Differentiation

Introduction to Rate of Change

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

-Understand concept of rate of change in daily life
-Distinguish between average and instantaneous rates
-Identify examples of changing quantities
-Connect rate of change to gradient concepts

-Discuss speed as rate of change of distance
-Examine population growth rates
-Analyze temperature change throughout the day
-Connect to gradients of lines from coordinate geometry

Exercise books
-Manila paper
-Real-world examples
-Graph examples

KLB Secondary Mathematics Form 4, Pages 177-182

Differentiation

Average Rate of Change
Instantaneous Rate of Change
Gradient of Curves at Points
Introduction to Delta Notation

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

-Calculate average rate of change between two points
-Use formula: average rate = Δy/Δx
-Apply to distance-time and other practical graphs
-Understand limitations of average rate calculations

-Calculate average speed between two time points
-Find average rate of population change
-Use coordinate points to find average rates
-Compare average rates over different intervals

Exercise books
-Manila paper
-Calculators
-Graph paper
-Tangent demonstrations
-Motion examples
-Rulers
-Curve examples
-Delta notation examples
-Symbol practice

KLB Secondary Mathematics Form 4, Pages 177-182

Differentiation

The Limiting Process
Introduction to Derivatives
Derivative of Linear Functions

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

-Understand concept of limit in differentiation
-Apply "as Δx approaches zero" reasoning
-Use limiting process to find exact derivatives
-Practice systematic limiting calculations

-Demonstrate limiting process with numerical examples
-Show chord approaching tangent as Δx → 0
-Calculate limits using table of values
-Practice systematic limit evaluation

Exercise books
-Manila paper
-Limit tables
-Systematic examples
-Derivative notation
-Function examples
-Linear function examples
-Verification methods

KLB Secondary Mathematics Form 4, Pages 182-184

Differentiation

Derivative of y = x^n (Basic Powers)
Derivative of Constant Functions
Derivative of Coefficient Functions
Derivative of Polynomial Functions

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

-Find derivatives of power functions
-Apply the rule d/dx(x^n) = nx^(n-1)
-Practice with x², x³, x⁴, etc.
-Verify using first principles for simple cases

-Derive d/dx(x²) = 2x using first principles
-Apply power rule to various functions
-Practice with x³, x⁴, x⁵ examples
-Verify selected results using definition

Exercise books
-Manila paper
-Power rule examples
-First principles verification
-Constant function graphs
-Geometric explanations
-Coefficient examples
-Rule combinations
-Polynomial examples
-Term-by-term method

KLB Secondary Mathematics Form 4, Pages 184-188

Differentiation

Applications to Tangent Lines
Applications to Normal Lines
Introduction to Stationary Points
Types of Stationary Points

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

-Find equations of tangent lines to curves
-Use derivatives to find tangent gradients
-Apply point-slope form for tangent equations
-Solve problems involving tangent lines

-Find tangent to y = x² at point (2, 4)
-Use derivative to get gradient at specific point
-Apply y - y₁ = m(x - x₁) formula
-Practice with various curves and points

Exercise books
-Manila paper
-Tangent line examples
-Point-slope applications
-Normal line examples
-Perpendicular concepts
-Curve sketches
-Stationary point examples
-Sign analysis charts
-Classification examples

KLB Secondary Mathematics Form 4, Pages 187-189

Differentiation

Finding and Classifying Stationary Points
Curve Sketching Using Derivatives
Introduction to Kinematics Applications

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

-Solve dy/dx = 0 to find stationary points
-Apply systematic classification method
-Use organized approach for point analysis
-Practice with polynomial functions

-Work through complete stationary point analysis
-Use systematic gradient sign testing
-Create organized solution format
-Practice with cubic and quartic functions

Exercise books
-Manila paper
-Systematic templates
-Complete examples
-Curve sketching templates
-Systematic method
-Motion examples
-Kinematics applications

KLB Secondary Mathematics Form 4, Pages 189-195

Differentiation

Acceleration as Second Derivative
Motion Problems and Applications
Introduction to Optimization
Geometric Optimization Problems

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

-Understand acceleration as derivative of velocity
-Apply a = dv/dt = d²s/dt² notation
-Find acceleration functions from displacement
-Apply to motion analysis problems

-Find acceleration from velocity functions
-Use second derivative notation
-Apply to projectile motion problems
-Practice with particle motion scenarios

