Matrices and Transformation

Matrices of 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:

-Define transformation and identify types
-Recognize that matrices can represent transformations
-Apply 2×2 matrices to position vectors
-Relate matrix operations to geometric transformations

-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

-Review transformation concepts from Form 2
-Demonstrate matrix multiplication using position vectors
-Plot objects and images on coordinate plane
-Practice identifying transformations from images

-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
-Pencils
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

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

Single Matrix for Successive Transformations
Inverse of a Transformation
Properties of Inverse Transformations

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

-Find single matrix equivalent to successive transformations
-Apply commutativity properties in matrix multiplication
-Determine order of operations in transformations
-Solve complex transformation problems efficiently

-Demonstrate equivalence of successive and single matrices
-Practice finding single equivalent matrices
-Compare geometric and algebraic approaches
-Solve real-world transformation problems

Exercise books
-Manila paper
-Ruler
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 21-24

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
Statistics II

Isometric and Non-isometric Transformations
Introduction to Advanced Statistics
Working Mean Concept

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

-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

-Compare congruent and non-congruent images using cutouts
-Classify transformations systematically
-Practice identification from matrices
-Discuss real-world applications of each type

-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
-Paper cutouts
-Manila paper
-Ruler
Exercise books
-Manila paper
-Real data examples
-Chalk/markers
-Sample datasets

KLB Secondary Mathematics Form 4, Pages 35-38
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
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
Introduction to Cumulative Frequency
Drawing Cumulative Frequency Curves (Ogives)

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

-Calculate specific deciles and percentiles
-Apply interpolation formulas for deciles/percentiles
-Interpret decile and percentile positions
-Use these measures for comparative analysis

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

-Calculate specific percentiles for class test scores
-Find deciles for sports performance data
-Compare students' positions using percentiles
-Practice with national examination statistics

-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
-Performance data
-Chalk/markers
Exercise books
-Manila paper
-Ruler
-Class data
-Pencils

KLB Secondary Mathematics Form 4, Pages 49-52
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
Range and Interquartile Range

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

-Define dispersion and its importance
-Understand limitations of central tendency alone
-Compare datasets with same mean but different spread
-Identify different measures of dispersion

-Compare test scores of two classes with same mean
-Show how different spreads affect interpretation
-Discuss variability in real-world data
-Introduce range as simplest measure

Exercise books
-Manila paper
-Comparative datasets
-Chalk/markers
-Student data
-Measuring tape

KLB Secondary Mathematics Form 4, Pages 60-65

Statistics II

Mean Absolute Deviation

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

-Calculate mean absolute deviation
-Use absolute values correctly in calculations
-Understand concept of average distance from mean
-Apply MAD to compare variability in datasets

-Calculate MAD for class test scores
-Practice with absolute value calculations
-Compare MAD values for different subjects
-Interpret MAD in context of data spread

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

KLB Secondary Mathematics Form 4, Pages 65-70

Statistics II

Introduction to Variance

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

-Define variance as mean of squared deviations
-Calculate variance using definition formula
-Understand why deviations are squared
-Compare variance with other dispersion measures

-Work through variance calculation step by step
-Explain squaring deviations eliminates negatives
-Calculate variance for simple datasets
-Compare with mean absolute deviation

Exercise books
-Manila paper
-Simple datasets
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 65-70

Statistics II

Variance Using Alternative Formula
Standard Deviation Calculations
Standard Deviation for Grouped Data

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

-Apply the formula: σ² = (Σx²/n) - x̄²
-Use alternative variance formula efficiently
-Compare computational methods
-Solve variance problems for frequency data

-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

-Demonstrate both variance formulas
-Show computational advantages of alternative formula
-Practice with frequency tables
-Students choose efficient method

