Trigonometry 

Trigonometry Tangent, sine and cosines

By the end of the lesson, the learner should be able to:
Define tangent, sine and cosine ratios from a right angles triangle

Defining what a tangent, Cosine and sine are using a right angled triangle

Charts illustrating tangent, sine and cosine

KLB BK2 Pg 123,132,133   Discovering secondary pg   70

Trigonometry 

Trigonometric Table
Angles and sides of a right angled triangle
Establishing Relationship of sine and cosine of complimentary angles
Sines and cosines of Complimentary angles
Relationship between tangent, sine and cosine
Trigonometric ratios of special angles 30, 45, 60 and 90

By the end of the lesson, the learner should be able to:
Use trigonometric tables to find the sine, cosine and tangent
Use the relationship of sine and cosine of complimentary angles in solving problems

Reading trigonometric tables of sines, cosines and tangent
Solving problems involving the sines and cosines of complimentary angles

Mathematical table
Mathematical table Charts Chalkboard
Chalkboards
Chalkboard Charts illustrating the relationship of sines and cosines of complimentary angles
Charts showing the three related trigonometric ratio
Charts showing isosceles right angled triangle Charts illustrating Equilateral triangle

KLB BK2 Pg 127, 138, 139   Discovering secondary pg 71
KLB BK2 Pg 145

Trigonometry 

Application of Trigonometric ratios in solving problems
Logarithms of Sines
Logarithms of cosines And tangents

By the end of the lesson, the learner should be able to:
Solve trigonometric problems without using tables

Solving trigonometric problems of special angles

Chalkboard
Chalkboard Mathematical tables
Chalkboard Mathematical table

KLB BK2 Pg 148

Trigonometry 

Reading tables of logarithms of sines, cosines and tangents
Application of trigonometry to real life situations
Area of a triangle Area of a triangle given the base and height (A = ? bh)

By the end of the lesson, the learner should be able to:
Read the logarithms of sines, cosines and tangents from tables

Solving problems through reading the table of logarithm of sines, cosines and tangents

Chalkboard Mathematical table
Mathematical table
Chart illustrating worked problem Chalkboard

KLB BK2 Pg 149-152

Trigonometry 

Area of a triangle using the formula (A = ? absin?)
Area of a triangle using the formula A = ?s(s-a)(s-b)(s-c)
Area of Quadrilateral and Polygons Area of a square, rectangle, rhombus, parallelogram and trapezium

By the end of the lesson, the learner should be able to:
- Derive the formula ? absinc - Using the formula derived in calculating the area of a triangle given two sides and an included angle

Deriving the formula ? absinc Using the formula to calculate the area of a triangle given two sides and an included angle

Charts illustrating a triangle with two sides and an included angle Charts showing derived formula
Charts illustrating a triangle with three sides Charts illustrating a worked example i.e. mathematical table
Charts illustrating formula used in calculating the areas of the quadrilateral

KLB BK2 Pg 156

Trigonometry 

Area of a kite
Area of other polygons (regular polygon) e.g. Pentagon
Area of irregular Polygon

By the end of the lesson, the learner should be able to:
Find the area of a kite

Calculating the area of a Kite

Model of a kite
Mathematical table Charts illustrating Polygons
Charts illustrating various irregular polygons Polygonal shapes

KLB BK2 Pg 163

Trigonometry 

Area of part of a circle Area of a sector (minor sector and a major sector)
Defining a segment of a circle Finding the area of a segment of a circle
Area of a common region between two circles given the angles and the radii
Area of a common region between two circles given only the radii of the two circles and a common chord
Surface area of solids Surface area of prisms Cylinder (ii) Triangular prism (iii) Hexagonal prism
Area of a square based Pyramid

By the end of the lesson, the learner should be able to:
- Find the area of a sector given the angle and the radius of a minor sector Calculate the area of a major sector of a circle
Calculate the area of common region between two circle given the radii of the two intersecting circles and the length of a common chord of the two circles

