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| WK | LSN | TOPIC | SUB-TOPIC | OBJECTIVES | T/L ACTIVITIES | T/L AIDS | REFERENCE | REMARKS |
|---|---|---|---|---|---|---|---|---|
| 1 |
SCHOOL OPENING AND OPENER EXAMINATIONS |
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| 2 | 1 |
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
|
|
| 2 | 2 |
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
|
|
| 2 | 3 |
Graphical Methods
|
Introduction to cubic equations
Graphical solution of 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
Chalk and blackboard, graph paper, cubic equation examples, exercise books |
KLB Mathematics Book Three Pg 301
|
|
| 2 | 4 |
Graphical Methods
|
Advanced cubic solutions
Introduction to rates of change |
By the end of the
lesson, the learner
should be able to:
Draw graphs of cubic equations Apply graphical methods to complex cubic problems Handle multiple root scenarios Verify solutions using graphical analysis |
Q/A on advanced cubic graphing using complex examples
Discussions on multiple root identification using graph analysis Solving challenging cubic problems using systematic methods Demonstrations using detailed cubic constructions Explaining verification methods using graphical checking |
Chalk and blackboard, advanced graph examples, exercise books
Chalk and blackboard, rate calculation examples, exercise books |
KLB Mathematics Book Three Pg 302-304
|
|
| 2 | 5 |
Graphical Methods
|
Average rates of change
Advanced average rates Introduction to instantaneous rates |
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
Chalk and blackboard, advanced rate scenarios, exercise books Chalk and blackboard, tangent line examples, exercise books |
KLB Mathematics Book Three Pg 304-306
|
|
| 2 | 6 |
Graphical Methods
|
Rate of change at an instant
Advanced instantaneous rates |
By the end of the
lesson, the learner
should be able to:
Calculate the rate of change at an instant 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
Chalk and blackboard, advanced rate examples, exercise books |
KLB Mathematics Book Three Pg 310-311
|
|
| 2 | 7 |
Graphical Methods
|
Empirical graphs
Advanced empirical methods |
By the end of the
lesson, the learner
should be able to:
Draw the empirical graphs Understand empirical data representation Plot experimental data systematically Analyze empirical relationships |
Q/A on empirical data plotting using experimental examples
Discussions on real data representation using practical scenarios Solving empirical graphing problems using systematic methods Demonstrations using experimental data examples Explaining empirical analysis using practical interpretations |
Chalk and blackboard, experimental data examples, exercise books
Chalk and blackboard, complex data examples, exercise books |
KLB Mathematics Book Three Pg 315-316
|
|
| 3 | 1 |
Circles: Chords and Tangents
|
Length of an arc
|
By the end of the
lesson, the learner
should be able to:
Calculate the length of an arc Apply arc length formula Understand arc-radius relationships |
Q/A on circle properties and terminology
Discussions on arc measurement concepts Solving basic arc length problems Demonstrations of formula application Explaining arc-angle relationships |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 124-125
|
|
| 3 | 2 |
Circles: Chords and Tangents
|
Chords
Parallel chords |
By the end of the
lesson, the learner
should be able to:
Calculate the length of a chord Apply chord properties and theorems Understand chord-radius relationships |
Q/A on chord definition and properties
Discussions on chord calculation methods Solving basic chord problems Demonstrations of geometric constructions Explaining chord theorems |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 126-128
|
|
| 3 | 3 |
Circles: Chords and Tangents
|
Equal chords
Intersecting chords Intersecting chords |
By the end of the
lesson, the learner
should be able to:
Find the length of equal chords Apply equal chord theorems Solve equal chord problems |
Q/A on equal chord properties
Discussions on chord equality conditions Solving equal chord problems Demonstrations of proof techniques Explaining theoretical foundations |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 131-132
|
|
| 3 | 4 |
Circles: Chords and Tangents
|
Chord properties
Tangent to a circle |
By the end of the
lesson, the learner
should be able to:
Solve comprehensive chord problems Integrate all chord concepts Apply chord knowledge systematically |
Q/A on comprehensive chord understanding
Discussions on integrated problem-solving Solving mixed chord problems Demonstrations of systematic approaches Explaining complete chord mastery |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 126-139
|
|
| 3 | 5 |
Circles: Chords and Tangents
|
Tangent to a circle
Properties of tangents to a circle from an external point |
By the end of the
lesson, the learner
should be able to:
Calculate the length of tangent Calculate the angle between tangents Apply tangent measurement techniques |
Q/A on tangent calculations
