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

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
Introduction to cubic equations

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
Chalk and blackboard, cubic function examples, exercise books

KLB Mathematics Book Three Pg 299-300

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

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

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

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

Graphical Methods

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
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
Chalk and blackboard, tangent line examples, exercise books

KLB Mathematics Book Three Pg 304-310

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

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

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

Graphical Methods

Advanced empirical methods

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

KLB Mathematics Book Three Pg 315-321

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

Compound Proportion and Rates of Work

Proportional Parts
Rates of Work

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
Chalk and blackboard, work scenario examples, exercise books

KLB Mathematics Book Three Pg 291-293

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

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

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

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

Probability

Combined Events OR probability
Independent Events

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
Chalk and blackboard, multiple coins and dice, independence demonstration materials, exercise books

KLB Mathematics Book Three Pg 272-274

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

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

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

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

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

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
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

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

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
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

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
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

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

Longitudes and Latitudes

Introduction to Earth as a Sphere
Great and Small Circles

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

-Understand Earth as a sphere for mathematical purposes
-Identify poles, equator, and axis of rotation
-Recognize Earth's dimensions and basic structure
-Connect Earth's rotation to day-night cycle

-Use globe or spherical ball to demonstrate Earth
-Identify North Pole, South Pole, and equator
-Discuss Earth's rotation and its effects
-Show axis of rotation through poles

Exercise books
-Globe/spherical ball
-Manila paper
-Chalk/markers
-Globe
-String

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Understanding Latitude

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

-Define latitude and its measurement
-Identify equator as 0° latitude reference
-Understand North and South latitude designations
-Recognize that latitude ranges from 0° to 90°

-Mark latitude lines on globe using tape
-Show equator as reference line (0°)
-Demonstrate measurement from equator to poles
-Practice identifying latitude positions

Exercise books
-Globe
-Tape/string
-Protractor

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Properties of Latitude Lines

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

-Understand that latitude lines are parallel circles
-Recognize that latitude lines are small circles (except equator)
-Calculate radii of latitude circles using trigonometry
-Apply formula r = R cos θ for latitude circle radius

-Demonstrate parallel nature of latitude lines
-Calculate radius of latitude circle at 60°N
-Show relationship between latitude and circle size
-Use trigonometry to find circle radii

Exercise books
-Globe
-Calculator
-Manila paper

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Understanding Longitude

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

-Define longitude and its measurement
-Identify Greenwich Meridian as 0° longitude reference
-Understand East and West longitude designations
-Recognize that longitude ranges from 0° to 180°

-Mark longitude lines on globe using string
-Show Greenwich Meridian as reference line
-Demonstrate measurement East and West from Greenwich
-Practice identifying longitude positions

Exercise books
-Globe
-String
-World map

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Properties of Longitude Lines

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

-Understand that longitude lines are great circles
-Recognize that all longitude lines pass through poles
-Understand that longitude lines converge at poles
-Identify that opposite longitudes differ by 180°

-Show longitude lines converging at poles
-Demonstrate that longitude lines are great circles
-Find opposite longitude positions
-Compare longitude and latitude line properties

Exercise books
-Globe
-String
-Manila paper

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Position of Places on Earth

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

-Express position using latitude and longitude coordinates
-Use correct notation for positions (e.g., 1°S, 37°E)
-Identify positions of major Kenyan cities
-Locate places given their coordinates

-Find positions of Nairobi, Mombasa, Kisumu on globe
-Practice writing coordinates in correct format
-Locate cities worldwide using coordinates
-Use maps to verify coordinate positions

Exercise books
-Globe
-World map
-Kenya map

KLB Secondary Mathematics Form 4, Pages 139-143

Longitudes and Latitudes

Latitude and Longitude Differences
Introduction to Distance Calculations

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

-Calculate latitude differences between two points
-Calculate longitude differences between two points
-Understand angular differences on same and opposite sides
-Apply difference calculations to navigation problems

-Calculate difference between Nairobi and Cairo
-Practice with points on same and opposite sides
-Work through systematic calculation methods
-Apply to real navigation scenarios

Exercise books
-Manila paper
-Calculator
-Navigation examples
-Globe
-Conversion charts

