Loci

Introduction to Loci
Basic Locus Concepts and Laws

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

-Define locus and understand its meaning
-Distinguish between locus of points, lines, and regions
-Identify real-world examples of loci
-Understand the concept of movement according to given laws

-Demonstrate door movement to show path traced by corner
-Use string and pencil to show circular locus
-Discuss examples: clock hands, pendulum swing
-Students trace paths of moving objects

Exercise books
-Manila paper
-String
-Chalk/markers
-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

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

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Locus of Points at Fixed Distance from a Point
Locus of Points at Fixed Distance from a Line

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

-Define circle as locus of points at fixed distance from center
-Construct circles with given radius using compass
-Understand sphere as 3D locus from fixed point
-Solve problems involving circular loci

-Construct circles of different radii
-Demonstrate with string of fixed length
-Discuss radar coverage, radio signal range
-Students create circles with various measurements

Exercise books
-Manila paper
-Compass
-String
-Ruler
-Set square

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Angle Bisector 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

-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

Exercise books
-Manila paper
-Compass
-Protractor

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Properties and Applications of Angle Bisector
Constant Angle Locus

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

-Understand relationship between angle bisectors in triangles
-Apply angle bisector theorem
-Solve problems involving inscribed circles
-Use angle bisectors in geometric constructions

-Construct inscribed circle using angle bisectors
-Apply angle bisector theorem to solve problems
-Find external angle bisectors
-Solve practical surveying problems

Exercise books
-Manila paper
-Compass
-Ruler
-Protractor

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

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

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

Exercise books
-Manila paper
-Ruler
-Colored pencils

KLB Secondary Mathematics Form 4, Pages 89-92

Loci

Advanced Inequality Applications
Introduction to Loci Involving Chords

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

-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

-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
-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
Three Dimensional Geometry

Integration of All Loci Types
Introduction to 3D Concepts

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
-Cardboard boxes
-Real 3D objects

KLB Secondary Mathematics Form 4, Pages 73-94

Three Dimensional Geometry

Properties of Common Solids

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

-Identify properties of cubes, cuboids, pyramids
-Count faces, edges, vertices systematically
-Apply Euler's formula (V - E + F = 2)
-Classify solids by their geometric properties

-Make models using cardboard and tape
-Create table of properties for different solids
-Verify Euler's formula with physical models
-Compare prisms and pyramids systematically

Exercise books
-Cardboard
-Scissors
-Tape/glue

KLB Secondary Mathematics Form 4, Pages 113-115

Three Dimensional Geometry

Understanding Planes in 3D Space
Lines 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
-Rulers/sticks
-3D models

KLB Secondary Mathematics Form 4, Pages 113-115

Three Dimensional Geometry

Introduction to Projections

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

-Understand concept of projection in 3D geometry
-Find projections of points onto planes
-Identify foot of perpendicular from point to plane
-Apply projection concept to shadow problems

-Use light source to create shadows (projections)
-Drop perpendiculars from corners to floor
-Identify projections in architectural drawings
-Practice finding feet of perpendiculars

Exercise books
-Manila paper
-Light source
-3D models

KLB Secondary Mathematics Form 4, Pages 115-123

Three Dimensional Geometry

Angle Between Line and Plane - Concept
Calculating Angles Between Lines and Planes

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
-Calculators
-3D problem diagrams

KLB Secondary Mathematics Form 4, Pages 115-123

Three Dimensional Geometry

Advanced Line-Plane Angle Problems

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

-Solve complex angle problems systematically
-Apply coordinate geometry methods where helpful
-Use multiple right-angled triangles in solutions
-Verify answers using different approaches

-Practice with tent and roof angle problems
-Solve ladder against wall problems in 3D
-Work through architectural angle calculations
-Use real-world engineering applications

Exercise books
-Manila paper
-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

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

KLB Secondary Mathematics Form 4, Pages 115-135

Three Dimensional Geometry

Volume and Surface Area Applications
Coordinate Geometry in 3D

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

-Connect 3D geometry to volume calculations
-Apply angle calculations to surface area problems
-Use 3D relationships in optimization
-Solve practical volume and area problems

-Calculate slant heights using 3D angles
-Find surface areas of pyramids using angles
-Apply to packaging and container problems
-Use in architectural space planning

Exercise books
-Manila paper
-Volume formulas
-Real containers
-3D coordinate grid
-Room corner reference

