Three Pg 258-259 |
|
| 4 | 5 |
Probability
|
Experimental probability
Range of probability measure |
By the end of the
lesson, the learner
should be able to:
Calculate the experimental probability |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 262-264 |
|
| 4 | 6 |
Probability
|
Probability space
Combined events |
By the end of the
lesson, the learner
should be able to:
Calculate the probability space for the theoretical probability |
Discussions
Solving Demonstrating Explaining |
Calculators, charts
|
KLB Mathematics
Book Three Pg 266-267 |
|
| 4 | 7 |
Probability
|
Combined events
Independent events Independent events |
By the end of the
lesson, the learner
should be able to:
Find the probability of a combined events |
Discussions
Solving Demonstrating Explaining |
Calculators, charts
|
KLB Mathematics
Book Three Pg 273-274 |
|
| 5 | 1 |
Probability
|
Independent events
Tree diagrams Tree diagrams |
By the end of the
lesson, the learner
should be able to:
Find the probability of independent events |
Discussions
Solving Demonstrating Explaining |
Calculators, charts
|
KLB Mathematics
Book Three Pg 278-280 |
|
| 5 | 2 |
Probability
Compound proportions and rate of work Compound proportions and rate of work |
Tree diagrams
Compound proportions Compound proportions |
By the end of the
lesson, the learner
should be able to:
Use tree diagrams to find probability |
Discussions
Solving Demonstrating Explaining |
Calculators, charts
Calculators |
KLB Mathematics
Book Three Pg 283-285 |
|
| 5 | 3 |
Compound proportions and rate of work
|
Proportional parts
Rates of work |
By the end of the
lesson, the learner
should be able to:
Calculate the proportional parts |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 291-293 |
|
| 5 | 4 |
Compound proportions and rate of work
Graphical methods |
Rates of work
Tables of given relations |
By the end of the
lesson, the learner
should be able to:
Calculate the rate of work |
Discussions
Solving Demonstrating Explaining |
Calculators
Geoboard & graph books |
KLB Mathematics
Book Three Pg 295-296 |
|
| 5 | 5 |
Graphical methods
|
Graphs of given relations
Graphical solution of cubic equations Graphical solution of cubic equations |
By the end of the
lesson, the learner
should be able to:
Draw graphs of given relations |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
|
KLB Mathematics
Book Three Pg 300 |
|
| 5 | 6 |
Graphical methods
|
Average rates of change
Rate of change at an instant Empirical graphs |
By the end of the
lesson, the learner
should be able to:
Calculate the average rates of change |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
|
KLB Mathematics
Book Three Pg 304-306 |
|
| 5 | 7 |
Graphical methods
|
Reduction of non-linear laws to linear form
|
By the end of the
lesson, the learner
should be able to:
Draw the graphs of reduction of non-linear laws to linear form |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
Geoboard & graph bookss |
KLB Mathematics
Book Three Pg 318-321 |
|
| 6 | 1 |
Graphical methods
|
Equation of a circle
|
By the end of the
lesson, the learner
should be able to:
Find the equation of a circle |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
|
KLB Mathematics
Book Three Pg 325-326 |
|
| 6 | 2 |
Matrices and Transformation
|
Matrices of Transformation
Identifying Common Transformation Matrices Finding the Matrix of a Transformation |
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 |
-Review transformation concepts from Form 2 -Demonstrate matrix multiplication using position vectors -Plot objects and images on coordinate plane -Practice identifying transformations from images |
Exercise books
-Manila paper -Ruler -Pencils -String -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 1-5
|
|
| 6 | 3 |
Matrices and Transformation
|
Using the Unit Square Method
Successive Transformations Matrix Multiplication for Combined Transformations |
By the end of the
lesson, the learner
should be able to:
-Use unit square to find transformation matrices -Read matrix elements directly from unit square images -Apply unit square method to various transformations -Compare unit square method with algebraic method |
-Demonstrate unit square method systematically -Practice reading transformation matrices from diagrams -Apply method to reflections, rotations, enlargements -Compare efficiency of different methods |
