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| WK | LSN | TOPIC | SUB-TOPIC | OBJECTIVES | T/L ACTIVITIES | T/L AIDS | REFERENCE | REMARKS |
|---|---|---|---|---|---|---|---|---|
| 1 |
OPENING OF SCHOOLS AND TRIAL EXAMINATIONS |
|||||||
| 2 | 1 |
Quadratic Expressions and Equations
|
Factorization of quadratic expressions
|
By the end of the
lesson, the learner
should be able to:
Factorize quadratic expressions Write the perfect squares |
Discussions
Solving Demonstrating Explaining |
calculators
|
KLB Mathematics
Book Three Pg 1 |
|
| 2 | 2 |
Quadratic Expressions and Equations
|
Completing squares
Completing squares |
By the end of the
lesson, the learner
should be able to:
Factorize quadratic expression by completing square method |
Discussions
Solving Demonstrating Explaining |
calculators
|
KLB Mathematics
Book Three Pg 1-2 |
|
| 2 | 3 |
Quadratic Expressions and Equations
|
Solving quadratic expression by completing square
Solving quadratic expression by factorization |
By the end of the
lesson, the learner
should be able to:
Factorize quadratic expressions Solve quadratic expressions by completing square Solve quadratic expressions by factorization |
Discussions
Solving Demonstrating Explaining |
Calculators
Calculators |
KLB Mathematics
Book Three Pg 5-6 |
|
| 2 | 4 |
Quadratic Expressions and Equations
|
The quadratic formula
The quadratic formula Formation of quadratic equations |
By the end of the
lesson, the learner
should be able to:
Solve quadratic expressions using the quadratic formula Form a quadratic equation from word problem Solve the quadratic equation |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 7-9 |
|
| 2 | 5 |
Quadratic Expressions and Equations
|
Graphs of quadratic functions
Graphs of quadratic functions |
By the end of the
lesson, the learner
should be able to:
Draw a table of the quadratic functions Draw graphs of quadratic functions |
Discussions
Solving Demonstrating Explaining |
graph papers & geoboard
|
KLB Mathematics
Book Three Pg 12-15 |
|
| 2 | 6 |
Quadratic Expressions and Equations
|
Graphical solutions of quadratic equation
Graphical solutions of quadratic equation |
By the end of the
lesson, the learner
should be able to:
Draw graphs of quadratic functions Solve quadratic equations using the graphs |
Discussions
Solving Demonstrating Explaining |
graph papers & geoboard
|
KLB Mathematics
Book Three Pg 15-17 |
|
| 2 | 7 |
Quadratic Expressions and Equations
Surds |
Graphical solutions of simultaneous equations
Further graphical solutions Rational and irrational numbers |
By the end of the
lesson, the learner
should be able to:
Draw tables for simultaneous equations Find the graphical solutions of simultaneous equations Draw tables of other related quadratic equations Solve other related quadratic functions graphically Classify numbers as rational and irrational numbers |
Discussions
Solving Demonstrating Explaining |
graph papers & geoboard
graph papers & geoboards Calculators |
KLB Mathematics
Book Three Pg 19-21 |
|
| 3 | 1 |
Surds
|
Surds
Addition of surds |
By the end of the
lesson, the learner
should be able to:
State the order of surds Simplify surds Add surds |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 78-79 |
|
| 3 | 2 |
Surds
|
Subtraction of surds
Multiplication of surds |
By the end of the
lesson, the learner
should be able to:
Subtract surds Multiply surds |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 80 |
|
| 3 | 3 |
Surds
|
Division of surds
Rationalizing the denominator Solving problem |
By the end of the
lesson, the learner
should be able to:
Divide surds Rationalize the denominator Solve problems on surds |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 81-82 |
|
| 3 | 4 |
Further Logarithms
|
Introduction
Laws of logarithms |
By the end of the
lesson, the learner
should be able to:
Use calculators to find the logarithm of numbers State the laws of logarithms Use laws of logarithms to solve problems |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 89 |
|
| 3 | 5 |
Further Logarithms
|
Laws of logarithms
Logarithmic equations and expressions Logarithmic equations and expressions |
By the end of the
lesson, the learner
should be able to:
State the laws of logarithms Use laws of logarithms to solve problems Solve the logarithmic equations and expressions |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 90-93 |
|
| 3 | 6 |
Further Logarithms
|
Further computation using logarithms
Further computation using logarithms |
By the end of the
lesson, the learner
should be able to:
Solve problems involving logarithms |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 95-96 |
|
| 3 | 7 |
Further Logarithms
|
Further computation using logarithms
Problem solving |
By the end of the
lesson, the learner
should be able to:
Solve problems involving logarithms |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 95-96 |
|
| 4 | 1 |
Further Logarithms
Commercial arithmetic Commercial arithmetic |
Problem solving
Simple interest Compound interest |
By the end of the
lesson, the learner
should be able to:
Solve problems involving logarithms Calculate simple interest Calculate the compound interest |
Discussions Solving
Demonstrating Explaining Discussions Solving Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 97 |
|
| 4 | 2 |
Commercial arithmetic
|
Appreciation
Depreciation |
By the end of the
lesson, the learner
should be able to:
Calculate the appreciation value of items Calculate the depreciation value of items |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 108 |
|
| 4 | 3 |
Commercial arithmetic
|
Hire purchase
Income tax |
By the end of the
lesson, the learner
should be able to:
Find the hire purchase Calculate the income tax |
Discussions
Solving Demonstrating Explaining |
,calculator
income tax table ,calculator |
KLB Mathematics
Book Three Pg 110-112 |
|
| 4 | 4 |
Commercial arithmetic
Matrices Matrices |
P.A.Y.E
Matrix representation and order of matrix Addition of matrix |
By the end of the
lesson, the learner
should be able to:
Calculate the p.a.y.e Represent matrix State the order of a matrix Add matrices |
Discussions
Solving Demonstrating Explaining |
Calculators s
Chart showing tabular data |
KLB Mathematics
Book Three Pg 114-117 |
|
| 4 | 5 |
Matrices
|
Subtraction of matrices
Combined addition and subtraction of matrices |
By the end of the
lesson, the learner
should be able to:
Subtract matrices Perform the combined operation on matrices |
Discussions
Solving Demonstrating Explaining |
Chart showing tabular data
|
KLB Mathematics
Book Three Pg 171 |
|
| 4 | 6 |
Matrices
|
Matrix multiplication
Matrix multiplication |
By the end of the
lesson, the learner
should be able to:
Multiply matrices |
Discussions
Solving Demonstrating Explaining |
Chart showing tabular data
|
KLB Mathematics
Book Three Pg 174-175 |
|
| 4 | 7 |
Matrices
|
Identity matrix
Determinant of a 2 Inverse of a 2 |
By the end of the
lesson, the learner
should be able to:
Find the identity matrix Find the determinant of a 2 Calculate the inverse of a 2 |
Discussions
Solving Demonstrating Explaining |
Calculator
|
KLB Mathematics
Book Three Pg 182-183 |
|
| 5 | 1 |
Matrices
|
Inverse of a 2
Solutions of simultaneous equations by matrix method |
By the end of the
lesson, the learner
should be able to:
Calculate the inverse of a 2 Solve simultaneous equations by matrix method |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 186-187 |
|
| 5 | 2 |
Matrices
|
Solutions of simultaneous equations by matrix method
Problem solving |
By the end of the
lesson, the learner
should be able to:
Solve simultaneous equations by matrix method Calculate the inverse of a matrix |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 188-190 |
|
| 5 | 3 |
Formulae and variations
|
Formulae
Direct variation Inverse variation |
By the end of the
lesson, the learner
should be able to:
Make subject of the given formula Solve problems involving direct variations Solve problems involving inverse variations |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 191-193 |
|
| 5 | 4 |
Formulae and variations
|
Partial variation
Joint variation |
By the end of the
lesson, the learner
should be able to:
Solve problems involving partial variations Solve problems involving join variations |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 201-203 |
|
| 5 | 5 |
Formulae and variations
Sequences and series |
Joint variation
Sequences |
By the end of the
lesson, the learner
should be able to:
Solve problems involving join variations Find the next terms |
Discussions
Solving Demonstrating Explaining |
|
KLB Mathematics
Book Three Pg 206 |
|
| 5 | 6 |
Sequences and series
|
Arithmetic sequences
Geometric sequence Arithmetic series |
By the end of the
lesson, the learner
should be able to:
Find the nth term of a given arithmetic sequence Find the nth term of a given geometric sequence Find the nth term of a given arithmetic series |
Discussions
Solving Demonstrating Explaining |
|
KLB Mathematics
Book Three Pg 209-210 |
|
| 5 | 7 |
Sequences and series
|
Geometric series
Geometric series |
By the end of the
lesson, the learner
should be able to:
Find the nth term of a given geometric series |
Discussions
Solving Demonstrating Explaining |
|
KLB Mathematics
Book Three Pg 216-219 |
|
| 6 | 1 |
Vectors II
|
Coordinates in two dimensions
Coordinates in three dimensions |
By the end of the
lesson, the learner
should be able to:
Identify the coordinates of appoint in two dimensions Identify the coordinates of appoint in three dimensions |
Discussions
Solving Demonstrating Explaining |
Wire mesh in 3 dimensions
|
KLB Mathematics
Book Three Pg 221 |
|
| 6 | 2 |
Vectors II
|
Column vectors
Position vector Unit vectors |
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 terms of unit vectors |
Discussions
Solving Demonstrating Explaining |
Wire mesh in 3 dimensions
|
KLB Mathematics
Book Three Pg 223-224 |
|
| 6 | 3 |
Vectors II
|
Unit vectors
Magnitude of a vector in three dimensions |
By the end of the
lesson, the learner
should be able to:
Express vectors in terms of unit vectors Calculate the magnitude of a vector in three dimensions |
Discussions
Solving Demonstrating Explaining |
calculators
|
KLB Mathematics
Book Three Pg 226-228 |
|
| 6 | 4 |
Vectors II
|
Parallel vectors
Collinear points |
By the end of the
lesson, the learner
should be able to:
Identify parallel vectors Show that points are collinear |
Discussions
Solving Demonstrating Explaining |
Geoboard
|
KLB Mathematics
Book Three Pg 231-232 |
|
| 6 | 5 |
Vectors II
|
Collinear points
Proportion division of a line Proportion division of a line |
By the end of the
lesson, the learner
should be able to:
Show that points are collinear Divide a line internally in the given ratio Divide a line externally in the given ratio |
Discussions
Solving Demonstrating Explaining |
Geoboard
Geoboard, calculators |
KLB Mathematics
Book Three Pg 233-234 |
|
| 6 | 6 |
Vectors II
|
Proportion division of a line
Ratio theorem |
By the end of the
lesson, the learner
should be able to:
Divide a line internally and externally in the given ratio Express position vectors |
Discussions
Solving Demonstrating Explaining |
Geoboard, calculators
|
KLB Mathematics
Book Three Pg 239 |
|
| 6 | 7 |
Vectors II
|
Ratio theorem
Mid-point Ratio theorem |
By the end of the
lesson, the learner
should be able to:
Find the position vector Find the mid-points of the given vectors Use ratio theorem to find the given vectors |
Discussions
Solving Demonstrating Explaining |
Geoboard, calculators
|
KLB Mathematics
Book Three Pg 242 |
|
| 7 | 1 |
Vectors II
|
Ratio theorem
Applications of vectors |
By the end of the
lesson, the learner
should be able to:
Use ratio theorem to find the given vectors Use vectors to show the diagonals of a parallelogram |
Discussions
Solving Demonstrating Explaining |
Geoboard, calculators
|
KLB Mathematics
Book Three Pg 246-248 |
|
| 7 | 2 |
Vectors II
Binomial expansion |
Applications of vectors
Binomial Expansion up to power four |
By the end of the
lesson, the learner
should be able to:
Use vectors to show the diagonals of a rectangle Expand binomial function up to power four |
Discussions
Solving Demonstrating Explaining |
Geoboard, calculators
calculators |
KLB Mathematics
Book Three Pg |
|
| 7 | 3 |
Binomial expansion
|
Pascal
Pascal Pascal |
By the end of the
lesson, the learner
should be able to:
Use Pascal |
Discussions
Solving Demonstrating Explaining |
calculators
|
KLB Mathematics
Book Three Pg 256-257 |
|
| 7 | 4 |
Binomial expansion
|
Applications to numerical cases
Applications to numerical cases |
By the end of the
lesson, the learner
should be able to:
Use binomial expansion to solve numerical problems |
Discussions