KLB Secondary Mathematics Form 4, Pages 115-135

Three Dimensional Geometry

Integration with Trigonometry

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

KLB Secondary Mathematics Form 4, Pages 115-135

Linear Programming

Introduction to Linear Programming
Forming Linear Inequalities from Word Problems

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

-Understand the concept of optimization in real life
-Identify decision variables in practical situations
-Recognize constraints and objective functions
-Understand applications of linear programming

-Discuss resource allocation problems in daily life
-Identify optimization scenarios in business and farming
-Introduce decision-making with limited resources
-Use simple examples from student experiences

Exercise books
-Manila paper
-Real-life examples
-Chalk/markers
-Local business examples
-Agricultural scenarios

KLB Secondary Mathematics Form 4, Pages 165-167

Linear Programming

Types of Constraints

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

-Identify non-negativity constraints
-Understand resource constraints and their implications
-Form demand and supply constraints
-Apply constraint formation to various industries

-Practice with non-negativity constraints (x ≥ 0, y ≥ 0)
-Form material and labor constraints
-Apply to manufacturing and service industries
-Use school resource allocation examples

Exercise books
-Manila paper
-Industry examples
-School scenarios

KLB Secondary Mathematics Form 4, Pages 165-167

Linear Programming

Objective Functions
Complete Problem Formulation

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

-Define objective functions for maximization problems
-Define objective functions for minimization problems
-Understand profit, cost, and other objective measures
-Connect objective functions to real-world goals

-Form profit maximization functions
-Create cost minimization functions
-Practice with revenue and efficiency objectives
-Apply to business and production scenarios

Exercise books
-Manila paper
-Business examples
-Production scenarios
-Complete examples
-Systematic templates

KLB Secondary Mathematics Form 4, Pages 165-167

Linear Programming

Introduction to Graphical Solution Method

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

-Understand graphical representation of inequalities
-Plot constraint lines on coordinate plane
-Identify feasible and infeasible regions
-Understand boundary lines and their significance

-Plot simple inequality x + y ≤ 10 on graph
-Shade feasible regions systematically
-Distinguish between ≤ and < inequalities
-Practice with multiple examples on manila paper

Exercise books
-Manila paper
-Rulers
-Colored pencils

KLB Secondary Mathematics Form 4, Pages 166-172

Linear Programming

Plotting Multiple Constraints

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

-Plot multiple inequalities on same graph
-Find intersection of constraint lines
-Identify feasible region bounded by multiple constraints
-Handle cases with no feasible solution

-Plot system of 3-4 constraints simultaneously
-Find intersection points of constraint lines
-Identify and shade final feasible region
-Discuss unbounded and empty feasible regions

Exercise books
-Manila paper
-Rulers
-Different colored pencils

KLB Secondary Mathematics Form 4, Pages 166-172

Linear Programming

Properties of Feasible Regions
Introduction to Optimization

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

-Understand that feasible region is convex
-Identify corner points (vertices) of feasible region
-Understand significance of corner points
-Calculate coordinates of corner points

-Identify all corner points of feasible region
-Calculate intersection points algebraically
-Verify corner points satisfy all constraints
-Understand why corner points are important

Exercise books
-Manila paper
-Calculators
-Algebraic methods
-Evaluation tables

KLB Secondary Mathematics Form 4, Pages 166-172

Linear Programming

The Corner Point Method

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

-Apply systematic corner point evaluation method
-Create organized tables for corner point analysis
-Identify optimal corner point efficiently
-Handle cases with multiple optimal solutions

-Create systematic evaluation table
-Work through corner point method step-by-step
-Practice with various objective functions
-Identify and handle tie cases

Exercise books
-Manila paper
-Evaluation templates
-Systematic approach

KLB Secondary Mathematics Form 4, Pages 172-176

Linear Programming

The Iso-Profit/Iso-Cost Line Method
Comparing Solution Methods

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

-Understand concept of iso-profit and iso-cost lines
-Draw family of parallel objective function lines
-Use slope to find optimal point graphically
-Apply sliding line method for optimization

-Draw iso-profit lines for given objective function
-Show family of parallel lines with different values
-Find optimal point by sliding line to extreme position
-Practice with both maximization and minimization

Exercise books
-Manila paper
-Rulers
-Sliding technique
-Method comparison
-Verification examples

KLB Secondary Mathematics Form 4, Pages 172-176

Linear Programming
Integration

Business Applications - Production Planning
Introduction to Reverse Differentiation

