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
Using the Unit Square Method

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

Successive Transformations
Matrix Multiplication for Combined Transformations
Single Matrix for Successive Transformations

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

-Understand the concept of successive transformations
-Apply transformations in correct order
-Recognize that order matters in matrix multiplication
-Perform multiple transformations step by step

-Demonstrate successive transformations with paper cutouts
-Practice applying transformations in sequence
-Compare results when order is changed
-Work through step-by-step examples

Exercise books
-Manila paper
-Ruler
-Coloured pencils
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 16-24

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
Shear Transformations

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
Exercise books
-Cardboard pieces
-Manila paper
-Ruler

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
Isometric and Non-isometric Transformations

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
-Paper cutouts

KLB Secondary Mathematics Form 4, Pages 28-34

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
Mean Using Working Mean - Simple Data

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
-Student data

KLB Secondary Mathematics Form 4, Pages 39-42

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
Advanced Working Mean Techniques

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
-Economic data

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
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

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
Drawing Cumulative Frequency Curves (Ogives)

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
-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
Introduction to Measures of Dispersion

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
-Comparative datasets
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 52-60

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
Standard Deviation for Grouped Data

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
-Agricultural data

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

Trigonometry III

Review of Basic Trigonometric Ratios
Deriving the Identity sin²θ + cos²θ = 1

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

-Recall sin, cos, tan from right-angled triangles
-Apply Pythagoras theorem with trigonometry
-Use basic trigonometric ratios to solve problems
-Establish relationship between trigonometric ratios

-Review right-angled triangle ratios from Form 2
-Practice calculating unknown sides and angles
-Work through examples using SOH-CAH-TOA
-Solve simple practical problems

Exercise books
-Manila paper
-Rulers
-Calculators (if available)
-Unit circle diagrams
-Calculators

KLB Secondary Mathematics Form 4, Pages 99-103

Trigonometry III

Applications of sin²θ + cos²θ = 1

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

KLB Secondary Mathematics Form 4, Pages 99-103

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

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

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

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

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

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

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

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

Trigonometry III

Equations Involving Multiple Angles
Using Graphs to Solve Trigonometric Equations

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

KLB Secondary Mathematics Form 4, Pages 109-112

Trigonometry III

Trigonometric Equations with Identities

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

-Use trigonometric identities to solve equations
-Apply sin²θ + cos²θ = 1 in equation solving
-Convert between different trigonometric functions
-Solve equations using multiple identities

-Solve equations using fundamental identity
-Convert tan equations to sin/cos form
-Practice identity-based equation solving
-Work through complex multi-step problems

Exercise books
-Manila paper
-Identity reference sheets
-Complex examples

KLB Secondary Mathematics Form 4, Pages 109-112

Three Dimensional Geometry

Introduction to 3D Concepts
Properties of Common Solids

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

-Distinguish between 1D, 2D, and 3D objects
-Identify vertices, edges, and faces of 3D solids
-Understand concepts of points, lines, and planes in space
-Recognize real-world 3D objects and their properties

-Use classroom objects to demonstrate dimensions
-Count vertices, edges, faces of cardboard models
-Identify 3D shapes in school environment
-Discuss difference between area and volume

Exercise books
-Cardboard boxes
-Manila paper
-Real 3D objects
-Cardboard
-Scissors
-Tape/glue

KLB Secondary Mathematics Form 4, Pages 113-115

Three Dimensional Geometry

Understanding Planes in 3D Space

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

-Define planes and their properties in 3D
-Identify parallel and intersecting planes
-Understand that planes extend infinitely
-Recognize planes formed by faces of solids

-Use books/boards to represent planes
-Demonstrate parallel planes using multiple books
-Show intersecting planes using book corners
-Identify planes in classroom architecture

