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

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

Graphical methods

Average rates of change
Rate of change at an instant

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

Discussions
Solving
Demonstrating
Explaining

Geoboard & graph books

KLB Mathematics
Book Three
Pg 304-306

Graphical methods

Empirical graphs
Reduction of non-linear laws to linear form

By the end of the lesson, the learner should be able to:
Draw the empirical graphs
Draw the graphs of reduction of non-linear laws to linear form

Discussions
Solving
Demonstrating
Explaining

Geoboard & graph books

KLB Mathematics
Book Three
Pg 315-316

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
Geoboard & graph bookss

KLB Mathematics
Book Three
Pg 318-321

Graphical methods

Equation of a circle
Equation of a circle

By the end of the lesson, the learner should be able to:
Find the equation of a circle

Discussions
Solving
Demonstrating
Explaining

Geoboard & graph books

KLB Mathematics
Book Three
Pg 325-326

Graphical methods
Matrices and Transformation

Equation of a circle
Transformation on a Cartesian plane

By the end of the lesson, the learner should be able to:
Find the equation of a circle
Relate image and objects under a given
transformation on the Cartesian plane

Discussions
Solving
Demonstrating
Explaining
Drawing objects and
their images on
Cartesian plane
Practice Ex 1.1 P5

Geoboard & graph books
Square boards
Peg boards and strings
Rubber band

KLB Mathematics
Book Three
Pg 327-328

Matrices and Transformation

Identification of transformation matrix

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


Determine the matrix of a
transformation

Practice exercise
KLB EX 1.2 and 1.3

Square boards
Peg boards and strings
Rubber band

- K.M, Advancing in
Math F4 Pg 3-9
- KLB Pg 6-16 

Matrices and Transformation

Successive transformation
Single matrix of transformation for successive transformation

By the end of the lesson, the learner should be able to:
Perform successive transformation
Determine and identify a single matrix
for successive transformation

Drawing objects and its
successive images
KLB Ex 1.4

Square boards
Peg boards and strings
Rubber band

- K.M, Advancing in
Math F4 Pg 15-17
- KLB Pg 16-24 

Matrices and Transformation

Relate Identity Matrix and Transformation
Inverse of a matrix area scale factor and determinant of a matrix

By the end of the lesson, the learner should be able to:
Relate identity matrix and
transformation
Determine the inverse of a

Practice exercise Ex 1.4
KLB BK 4
Practice exercise Ex 1.5

Calculators

- K.M, Advancing in
Math F4 Pg 13-14
- KLB Pg 22-24 

Matrices and Transformation

Area of scale factor and determinant of a matrix

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


Establish and use the relationship between
area scale factor and determinant of a
matrix

Practice exercise Ex 1.5
KLB BK 4 pg 27

Boards and strings
Peg boards and strings
Rubber band
Calculators

- K.M, Advancing in
Math F4 Pg 17-19
- KLB Pg 26-27 

Matrices and Transformation

Shear and stretch

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


Determine shear and stretch

Drawing objects and
images under shear and
stretch. Ex 1.6

Square boards
Peg boards and strings
Rubber band
Calculators

- K.M, Advancing in
Math F4 Pg 10-13
- KLB Pg 28-34 

Statistics

Ogive

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


Use cumulative frequency tables to
Draw the ogive

Drawing cumulative
frequency curve (ogive)
KLB Pg 4, Ex. 2.2

Square boards
Graph papers

- K.M, Advancing in
Math F4 Pg 28-29
- KLB Pg 51-52 

Statistics

Median

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


Estimate the median and quartiles by
Calculations
Ogive

Practice exercise
KLB Pg 4, Ex. 2.2

Square boards
Graph papers
Calculators

- K.M, Advancing in
Math F4 Pg 29-31
- KLB Pg 48 

Statistics

Quartile

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


Estimate median and quartiles by
Calculations
ogive

Practice exercise
KLB Pg 4, Ex. 2.2

Square boards
Graph papers
Calculators

- K.M, Advancing in
Math F4 Pg 29-31
- KLB Pg 46 

Statistics

Range- inter quartile range

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


Define and calculate measure of
dispersion-range, quartiles and
inter-quartile range