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

-Apply linear programming to production problems
-Solve manufacturing optimization problems
-Handle resource allocation in production
-Apply to Kenyan manufacturing scenarios

-Solve factory production optimization problem
-Apply to textile or food processing examples
-Use local manufacturing scenarios
-Calculate optimal production mix

Exercise books
-Manila paper
-Manufacturing examples
-Kenyan industry data
Graph papers
-Differentiation charts
-Exercise books
-Function examples

KLB Secondary Mathematics Form 4, Pages 172-176

Integration

Basic Integration Rules - Power Functions
Integration of Polynomial Functions

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

KLB Secondary Mathematics Form 4, Pages 223-225

Integration

Finding Particular Solutions
Introduction to Definite Integrals
Evaluating Definite Integrals

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

-Use initial conditions to find specific values of constant c
-Solve problems involving boundary conditions
-Apply integration to find equations of curves
-Distinguish between general and particular solutions

-Working examples with given initial conditions
-Finding curve equations when gradient function and point are known
-Practice problems from various contexts
-Discussion on why particular solutions are important
-Problem-solving session with curve-finding exercises

Graph papers
-Calculators
-Curve examples
-Exercise books
-Geometric models
-Integration notation charts
Calculators
-Step-by-step worksheets
-Evaluation charts

KLB Secondary Mathematics Form 4, Pages 223-225

Integration

Area Under Curves - Single Functions
Areas Below X-axis and Mixed Regions
Area Between Two Curves

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

-Understand integration as area calculation tool
-Calculate area between curve and x-axis
-Handle regions bounded by curves and vertical lines
-Apply definite integrals to find exact areas

-Geometric demonstration of area under curves
-Drawing and shading regions on graph paper
-Working examples: area under y = x², y = 2x + 3, etc.
-Comparison with approximation methods from Chapter 9
-Practice finding areas of various regions

Graph papers
-Curve sketching tools
-Colored pencils
-Calculators
-Area grids
-Curve examples
-Colored materials
-Exercise books
-Equation solving aids

KLB Secondary Mathematics Form 4, Pages 230-233

REVISION

Paper 1 Revision
Paper 1 Revision
Paper 1 Revision

Section I: Short Answer Questions
Section I: Short Answer Questions
Section I: Mixed Question Practice

By the end of the lesson, the learner should be able to:
– attempt compulsory short-answer questions – show clear working for full marks – apply speed and accuracy in solving problems

Students attempt selected questions individually Peer-marking and teacher correction

Past Paper 1 exams, Marking Schemes
Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes

KLB Math Bk 1–4, paper 1 question paper

Paper 1 Revision
paper 2 Revision

Section II: Structured Questions
Section I: Short Answer Questions

By the end of the lesson, the learner should be able to:
– develop detailed structured responses – organize answers step by step – apply concepts in real-life problem settings

Group brainstorming on selected structured questions Teacher gives feedback on presentation

Past Paper 1s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers
Past paper 2 exams, Marking Schemes

KLB Math Bk 1–4
paper 1 question paper

paper 2 Revision

Section I: Short Answer Questions
Section I: Mixed Question Practice
Section II: Structured Questions

By the end of the lesson, the learner should be able to:
– practice a variety of short-answer styles – apply problem-solving strategies – build confidence in tackling compulsory questions

Teacher demonstrates approaches Students work in pairs and discuss solutions

Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes
Past Paper 2s, Marking Schemes

KLB Math Bk 1–4
paper 2 question paper

paper 2 Revision
Paper 1 Revision

Section II: Structured Questions
Section I: Short Answer Questions

By the end of the lesson, the learner should be able to:
– practice extended problem solving – interpret and use graphs, diagrams and data – present answers clearly for maximum marks

Students attempt structured questions under timed conditions Peer review and corrections

Graph Papers, Geometry Sets, Past Papers
Past Paper 1 exams, Marking Schemes

KLB Math Bk 1–4
paper 2 question paper

Paper 1 Revision

Section I: Short Answer Questions
Section I: Mixed Question Practice
Section II: Structured Questions

By the end of the lesson, the learner should be able to:
– practice a variety of short-answer styles – apply problem-solving strategies – build confidence in tackling compulsory questions

Teacher demonstrates approaches Students work in pairs and discuss solutions

Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes
Past Paper 1s, Marking Schemes

KLB Math Bk 1–4
paper 1 question paper

Paper 1 Revision
paper 2 Revision
paper 2 Revision

Section II: Structured Questions
Section I: Short Answer Questions
Section I: Short Answer Questions