Finding the area of a minor and a major sector of a circle
Finding the area of a common region between two intersecting

Charts illustrating sectors
Chart illustrating a Segment
Charts illustrating common region between the circles Use of a mathematical table during calculation
Charts illustrating common region between two intersecting circles
Models of cylinder, triangular and hexagonal prisms
Models of a square based pyramid

KLB BK 2 Pg 167
KLB BK 2 Pg 176

Trigonometry 

Surface area of a Rectangular based Pyramid
Surface area of a cone using the formula A = ?r2 + ?rl
Surface area of a frustrum of a cone and a pyramid

By the end of the lesson, the learner should be able to:
Find the surface area of a rectangular based pyramid

Finding the surface area of a rectangular based pyramid

Models of a Rectangular based pyramid
Models of a cone
Models of frustrum of a cone and a pyramid

KLB BK 2 Pg 179-180

Trigonometry 

Finding the surface area of a sphere
Surface area of a Hemispheres
Volume of Solids Volume of prism (triangular based prism)

By the end of the lesson, the learner should be able to:
Find the surface area of a sphere given the radius of a sphere

Finding the surface area of a sphere

Models of a sphere Charts illustrating formula for finding the surface area of a sphere
Models of a hemisphere
Models of a triangular based prism

KLB BK 2 Pg 183

Trigonometry 

Volume of prism (hexagonal based prism) given the sides and angle
Volume of a pyramid (square based and rectangular based)
Volume of a cone

By the end of the lesson, the learner should be able to:
Find the volume of a hexagonal based prism

Calculating the volume of an hexagonal prism

Models of hexagonal based prism
Models of square and Rectangular based Pyramids
Model of a cone

KLB BK 2 Pg 187

Trigonometry 

Volume of a frustrum of a cone
Volume of a frustrum of a pyramid
Volume of a sphere (v = 4/3?r3)

By the end of the lesson, the learner should be able to:
Find the volume of a frustrum of a cone

Finding the volume of a full cone before its cutoff Finding the volume of a cut cone then subtracting

Models of a frustrum of a cone
Models of frustrum of a pyramid
Model of a sphere Mathematical table

KLB BK 2 Pg 192

Trigonometry 
Trigonometric Ratios

Volume of a Hemisphere {(v = ? (4/3?r3)}
Application of area of triangles to real life
Tangent of an angle
Tangent of an angle
Using tangents in calculations
Application of tangents

By the end of the lesson, the learner should be able to:
Find the volume of a hemisphere

find the tangent of an angle from tables

Working out the volume of a hemisphere
Measuring lengths/angles
Dividing numbers
Drawing right angles
Reading mathematical tables

Models of hemisphere
Mathematical table Chart illustrating formula used
Protractor
Ruler
Right corners
Mathematical tables

Macmillan BK 2 Pg 173
KLB Maths Bk2 Pg. 119-122

Trigonometric Ratios

The sine of an angle
The cosine of an angle
Application of sine and cosine

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

find the sine of an angle by calculations and through tables

Measuring lengths/angles
Dividing numbers
Drawing right angles
Reading mathematical tables

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 119-122

Trigonometric Ratios

Complementary angles
Special angles
Application of Special angles

By the end of the lesson, the learner should be able to:
define complementary angles. Work out sines of an angle given the cosine of its complimentary and vice versa

Measuring lengths/angles
Dividing numbers
Drawing right angles
Reading mathematical tables

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 119-122

Trigonometric Ratios

Logarithms of sines, cosines and tangents
Relationship between sin, cos and tan
Application to real life situation

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

solve problems using logarithms of sines cosines and tangents

Measuring lengths/angles
Dividing numbers
Drawing right angles
Reading mathematical tables

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 119-122

Trigonometric Ratios
Area of A Triangle
Area of A Triangle

Problem solving
Area =
Solve problems involving =

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

solve problems on trigonometry

Problem solving

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 119-122

Area of A Triangle
Area of Quadrilaterals

A =?s(s-a) (s-b) (s-c)
Problem solving
Area of parallelogram
Area of Rhombus
Area of trapezium and kite
Area of regular polygons

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

find the area of a triangle given the three sides

find the area of a regular polygon.