Exercise books
-Manila paper
-Second derivative examples
-Motion analysis
-Complete motion examples
-Real scenarios
-Optimization examples
-Real applications
-Geometric examples
-Design applications

KLB Secondary Mathematics Form 4, Pages 197-201

Differentiation
Matrices and Transformations
Matrices and Transformations
Matrices and Transformations

Business and Economic Applications
Advanced Optimization Problems
Transformation on a Cartesian plane
Basic Transformation Matrices
Identification of transformation matrix

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

-Apply derivatives to profit and cost functions
-Find marginal cost and marginal revenue
-Use calculus for business optimization
-Apply to Kenyan business scenarios

-Find maximum profit using calculus
-Calculate marginal cost and revenue
-Apply to agricultural and manufacturing examples
-Use derivatives for business decision-making

Exercise books
-Manila paper
-Business examples
-Economic applications
-Complex examples
-Engineering applications
Square boards
-Peg boards
-Graph papers
-Mirrors
-Rulers
-Protractors
-Calculators
Graph papers
-Exercise books
-Matrix examples

KLB Secondary Mathematics Form 4, Pages 201-204

Matrices and Transformations

Two Successive Transformations
Complex Successive Transformations
Single matrix of transformation for successive transformations
Matrix Multiplication Properties
Identity Matrix and Transformation
Inverse of a matrix

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

-Apply two transformations in sequence
-Understand that order of transformations matters
-Find final image after two transformations
-Compare results of different orders

-Physical demonstration of successive transformations
-Step-by-step working showing AB ≠ BA
-Drawing intermediate and final images
-Practice with reflection followed by rotation
-Group work comparing different orders

Square boards
-Peg boards
-Graph papers
-Colored pencils
-Rulers
-Calculators
Calculators
-Matrix multiplication charts
-Exercise books
-Matrix worksheets
-Formula sheets
-Matrix examples

KLB Secondary Mathematics Form 4, Pages 15-17

Matrices and Transformations
Integration

Determinant and Area Scale Factor
Area scale factor and determinant relationship
Shear Transformation
Stretch Transformation and Review
Introduction to Reverse Differentiation

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

-Calculate determinant of 2×2 matrix
-Understand relationship between determinant and area scaling
-Apply formula: area scale factor =

det(matrix)

-Solve problems involving area changes under transformations
Calculators
-Graph papers
-Formula sheets
-Area calculation tools
Square boards
-Flexible materials
-Rulers
-Calculators
Graph papers
-Elastic materials
-Comparison charts
-Review materials
-Differentiation charts
-Exercise books
-Function examples

-Determinant calculation practice
-Demonstration using shapes with known areas
-Establishing that area scale factor =

Integration

Basic Integration Rules - Power Functions
Integration of Polynomial Functions
Finding Particular Solutions
Introduction to Definite Integrals
Evaluating Definite Integrals
Area Under Curves - Single Functions
Areas Below X-axis and Mixed Regions

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

-Apply power rule for integration: ∫xⁿ dx = xⁿ⁺¹/(n+1) + c
-Understand the constant of integration and why it's necessary
-Integrate simple power functions where n ≠ -1
-Practice with positive, negative, and fractional powers

-Derivation of power rule through reverse differentiation
-Multiple examples with different values of n
-Explanation of arbitrary constant using family of curves
-Practice exercises with various power functions
-Common mistakes discussion and correction

Calculators
-Graph papers
-Power rule charts
-Exercise books
-Algebraic worksheets
-Polynomial examples
Graph papers
-Calculators
-Curve examples
-Geometric models
-Integration notation charts
-Step-by-step worksheets
-Evaluation charts
-Curve sketching tools
-Colored pencils
-Area grids
-Colored materials

KLB Secondary Mathematics Form 4, Pages 223-225

Integration
Quadratic Expressions and Equations
Quadratic Expressions and Equations
Quadratic Expressions and Equations
Quadratic Expressions and Equations
Quadratic Expressions and Equations
Quadratic Expressions and Equations

Area Between Two Curves
Factorisation of quadratic expressions
Factorisation of quadratic expressions
Completing squares
Completing squares
Solving quadratic expressions by completing square
Solving quadratic expressions by factorization

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

-Calculate area between two intersecting curves
-Find intersection points as integration limits
-Apply method: Area = ∫ₐᵇ [f(x) - g(x)]dx
-Handle multiple intersection scenarios