Practice exercise
KLB Pg 4, Ex. 2.2

Calculators

- K.M, Advancing in
Math F4 Pg 32-33
- KLB BK 4 

Statistics

Quartile deviation
Variance

By the end of the lesson, the learner should be able to:
Define and calculate measures of
dispersion ? quartile deviation
Dispersion, variance interpret measure
of dispersion

Practice exercise
KLB Pg 4, Ex. 2.2

Calculators

- K.M, Advancing in
Math F4 Pg 34-35
- KLB Bk4 Pg 57-59 

Statistics

Standard deviation

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


- Define and calculate measures of
dispersion, standard deviation
- Interpret measures of dispersion

Ex. 2.3
Exams ? CATS

Calculators

- K.M, Advancing in
Math F4 Pg 34-39
- KLB Bk4 Pg 60 

Loci

Common types of Loci

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


Define locus

Practice exercise
KLB Pg 4, Ex. 3.2

Geometrical patterns

- K.M, Advancing in
Math F4 Pg 40-41
- KLB Bk4 Pg 68 

Loci

Perpendicular bisector Loci

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


Describe common types of loci

Practice exercise
KLB Pg 4, Ex. 3.2

Geometrical patterns

- K.M, Advancing in
Math F4 Pg 40
- KLB Bk4 Pg 69

Loci

Loci of a point at a given distance from a fixed point and fixed line

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


Describe common types of loci

Practice exercise
KLB Pg 4, Ex. 3.2

Geometrical patterns

- K.M, Advancing in
Math F4 Pg 40
- KLB Bk4 Pg 70-71 

Loci

Angle bisector Loci

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


Describe common types of loci

Practice exercise
KLB Pg 4, Ex. 3.2

Geometrical patterns

- K.M, Advancing in
Math F4 Pg 41
- KLB Bk4 Pg 71-72 

Loci

Constant angle loci
Construction:- loci of the equalities

By the end of the lesson, the learner should be able to:
Describe common types of loci
Construct loci

Practice exercise
KLB Pg 4, Ex. 3.2
Involving inequalities

Geometrical patterns
Geometrical
instruments

- K.M, Advancing in
Math F4 Pg 42-43
- KLB Bk4 Pg 72-74 

Loci

Loci involving chords

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


Construct loci involving chords

Practice exercise
KLB Pg 4, Ex. 3.5

Geometrical
instruments

- K.M, Advancing in
Math F4 Pg 45-47
- KLB Bk4 Pg 84 

Loci

Loci involving chords

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


Construct loci involving chords

Practice exercise
KLB Pg 4, Ex. 3.5

Geometrical
instruments

- K.M, Advancing in
Math F4 Pg 45-47
- KLB Bk4 Pg 84 

Loci
Trigonometry

Loci under given conditions including intersecting chords
Trigonometric ratios

By the end of the lesson, the learner should be able to:
Construct loci involving intersecting
Loci and under given conditions
Recall and define trigonometric ratios

Practice exercise
KLB Pg 4, Ex. 3.4
KLB Pg 4, Ex. 4.1
Advancing BK 4, Ex. 4.1

Geometrical
instruments
Chart illustrating
Trigonometric ratios

- K.M, Advancing in
Math F4 Pg 47-49 

Three Dimensional Geometry

Geometrical properties of common solids
Skew lines projection of a line onto a plane

By the end of the lesson, the learner should be able to:
State the geometric properties of
common solids
? Education Plus Agencies
Identify projection of a line onto a
Plane

Practice exercise
Advancing BK 4,
Ex. 5.1
KLB Pg 4, Ex. 5.1
KLB Pg 4, Ex. 5.2

3-D models

- K.M, Advancing in
Math F4 Pg 72-73
- KLB BK 4
Pg 104-106 

Three Dimensional Geometry

Length of a line in 3D geometry
Angle between a line and a line

By the end of the lesson, the learner should be able to:
Calculate the length between two points
in 3D geometry
Identify and calculate the angle between
a line and a line