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

KLB Secondary Mathematics Form 4, Pages 65-70

Statistics II
Loci

Advanced Standard Deviation Techniques
Introduction to Loci

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
-String

KLB Secondary Mathematics Form 4, Pages 65-70

Loci

Basic Locus Concepts and Laws

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

-Understand that loci follow specific laws or conditions
-Identify the laws governing different types of movement
-Distinguish between 2D and 3D loci
-Apply locus concepts to simple problems

-Physical demonstrations with moving objects
-Students track movement of classroom door
-Identify laws governing pendulum movement
-Practice stating locus laws clearly

Exercise books
-Manila paper
-String
-Real objects

KLB Secondary Mathematics Form 4, Pages 73-75

Loci

Perpendicular Bisector Locus

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

-Define perpendicular bisector locus
-Construct perpendicular bisector using compass and ruler
-Prove that points on perpendicular bisector are equidistant from endpoints
-Apply perpendicular bisector to solve problems

-Construct perpendicular bisector on manila paper
-Measure distances to verify equidistance property
-Use folding method to find perpendicular bisector
-Practice with different line segments

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Properties and Applications of Perpendicular Bisector
Locus of Points at Fixed Distance from a Point

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

-Understand perpendicular bisector in 3D space
-Apply perpendicular bisector to find circumcenters
-Solve practical problems using perpendicular bisector
-Use perpendicular bisector in triangle constructions

-Find circumcenter of triangle using perpendicular bisectors
-Solve water pipe problems (equidistant from two points)
-Apply to real-world location problems
-Practice with various triangle types

Exercise books
-Manila paper
-Compass
-Ruler
-String

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Locus of Points at Fixed Distance from a Line

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

-Define locus of points at fixed distance from straight line
-Construct parallel lines at given distances
-Understand cylindrical surface in 3D
-Apply to practical problems like road margins

-Construct parallel lines using ruler and set square
-Mark points at equal distances from given line
-Discuss road design, river banks, field boundaries
-Practice with various distances and orientations

Exercise books
-Manila paper
-Ruler
-Set square

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Angle Bisector Locus
Properties and Applications of Angle Bisector
Constant Angle Locus

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

-Define angle bisector locus
-Construct angle bisectors using compass and ruler
-Prove equidistance property of angle bisector
-Apply angle bisector to find incenters

-Understand constant angle locus concept
-Construct constant angle loci using arc method
-Apply circle theorems to constant angle problems
-Solve problems involving angles in semicircles

-Construct angle bisectors for various angles
-Verify equidistance from angle arms
-Find incenter of triangle using angle bisectors
-Practice with acute, obtuse, and right angles

-Demonstrate constant angle using protractor
-Construct arc passing through two points
-Use angles in semicircle property
-Practice with different angle measures

Exercise books
-Manila paper
-Compass
-Protractor
-Ruler

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Advanced Constant Angle Constructions

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

-Construct constant angle loci for various angles
-Find centers of constant angle arcs
-Solve complex constant angle problems
-Apply to geometric theorem proving

-Find centers for 60°, 90°, 120° angle loci
-Construct major and minor arcs
-Solve problems involving multiple angle constraints
-Verify constructions using measurement

Exercise books
-Manila paper
-Compass
-Protractor

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Introduction to Intersecting Loci
Intersecting Circles and Lines

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

-Understand concept of intersecting loci
-Identify points satisfying multiple conditions
-Find intersection points of two loci
-Apply intersecting loci to solve practical problems

-Demonstrate intersection of two circles
-Find points equidistant from two points AND at fixed distance from third point
-Solve simple two-condition problems
-Practice identifying intersection points

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 83-89

Loci

Triangle Centers Using Intersecting Loci

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

-Find circumcenter using perpendicular bisector intersections
-Locate incenter using angle bisector intersections
-Determine centroid and orthocenter
-Apply triangle centers to solve problems

-Construct all four triangle centers
-Compare properties of different triangle centers
-Use triangle centers in geometric proofs
-Solve problems involving triangle center properties