-Method for finding curve intersection points
-Working examples: area between y = x² and y = x
-Step-by-step process for area between curves
-Practice with linear and quadratic function pairs
-Advanced examples with multiple intersections

Graph papers
-Equation solving aids
-Calculators
-Colored pencils
-Exercise books
Calculators, charts showing factorization patterns
Calculators, factorization method charts
Calculators, perfect square charts
Calculators, vertex form examples
Calculators, equation solving guides
Calculators, method selection charts

KLB Secondary Mathematics Form 4, Pages 233-235

Quadratic Expressions and Equations

The quadratic formula
Formation of quadratic equations
Graphs of quadratic functions
Graphs of quadratic functions

By the end of the lesson, the learner should be able to:
Solve quadratic expressions using the quadratic formula
Apply quadratic formula to any quadratic equation
Derive the quadratic formula

Q/A on formula derivation steps
Discussions on formula applications
Solving equations using formula
Demonstrations of derivation process
Explaining formula structure

Calculators, formula derivation charts
Calculators, discriminant interpretation guides
Calculators, word problem templates
Graph papers, calculators, plotting guides
Graph papers, calculators, rulers

KLB Mathematics Book Three Pg 7-9

Quadratic Expressions and Equations

Graphical solutions of quadratic equation
Graphical solutions of simultaneous equations

By the end of the lesson, the learner should be able to:
Draw graphs of quadratic functions
Solve quadratic equations using the graphs
Find roots as x-intercepts

Q/A on graph-equation relationships
Discussions on graphical solutions
Solving equations graphically
Demonstrations of root finding
Explaining intersection concepts

Graph papers, calculators, rulers
Graph papers, calculators, estimation guides
Graph papers, calculators, intersection analysis guides

KLB Mathematics Book Three Pg 15-17

Approximations and Errors

Computing using calculators
Approximation
Estimation

By the end of the lesson, the learner should be able to:
Solve basic operations using calculators
Use calculator functions effectively
Apply calculator to mathematical computations

Q/A on calculator familiarity
Discussions on calculator operations
Solving basic arithmetic problems
Demonstrations of calculator functions
Explaining proper calculator usage

Calculators, operation guides
Calculators, verification worksheets
Calculators, rounding charts
Calculators, estimation guides

KLB Mathematics Book Three Pg 24-26

Approximations and Errors

Accuracy and errors
Percentage error
Rounding off error and truncation error
Propagation of errors

By the end of the lesson, the learner should be able to:
Find the absolute error
Calculate relative error
Distinguish between different error types

Q/A on error concepts
Discussions on error calculations
Solving absolute and relative error problems
Demonstrations of error computation
Explaining error significance

Calculators, error calculation sheets
Calculators, percentage error worksheets
Calculators, error comparison charts
Calculators, error propagation guides

KLB Mathematics Book Three Pg 31-32

Approximations and Errors

Propagation of errors
Propagation of errors in multiplication
Propagation of errors in multiplication

By the end of the lesson, the learner should be able to:
Find the propagation of errors in addition and subtraction
Apply error propagation to complex problems
Verify error calculations

Q/A on propagation mastery
Discussions on complex error scenarios
Solving advanced propagation problems
Demonstrations of verification methods
Explaining error validation

Calculators, verification worksheets
Calculators, multiplication error guides
Calculators, method comparison charts

KLB Mathematics Book Three Pg 35-36

Approximations and Errors
Trigonometry (II)

Propagation of errors in division
Word problems
The unit circle

By the end of the lesson, the learner should be able to:
Find the propagation of errors in division
Calculate errors in quotients
Apply division error rules

Q/A on division error concepts
Discussions on quotient error calculation
Solving division error problems
Demonstrations of division error methods
Explaining division error principles

Calculators, division error worksheets
Calculators, verification guides
Calculators, word problem sets, comprehensive review sheets
Calculators, protractors, rulers, pair of compasses

KLB Mathematics Book Three Pg 37-38

Trigonometry (II)

The unit circle
Trigonometric ratios of angles greater than 90°
Trigonometric ratios of angles greater than 90°

By the end of the lesson, the learner should be able to:
Solve problems using the unit circle
Apply unit circle to find trigonometric values
Use unit circle for angle measurement