Practice exercise
Advancing BK 4,
Ex. 5.4

3-D models

- K.M, Advancing in
Math F4 Pg 78-80 

Three Dimensional Geometry

A line and a plane
A plane and a plane

By the end of the lesson, the learner should be able to:
Identify and calculate the angle between
a line and a plane
Identify and calculate the angle
between a line and a plane

Practice exercise
Advancing BK 4,
Ex. 5.3 and 5.4
KLB Pg 4, Ex. 5.1
Ex. 5.4
KLB Pg 4, Ex. 5.2

3-D models

- K.M, Advancing in
Math F4 Pg 78-80
- KLB BK 4
Pg 106-109 

Three Dimensional Geometry

Angles between skew lines

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


Identify and calculate the angle
between skew lines

Practice exercise
Advancing BK 4,
Ex. 5.4
KLB Pg 4, Ex. 5.2

3-D models

- K.M, Advancing in
Math F4 Pg 78-80
- KLB BK 4
Pg 118-119 

Longitudes and Latitudes

Latitudes and longitudes (great and small circle)

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


Define the great and small circle in
relation to a sphere (including the earth)

Practice exercise
Advancing BK 4,
Ex. 6.2
KLB Pg 4, Ex. 6.1

Globe
Ball

- K.M, Advancing in
Math F4 Pg 81-83
- KLB BK 4
Pg 125-126 

Longitudes and Latitudes

The equator and Greenwich meridian
Longitudes and Latitudes Position of a place on the surface of the earth

By the end of the lesson, the learner should be able to:
Define the great and small circle in
relation to a sphere (including the earth)
Locate a place on the earth?s surface in
terms of latitude and longitude

Practice exercise
Advancing BK 4,
Ex. 6.2
KLB Pg 4, Ex. 6.1

Globe
Ball

- K.M, Advancing in
Math F4 Pg 83
- KLB BK 4
Pg 126-127 

Longitudes and Latitudes

Radii of small and great circles
Distance between two points along the small and great circle in nautical miles and kilometres

By the end of the lesson, the learner should be able to:
Establish the relationship between the
radii of small and great circles
Calculate the distance between two
points along the great circles and small
circles (longitudes and latitudes) in
nautical miles (nm) and kilometres (km)

Practice exercise
Advancing BK 4,
Ex. 6.4
KLB Pg 4, Ex. 6.2

Globe
Ball

- K.M, Advancing in
Math F4 Pg 89
- KLB BK 4
Pg 133-134 

Longitudes and Latitudes

Distance in nautical miles and kilometers along a circle of latitude

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


Calculate the distance in nautical miles
and kilometers along a circle of
latitude