Discussions
Drawing triangles
Measuring lengths/angles
Calculating area
Drawing trapeziums/polygons
Measuring lengths/angles
Reading mathematical tables
Discussions

Protractor
Ruler
Right corners
Mathematical tables
Parallelograms
Trapeziums
Polygons
Squares/rectangles
Parallelograms
Trapeziums
Polygons
Squares/rectangles
Mathematical tables
Mathematical tables Chalkboard illustrations

KLB Maths Bk2 Pg. 155-157

KLB Maths Bk2 Pg. 161

Area of Quadrilaterals
Area of Part of a Circle
Area of Part of a Circle

Problem solving
Area of a sector
Area of a segment

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

solve problems on area of quadrilaterals and other polygons

Learners solve problems

Parallelograms
Trapeziums
Polygons
Squares/rectangles
Mathematical tables
Circles
Chart illustrating the area of a sector
Chart illustrating the area of a minor segment

KLB Maths Bk2 Pg. 165-166

Area of Part of a Circle

Common region between two circles
Common region between two circles
Problem solving

By the end of the lesson, the learner should be able to:
find the area of the common region between two circles.

Drawing circles
Measuring radii/diameters
Measuring angles
Calculating the area of a circle
Discussions

Circles
Chart illustrating the area of a minor segment
Chart illustrating the area of a minor segment Chalkboard illustrations

KLB Maths Bk2 Pg. 167-169

Surface Area of Solids

Surface area of prisms
Surface area of pyramid
Surface area of a cone

By the end of the lesson, the learner should be able to:
find the surface area of a prism.

Drawing prisms
Measuring lengths
Opening prisms to form
nets
Discussions
Calculating area

Prism Chalkboard illustrations
Pyramids with square base, rectangular base, triangular base
Cone

KLB Maths Bk2 Pg. 177

Surface Area of Solids

Surface area of frustrum with circular base
Surface area of frustrum with square base
Surface area of frustrum with rectangular base

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

find the surface area of frustrum with circular base

Drawing cones/frustums
Making cones/frustums
Measuring lengths/
angles
Discussions

Chart illustrating the surface area of a frustrum
Chart illustrating frustrum with a square base
Chart illustrating frustrum with a rectangular base

KLB Maths Bk2 Pg. 181-283
KLBMathematics Bk2
Discovering Secondary Mathematics Bk2

Surface Area of Solids
Volume of Solids

Surface area of spheres
Problem solving
Volume of prism
Volume of pyramid
Volume of a cone
Volume of a sphere

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

find the surface area of a sphere

find the volume of a pyramid

Sketching spheres
Making spheres
Measuring diameters/
radii of spheres
Discussions
Drawing pyramids
Making pyramids
Opening pyramids to
form nets
Discussions

Chalkboard illustrations
Past paper questions
Prism
Pyramid
Cone
Sphere

KLB Maths Bk2 Pg. 183

KLB Maths Bk2 Pg. 189-190

Volume of Solids

Volume of frustrum
Volume of frustrum with a square base
Volume of frustrum with a rectangular base

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

find the volume of a frustrum with a circular base

Making cones/frustums
Opening cones/frustums
to form nets

Frustrum with circular base
Frustrum with square base
Frustrum with rectangular base

KLB Maths Bk2 Pg. 192-193

Volume of Solids
Quadratic Expressions and Equations

Application to real life situation
Problem solving
Expansion of Algebraic Expressions

By the end of the lesson, the learner should be able to:
apply the knowledge of volume of solids to real life situations.