Solving Demonstrating Explaining |
calculators
Calculators |
KLB Mathematics
Book Three Pg 259-260 |
|
| 7 | 5 |
Probability
|
Experimental probability
Experimental probability |
By the end of the
lesson, the learner
should be able to:
Calculate the experimental probability |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 262-264 |
|
| 7 | 6 |
Probability
|
Range of probability measure
Probability space Probability space |
By the end of the
lesson, the learner
should be able to:
Calculate the range of probability measure Calculate the probability space for the theoretical probability |
Discussions
Solving Demonstrating Explaining |
Calculators
Calculators, charts |
KLB Mathematics
Book Three Pg 265-266 |
|
| 7 | 7 |
Probability
|
Combined events
Combined events |
By the end of the
lesson, the learner
should be able to:
Find the probability of a combined events |
Discussions
Solving Demonstrating Explaining |
Calculators, charts
|
KLB Mathematics
Book Three Pg 272-273 |
|
| 8 | 1 |
Probability
|
Independent events
Independent events |
By the end of the
lesson, the learner
should be able to:
Find the probability of independent events |
Discussions
Solving Demonstrating Explaining |
Calculators, charts
|
KLB Mathematics
Book Three Pg 274-275 |
|
| 8 | 2 |
Probability
|
Independent events
Tree diagrams Tree diagrams |
By the end of the
lesson, the learner
should be able to:
Find the probability of independent events Draw tree diagrams to show the probability space Use tree diagrams to find probability |
Discussions
Solving Demonstrating Explaining |
Calculators, charts
|
KLB Mathematics
Book Three Pg 278-280 |
|
| 8 | 3 |
Probability
Compound proportions and rate of work |
Tree diagrams
Compound proportions |
By the end of the
lesson, the learner
should be able to:
Use tree diagrams to find probability Find the compound proportions |
Discussions
Solving Demonstrating Explaining |
Calculators, charts
Calculators |
KLB Mathematics
Book Three Pg 283-285 |
|
| 8 | 4 |
Compound proportions and rate of work
|
Compound proportions
Proportional parts |
By the end of the
lesson, the learner
should be able to:
Find the compound proportions Calculate the proportional parts |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 290-291 |
|
| 8 | 5 |
Compound proportions and rate of work
|
Rates of work
Rates of work Rates of work |
By the end of the
lesson, the learner
should be able to:
Calculate the rate of work |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 294-295 |
|
| 8 | 6 |
Graphical methods
|
Tables of given relations
Graphs of given relations |
By the end of the
lesson, the learner
should be able to:
Draw tables of given relations Draw graphs of given relations |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
|
KLB Mathematics
Book Three Pg 299 |
|
| 8 | 7 |
Graphical methods
|
Graphical solution of cubic equations
Graphical solution of cubic equations |
By the end of the
lesson, the learner
should be able to:
Draw tables of cubic functions Draw graphs of cubic equations |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
|
KLB Mathematics
Book Three Pg 301 |
|
| 9 | 1 |
Graphical methods
|
Average rates of change
Rate of change at an instant Empirical graphs |
By the end of the
lesson, the learner
should be able to:
Calculate the average rates of change Calculate the rate of change at an instant Draw the empirical graphs |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
|
KLB Mathematics
Book Three Pg 304-306 |
|
| 9 | 2 |
Graphical methods
|
Reduction of non-linear laws to linear form
Reduction of non-linear laws to linear form |
By the end of the
lesson, the learner
should be able to:
Draw the graphs of reduction of non-linear laws to linear form |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
|
KLB Mathematics
Book Three Pg 318-321 |
|
| 9 | 3 |
Graphical methods
|
Reduction of non-linear laws to linear form
Equation of a circle |
By the end of the
lesson, the learner
should be able to:
Draw the graphs of reduction of non-linear laws to linear form Find the equation of a circle |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph bookss
Geoboard & graph books |
KLB Mathematics
Book Three Pg 318-321 |
|
| 9 | 4 |
Graphical methods
Differentiation |