Exercise books
-Manila paper -Ruler -String -Coloured pencils -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 6-16
|
|
| 6 | 4 |
Matrices and Transformation
|
Single Matrix for Successive Transformations
Inverse of a Transformation Properties of Inverse 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
|
|
| 6 | 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
|
|
|
| 6 | 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
|
|
| 6 | 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
|
|
| 7 | 1 |
Matrices and Transformation
Statistics II |
Isometric and Non-isometric Transformations
Introduction to Advanced Statistics |
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 -Real data examples -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 35-38
|
|
| 7 | 2 |
Statistics II
|
Working Mean Concept
|
By the end of the
lesson, the learner
should be able to:
-Define working mean (assumed mean) -Explain why working mean simplifies calculations -Identify appropriate working mean values -Apply working mean to reduce calculation errors |
-Demonstrate calculation difficulties with large numbers -Show how working mean simplifies arithmetic -Practice selecting suitable working means -Compare results with and without working mean |
Exercise books
-Manila paper -Sample datasets -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 39-42
|
|
| 7 | 3 |
Statistics II
|
Mean Using Working Mean - Simple Data
Mean Using Working Mean - Frequency Tables |
By the end of the
lesson, the learner
should be able to:
-Calculate mean using working mean for ungrouped data -Apply the formula: mean = working mean + mean of deviations -Verify results using direct calculation method -Solve problems with whole numbers |
-Work through step-by-step examples on chalkboard -Practice with student marks and heights data -Verify answers using traditional method -Individual practice with guided support |
Exercise books
-Manila paper -Student data -Chalk/markers -Community data |
KLB Secondary Mathematics Form 4, Pages 42-48
|
|
| 7 | 4 |
Statistics II
|
Mean for Grouped Data Using Working Mean
|
By the end of the
lesson, the learner
should be able to:
-Calculate mean for grouped continuous data -Select appropriate working mean for grouped data -Use midpoints of class intervals correctly -Apply working mean formula to grouped data |
-Use height/weight data of students in class -Practice finding midpoints of class intervals -Work through complex calculations step by step -Students practice with agricultural production data |
Exercise books
-Manila paper -Real datasets -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 42-48
|
|
| 7 | 5 |
Statistics II
|
Advanced Working Mean Techniques
|
By the end of the
lesson, the learner
should be able to:
-Apply coding techniques with working mean -Divide by class width to simplify further -Use transformation methods efficiently -Solve complex grouped data problems |
-Demonstrate coding method on chalkboard -Show how dividing by class width helps -Practice reverse calculations to get original mean -Work with economic data from Kenya |
Exercise books
-Manila paper -Economic data -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 42-48
|
|
| 7 | 6 |
Statistics II
|
Introduction to Quartiles, Deciles, Percentiles
Calculating Quartiles for Ungrouped Data |
By the end of the
lesson, the learner
should be able to:
-Define quartiles, deciles, and percentiles -Understand how they divide data into parts -Explain the relationship between these measures -Identify their importance in data analysis |
-Use physical demonstration with student heights -Arrange 20 students by height to show quartiles -Explain percentile ranks in exam results -Discuss applications in grading systems |
Exercise books
-Manila paper -Student height data -Measuring tape -Test score data -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 49-52
|
|
| 7 | 7 |
Statistics II
|
Quartiles for Grouped Data
|
By the end of the
lesson, the learner
should be able to:
-Calculate quartiles using interpolation formula -Identify quartile classes correctly -Apply the formula: Q = L + [(n/4 - CF)/f] × h -Solve problems with continuous grouped data |