Q/A on unit circle mastery
Discussions on practical applications
Solving trigonometric problems
Demonstrations of value finding
Explaining angle relationships

Calculators, protractors, rulers, pair of compasses
Calculators, quadrant charts

KLB Mathematics Book Three Pg 43-44

Trigonometry (II)

Trigonometric ratios of negative angles
Trigonometric ratios of angles greater than 360°
Use of mathematical tables
Use of mathematical tables

By the end of the lesson, the learner should be able to:
Find the trigonometric values of negative angles
Apply negative angle identities
Solve problems involving negative angles

Q/A on negative angle concepts
Discussions on angle direction
Solving negative angle problems
Demonstrations of identity applications
Explaining clockwise rotations

Geoboards, graph books, calculators
Mathematical tables, calculators

KLB Mathematics Book Three Pg 48-49

Trigonometry (II)

Use of calculators
Radian measure
Simple trigonometric graphs
Graphs of cosines

By the end of the lesson, the learner should be able to:
Use calculators to find sine, cosine and tan
Apply calculator functions for trigonometry
Verify calculator accuracy

Q/A on calculator trigonometric functions
Discussions on calculator modes
Solving problems using calculators
Demonstrations of function keys
Explaining degree vs radian modes

Calculators, function guides
Calculators, conversion charts
Calculators, graph papers, plotting guides

KLB Mathematics Book Three Pg 56-58

Trigonometry (II)

Graphs of tan
The sine rule
Cosine rule

By the end of the lesson, the learner should be able to:
Draw tables for tan of values
Plot graphs of tan functions
Identify asymptotes and discontinuities

Q/A on tangent behavior
Discussions on function domains
Solving tangent graphing problems
Demonstrations of asymptote identification
Explaining discontinuous functions

Calculators, graph papers, plotting guides
Calculators, triangle worksheets

KLB Mathematics Book Three Pg 64-65

Trigonometry (II)
Surds
Surds
Surds

Problem solving
Rational and irrational numbers
Order of surds and simplification
Simplification of surds practice

By the end of the lesson, the learner should be able to:
Solve problems on cosines, sines and tan
Apply trigonometry to real-world situations
Integrate all trigonometric concepts

Q/A on chapter consolidation
Discussions on practical applications
Solving comprehensive problems
Demonstrations of problem-solving strategies
Explaining real-world trigonometry

Calculators, comprehensive problem sets, real-world examples
Calculators, number classification charts
Calculators, surd order examples
Calculators, factor trees, simplification worksheets

KLB Mathematics Book Three Pg 76-77

Surds

Addition of surds
Subtraction of surds
Multiplication of surds

By the end of the lesson, the learner should be able to:
Add surds with like terms
Combine surds of the same order
Simplify surd addition expressions

Q/A on like term concepts
Discussions on surd addition rules
Solving addition problems systematically
Demonstrations of combining techniques
Explaining when surds can be added

Calculators, addition rule charts
Calculators, subtraction worksheets
Calculators, multiplication rule guides

KLB Mathematics Book Three Pg 79-80

Surds
Further Logarithms

Division of surds
Rationalizing the denominator
Advanced rationalization techniques
Introduction

By the end of the lesson, the learner should be able to:
Divide surds of the same order
Apply division rules to surds
Simplify quotients of surds

Q/A on division concepts
Discussions on surd division methods
Solving division problems systematically
Demonstrations of quotient simplification
Explaining division techniques

Calculators, division worksheets
Calculators, rationalization guides
Calculators, advanced technique sheets
Calculators, logarithm definition charts

KLB Mathematics Book Three Pg 81-82

Further Logarithms

Laws of logarithms

By the end of the lesson, the learner should be able to:
State the laws of logarithms
Apply basic logarithmic laws
Use logarithm laws for simple calculations

Q/A on logarithmic law foundations
Discussions on multiplication and division laws
Solving problems using basic laws
Demonstrations of law applications
Explaining law derivations

Calculators, logarithm law charts
Calculators, advanced law worksheets
Calculators, challenging problem sets

KLB Mathematics Book Three Pg 90-93

Further Logarithms

Logarithmic equations and expressions
Further computation using logarithms
Further computation using logarithms

By the end of the lesson, the learner should be able to:
Solve the logarithmic equations and expressions
Apply algebraic methods to logarithmic equations
Verify solutions of logarithmic equations