By the end of the lesson, the learner should be able to:
– practice extended problem solving – interpret and use graphs, diagrams and data – present answers clearly for maximum marks

Students attempt structured questions under timed conditions Peer review and corrections

Graph Papers, Geometry Sets, Past Papers
Past paper 2 exams, Marking Schemes
Chalkboard, Past Papers, Calculators

KLB Math Bk 1–4
paper 1 question paper

paper 2 Revision

Section I: Mixed Question Practice
Section II: Structured Questions
Section II: Structured Questions

By the end of the lesson, the learner should be able to:
– integrate knowledge to solve mixed short questions – apply logical reasoning and time management – identify common errors and correct them

Timed practice with mixed short-answer questions Class discussion of solutions

Past Papers, Marking Schemes
Past Paper 2s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers

Students’ Notes, Revision Texts
Paper 2 question paper

Paper 1 Revision

Section I: Short Answer Questions
Section I: Short Answer Questions
Section I: Mixed Question Practice

By the end of the lesson, the learner should be able to:
– attempt compulsory short-answer questions – show clear working for full marks – apply speed and accuracy in solving problems

Students attempt selected questions individually Peer-marking and teacher correction

Past Paper 1 exams, Marking Schemes
Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes

KLB Math Bk 1–4, paper 1 question paper

Paper 1 Revision
paper 2 Revision

Section II: Structured Questions
Section I: Short Answer Questions

By the end of the lesson, the learner should be able to:
– develop detailed structured responses – organize answers step by step – apply concepts in real-life problem settings

Group brainstorming on selected structured questions Teacher gives feedback on presentation

Past Paper 1s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers
Past paper 2 exams, Marking Schemes

KLB Math Bk 1–4
paper 1 question paper

paper 2 Revision

Section I: Short Answer Questions
Section I: Mixed Question Practice

By the end of the lesson, the learner should be able to:
– practice a variety of short-answer styles – apply problem-solving strategies – build confidence in tackling compulsory questions

Teacher demonstrates approaches Students work in pairs and discuss solutions

Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes

KLB Math Bk 1–4
paper 2 question paper

paper 2 Revision
Paper 1 Revision

Section II: Structured Questions
Section I: Short Answer Questions

By the end of the lesson, the learner should be able to:
– develop detailed structured responses – organize answers step by step – apply concepts in real-life problem settings

Group brainstorming on selected structured questions Teacher gives feedback on presentation

Past Paper 2s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers
Past Paper 1 exams, Marking Schemes

KLB Math Bk 1–4
paper 2 question paper

Paper 1 Revision

Section I: Short Answer Questions
Section I: Mixed Question Practice
Section II: Structured Questions

By the end of the lesson, the learner should be able to:
– practice a variety of short-answer styles – apply problem-solving strategies – build confidence in tackling compulsory questions

Teacher demonstrates approaches Students work in pairs and discuss solutions

Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes
Past Paper 1s, Marking Schemes

KLB Math Bk 1–4
paper 1 question paper

Paper 1 Revision
paper 2 Revision
paper 2 Revision

Section II: Structured Questions
Section I: Short Answer Questions
Section I: Short Answer Questions

By the end of the lesson, the learner should be able to:
– practice extended problem solving – interpret and use graphs, diagrams and data – present answers clearly for maximum marks

Students attempt structured questions under timed conditions Peer review and corrections

Graph Papers, Geometry Sets, Past Papers
Past paper 2 exams, Marking Schemes
Chalkboard, Past Papers, Calculators

KLB Math Bk 1–4
paper 1 question paper

paper 2 Revision

Section I: Mixed Question Practice
Section II: Structured Questions
Section II: Structured Questions

By the end of the lesson, the learner should be able to:
– integrate knowledge to solve mixed short questions – apply logical reasoning and time management – identify common errors and correct them

Timed practice with mixed short-answer questions Class discussion of solutions

Past Papers, Marking Schemes
Past Paper 2s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers

Students’ Notes, Revision Texts
Paper 2 question paper

Paper 1 Revision

Section I: Short Answer Questions
Section I: Short Answer Questions
Section I: Mixed Question Practice

By the end of the lesson, the learner should be able to:
– attempt compulsory short-answer questions – show clear working for full marks – apply speed and accuracy in solving problems

Students attempt selected questions individually Peer-marking and teacher correction