-Work through detailed examples on chalkboard -Practice identifying quartile positions -Use cumulative frequency systematically -Apply to real examination grade data |
Exercise books
-Manila paper -Grade data -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 49-52
|
|
| 8 | 1 |
Statistics II
|
Deciles and Percentiles Calculations
Introduction to Cumulative Frequency |
By the end of the
lesson, the learner
should be able to:
-Calculate specific deciles and percentiles -Apply interpolation formulas for deciles/percentiles -Interpret decile and percentile positions -Use these measures for comparative analysis |
-Calculate specific percentiles for class test scores -Find deciles for sports performance data -Compare students' positions using percentiles -Practice with national examination statistics |
Exercise books
-Manila paper -Performance data -Chalk/markers -Ruler -Class data |
KLB Secondary Mathematics Form 4, Pages 49-52
|
|
| 8 | 2 |
Statistics II
|
Drawing Cumulative Frequency Curves (Ogives)
|
By the end of the
lesson, the learner
should be able to:
-Draw accurate ogives using proper scales -Plot cumulative frequency against upper boundaries -Create smooth curves through plotted points -Label axes and scales correctly |
-Practice plotting on large manila paper -Use rulers for accurate scales -Demonstrate smooth curve drawing technique -Students create their own ogives |
Exercise books
-Manila paper -Ruler -Pencils |
KLB Secondary Mathematics Form 4, Pages 52-60
|
|
| 8 | 3 |
Statistics II
|
Reading Values from Ogives
Applications of Ogives |
By the end of the
lesson, the learner
should be able to:
-Read median from cumulative frequency curve -Find quartiles using ogive -Estimate any percentile from the curve -Interpret readings in real-world context |
-Demonstrate reading techniques on large ogive -Practice finding median position (n/2) -Read quartile positions systematically -Students practice reading their own curves |
Exercise books
-Manila paper -Completed ogives -Ruler -Real problem datasets |
KLB Secondary Mathematics Form 4, Pages 52-60
|
|
| 8 | 4 |
Statistics II
|
Introduction to Measures of Dispersion
|
By the end of the
lesson, the learner
should be able to:
-Define dispersion and its importance -Understand limitations of central tendency alone -Compare datasets with same mean but different spread -Identify different measures of dispersion |
-Compare test scores of two classes with same mean -Show how different spreads affect interpretation -Discuss variability in real-world data -Introduce range as simplest measure |
Exercise books
-Manila paper -Comparative datasets -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 60-65
|
|
| 8 | 5 |
Statistics II
|
Range and Interquartile Range
Mean Absolute Deviation |
By the end of the
lesson, the learner
should be able to:
-Calculate range for different datasets -Find interquartile range (Q3 - Q1) -Calculate quartile deviation (semi-interquartile range) -Compare advantages and limitations of each measure |
-Calculate range for student heights in class -Find IQR for the same data -Discuss effect of outliers on range -Compare IQR stability with range |
Exercise books
-Manila paper -Student data -Measuring tape -Test score data -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 60-65
|
|
| 8 | 6 |
Statistics II
|
Introduction to Variance
|
By the end of the
lesson, the learner
should be able to:
-Define variance as mean of squared deviations -Calculate variance using definition formula -Understand why deviations are squared -Compare variance with other dispersion measures |
-Work through variance calculation step by step -Explain squaring deviations eliminates negatives -Calculate variance for simple datasets -Compare with mean absolute deviation |
Exercise books
-Manila paper -Simple datasets -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 65-70
|
|
| 8 | 7 |
Statistics II
|
Variance Using Alternative Formula
Standard Deviation Calculations |
By the end of the
lesson, the learner
should be able to:
-Apply the formula: σ² = (Σx²/n) - x̄² -Use alternative variance formula efficiently -Compare computational methods -Solve variance problems for frequency data |
-Demonstrate both variance formulas -Show computational advantages of alternative formula -Practice with frequency tables -Students choose efficient method |