Q/A on equation-solving techniques
Discussions on logarithmic equation types
Solving basic logarithmic equations
Demonstrations of solution methods
Explaining verification techniques

Calculators, equation-solving guides
Calculators, advanced equation worksheets
Calculators, computation worksheets
Calculators, intermediate problem sets

KLB Mathematics Book Three Pg 93-95

Further Logarithms
Commercial Arithmetic

Further computation using logarithms
Problem solving
Problem solving
Simple interest

By the end of the lesson, the learner should be able to:
Solve problems involving logarithms
Master advanced logarithmic computations
Apply logarithms to complex mathematical scenarios

Q/A on advanced computational mastery
Discussions on complex calculation strategies
Solving advanced computation problems
Demonstrations of sophisticated methods
Explaining optimal computational approaches

Calculators, advanced computation guides
Calculators, comprehensive problem sets
Calculators, real-world application examples
Calculators, simple interest charts

KLB Mathematics Book Three Pg 95-96

Commercial Arithmetic

Simple interest
Compound interest
Compound interest

By the end of the lesson, the learner should be able to:
Calculate simple interest
Solve complex simple interest problems
Apply simple interest to real-world situations

Q/A on advanced simple interest concepts
Discussions on practical applications
Solving complex interest problems
Demonstrations of real-world scenarios
Explaining business applications

Calculators, real-world problem sets
Calculators, compound interest tables
Calculators, comparison worksheets

KLB Mathematics Book Three Pg 98-101

Commercial Arithmetic

Appreciation
Depreciation
Hire purchase
Hire purchase

By the end of the lesson, the learner should be able to:
Calculate the appreciation value of items
Apply appreciation concepts
Solve appreciation problems

Q/A on appreciation concepts
Discussions on asset value increases
Solving appreciation calculation problems
Demonstrations of value growth
Explaining appreciation applications

Calculators, appreciation examples
Calculators, depreciation charts
Calculators, hire purchase examples
Calculators, complex hire purchase worksheets

KLB Mathematics Book Three Pg 108

Commercial Arithmetic
Circles: Chords and Tangents
Circles: Chords and Tangents

Income tax and P.A.Y.E
Length of an arc
Length of an arc

By the end of the lesson, the learner should be able to:
Calculate the income tax
Calculate the P.A.Y.E
Apply tax calculation methods

Q/A on tax system concepts
Discussions on income tax and P.A.Y.E systems
Solving tax calculation problems
Demonstrations of tax computation
Explaining taxation principles

Income tax tables, calculators
Geometrical set, calculators

KLB Mathematics Book Three Pg 112-117

Circles: Chords and Tangents

Chords
Parallel chords
Equal chords
Intersecting chords

By the end of the lesson, the learner should be able to:
Calculate the length of a chord
Apply chord properties and theorems
Understand chord-radius relationships

Q/A on chord definition and properties
Discussions on chord calculation methods
Solving basic chord problems
Demonstrations of geometric constructions
Explaining chord theorems

Geometrical set, calculators

KLB Mathematics Book Three Pg 126-128

Circles: Chords and Tangents

Intersecting chords
Chord properties
Tangent to a circle
Tangent to a circle

By the end of the lesson, the learner should be able to:
Calculate the length of intersecting chords
Solve complex intersection problems
Apply advanced chord theorems

Q/A on advanced intersection scenarios
Discussions on complex chord relationships
Solving challenging intersection problems
Demonstrations of advanced techniques
Explaining sophisticated applications

Geometrical set, calculators

KLB Mathematics Book Three Pg 135-139

Circles: Chords and Tangents

Properties of tangents to a circle from an external point
Tangent properties
Tangents to two circles

By the end of the lesson, the learner should be able to:
State the properties of tangents to a circle from an external point
Apply external tangent properties
Solve external tangent problems

Q/A on external tangent concepts
Discussions on tangent properties
Solving external tangent problems
Demonstrations of property applications
Explaining theoretical foundations

Geometrical set, calculators

KLB Mathematics Book Three Pg 142-144

Circles: Chords and Tangents

Tangents to two circles
Contact of circles
Contact of circles
Circle contact

By the end of the lesson, the learner should be able to:
Calculate the tangents of transverse common tangents
Find transverse tangent properties
Compare direct and transverse tangents