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 83-89

Loci

Complex Intersecting Loci Problems

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

-Solve problems with three or more conditions
-Find regions satisfying multiple constraints
-Apply intersecting loci to optimization problems
-Use systematic approach to complex problems

-Solve treasure hunt type problems
-Find optimal locations for facilities
-Apply to surveying and engineering problems
-Practice systematic problem-solving approach

Exercise books
-Manila paper
-Compass
-Real-world scenarios

KLB Secondary Mathematics Form 4, Pages 83-89

Loci

Introduction to Loci of Inequalities
Distance Inequality Loci

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

-Understand graphical representation of inequalities
-Identify regions satisfying inequality conditions
-Distinguish between boundary lines and regions
-Apply inequality loci to practical constraints

-Shade regions representing simple inequalities
-Use broken and solid lines appropriately
-Practice with distance inequalities
-Apply to real-world constraint problems

Exercise books
-Manila paper
-Ruler
-Colored pencils
-Compass

KLB Secondary Mathematics Form 4, Pages 89-92

Loci

Combined Inequality Loci
Advanced Inequality Applications
Introduction to Loci Involving Chords

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

-Solve problems with multiple inequality constraints
-Find intersection regions of inequality loci
-Apply to optimization and feasibility problems
-Use systematic shading techniques

-Apply inequality loci to linear programming introduction
-Solve real-world optimization problems
-Find maximum and minimum values in regions
-Use graphical methods for decision making

-Find feasible regions for multiple constraints
-Solve planning problems with restrictions
-Apply to resource allocation scenarios
-Practice systematic region identification

-Solve simple linear programming problems
-Find optimal points in feasible regions
-Apply to business and farming scenarios
-Practice identifying corner points

Exercise books
-Manila paper
-Ruler
-Colored pencils
Exercise books
-Manila paper
-Ruler
-Real problem data
-Compass

KLB Secondary Mathematics Form 4, Pages 89-92

Loci

Chord-Based Constructions

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

-Construct circles through three points using chords
-Find loci of chord midpoints
-Solve problems with intersecting chords
-Apply chord properties to geometric constructions

-Construct circles using three non-collinear points
-Find locus of midpoints of parallel chords
-Solve chord intersection problems
-Practice with chord-tangent relationships

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 92-94

Loci

Advanced Chord Problems

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

-Solve complex problems involving multiple chords
-Apply power of point theorem
-Find loci related to chord properties
-Use chords in circle geometry proofs

-Apply intersecting chords theorem
-Solve problems with chord-secant relationships
-Find loci of points with equal power
-Practice with tangent-chord angles

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 92-94

Loci
Vectors (II)

Integration of All Loci Types
Coordinates in two dimensions

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

-Combine different types of loci in single problems
-Solve comprehensive loci challenges
-Apply multiple loci concepts simultaneously
-Use loci in geometric investigations

-Solve multi-step loci problems
-Combine circle, line, and angle loci
-Apply to real-world complex scenarios
-Practice systematic problem-solving

Exercise books
-Manila paper
-Compass
-Ruler
Chalk and blackboard, squared paper or grid drawn on ground, exercise books

KLB Secondary Mathematics Form 4, Pages 73-94

Vectors (II)

Coordinates in three dimensions

By the end of the lesson, the learner should be able to:
Identify the coordinates of a point in three dimensions
Understand the three-dimensional coordinate system
Plot points in 3D space systematically
Apply 3D coordinates to spatial problems

Q/A on 3D coordinate understanding using room corner references
Discussions on height, length, and width measurements
Solving 3D coordinate problems using systematic approaches
Demonstrations using classroom corners and building structures
Explaining 3D visualization using physical room examples

Chalk and blackboard, 3D models made from sticks and clay, exercise books

KLB Mathematics Book Three Pg 222

Vectors (II)

Column and position vectors in three dimensions
Position vectors and applications