Exercise books
-Manila paper
-Books/boards
-Classroom examples

KLB Secondary Mathematics Form 4, Pages 113-115

Three Dimensional Geometry

Lines in 3D Space
Introduction to Projections

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

-Understand different types of lines in 3D
-Identify parallel, intersecting, and skew lines
-Recognize that skew lines don't intersect and aren't parallel
-Find examples of different line relationships

-Use rulers/sticks to demonstrate line relationships
-Show parallel lines using parallel rulers
-Demonstrate skew lines using classroom edges
-Practice identifying line relationships in models

Exercise books
-Rulers/sticks
-3D models
-Manila paper
-Light source

KLB Secondary Mathematics Form 4, Pages 113-115

Three Dimensional Geometry

Angle Between Line and Plane - Concept

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

-Define angle between line and plane
-Understand that angle is measured with projection
-Identify the projection of line on plane
-Recognize when line is perpendicular to plane

-Demonstrate using stick against book (plane)
-Show that angle is with projection, not plane itself
-Use protractor to measure angles with projections
-Identify perpendicular lines to planes

Exercise books
-Manila paper
-Protractor
-Rulers/sticks

KLB Secondary Mathematics Form 4, Pages 115-123

Three Dimensional Geometry

Calculating Angles Between Lines and Planes
Advanced Line-Plane Angle Problems

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

-Calculate angles using right-angled triangles
-Apply trigonometry to 3D angle problems
-Use Pythagoras theorem in 3D contexts
-Solve problems involving cuboids and pyramids

-Work through step-by-step calculations
-Use trigonometric ratios in 3D problems
-Practice with cuboid diagonal problems
-Apply to pyramid and cone angle calculations

Exercise books
-Manila paper
-Calculators
-3D problem diagrams
-Real scenarios
-Problem sets

KLB Secondary Mathematics Form 4, Pages 115-123

Three Dimensional Geometry

Introduction to Plane-Plane Angles

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

-Define angle between two planes
-Understand concept of dihedral angles
-Identify line of intersection of two planes
-Find perpendiculars to intersection line

-Use two books to demonstrate intersecting planes
-Show how planes meet along an edge
-Identify dihedral angles in classroom
-Demonstrate using folded paper

Exercise books
-Manila paper
-Books
-Folded paper

KLB Secondary Mathematics Form 4, Pages 123-128

Three Dimensional Geometry

Finding Angles Between Planes
Complex Plane-Plane Angle Problems

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

-Construct perpendiculars to find plane angles
-Apply trigonometry to calculate dihedral angles
-Use right-angled triangles in plane intersection
-Solve angle problems in prisms and pyramids

-Work through construction method step-by-step
-Practice finding intersection lines first
-Calculate angles in triangular prisms
-Apply to roof and building angle problems

Exercise books
-Manila paper
-Protractor
-Building examples
-Complex 3D models
-Architecture examples

KLB Secondary Mathematics Form 4, Pages 123-128

Three Dimensional Geometry

Practical Applications of Plane Angles

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

-Apply plane angles to real-world problems
-Solve engineering and construction problems
-Calculate angles in roof structures
-Use in navigation and surveying contexts

-Calculate roof pitch angles
-Solve bridge construction angle problems
-Apply to mining and tunnel excavation
-Use in aerial navigation problems

Exercise books
-Manila paper
-Real engineering data
-Construction examples

KLB Secondary Mathematics Form 4, Pages 123-128

Three Dimensional Geometry

Understanding Skew Lines
Angle Between Skew Lines

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

-Define skew lines and their properties
-Distinguish skew lines from parallel/intersecting lines
-Identify skew lines in 3D models
-Understand that skew lines exist only in 3D

-Use classroom edges to show skew lines
-Demonstrate with two rulers in space
-Identify skew lines in building frameworks
-Practice recognition in various 3D shapes

Exercise books
-Manila paper
-Rulers
-Building frameworks
-Translation examples

KLB Secondary Mathematics Form 4, Pages 128-135

Three Dimensional Geometry

Advanced Skew Line Problems

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

-Solve complex skew line angle calculations
-Apply to engineering and architectural problems
-Use systematic approach for difficult problems
-Combine with other 3D geometric concepts