Q/A on transverse tangent concepts
Discussions on tangent type differences
Solving transverse tangent problems
Demonstrations of comparison methods
Explaining tangent classifications

Geometrical set, calculators

KLB Mathematics Book Three Pg 150-151

Circles: Chords and Tangents

Angle in alternate segment
Circumscribed circle

By the end of the lesson, the learner should be able to:
Calculate the angles in alternate segments
Apply alternate segment theorem
Understand segment angle properties

Q/A on alternate segment concepts
Discussions on segment angle relationships
Solving basic segment problems
Demonstrations of theorem application
Explaining geometric proofs

Geometrical set, calculators

KLB Mathematics Book Three Pg 157-160

Circles: Chords and Tangents

Escribed circles
Centroid
Orthocenter
Circle and triangle relationships

By the end of the lesson, the learner should be able to:
Construct escribed circles
Find escribed circle properties
Apply escription concepts

Q/A on escription concepts
Discussions on escribed circle construction
Solving escription problems
Demonstrations of construction methods
Explaining escription applications

Geometrical set, calculators

KLB Mathematics Book Three Pg 165-166

Matrices

Introduction and real-life applications
Order of a matrix and elements
Square matrices, row and column matrices
Addition of matrices
Subtraction of matrices
Combined addition and subtraction
Scalar multiplication
Introduction to matrix multiplication

By the end of the lesson, the learner should be able to:
Define matrices and identify matrix applications
Recognize matrices in everyday contexts
Understand tabular data representation
Appreciate the importance of matrices

Q/A on tabular data in daily life
Discussions on school exam results tables
Analyzing bus timetables and price lists
Demonstrations using newspaper sports tables
Explaining matrix notation using grid patterns

Old newspapers with league tables, chalk and blackboard, exercise books
Chalk and blackboard, ruled exercise books, class register
Paper cutouts, chalk and blackboard, counters or bottle tops
Counters or stones, chalk and blackboard, exercise books
Chalk and blackboard, exercise books, number cards made from cardboard
Chalk and blackboard, exercise books, locally made operation cards
Beans or stones for grouping, chalk and blackboard, exercise books
Chalk and blackboard, rulers for tracing, exercise books

KLB Mathematics Book Three Pg 168-169

Matrices

Matrix multiplication (2×2 matrices)
Matrix multiplication (larger matrices)
Properties of matrix multiplication
Real-world matrix multiplication applications

By the end of the lesson, the learner should be able to:
Multiply 2×2 matrices systematically
Apply correct multiplication procedures
Calculate matrix products accurately
Understand result matrix dimensions

Q/A on 2×2 matrix multiplication using simple numbers
Discussions on systematic calculation methods
Solving 2×2 problems using step-by-step approach
Demonstrations using organized blackboard layout
Explaining product formation using grid method

Chalk and blackboard, exercise books, homemade grid templates
Chalk and blackboard, large sheets of paper for working, exercise books
Chalk and blackboard, exercise books, cardboard for property cards
Chalk and blackboard, local price lists, exercise books

KLB Mathematics Book Three Pg 176-179

Matrices

Identity matrix
Determinant of 2×2 matrices
Inverse of 2×2 matrices - theory

By the end of the lesson, the learner should be able to:
Define and identify identity matrices
Understand identity matrix properties
Apply identity matrices in multiplication
Recognize the multiplicative identity role

Q/A on identity concepts using number 1 analogy
Discussions on multiplicative identity using examples
Solving identity problems using pattern recognition
Demonstrations using multiplication by 1 concept
Explaining diagonal properties using visual patterns

Chalk and blackboard, exercise books, pattern cards made from paper
Chalk and blackboard, exercise books, crossed sticks for demonstration
Chalk and blackboard, exercise books, fraction examples

KLB Mathematics Book Three Pg 182-183

Matrices

Inverse of 2×2 matrices - practice
Introduction to solving simultaneous equations
Solving 2×2 simultaneous equations using matrices
Advanced simultaneous equation problems

By the end of the lesson, the learner should be able to:
Calculate inverses of 2×2 matrices systematically
Verify inverse calculations through multiplication
Apply inverse properties correctly
Solve complex inverse problems

Q/A on inverse calculation verification methods
Discussions on accuracy checking using multiplication
Solving advanced inverse problems using practice
Demonstrations using verification procedures
Explaining checking methods using examples