KLB Secondary Mathematics Form 4, Pages 139-143

Longitudes and Latitudes

Distance Along Great Circles

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

-Calculate distances along meridians (longitude lines)
-Calculate distances along equator
-Apply formula: distance = angle × 60 nm
-Convert distances between nautical miles and kilometers

-Calculate distance from Nairobi to Cairo (same longitude)
-Find distance between two points on equator
-Practice conversion between units
-Apply to real geographical examples

Exercise books
-Manila paper
-Calculator
-Real examples

KLB Secondary Mathematics Form 4, Pages 143-156

Longitudes and Latitudes

Distance Along Small Circles (Parallels)

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

-Understand that parallel distances use different formula
-Apply formula: distance = longitude difference × 60 × cos(latitude)
-Calculate radius of latitude circles
-Solve problems involving parallel of latitude distances

-Derive formula using trigonometry
-Calculate distance between Mombasa and Lagos
-Show why latitude affects distance calculations
-Practice with various latitude examples

Exercise books
-Manila paper
-Calculator
-African city examples

KLB Secondary Mathematics Form 4, Pages 143-156

Longitudes and Latitudes

Shortest Distance Problems

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

-Understand that shortest distance is along great circle
-Compare great circle and parallel distances
-Calculate shortest distances between any two points
-Apply to navigation and flight path problems

-Compare distances: parallel vs great circle routes
-Calculate shortest distance between London and New York
-Apply to aircraft flight planning
-Discuss practical navigation implications

Exercise books
-Manila paper
-Calculator
-Flight path examples

KLB Secondary Mathematics Form 4, Pages 143-156

Longitudes and Latitudes

Advanced Distance Calculations

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

-Solve complex distance problems with multiple steps
-Calculate distances involving multiple coordinate differences
-Apply to surveying and mapping problems
-Use systematic approaches for difficult calculations

-Work through complex multi-step distance problems
-Apply to surveying land boundaries
-Calculate perimeters of geographical regions
-Practice with examination-style problems

Exercise books
-Manila paper
-Calculator
-Surveying examples

KLB Secondary Mathematics Form 4, Pages 143-156

Longitudes and Latitudes

Introduction to Time and Longitude
Local Time Calculations

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

-Understand relationship between longitude and time
-Learn that Earth rotates 360° in 24 hours
-Calculate that 15° longitude = 1 hour time difference
-Understand concept of local time

-Demonstrate Earth's rotation using globe
-Show how sun position determines local time
-Calculate time differences for various longitudes
-Apply to understanding sunrise/sunset times

Exercise books
-Globe
-Light source
-Time zone examples
-Manila paper
-World time examples
-Calculator

KLB Secondary Mathematics Form 4, Pages 156-161

Longitudes and Latitudes

Greenwich Mean Time (GMT)

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

-Understand Greenwich as reference for world time
-Calculate local times relative to GMT
-Apply GMT to solve international time problems
-Understand time zones and their practical applications

-Use Greenwich as time reference point
-Calculate local times for cities worldwide
-Apply to international business scenarios
-Discuss practical applications of GMT

Exercise books
-Manila paper
-World map
-Time zone charts

KLB Secondary Mathematics Form 4, Pages 156-161

Longitudes and Latitudes

Complex Time Problems

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

-Solve time problems involving date changes
-Handle calculations crossing International Date Line
-Apply to travel and communication scenarios
-Calculate arrival times for international flights

-Work through International Date Line problems
-Calculate flight arrival times across time zones
-Apply to international communication timing
-Practice with business meeting scheduling

Exercise books
-Manila paper
-International examples
-Travel scenarios

KLB Secondary Mathematics Form 4, Pages 156-161

Longitudes and Latitudes

Speed Calculations

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

-Define knot as nautical mile per hour
-Calculate speeds in knots and km/h
-Apply speed calculations to navigation problems
-Solve problems involving time, distance, and speed

-Calculate ship speeds in knots
-Convert between knots and km/h
-Apply to aircraft and ship navigation
-Practice with maritime and aviation examples

Exercise books
-Manila paper
-Calculator
-Navigation examples

KLB Secondary Mathematics Form 4, Pages 156-161