By the end of the lesson, the learner should be able to:
Find a displacement and represent it in column vector
Calculate the position vector
Express vectors in column form
Apply column vector notation systematically

Q/A on displacement representation using movement examples
Discussions on vector notation using organized column format
Solving column vector problems using systematic methods
Demonstrations using physical movement and direction examples
Explaining vector components using practical displacement

Chalk and blackboard, movement demonstration space, exercise books
Chalk and blackboard, origin marking systems, exercise books

KLB Mathematics Book Three Pg 223-224

Vectors (II)

Column vectors in terms of unit vectors i, j, k
Vector operations using unit vectors

By the end of the lesson, the learner should be able to:
Express vectors in terms of unit vectors
Convert between column and unit vector notation
Understand the standard basis vector system
Apply unit vector representation systematically
Express vectors in terms of unit vectors
Perform vector addition using unit vector notation
Calculate vector subtraction with i, j, k components
Apply scalar multiplication to unit vectors

Q/A on unit vector concepts using direction examples
Discussions on component representation using organized methods
Solving unit vector problems using systematic conversion
Demonstrations using perpendicular direction examples
Explaining basis vector concepts using coordinate axes
Q/A on vector operations using component-wise calculation
Discussions on systematic operation methods
Solving vector operation problems using organized approaches
Demonstrations using component separation and combination
Explaining operation logic using algebraic reasoning

Chalk and blackboard, direction indicators, unit vector reference charts, exercise books
Chalk and blackboard, component calculation aids, exercise books

KLB Mathematics Book Three Pg 226-228

Vectors (II)

Magnitude of a vector in three dimensions
Magnitude applications and unit vectors

By the end of the lesson, the learner should be able to:
Calculate the magnitude of a vector in three dimensions
Apply the 3D magnitude formula systematically
Find vector lengths in spatial contexts
Solve magnitude problems accurately

Q/A on 3D magnitude using extended Pythagorean methods
Discussions on spatial distance calculation using 3D techniques
Solving 3D magnitude problems using systematic calculation
Demonstrations using 3D distance examples
Explaining 3D magnitude using practical spatial examples

Chalk and blackboard, 3D measurement aids, exercise books
Chalk and blackboard, direction finding aids, exercise books

KLB Mathematics Book Three Pg 229-230

Vectors (II)

Parallel vectors
Collinearity
Advanced collinearity applications

By the end of the lesson, the learner should be able to:
Identify parallel vectors
Determine when vectors are parallel
Apply parallel vector properties
Use scalar multiples in parallel relationships
Show that points are collinear
Apply vector methods to prove collinearity
Test for collinear points using vector techniques
Solve collinearity problems systematically

Q/A on parallel identification using scalar multiple methods
Discussions on parallel relationships using geometric examples
Solving parallel vector problems using systematic testing
Demonstrations using parallel line and direction examples
Explaining parallel concepts using geometric reasoning
Q/A on collinearity testing using vector proportion methods
Discussions on point alignment using vector analysis
Solving collinearity problems using systematic verification
Demonstrations using straight-line point examples
Explaining collinearity using geometric alignment concepts

Chalk and blackboard, parallel line demonstrations, exercise books
Chalk and blackboard, straight-line demonstrations, exercise books
Chalk and blackboard, complex geometric aids, exercise books

KLB Mathematics Book Three Pg 231-232
KLB Mathematics Book Three Pg 232-234

Vectors (II)

Proportional division of a line

By the end of the lesson, the learner should be able to:
Divide a line internally in the given ratio
Apply the internal division formula
Calculate division points using vector methods
Understand proportional division concepts

Q/A on internal division using systematic formula application
Discussions on ratio division using proportional methods
Solving internal division problems using organized approaches
Demonstrations using internal point construction examples
Explaining internal division using geometric visualization

Chalk and blackboard, internal division models, exercise books

KLB Mathematics Book Three Pg 237-238

Vectors (II)