Discussions on tangent measurement Solving tangent calculation problems Demonstrations of measurement methods Explaining tangent applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 141-142
|
|
| 3 | 6 |
Circles: Chords and Tangents
|
Tangent properties
Tangents to two circles |
By the end of the
lesson, the learner
should be able to:
Solve comprehensive tangent problems Apply all tangent concepts Integrate tangent knowledge systematically |
Q/A on comprehensive tangent mastery
Discussions on integrated applications Solving mixed tangent problems Demonstrations of complete understanding Explaining systematic problem-solving |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 139-147
|
|
| 3 | 7 |
Circles: Chords and Tangents
|
Tangents to two circles
Contact of circles Contact of circles |
By the end of the
lesson, the learner
should be able to:
Calculate the tangents of transverse common tangents Find transverse tangent properties Compare direct and transverse tangents |
Q/A on transverse tangent concepts
Discussions on tangent type differences Solving transverse tangent problems Demonstrations of comparison methods Explaining tangent classifications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 150-151
|
|
| 4 | 1 |
Circles: Chords and Tangents
|
Circle contact
Angle in alternate segment |
By the end of the
lesson, the learner
should be able to:
Solve problems involving chords, tangents and contact circles Integrate all contact concepts Apply comprehensive contact knowledge |
Q/A on comprehensive contact understanding
Discussions on integrated problem-solving Solving complex contact problems Demonstrations of systematic approaches Explaining complete contact mastery |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 154-157
|
|
| 4 | 2 |
Circles: Chords and Tangents
|
Angle in alternate segment
Circumscribed circle |
By the end of the
lesson, the learner
should be able to:
Calculate the angles in alternate segments Solve complex segment problems Apply advanced segment theorems |
Q/A on advanced segment applications
Discussions on complex angle relationships Solving challenging segment problems Demonstrations of sophisticated techniques Explaining advanced applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 160-161
|
|
| 4 | 3 |
Circles: Chords and Tangents
|
Escribed circles
Centroid |
By the end of the
lesson, the learner
should be able to:
Construct escribed circles Find escribed circle properties Apply escription concepts |
Q/A on escription concepts
Discussions on escribed circle construction Solving escription problems Demonstrations of construction methods Explaining escription applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 165-166
|
|
| 4 | 4 |
Circles: Chords and Tangents
|
Orthocenter
Circle and triangle relationships |
By the end of the
lesson, the learner
should be able to:
Construct orthocenter Find orthocenter properties Apply orthocenter concepts |
Q/A on orthocenter concepts
Discussions on orthocenter construction Solving orthocenter problems Demonstrations of construction methods Explaining orthocenter applications |
Geometrical set, calculators
|
KLB Mathematics Book Three Pg 167
|
|
| 4 | 5 |
Statistics II
|
Introduction to Advanced Statistics
Working Mean Concept Mean Using Working Mean - Simple Data |
By the end of the
lesson, the learner
should be able to:
-Review measures of central tendency from Form 2 -Identify limitations of simple mean calculations -Understand need for advanced statistical methods -Recognize patterns in large datasets |
-Review mean, median, mode from previous work -Discuss challenges with large numbers -Examine real data from Kenya (population, rainfall) -Q&A on statistical applications in daily life |
Exercise books
-Manila paper -Real data examples -Chalk/markers -Sample datasets -Student data |
KLB Secondary Mathematics Form 4, Pages 39-42
|
|
| 4 | 6 |
Statistics II
|
Mean Using Working Mean - Frequency Tables
Mean for Grouped Data Using Working Mean |
By the end of the
lesson, the learner
should be able to:
-Calculate mean using working mean for frequency data -Apply working mean to discrete frequency distributions -Use the formula with frequencies correctly -Solve real-world problems with frequency data |
-Demonstrate with family size data from local community -Practice calculating fx and fd systematically -Work through examples step-by-step -Students practice with their own collected data |
Exercise books
-Manila paper -Community data -Chalk/markers -Real datasets |
KLB Secondary Mathematics Form 4, Pages 42-48
|
|
| 4 | 7 |
Statistics II
|
Advanced Working Mean Techniques
Introduction to Quartiles, Deciles, Percentiles |
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 -Student height data -Measuring tape |
KLB Secondary Mathematics Form 4, Pages 42-48
|
|
| 5 | 1 |
Statistics II
|
Calculating Quartiles for Ungrouped Data
Quartiles for Grouped Data |
By the end of the
lesson, the learner
should be able to:
-Find lower quartile, median, upper quartile for raw data -Apply the position formulas correctly -Arrange data in ascending order systematically -Interpret quartile values in context |