Practice exercise
Advancing BK 4,
Ex. 6.5
KLB Pg 4, Ex. 6.3

Globe
Ball
Calculators

- K.M, Advancing in
Math F4 Pg 87-98
- KLB BK 4
Pg 130-133 

Longitudes and Latitudes

Time and longitude

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


Calculate time in relation to kilometers
per hour

Practice exercise
Advancing BK 4,
Ex. 6.5
KLB Pg 4, Ex. 6.3

Globe
Ball
Calculators

- K.M, Advancing in
Math F4 Pg 91-92
- KLB Bk4Pg141-142 

Longitudes and Latitudes

Speed in knots and kilometer per hour

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


Calculate speed in knots and
kilometer per hour

Practice exercise
Advancing BK 4,
Ex. 6.6
KLB Pg 4, Ex. 6.3

Real life situation

- K.M, Advancing in
Math F4 Pg 96-98
- KLB BK 4 Pg 150 

Linear Programming

Formation of linear Inequalities

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


Form linear inequalities based on real
life situations

Practice exercise
Advancing BK 4,
Ex. 7.3
KLB BK 4, Ex. 7.1

Inequalities

- K.M, Advancing in
Math F4 Pg 94-95
- KLB BK 4
Pg 151-152 

Linear Programming

Formation of linear Inequalities

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


Form linear inequalities based on real
life situations

Practice exercise
Advancing BK 4,
Ex. 7.3
KLB BK 4, Ex. 7.1

Inequalities

- K.M, Advancing in
Math F4 Pg 94-95
- KLB BK 4
Pg 151-152 

Linear Programming

Analytical solutions of linear inequalities

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


Analyze solutions of linear inequalities

Practice exercise
Advancing BK 4,
Ex. 7.1
KLB BK 4, Ex. 7.2

Square boards
Graph papers

- K.M, Advancing in
Math F4 Pg 95-96
- KLB BK 4
Pg 152-155 

Linear Programming

Solutions of linear inequalities by graph

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


Represent the linear inequalities on a
graph

Representing inequalities
in a graph
Advancing BK 4,
Ex. 7.2
KLB BK 4, Ex. 7.2

Square boards

- K.M, Advancing in
Math F4 Pg 94-95
- KLB BK 4
Pg 151-152 

Linear Programming

Optimization (include objective)

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


Solve and interpret the optimum
solution of the linear inequalities

Practice exercise
Advancing BK 4,
Ex. 7.5
KLB BK 4, Ex. 7.3

Graph paper

- K.M, Advancing in
Math F4 Pg 95-96
- KLB BK 4
Pg 152-155

Linear Programming

Application of linear programming to real life situation

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


Solve and interpret the optimum
solution of the linear programming to
real life situations

Practice exercise
Advancing BK 4,
Ex. 7.5
KLB BK 4, Ex. 7.3

Real life situations
Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg 99-100
- KLB BK 4
Pg 157-159 

Differentiation

Average and instantaneous rates of change

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


Find out the average rates of change
and instantaneous rate of change

Practice exercise
Advancing BK 4,
Ex. 8.1
KLB BK 4, Ex. 8.1

Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg100-103
- KLB BK 4
Pg 157-159 

Differentiation

Differentiation Gradient of a curve at a point

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


Find the gradient of a curve at a point
using tangent

Practice exercise
Advancing BK 4,
Ex. 8.2
KLB BK 4, Ex. 8.1

Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg 109
- KLB BK 4
Pg 162-163 

Differentiation

Gradient of y = xn where n is a positive interger
Delta notation (?)

By the end of the lesson, the learner should be able to:
Find the gradient function of the form
y = xn (n = positive interger)
- Relate the delta notation to rates of
change
- Define derivative of a function
polynomial and differentiation

Practice exercise
Advancing BK 4,
Ex. 8.2 and 8.3
KLB BK 4, Ex. 8.1
Ex. 8.2 and 8.4

Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg 110
- KLB BK 4
Pg 164-167 

Differentiation

Derivation of a Polynomial
Equations of tangents And normal to the Curve

By the end of the lesson, the learner should be able to:
Determine the derivate of a polynomial
Find the equations of tangents and
normals to the curves

Practice exercise
Advancing BK 4,
Ex. 8.1
KLB BK 4, Ex. 8.1
Ex. 8.5
KLB BK 4, Ex. 8.2

Polynomials
Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg116-117
- KLB BK 4
Pg 170-171 

Differentiation

Stationery point
Curve sketching

By the end of the lesson, the learner should be able to:
Sketch a sketch
Sketch a curve

Practice exercise
Advancing BK 4,
Ex. 8.6
KLB BK 4, Ex. 8.3
Ex. 8.7
KLB BK 4, Ex. 8.4

Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg118-120
- KLB BK 4
Pg 174-179 

Differentiation

Application of differentiation to calculation of distance velocity and acceleration

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


Apply differentiation in calculating
distance, velocity and accelaration

Practice exercise
Advancing BK 4,
Ex. 8.8
KLB BK 4, Ex. 8.5

Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg121-123
- KLB BK 4
Pg 182-183 

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