External division of a line

By the end of the lesson, the learner should be able to:
Divide a line externally in the given ratio
Apply the external division formula
Distinguish between internal and external division
Solve external division problems accurately

Q/A on external division using systematic formula application
Discussions on external point calculation using vector methods
Solving external division problems using careful approaches
Demonstrations using external point construction examples
Explaining external division using extended line concepts

Chalk and blackboard, external division models, exercise books

KLB Mathematics Book Three Pg 238-239

Vectors (II)

Combined internal and external division
Ratio theorem

By the end of the lesson, the learner should be able to:
Divide a line internally and externally in the given ratio
Apply both division formulas systematically
Compare internal and external division results
Handle mixed division problems

Q/A on combined division using comparative methods
Discussions on division type selection using problem analysis
Solving combined division problems using systematic approaches
Demonstrations using both division types
Explaining division relationships using geometric reasoning

Chalk and blackboard, combined division models, exercise books
Chalk and blackboard, ratio theorem aids, exercise books

KLB Mathematics Book Three Pg 239

Vectors (II)

Advanced ratio theorem applications

By the end of the lesson, the learner should be able to:
Find the position vector
Apply ratio theorem to complex scenarios
Solve multi-step ratio problems
Use ratio theorem in geometric proofs

Q/A on advanced ratio applications using complex problems
Discussions on multi-step ratio calculation
Solving challenging ratio problems using systematic methods
Demonstrations using comprehensive ratio examples
Explaining advanced applications using detailed reasoning

Chalk and blackboard, advanced ratio models, exercise books

KLB Mathematics Book Three Pg 242

Vectors (II)

Mid-point

By the end of the lesson, the learner should be able to:
Find the mid-points of the given vectors
Apply midpoint formulas in vector contexts
Use midpoint concepts in geometric problems
Calculate midpoints systematically

Q/A on midpoint calculation using vector averaging methods
Discussions on midpoint applications using geometric examples
Solving midpoint problems using systematic approaches
Demonstrations using midpoint construction and calculation
Explaining midpoint concepts using practical examples

Chalk and blackboard, midpoint demonstration aids, exercise books

KLB Mathematics Book Three Pg 243

Vectors (II)

Ratio theorem and midpoint integration
Advanced ratio theorem applications
Applications of vectors in geometry

By the end of the lesson, the learner should be able to:
Use ratio theorem to find the given vectors
Apply midpoint and ratio concepts together
Solve complex ratio and midpoint problems
Integrate division and midpoint methods
Use vectors to show the diagonals of a parallelogram
Apply vector methods to geometric proofs
Demonstrate parallelogram properties using vectors
Solve geometric problems using vector techniques

Q/A on integrated problem-solving using combined methods
Discussions on complex scenario analysis using systematic approaches
Solving challenging problems using integrated techniques
Demonstrations using comprehensive geometric examples
Explaining integration using logical problem-solving
Q/A on geometric proof using vector methods
Discussions on parallelogram properties using vector analysis
Solving geometric problems using systematic vector techniques
Demonstrations using vector-based geometric constructions
Explaining geometric relationships using vector reasoning

Chalk and blackboard, complex problem materials, exercise books
Chalk and blackboard, advanced geometric aids, exercise books
Chalk and blackboard, parallelogram models, exercise books

KLB Mathematics Book Three Pg 244-245
KLB Mathematics Book Three Pg 248-249

Vectors (II)

Rectangle diagonal applications
Advanced geometric applications

By the end of the lesson, the learner should be able to:
Use vectors to show the diagonals of a rectangle
Apply vector methods to rectangle properties
Prove rectangle theorems using vectors
Compare parallelogram and rectangle diagonal properties

Q/A on rectangle properties using vector analysis
Discussions on diagonal relationships using vector methods
Solving rectangle problems using systematic approaches
Demonstrations using rectangle constructions and vector proofs
Explaining rectangle properties using vector reasoning