-Practice with test scores from the class -Arrange data systematically on chalkboard -Calculate Q1, Q2, Q3 step by step -Students work with their own datasets |
Exercise books
-Manila paper -Test score data -Chalk/markers -Grade data |
KLB Secondary Mathematics Form 4, Pages 49-52
|
|
| 5 | 2 |
Statistics II
|
Deciles and Percentiles Calculations
Introduction to Cumulative Frequency Drawing Cumulative Frequency Curves (Ogives) |
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 -Pencils |
KLB Secondary Mathematics Form 4, Pages 49-52
|
|
| 5 | 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
|
|
| 5 | 4 |
Statistics II
|
Introduction to Measures of Dispersion
Range and Interquartile Range |
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 -Student data -Measuring tape |
KLB Secondary Mathematics Form 4, Pages 60-65
|
|
| 5 | 5 |
Statistics II
|
Mean Absolute Deviation
Introduction to Variance |
By the end of the
lesson, the learner
should be able to:
-Calculate mean absolute deviation -Use absolute values correctly in calculations -Understand concept of average distance from mean -Apply MAD to compare variability in datasets |
-Calculate MAD for class test scores -Practice with absolute value calculations -Compare MAD values for different subjects -Interpret MAD in context of data spread |
Exercise books
-Manila paper -Test score data -Chalk/markers -Simple datasets |
KLB Secondary Mathematics Form 4, Pages 65-70
|
|
| 5 | 6 |
Statistics II
|
Variance Using Alternative Formula
Standard Deviation Calculations Standard Deviation for Grouped Data |
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 -Agricultural data |
KLB Secondary Mathematics Form 4, Pages 65-70
|
|
| 5 | 7 |
Statistics II
Trigonometry III |
Advanced Standard Deviation Techniques
Review of Basic Trigonometric Ratios |
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 -Rulers -Calculators (if available) |
KLB Secondary Mathematics Form 4, Pages 65-70
|
|
| 6 | 1 |
Trigonometry III
|
Deriving the Identity sin²θ + cos²θ = 1
Applications of 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 -Trigonometric tables -Real-world examples |
KLB Secondary Mathematics Form 4, Pages 99-103
|
|
| 6 | 2 |
Trigonometry III
|
Additional Trigonometric Identities
Introduction to Waves |
By the end of the
lesson, the learner
should be able to:
-Derive and apply tan θ = sin θ/cos θ -Use reciprocal ratios (sec, cosec, cot) -Apply multiple identities in problem solving -Verify trigonometric identities algebraically |
-Demonstrate relationship between tan, sin, cos -Introduce reciprocal ratios with examples -Practice identity verification techniques -Solve composite identity problems |
Exercise books
-Manila paper -Identity reference sheet -Calculators -String/rope -Wave diagrams |
KLB Secondary Mathematics Form 4, Pages 99-103
|
|
| 6 | 3 |
Trigonometry III
|
Sine and Cosine Waves
Transformations of Sine 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) -Colored pencils |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 6 | 4 |
Trigonometry III
|
Period Changes in Trigonometric Functions
Combined Amplitude and Period Transformations Phase Angles and Wave Shifts |
By the end of the
lesson, the learner
should be able to:
-Understand effect of coefficient on period -Plot graphs of y = sin(bx) for different values of b -Calculate periods of transformed functions -Apply period changes to cyclical phenomena |
-Plot y = sin(2x), y = sin(x/2) on manila paper -Compare periods with y = sin x -Calculate period using formula 360°/b -Apply to frequency and musical pitch examples |
Exercise books
-Manila paper -Rulers -Period calculation charts -Transformation examples -Colored pencils -Phase shift examples |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 6 | 5 |
Trigonometry III
|
General Trigonometric Functions
Cosine Wave Transformations |
By the end of the
lesson, the learner
should be able to:
-Work with y = a sin(bx + c) functions -Identify amplitude, period, and phase angle -Plot complex trigonometric functions -Solve problems involving all transformations |
-Plot y = 2 sin(3x + 60°) step by step -Identify all transformation parameters -Practice reading values from complex waves -Apply to real-world periodic phenomena |
Exercise books
-Manila paper -Rulers -Complex function examples -Temperature data |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 6 | 6 |
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
|
|
| 6 | 7 |
Trigonometry III
|
Quadratic Trigonometric Equations
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 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 -Multiple angle examples -Real applications -Rulers -Graphing examples -Identity reference sheets -Complex examples |
KLB Secondary Mathematics Form 4, Pages 109-112
|
|
| 7-8 |
END OF TERM EXAMINATIONS |
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| 9 |
MARKING OF EXAMINATIONS AND CLOSING OF THE SCHOOL |
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