Exercise books
-Manila paper -Frequency data -Chalk/markers -Exam score data |
KLB Secondary Mathematics Form 4, Pages 65-70
|
|
| 9 | 1 |
Statistics II
|
Standard Deviation for Grouped Data
|
By the end of the
lesson, the learner
should be able to:
-Calculate standard deviation for frequency distributions -Use working mean with grouped data for SD -Apply coding techniques to simplify calculations -Solve complex grouped data problems |
-Work with agricultural yield data from local farms -Use coding method to simplify calculations -Calculate SD step by step for grouped data -Compare variability in different crops |
Exercise books
-Manila paper -Agricultural data -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 65-70
|
|
| 9 | 2 |
Statistics II
Loci |
Advanced Standard Deviation Techniques
Introduction to Loci |
By the end of the
lesson, the learner
should be able to:
-Apply transformation properties of standard deviation -Use coding with class width division -Solve problems with multiple transformations -Verify results using different methods |
-Demonstrate coding transformations -Show how SD changes with data transformations -Practice reverse calculations -Verify using alternative methods |
Exercise books
-Manila paper -Transformation examples -Chalk/markers -String |
KLB Secondary Mathematics Form 4, Pages 65-70
|
|
| 9 | 3 |
Loci
|
Basic Locus Concepts and Laws
|
By the end of the
lesson, the learner
should be able to:
-Understand that loci follow specific laws or conditions -Identify the laws governing different types of movement -Distinguish between 2D and 3D loci -Apply locus concepts to simple problems |
-Physical demonstrations with moving objects -Students track movement of classroom door -Identify laws governing pendulum movement -Practice stating locus laws clearly |
Exercise books
-Manila paper -String -Real objects |
KLB Secondary Mathematics Form 4, Pages 73-75
|
|
| 9 | 4 |
Loci
|
Perpendicular Bisector Locus
Properties and Applications of Perpendicular Bisector |
By the end of the
lesson, the learner
should be able to:
-Define perpendicular bisector locus -Construct perpendicular bisector using compass and ruler -Prove that points on perpendicular bisector are equidistant from endpoints -Apply perpendicular bisector to solve problems |
-Construct perpendicular bisector on manila paper -Measure distances to verify equidistance property -Use folding method to find perpendicular bisector -Practice with different line segments |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 9 | 5 |
Loci
|
Locus of Points at Fixed Distance from a Point
|
By the end of the
lesson, the learner
should be able to:
-Define circle as locus of points at fixed distance from center -Construct circles with given radius using compass -Understand sphere as 3D locus from fixed point -Solve problems involving circular loci |
-Construct circles of different radii -Demonstrate with string of fixed length -Discuss radar coverage, radio signal range -Students create circles with various measurements |
Exercise books
-Manila paper -Compass -String |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 9 | 6 |
Loci
|
Locus of Points at Fixed Distance from a Line
|
By the end of the
lesson, the learner
should be able to:
-Define locus of points at fixed distance from straight line -Construct parallel lines at given distances -Understand cylindrical surface in 3D -Apply to practical problems like road margins |
-Construct parallel lines using ruler and set square -Mark points at equal distances from given line -Discuss road design, river banks, field boundaries -Practice with various distances and orientations |
Exercise books
-Manila paper -Ruler -Set square |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 9 | 7 |
Loci
|
Angle Bisector Locus
Properties and Applications of Angle Bisector |
By the end of the
lesson, the learner
should be able to:
-Define angle bisector locus -Construct angle bisectors using compass and ruler -Prove equidistance property of angle bisector -Apply angle bisector to find incenters |
-Construct angle bisectors for various angles -Verify equidistance from angle arms -Find incenter of triangle using angle bisectors -Practice with acute, obtuse, and right angles |