Chalk and blackboard, exercise books, scrap paper for verification
Chalk and blackboard, exercise books, equation examples from previous topics
Chalk and blackboard, exercise books, previous elimination method examples
Chalk and blackboard, exercise books, graph paper if available

KLB Mathematics Book Three Pg 185-187

Matrices

Matrix applications in real-world problems
Transpose of matrices
Matrix equation solving

By the end of the lesson, the learner should be able to:
Apply matrix operations to practical scenarios
Solve business, engineering, and scientific problems
Model real situations using matrices
Interpret matrix solutions in context

Q/A on practical applications using local examples
Discussions on modeling using familiar situations
Solving comprehensive problems using matrix tools
Demonstrations using community-based scenarios
Explaining solution interpretation using meaningful contexts

Chalk and blackboard, local business examples, exercise books
Chalk and blackboard, exercise books, paper cutouts for demonstration
Chalk and blackboard, exercise books, algebra reference examples

KLB Mathematics Book Three Pg 168-190

Formulae and Variations

Introduction to formulae
Subject of a formula - basic cases
Subject of a formula - intermediate cases
Subject of a formula - advanced cases

By the end of the lesson, the learner should be able to:
Define formulae and identify formula components
Recognize formulae in everyday contexts
Understand the relationship between variables
Appreciate the importance of formulae in mathematics

Q/A on familiar formulae from daily life
Discussions on cooking recipes as formulae
Analyzing distance-time relationships using walking examples
Demonstrations using perimeter and area calculations
Explaining formula notation using simple examples

Chalk and blackboard, measuring tape or string, exercise books
Chalk and blackboard, simple balance (stones and stick), exercise books
Chalk and blackboard, fraction strips made from paper, exercise books
Chalk and blackboard, squared paper patterns, exercise books

KLB Mathematics Book Three Pg 191-193

Formulae and Variations
Sequences and Series

Applications of formula manipulation
Introduction to variation
Direct variation - introduction
Introduction to sequences and finding terms

By the end of the lesson, the learner should be able to:
Apply formula rearrangement to practical problems
Solve real-world problems using formula manipulation
Calculate unknown quantities in various contexts
Interpret results in meaningful situations

Q/A on practical applications using local examples
Discussions on real-world formula use in farming/building
Solving application problems using formula rearrangement
Demonstrations using construction and farming scenarios
Explaining practical interpretation using community examples

Chalk and blackboard, local measurement tools, exercise books
Chalk and blackboard, local price lists from markets, exercise books
Chalk and blackboard, beans or stones for counting, exercise books
Chalk and blackboard, stones or beans for patterns, exercise books

KLB Mathematics Book Three Pg 191-193

Sequences and Series

General term of sequences and applications
Arithmetic sequences and nth term
Arithmetic sequence applications

By the end of the lesson, the learner should be able to:
Develop general rules for sequences
Express the nth term using algebraic notation
Find specific terms using general formulas
Apply sequence concepts to practical problems

Q/A on rule formulation using systematic approach
Discussions on algebraic expression development
Solving general term and application problems
Demonstrations using position-value relationships
Explaining practical relevance using community examples

Chalk and blackboard, numbered cards made from paper, exercise books
Chalk and blackboard, measuring tape or string, exercise books
Chalk and blackboard, local employment/savings examples, exercise books

KLB Mathematics Book Three Pg 207-208

Sequences and Series

Geometric sequences and nth term
Geometric sequence applications
Arithmetic series and sum formula
Geometric series and applications
Mixed problems and advanced applications
Sequences in nature and technology

By the end of the lesson, the learner should be able to:
Define geometric sequences and common ratios
Calculate common ratios correctly
Derive and apply the geometric nth term formula
Understand exponential growth patterns

Q/A on geometric patterns using multiplication examples
Discussions on ratio-based progressions and formula derivation
Solving geometric sequence problems systematically
Demonstrations using doubling and scaling examples
Explaining exponential structure using practical examples

Chalk and blackboard, objects for doubling demonstrations, exercise books
Chalk and blackboard, population/growth data examples, exercise books
Chalk and blackboard, counting materials for summation, exercise books
Chalk and blackboard, convergence demonstration materials, exercise books
Chalk and blackboard, mixed problem collections, exercise books
Chalk and blackboard, natural and technology examples, exercise books

KLB Mathematics Book Three Pg 211-213