-Work through power line and cable problems
-Solve bridge and tower construction angles
-Practice with space frame structures
-Apply to antenna and communication tower problems

Exercise books
-Manila paper
-Engineering examples
-Structure diagrams

KLB Secondary Mathematics Form 4, Pages 128-135

Three Dimensional Geometry

Distance Calculations in 3D
Volume and Surface Area Applications

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

-Calculate distances between points in 3D
-Find shortest distances between lines and planes
-Apply 3D Pythagoras theorem
-Use distance formula in coordinate geometry

-Calculate space diagonals in cuboids
-Find distances from points to planes
-Apply 3D distance formula systematically
-Solve minimum distance problems

Exercise books
-Manila paper
-Distance calculation charts
-3D coordinate examples
-Volume formulas
-Real containers

KLB Secondary Mathematics Form 4, Pages 115-135

Three Dimensional Geometry

Coordinate Geometry in 3D

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

-Extend coordinate geometry to three dimensions
-Plot points in 3D coordinate system
-Calculate distances and angles using coordinates
-Apply vector concepts to 3D problems

-Set up 3D coordinate system using room corners
-Plot simple points in 3D space
-Calculate distances using coordinate formula
-Introduce basic vector concepts

Exercise books
-Manila paper
-3D coordinate grid
-Room corner reference

KLB Secondary Mathematics Form 4, Pages 115-135

Three Dimensional Geometry
Compound Proportion and Rates of Work

Integration with Trigonometry
Compound Proportions

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

-Apply trigonometry extensively to 3D problems
-Use multiple trigonometric ratios in solutions
-Combine trigonometry with 3D geometric reasoning
-Solve complex problems requiring trig and geometry

-Work through problems requiring sin, cos, tan
-Use trigonometric identities in 3D contexts
-Practice angle calculations in pyramids
-Apply to navigation and astronomy problems

Exercise books
-Manila paper
-Trigonometric tables
-Astronomy examples
Chalk and blackboard, local business examples, calculators if available, exercise books

KLB Secondary Mathematics Form 4, Pages 115-135

Compound Proportion and Rates of Work

Compound Proportions applications

By the end of the lesson, the learner should be able to:
Find the compound proportions
Apply compound proportions to complex problems
Handle multi-step compound proportion scenarios
Solve real-world compound proportion problems

Q/A on advanced compound proportion using complex scenarios
Discussions on multi-variable relationships using practical contexts
Solving challenging compound problems using systematic approaches
Demonstrations using construction and farming examples
Explaining practical applications using community-based scenarios

Chalk and blackboard, construction/farming examples, exercise books

KLB Mathematics Book Three Pg 290-291

Compound Proportion and Rates of Work

Proportional Parts
Proportional Parts applications

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, business partnership examples, exercise books

KLB Mathematics Book Three Pg 291-293

Compound Proportion and Rates of Work

Rates of Work

By the end of the lesson, the learner should be able to:
Calculate the rate of work
Understand work rate relationships
Apply time-work-efficiency concepts
Solve basic rate of work problems

Q/A on work rate calculation using practical examples
Discussions on efficiency and time relationships using work scenarios
Solving basic rate of work problems using systematic methods
Demonstrations using construction and labor examples
Explaining work rate concepts using practical work situations

Chalk and blackboard, work scenario examples, exercise books

KLB Mathematics Book Three Pg 294-295

Compound Proportion and Rates of Work
Graphical Methods

Rates of Work and Mixtures
Tables of given relations

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
Chalk and blackboard, ruled paper for tables, exercise books

KLB Mathematics Book Three Pg 295-296

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
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

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
Empirical graphs
Advanced empirical methods

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
Chalk and blackboard, experimental data examples, exercise books
Chalk and blackboard, complex data examples, exercise books

KLB Mathematics Book Three Pg 310-315