Exercise books
-Manila paper -Compass -Protractor -Ruler |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 10 | 1 |
Loci
|
Constant Angle Locus
|
By the end of the
lesson, the learner
should be able to:
-Understand constant angle locus concept -Construct constant angle loci using arc method -Apply circle theorems to constant angle problems -Solve problems involving angles in semicircles |
-Demonstrate constant angle using protractor -Construct arc passing through two points -Use angles in semicircle property -Practice with different angle measures |
Exercise books
-Manila paper -Compass -Protractor |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 10 | 2 |
Loci
|
Advanced Constant Angle Constructions
Introduction to Intersecting Loci |
By the end of the
lesson, the learner
should be able to:
-Construct constant angle loci for various angles -Find centers of constant angle arcs -Solve complex constant angle problems -Apply to geometric theorem proving |
-Find centers for 60°, 90°, 120° angle loci -Construct major and minor arcs -Solve problems involving multiple angle constraints -Verify constructions using measurement |
Exercise books
-Manila paper -Compass -Protractor -Ruler |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 10 | 3 |
Loci
|
Intersecting Circles and Lines
|
By the end of the
lesson, the learner
should be able to:
-Find intersections of circles with lines -Determine intersections of two circles -Solve problems with line and circle combinations -Apply to geometric construction problems |
-Construct intersecting circles and lines -Find common tangents to circles -Solve problems involving circle-line intersections -Apply to wheel and track problems |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 83-89
|
|
| 10 | 4 |
Loci
|
Triangle Centers Using Intersecting Loci
Complex Intersecting Loci Problems |
By the end of the
lesson, the learner
should be able to:
-Find circumcenter using perpendicular bisector intersections -Locate incenter using angle bisector intersections -Determine centroid and orthocenter -Apply triangle centers to solve problems |
-Construct all four triangle centers -Compare properties of different triangle centers -Use triangle centers in geometric proofs -Solve problems involving triangle center properties |
Exercise books
-Manila paper -Compass -Ruler -Real-world scenarios |
KLB Secondary Mathematics Form 4, Pages 83-89
|
|
| 10 | 5 |
Loci
|
Introduction to Loci of Inequalities
|
By the end of the
lesson, the learner
should be able to:
-Understand graphical representation of inequalities -Identify regions satisfying inequality conditions -Distinguish between boundary lines and regions -Apply inequality loci to practical constraints |
-Shade regions representing simple inequalities -Use broken and solid lines appropriately -Practice with distance inequalities -Apply to real-world constraint problems |
Exercise books
-Manila paper -Ruler -Colored pencils |
KLB Secondary Mathematics Form 4, Pages 89-92
|
|
| 10 | 6 |
Loci
|
Distance Inequality Loci
Combined Inequality Loci |
By the end of the
lesson, the learner
should be able to:
-Represent distance inequalities graphically -Solve problems with "less than" and "greater than" distances -Find regions satisfying distance constraints -Apply to safety zone problems |
-Shade regions inside and outside circles -Solve exclusion zone problems -Apply to communication range problems -Practice with multiple distance constraints |
Exercise books
-Manila paper -Compass -Colored pencils -Ruler |
KLB Secondary Mathematics Form 4, Pages 89-92
|
|
| 10 | 7 |
Loci
|
Advanced Inequality Applications
|
By the end of the
lesson, the learner
should be able to:
-Apply inequality loci to linear programming introduction -Solve real-world optimization problems -Find maximum and minimum values in regions -Use graphical methods for decision making |
-Solve simple linear programming problems -Find optimal points in feasible regions -Apply to business and farming scenarios -Practice identifying corner points |
Exercise books
-Manila paper -Ruler -Real problem data |
KLB Secondary Mathematics Form 4, Pages 89-92
|
|
| 11 | 1 |
Loci
|
Introduction to Loci Involving Chords
Chord-Based Constructions |
By the end of the