Equation of a circle
Equation of a circle Derivation of a Polynomial |
By the end of the
lesson, the learner
should be able to:
Find the equation of a circle Determine the derivate of a polynomial |
Discussions
Solving Demonstrating Explaining Practice exercise Advancing BK 4, Ex. 8.1 KLB BK 4, Ex. 8.1 |
Geoboard & graph books
Polynomials |
KLB Mathematics
Book Three Pg 327-328 |
|
| 9 | 5 |
Differentiation
|
Equations of tangents
And normal to the
Curve
Stationery point |
By the end of the
lesson, the learner
should be able to:
Find the equations of tangents and normals to the curves Sketch a sketch |
Practice exercise
Advancing BK 4, Ex. 8.5 KLB BK 4, Ex. 8.2 Ex. 8.6 KLB BK 4, Ex. 8.3 |
Square boards
Graph paper |
- K.M, Advancing in
Math F4 Pg117-118 - KLB BK 4 Pg 173-174 |
|
| 9 | 6 |
Differentiation
|
Curve sketching
Application of differentiation to calculation of distance velocity and acceleration |
By the end of the
lesson, the learner
should be able to:
Sketch a curve Apply differentiation in calculating distance, velocity and accelaration |
Practice exercise
Advancing BK 4, Ex. 8.7 KLB BK 4, Ex. 8.4 Ex. 8.8 KLB BK 4, Ex. 8.5 |
Square boards
Graph paper |
- K.M, Advancing in
Math F4 Pg120-121 - KLB BK 4 Pg 180-181 |
|
| 9 | 7 |
Differentiation
|
Maxima and minima
|
By the end of the
lesson, the learner
should be able to:
Apply differentiation in finding maxima and minima of a function |
Practice exercise Advancing BK 4, Ex. 8.9 KLB BK 4, Ex. 8.6 |
Square boards Graph paper |
- K.M, Advancing in
Math F4 Pg118-120 - KLB BK 4 Pg 186-188 |
|
| 10 | 1 |
Area Approximations
|
Area by counting
technique
Trapezium rule |
By the end of the
lesson, the learner
should be able to:
Relate approximate area of irregular shapes by counting technique Find and derive trapezium rule |
Practice exercise
Advancing BK 4, Ex. 9.1 KLB BK 4, Ex. 9.1 Advancing BK 4, Ex. 9.3 KLB BK 4, Ex. 9.2 |
Irregular shapes from
Maps Tracing papers Square boards Graph paper |
- K.M, Advancing in
Math F4 Pg125-127 - KLB BK 4 Pg 190-193 |
|
| 10 | 2 |
Area Approximations
|
Area using trapezium
rule
Mid ordinate rule |
By the end of the
lesson, the learner
should be able to:
Apply trapezium rule estimate area under curves Derive the mid ordinate rule |
Practice exercise
Advancing BK 4, Ex. 9.4 KLB BK 4, Ex. 9.2 Advancing BK 4, Ex. 9.5 KLB BK 4, Ex. 9.3 |
Square boards
Graph paper |
- K.M, Advancing in
Math F4 Pg130-132 - KLB BK 4 Pg 195-199 |
|
| 10 | 3 |
Area Approximations
|
Area by mid ordinate
rule
|
By the end of the
lesson, the learner
should be able to:
Apply mid ordinate rule to approximate area under a curve |
Practice exercise Advancing BK 4, Ex. 9.5 KLB BK 4, Ex. 9.3 |
Real life situations |
- K.M, Advancing in
Math F4 Pg132-133 - KLB BK 4 Pg 202-205 |
|
| 10 | 4 |
Integration
|
Differentiation
|
By the end of the
lesson, the learner
should be able to:
Carry out the process of differentiation |
Practice exercise Advancing BK 4, Ex. 10.1 KLB BK 4, Ex. 10.1 |
Real life situations |
- K.M, Advancing in
Math F4 Pg133-134 - KLB BK 4 Pg 202-205 |
|
| 10 | 5 |
Integration
|
Reverse differentiation
Integration, notation and sum of area trapezia |
By the end of the
lesson, the learner
should be able to:
Reverse differentiation Integrate notations and sum of areas of trapezia |
Practice exercise
Advancing BK 4, Ex. 10.1 and 10.2 KLB BK 4, Ex. 10.1 Ex. 10.3 |
Real life situations
Square boards Graph paper |
- K.M, Advancing in
Math F4 Pg135-138 - KLB BK4 Pg207-210 |
|
| 10 | 6 |
Integration
|
Indefinite and definite
intergral
|
By the end of the
lesson, the learner
should be able to:
Indefine and define intergral |
Practice exercise Advancing BK 4, Ex. 10.4 KLB BK 4, Ex. 10.2 |
Square boards Graph paper |
- K.M, Advancing in
Math F4 Pg140-142 - KLB BK 4 Pg 212-215 |
|
| 10 | 7 |
Integration
|
Integral notation
Application in Kinematics |
By the end of the
lesson, the learner
should be able to:
Intergral notation Apply in kinematics |
Practice exercise
Advancing BK 4, Ex. 10.5 KLB BK 4, Ex. 10.3 Ex. 10.6 KLB BK 4, Ex. 10.4 |
Polynomials
Real life situations |
- K.M, Advancing in
Math F4 Pg142-145 - KLB BK 4 Pg 215-220 |
|
| 11-14 |
K.C.S.E EXAMINATIONS |
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