Making cones/frustums
Opening cones/frustums
to form nets

Models of pyramids, prism, cones and spheres
Past paper questions
Real-life experiences
Worked out
expressions

KLB Maths Bk2 Pg. 193-194

Quadratic Expressions and Equations

Quadratic identities
Application of identities
Factorise the Identities

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

derive the three Algebraic identities

Discussions
Multiplying numbers
Dividing numbers
Adding numbers
Subtracting numbers
Exercises

Real-life experiences
Worked out
expressions

KLB Maths Bk2 Pg. 204-205

Quadratic Expressions and Equations

Factorise other quadratic expressions
Factorisation of expressions of the form k2-9y2
Simplification of an expression by factorisation

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

Discussions
Multiplying numbers
Dividing numbers
Adding numbers
Subtracting numbers
Exercises

Chart illustrating factorization of a quadratic expression
Real-life experiences
Worked out
expressions

KLB Maths Bk2 Pg. 119-122

Quadratic Expressions and Equations
Quadratic Expressions and Equations
Linear Inequalities

Solving quadratic equations
The formation of quadratic equations
Formation and solving of quadratic equations from word problems
Solving on quadratic equations
Forming quadratic equations from the roots
Inequalities symbols

By the end of the lesson, the learner should be able to:
solve quadratic equations
solve problems on quadratic equations

Discussions
Multiplying numbers
Dividing numbers
Adding numbers
Subtracting numbers
Exercises

Real-life experiences
Worked out
expressions
Real-life experiences
Worked out
expressions
Number lines
Graph papers
Square boards
Negative and positive numbers

KLB Maths Bk2 Pg. 208

KLB Maths Bk2 Pg. 208-210

Linear Inequalities

Number line
Inequalities in one unknown
Graphical representation

By the end of the lesson, the learner should be able to:
illustrate inequalities on a number line

Drawing graphs of
inequalities
Determining the scale of a graph
Shading unwanted regions
Discussions

Number lines
Graph papers
Square boards
Negative and positive
numbers
Number lines Graph papers

KLB Maths Bk2 Pg. 213-224

Linear Inequalities

Graphical solutions of simultaneous linear inequalities
Area of the wanted region

By the end of the lesson, the learner should be able to:
solve the linear inequalities in two unknowns graphically

Drawing graphs of
inequalities
Determining the scale of a graph
Shading unwanted regions
Discussions

Number lines
Graph papers
Square boards
Negative and positive
numbers

KLB Maths Bk2 Pg. 213-224

Linear Inequalities
Linear Motion

Inequalities from inequality graphs
Problem solving.
Displacement, velocity, speed and acceleration

By the end of the lesson, the learner should be able to:
form simple linear inequalities from inequality graphs

Drawing graphs of
inequalities
Determining the scale of a graph
Shading unwanted regions
Discussions

Number lines
Graph papers
Square boards
Negative and positive
numbers
Stones
Pieces of paper

KLB Maths Bk2 Pg. 213-224

Linear Motion

Distinguishing terms
Distinguishing velocity and acceleration
Distance time graphs

By the end of the lesson, the learner should be able to:
distinguish between distance and displacement, speed and velocity

Plotting graphs
Drawing graphs

Graph papers
Stones
Pieces of paper

KLB Maths Bk2 Pg. 228-238

Linear Motion
Linear Motion
Statistics
Statistics

Interpret the velocity time graph
Interpreting graphs
Relative speed (objects moving in the same direction)
Problem solving
Definition
Collection and organization of data

By the end of the lesson, the learner should be able to:
interpret a velocity time graph

solve problems on linear motion

Learners interpret a velocity time graph
Question answer method

Drawn graphs
Real life situation
Chalkboard illustrations
Past paper questions
Weighing balance
Ruler
Tape measure
Pieces of stick
Arm length
Foot length
Graph papers

KLB
Maths Bk2
Pg.333
KLB
Maths Bk2
Pg.330

Statistics

Frequency tables
Grouped data
Mean of ungrouped data

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

draw a frequency distribution table

Collecting data
Measuring length/mass/age
Drawing graphs
Drawing tables
Using symbols to represent data
Discussion