lesson, the learner
should be able to:
-Review chord properties in circles -Understand perpendicular bisector of chords -Apply chord theorems to loci problems -Construct equal chords in circles |
-Review chord bisector theorem -Construct chords of given lengths -Find centers using chord properties -Practice with chord intersection theorems |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 92-94
|
|
| 11 | 2 |
Loci
|
Advanced Chord Problems
|
By the end of the
lesson, the learner
should be able to:
-Solve complex problems involving multiple chords -Apply power of point theorem -Find loci related to chord properties -Use chords in circle geometry proofs |
-Apply intersecting chords theorem -Solve problems with chord-secant relationships -Find loci of points with equal power -Practice with tangent-chord angles |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 92-94
|
|
| 11 | 3 |
Loci
Trigonometry III |
Integration of All Loci Types
Review of Basic Trigonometric Ratios |
By the end of the
lesson, the learner
should be able to:
-Combine different types of loci in single problems -Solve comprehensive loci challenges -Apply multiple loci concepts simultaneously -Use loci in geometric investigations |
-Solve multi-step loci problems -Combine circle, line, and angle loci -Apply to real-world complex scenarios -Practice systematic problem-solving |
Exercise books
-Manila paper -Compass -Ruler -Rulers -Calculators (if available) |
KLB Secondary Mathematics Form 4, Pages 73-94
|
|
| 11 | 4 |
Trigonometry III
|
Deriving the Identity sin²θ + cos²θ = 1
|
By the end of the
lesson, the learner
should be able to:
-Understand the derivation of fundamental identity -Apply Pythagoras theorem to unit circle -Use the identity to solve trigonometric equations -Convert between sin, cos using the identity |
-Demonstrate using right-angled triangle with hypotenuse 1 -Show algebraic derivation step by step -Practice substituting values to verify identity -Solve equations using the fundamental identity |
Exercise books
-Manila paper -Unit circle diagrams -Calculators |
KLB Secondary Mathematics Form 4, Pages 99-103
|
|
| 11 | 5 |
Trigonometry III
|
Applications of sin²θ + cos²θ = 1
Additional Trigonometric Identities |
By the end of the
lesson, the learner
should be able to:
-Solve problems using the fundamental identity -Find missing trigonometric ratios given one ratio -Apply identity to simplify trigonometric expressions -Use identity in geometric problem solving |
-Work through examples finding cos when sin is given -Practice simplifying complex trigonometric expressions -Solve problems involving unknown angles -Apply to real-world navigation problems |
Exercise books
-Manila paper -Trigonometric tables -Real-world examples -Identity reference sheet -Calculators |
KLB Secondary Mathematics Form 4, Pages 99-103
|
|
| 11 | 6 |
Trigonometry III
|
Introduction to Waves
|
By the end of the
lesson, the learner
should be able to:
-Define amplitude and period of waves -Understand wave characteristics and properties -Identify amplitude and period from graphs -Connect waves to trigonometric functions |
-Use physical demonstrations with string/rope -Draw simple wave patterns on manila paper -Measure amplitude and period from wave diagrams -Discuss real-world wave examples (sound, light) |
Exercise books
-Manila paper -String/rope -Wave diagrams |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 11 | 7 |
Trigonometry III
|
Sine and Cosine Waves
|
By the end of the
lesson, the learner
should be able to:
-Plot graphs of y = sin x and y = cos x -Identify amplitude and period of basic functions -Compare sine and cosine wave patterns -Read values from trigonometric graphs |
-Plot sin x and cos x on same axes using manila paper -Mark key points (0°, 90°, 180°, 270°, 360°) -Measure and compare wave characteristics -Practice reading values from completed graphs |
Exercise books
-Manila paper -Rulers -Graph paper (if available) |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 12 | 1 |
Trigonometry III
|
Transformations of Sine Waves
Period Changes in Trigonometric Functions |
By the end of the
lesson, the learner
should be able to:
-Understand effect of coefficient on amplitude -Plot graphs of y = k sin x for different values of k -Compare transformed waves with basic sine wave -Apply amplitude changes to real situations |