Chalk and blackboard, rectangle models, exercise books
Chalk and blackboard, advanced geometric models, exercise books

KLB Mathematics Book Three Pg 248-250

Binomial Expansion

Binomial expansions up to power four

By the end of the lesson, the learner should be able to:
Expand binomial function up to power four
Apply systematic multiplication methods
Recognize coefficient patterns in expansions
Use multiplication to expand binomial expressions

Q/A on algebraic multiplication using familiar expressions
Discussions on systematic expansion using step-by-step methods
Solving basic binomial multiplication problems
Demonstrations using area models and rectangular arrangements
Explaining pattern recognition using organized layouts

Chalk and blackboard, rectangular cutouts from paper, exercise books

KLB Mathematics Book Three Pg 256

Binomial Expansion

Binomial expansions up to power four (continued)

By the end of the lesson, the learner should be able to:
Expand binomial function up to power four
Handle increasingly complex coefficient patterns
Apply systematic expansion techniques efficiently
Verify expansions using substitution methods

Q/A on power expansion using multiplication techniques
Discussions on coefficient identification using pattern analysis
Solving expansion problems using systematic approaches
Demonstrations using geometric representations
Explaining verification methods using numerical substitution

Chalk and blackboard, squared paper for geometric models, exercise books

KLB Mathematics Book Three Pg 256

Binomial Expansion

Pascal's triangle
Pascal's triangle applications

By the end of the lesson, the learner should be able to:
Use Pascal's triangle
Construct Pascal's triangle systematically
Apply triangle coefficients for binomial expansions
Recognize number patterns in the triangle

Q/A on triangle construction using addition patterns
Discussions on coefficient relationships using triangle analysis
Solving triangle construction and application problems
Demonstrations using visual triangle building
Explaining pattern connections using systematic observation

Chalk and blackboard, triangular patterns drawn/cut from paper, exercise books
Chalk and blackboard, Pascal's triangle reference charts, exercise books

KLB Mathematics Book Three Pg 256-257

Binomial Expansion

Pascal's triangle (continued)

By the end of the lesson, the learner should be able to:
Use Pascal's triangle
Apply triangle to complex expansion problems
Handle higher powers using Pascal's triangle
Integrate triangle concepts with algebraic expansion

Q/A on advanced triangle applications using complex examples
Discussions on higher power expansion using triangle methods
Solving challenging problems using Pascal's triangle
Demonstrations using detailed triangle constructions
Explaining integration using comprehensive examples

Chalk and blackboard, advanced triangle patterns, exercise books

KLB Mathematics Book Three Pg 258-259

Binomial Expansion

Pascal's triangle advanced
Applications to numerical cases
Applications to numerical cases (continued)

By the end of the lesson, the learner should be able to:
Use Pascal's triangle
Apply general binomial theorem concepts
Understand combination notation in expansions
Use general term formula applications
Use binomial expansion to solve numerical problems
Apply binomial methods to complex calculations
Handle decimal approximations using expansions
Solve practical numerical problems

Q/A on general formula understanding using pattern analysis
Discussions on combination notation using counting principles
Solving general term problems using formula application
Demonstrations using systematic formula usage
Explaining general principles using algebraic reasoning
Q/A on advanced numerical applications using complex scenarios
Discussions on decimal approximation using expansion techniques
Solving challenging numerical problems using systematic methods
Demonstrations using detailed calculation procedures
Explaining practical relevance using real-world examples

Chalk and blackboard, combination calculation aids, exercise books
Chalk and blackboard, simple calculation aids, exercise books
Chalk and blackboard, advanced calculation examples, exercise books

KLB Mathematics Book Three Pg 258-259
KLB Mathematics Book Three Pg 259-260

Probability

Introduction

By the end of the lesson, the learner should be able to:
Calculate the experimental probability
Understand probability concepts in daily life
Distinguish between certain and uncertain events
Recognize probability situations