Past Paper 1 exams, Marking Schemes
Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes

KLB Math Bk 1–4, paper 1 question paper

Paper 1 Revision

Section II: Structured Questions

By the end of the lesson, the learner should be able to:
– develop detailed structured responses – organize answers step by step – apply concepts in real-life problem settings

Group brainstorming on selected structured questions Teacher gives feedback on presentation

Past Paper 1s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers

KLB Math Bk 1–4
paper 1 question paper

paper 2 Revision

Section I: Short Answer Questions
Section I: Short Answer Questions
Section I: Mixed Question Practice

By the end of the lesson, the learner should be able to:
– attempt compulsory short-answer questions – show clear working for full marks – apply speed and accuracy in solving problems

Students attempt selected questions individually Peer-marking and teacher correction

Past paper 2 exams, Marking Schemes
Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes

KLB Math Bk 1–4, paper 2 question paper

paper 2 Revision
Paper 1 Revision

Section II: Structured Questions
Section I: Short Answer Questions

By the end of the lesson, the learner should be able to:
– develop detailed structured responses – organize answers step by step – apply concepts in real-life problem settings

Group brainstorming on selected structured questions Teacher gives feedback on presentation

Past Paper 2s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers
Past Paper 1 exams, Marking Schemes

KLB Math Bk 1–4
paper 2 question paper

Paper 1 Revision

Section I: Short Answer Questions
Section I: Mixed Question Practice
Section II: Structured Questions

By the end of the lesson, the learner should be able to:
– practice a variety of short-answer styles – apply problem-solving strategies – build confidence in tackling compulsory questions

Teacher demonstrates approaches Students work in pairs and discuss solutions

Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes
Past Paper 1s, Marking Schemes

KLB Math Bk 1–4
paper 1 question paper

Paper 1 Revision
paper 2 Revision
paper 2 Revision

Section II: Structured Questions
Section I: Short Answer Questions
Section I: Short Answer Questions

By the end of the lesson, the learner should be able to:
– practice extended problem solving – interpret and use graphs, diagrams and data – present answers clearly for maximum marks

Students attempt structured questions under timed conditions Peer review and corrections

Graph Papers, Geometry Sets, Past Papers
Past paper 2 exams, Marking Schemes
Chalkboard, Past Papers, Calculators

KLB Math Bk 1–4
paper 1 question paper

paper 2 Revision

Section I: Mixed Question Practice
Section II: Structured Questions
Section II: Structured Questions

By the end of the lesson, the learner should be able to:
– integrate knowledge to solve mixed short questions – apply logical reasoning and time management – identify common errors and correct them

Timed practice with mixed short-answer questions Class discussion of solutions

Past Papers, Marking Schemes
Past Paper 2s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers

Students’ Notes, Revision Texts
Paper 2 question paper

Paper 1 Revision

Section I: Short Answer Questions
Section I: Short Answer Questions

By the end of the lesson, the learner should be able to:
– attempt compulsory short-answer questions – show clear working for full marks – apply speed and accuracy in solving problems

Students attempt selected questions individually Peer-marking and teacher correction

Past Paper 1 exams, Marking Schemes
Chalkboard, Past Papers, Calculators

KLB Math Bk 1–4, paper 1 question paper

Paper 1 Revision

Section I: Mixed Question Practice
Section II: Structured Questions
Section II: Structured Questions

By the end of the lesson, the learner should be able to:
– integrate knowledge to solve mixed short questions – apply logical reasoning and time management – identify common errors and correct them

Timed practice with mixed short-answer questions Class discussion of solutions

Past Papers, Marking Schemes
Past Paper 1s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers

Students’ Notes, Revision Texts
paper 1 question paper

paper 2 Revision

Section I: Short Answer Questions
Section I: Short Answer Questions
Section I: Mixed Question Practice

By the end of the lesson, the learner should be able to:
– attempt compulsory short-answer questions – show clear working for full marks – apply speed and accuracy in solving problems

Students attempt selected questions individually Peer-marking and teacher correction

Past paper 2 exams, Marking Schemes
Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes

KLB Math Bk 1–4, paper 2 question paper

paper 2 Revision

Section II: Structured Questions

By the end of the lesson, the learner should be able to:
– develop detailed structured responses – organize answers step by step – apply concepts in real-life problem settings

Group brainstorming on selected structured questions Teacher gives feedback on presentation

Past Paper 2s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers

KLB Math Bk 1–4
paper 2 question paper