-Plot y = 2 sin x, y = 3 sin x on manila paper -Compare amplitudes with y = sin x -Demonstrate stretching effect of coefficient -Apply to sound volume or signal strength examples |
Exercise books
-Manila paper -Colored pencils -Rulers -Period calculation charts |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 12 | 2 |
Trigonometry III
|
Combined Amplitude and Period Transformations
|
By the end of the
lesson, the learner
should be able to:
-Plot graphs of y = a sin(bx) functions -Identify both amplitude and period changes -Solve problems with multiple transformations -Apply to complex wave phenomena |
-Plot y = 2 sin(3x), y = 3 sin(x/2) on manila paper -Calculate both amplitude and period for each function -Compare multiple transformed waves -Apply to radio waves or tidal patterns |
Exercise books
-Manila paper -Rulers -Transformation examples |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 12 | 3 |
Trigonometry III
|
Phase Angles and Wave Shifts
General Trigonometric Functions |
By the end of the
lesson, the learner
should be able to:
-Understand concept of phase angle -Plot graphs of y = sin(x + θ) functions -Identify horizontal shifts in wave patterns -Apply phase differences to wave analysis |
-Plot y = sin(x + 45°), y = sin(x - 30°) -Demonstrate horizontal shifting of waves -Compare leading and lagging waves -Apply to electrical circuits or sound waves |
Exercise books
-Manila paper -Colored pencils -Phase shift examples -Rulers -Complex function examples |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 12 | 4 |
Trigonometry III
|
Cosine Wave Transformations
|
By the end of the
lesson, the learner
should be able to:
-Apply transformations to cosine functions -Plot y = a cos(bx + c) functions -Compare cosine and sine transformations -Use cosine functions in modeling |
-Plot various cosine transformations on manila paper -Compare with equivalent sine transformations -Practice identifying cosine wave parameters -Model temperature variations using cosine |
Exercise books
-Manila paper -Rulers -Temperature data |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 12 | 5 |
Trigonometry III
|
Introduction to Trigonometric Equations
Solving Basic Trigonometric Equations |
By the end of the
lesson, the learner
should be able to:
-Understand concept of trigonometric equations -Identify that trig equations have multiple solutions -Solve simple equations like sin x = 0.5 -Find all solutions in given ranges |
-Demonstrate using unit circle or graphs -Show why sin x = 0.5 has multiple solutions -Practice finding principal values -Use graphs to identify all solutions in range |
Exercise books
-Manila paper -Unit circle diagrams -Trigonometric tables -Calculators -Solution worksheets |
KLB Secondary Mathematics Form 4, Pages 109-112
|
|
| 12 | 6 |
Trigonometry III
|
Quadratic Trigonometric Equations
|
By the end of the
lesson, the learner
should be able to:
-Solve equations like sin²x - sin x = 0 -Apply factoring techniques to trigonometric equations -Use substitution methods for complex equations -Find all solutions systematically |
-Demonstrate substitution method (let y = sin x) -Factor quadratic expressions in trigonometry -Solve resulting quadratic equations -Back-substitute to find angle solutions |
Exercise books
-Manila paper -Factoring techniques -Substitution examples |
KLB Secondary Mathematics Form 4, Pages 109-112
|
|
| 12 | 7 |
Trigonometry III
|
Equations Involving Multiple Angles
Using Graphs to Solve Trigonometric Equations Trigonometric Equations with Identities |
By the end of the
lesson, the learner
should be able to:
-Solve equations like sin(2x) = 0.5 -Handle double and triple angle cases -Find solutions for compound angle equations -Apply to periodic motion problems |
-Work through sin(2x) = 0.5 systematically -Show relationship between 2x solutions and x solutions -Practice with cos(3x) and tan(x/2) equations -Apply to pendulum and rotation problems |
Exercise books
-Manila paper -Multiple angle examples -Real applications -Rulers -Graphing examples -Identity reference sheets -Complex examples |
KLB Secondary Mathematics Form 4, Pages 109-112
|
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