Q/A on uncertain events from daily life experiences
Discussions on weather prediction and game outcomes
Analyzing chance events using coin tossing and dice rolling
Demonstrations using simple probability experiments
Explaining probability language using familiar examples

Chalk and blackboard, coins, dice made from cardboard, exercise books

KLB Mathematics Book Three Pg 262-264

Probability

Experimental Probability
Experimental Probability applications

By the end of the lesson, the learner should be able to:
Calculate the experimental probability
Conduct probability experiments systematically
Record and analyze experimental data
Compare experimental results with expectations

Q/A on frequency counting using repeated experiments
Discussions on trial repetition and result recording
Solving experimental probability problems using data collection
Demonstrations using coin toss and dice roll experiments
Explaining frequency ratio calculations using practical examples

Chalk and blackboard, coins, cardboard dice, tally charts, exercise books
Chalk and blackboard, extended experimental materials, data recording sheets, exercise books

KLB Mathematics Book Three Pg 262-264

Probability

Range of Probability Measure

By the end of the lesson, the learner should be able to:
Calculate the range of probability measure
Express probabilities on scale from 0 to 1
Convert between fractions, decimals, and percentages
Interpret probability values correctly

Q/A on probability scale using number line representations
Discussions on probability conversion between forms
Solving probability scale problems using systematic methods
Demonstrations using probability line and scale examples
Explaining scale interpretation using practical scenarios

Chalk and blackboard, number line drawings, probability scale charts, exercise books

KLB Mathematics Book Three Pg 265-266

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
Theoretical Probability advanced

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
Chalk and blackboard, complex probability materials, advanced calculation aids, exercise books

KLB Mathematics Book Three Pg 266-268

Probability

Theoretical Probability applications
Combined Events
Combined Events OR probability

By the end of the lesson, the learner should be able to:
Calculate the probability space for the theoretical probability
Apply theoretical concepts to real situations
Solve practical probability problems
Interpret results in meaningful contexts
Find the probability of a combined events
Understand compound events and combinations
Distinguish between different event types
Apply basic combination rules

Q/A on practical probability using local examples
Discussions on real-world applications using community scenarios
Solving application problems using theoretical methods
Demonstrations using local games and practical situations
Explaining practical interpretation using meaningful contexts
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, local game examples, practical scenario materials, exercise books
Chalk and blackboard, playing cards, multiple dice, Venn diagram drawings, exercise books
Chalk and blackboard, Venn diagram materials, card examples, exercise books

KLB Mathematics Book Three Pg 268-270
KLB Mathematics Book Three Pg 272-273

Probability

Independent Events

By the end of the lesson, the learner should be able to:
Find the probability of independent events
Apply multiplication rule for independent events
Calculate "A and B" probabilities
Understand independence concepts

Q/A on multiplication rule using independent event examples
Discussions on independence identification and verification
Solving AND probability problems using systematic calculation
Demonstrations using multiple coin tosses and dice combinations
Explaining multiplication rule using logical reasoning

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

KLB Mathematics Book Three Pg 274-275

Probability

Independent Events advanced

By the end of the lesson, the learner should be able to:
Find the probability of independent events
Distinguish between independent and dependent events
Apply conditional probability concepts
Handle complex independence scenarios

Q/A on independence verification using mathematical methods
Discussions on dependence concepts using card drawing examples
Solving dependent and independent event problems using systematic approaches
Demonstrations using replacement and non-replacement scenarios
Explaining conditional probability using practical examples

Chalk and blackboard, playing cards for replacement scenarios, multiple experimental setups, exercise books

KLB Mathematics Book Three Pg 276-278

Probability

Independent Events applications
Tree Diagrams
Tree Diagrams advanced

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
Chalk and blackboard, tree diagram templates, branching materials, exercise books
Chalk and blackboard, complex tree examples, detailed calculation aids, exercise books

KLB Mathematics Book Three Pg 278-280