Weighing balance
Ruler
Tape measure
Pieces of stick
Arm length
Foot length
Graph papers

KLB Maths Bk2 Pg. 241-252

Statistics

Median of ungrouped data
Mean of ungrouped data
Median of a grouped data modal class

By the end of the lesson, the learner should be able to:
calculate the median of ungrouped data and state the mode

Collecting data
Measuring length/mass/age
Drawing graphs
Drawing tables
Using symbols to represent data
Discussion

Weighing balance
Ruler
Tape measure
Pieces of stick
Arm length
Foot length
Graph papers

KLB Maths Bk2 Pg. 241-252

Statistics

Data Representation. Line graphs
Bar graphs
Pictogram

By the end of the lesson, the learner should be able to:
represent data in form of a line graph

Collecting data
Measuring length/mass/age
Drawing graphs
Drawing tables
Using symbols to represent data
Discussion

Weighing balance
Ruler
Tape measure
Pieces of stick
Arm length
Foot length
Graph papers
Pictures which are whole, half, quarter

KLB Maths Bk2 Pg. 241-252

Statistics

Histograms
Frequency polygons
Histograms with uneven distribution

By the end of the lesson, the learner should be able to:
represent data in form of histograms

Collecting data
Measuring length/mass/age
Drawing graphs
Drawing tables
Using symbols to represent data
Discussion

Weighing balance
Ruler
Tape measure
Pieces of stick
Arm length
Foot length
Graph papers
Histograms drawn. Data
Data with uneven classes

KLB Maths Bk2 Pg. 241-252

Statistics
Angle Properties of a Circle

Interpretation of data
Problem solving
Arc chord segment
Angles subtended by the same arc in the same segment
Angle at the centre and at the circumference
Angles subtended by the diameter at the circumference

By the end of the lesson, the learner should be able to:
interpret data from real life situation

relate and compute angles subtended by an arc of a circle at the circumference

Collecting data
Measuring length/mass/age
Drawing graphs
Drawing tables
Using symbols to represent data
Discussion
Discussions
Drawing circles
Measuring radii/diameters/angles
Identifying the parts of a circle

Real life situations
Past paper questions
Chart illustrating arc chord and segment
Chart illustrating Angles subtended by the same arc in same segment are equal
Chart illustrating Angles subtended at the centre by an arc and one subtended at the circumference
Circles showing the
different parts

KLB Maths Bk2 Pg. 241-252

KLB Maths Bk2 Pg. 264-278

Angle Properties of a Circle

Cyclic quadrilateral
Exterior angle property

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

state the angle properties of a cyclic quadrilateral

Discussions
Drawing circles
Measuring radii/diameters/angles
Identifying the parts of a circle

Circles showing the
different parts

KLB Maths Bk2 Pg. 264-278

Angle Properties of a Circle
Vectors

Problem solving
Problem solving
Definition and Representation of vectors

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

solve problems on angle properties of a circle

Discussions
Drawing circles
Measuring radii/diameters/angles
Identifying the parts of a circle

Circles showing the
different parts Past paper questions
different parts Past paper questions
1x2 matrices
Graph papers
Square boards
Ruler

KLB Maths Bk2 Pg. 264-278

Vectors

Equivalent vectors
Addition of vectors
Multiplication of vectors

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

Writing position vectors
Adding/subtracting
numbers
Squaring and getting the
square root of numbers

1x2 matrices
Graph papers
Square boards
Ruler

KLB Maths Bk2 Pg. 285

Vectors

Position vectors
Column vector
Magnitude of a vector
Mid - point
Translation vector

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

define a position vector
illustrate position vectors on a Cartesian plane

Writing position vectors
Adding/subtracting
numbers
Squaring and getting the
square root of numbers

1x2 matrices
Graph papers
Square boards
Ruler

KLB Maths Bk2 Pg.298