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

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

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

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

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

Matrices and Transformation

Matrices of 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

KLB Secondary Mathematics Form 4, Pages 1-5

Matrices and Transformation

Identifying Common Transformation Matrices
Finding the Matrix of a Transformation

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
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 1-5

Matrices and Transformation

Using the Unit Square Method
Successive 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

KLB Secondary Mathematics Form 4, Pages 6-16

Matrices and Transformation

Matrix Multiplication for Combined Transformations
Single Matrix for Successive Transformations

By the end of the lesson, the learner should be able to:

-Multiply 2×2 matrices to find combined transformations
-Apply matrix multiplication rules correctly
-Verify combined transformations geometrically
-Solve problems involving multiple transformations

-Practice matrix multiplication systematically on chalkboard
-Verify results by applying to test objects
-Work through complex transformation sequences
-Check computations step by step

Exercise books
-Manila paper
-Ruler
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 16-24

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

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

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

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

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

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

Matrices and Transformation

Isometric and Non-isometric Transformations

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

Statistics II

Introduction to Advanced Statistics

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

KLB Secondary Mathematics Form 4, Pages 39-42

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

Statistics II

Mean Using Working Mean - Simple Data

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

KLB Secondary Mathematics Form 4, Pages 42-48

Statistics II

Mean Using Working Mean - Frequency Tables

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

KLB Secondary Mathematics Form 4, Pages 42-48

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

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

Statistics II

Introduction to Quartiles, Deciles, Percentiles

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

KLB Secondary Mathematics Form 4, Pages 49-52

Statistics II

Introduction to Quartiles, Deciles, Percentiles

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

KLB Secondary Mathematics Form 4, Pages 49-52

Statistics II

Calculating Quartiles for Ungrouped 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

KLB Secondary Mathematics Form 4, Pages 49-52

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

Statistics II

Deciles and Percentiles Calculations

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

KLB Secondary Mathematics Form 4, Pages 49-52

Statistics II

Introduction to Cumulative Frequency

By the end of the lesson, the learner should be able to:

-Construct cumulative frequency tables
-Understand "less than" cumulative frequencies
-Plot cumulative frequency against class boundaries
-Identify the characteristic S-shape of ogives

-Create cumulative frequency table with class data
-Plot points on manila paper grid
-Join points to form smooth curve
-Discuss properties of ogive curves

Exercise books
-Manila paper
-Ruler
-Class data

KLB Secondary Mathematics Form 4, Pages 52-60

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

Statistics II

Reading Values from 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

KLB Secondary Mathematics Form 4, Pages 52-60

Statistics II

Applications of Ogives

By the end of the lesson, the learner should be able to:

-Use ogives to solve real-world problems
-Find number of values above/below certain points
-Calculate percentage of data in given ranges
-Compare different datasets using ogives

-Solve problems about pass rates in examinations
-Find how many students scored above average
-Calculate percentages for different grade ranges
-Use agricultural production data for analysis

Exercise books
-Manila paper
-Real problem datasets
-Ruler

KLB Secondary Mathematics Form 4, Pages 52-60

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

Statistics II

Range and Interquartile Range

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

KLB Secondary Mathematics Form 4, Pages 60-65

Statistics II

Mean Absolute Deviation

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

KLB Secondary Mathematics Form 4, Pages 65-70

Statistics II

Mean Absolute Deviation

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

KLB Secondary Mathematics Form 4, Pages 65-70

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

Statistics II

Variance Using Alternative Formula

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

KLB Secondary Mathematics Form 4, Pages 65-70

Statistics II

Standard Deviation Calculations

By the end of the lesson, the learner should be able to:

-Calculate standard deviation as square root of variance
-Apply standard deviation to ungrouped data
-Use standard deviation to compare datasets
-Interpret standard deviation in practical contexts

-Calculate SD for student exam scores
-Compare SD values for different subjects
-Interpret what high/low SD means
-Use SD to identify consistent performance

Exercise books
-Manila paper
-Exam score data
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 65-70

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

Statistics II

Advanced Standard Deviation Techniques

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

KLB Secondary Mathematics Form 4, Pages 65-70