Trigonometry 

Pythagoras Theorem

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

Deriving Pythagoras Theorem

Chalkboard Charts Illustrating derived theorem

KLB BK2 Pg 120   Discovering secondary pg 67

Trigonometry 

Solutions of problems Using Pythagoras Theorem
Application to real life Situation

By the end of the lesson, the learner should be able to:
Solve problems using Pythagoras Theorem

Solving problems using Pythagoras theorem

Charts illustrating Pythagoras theorem
Mathematical table

KLB BK2 Pg 121   Discovering secondary pg 67

Trigonometry 

Trigonometry Tangent, sine and cosines
Trigonometric Table

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
Mathematical table

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

Trigonometry 

Angles and sides of a right angled triangle
Establishing Relationship of sine and cosine of complimentary angles

By the end of the lesson, the learner should be able to:
Use the sine, cosine and tangent in calculating the length of a right angled triangle and also finding the angle given two sides and unknown angle The length can be obtained if one side is given and an angle

Using mathematical tables Finding the length using sine ratio Finding the length using Cosine and tangent ratio Finding the angle using Sine, cosine and tangent

Mathematical table Charts Chalkboard
Chalkboards

KLB BK2 Pg 125, 139, 140  Discovering secondary pg  

Trigonometry 

Sines and cosines of Complimentary angles
Relationship between tangent, sine and cosine

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

Solving problems involving the sines and cosines of complimentary angles

Chalkboard Charts illustrating the relationship of sines and cosines of complimentary angles
Charts showing the three related trigonometric ratio

KLB BK2 Pg 145

Trigonometry 

Trigonometric ratios of special angles 30, 45, 60 and 90
Application of Trigonometric ratios in solving problems
Logarithms of Sines

By the end of the lesson, the learner should be able to:
Determine the trigonometric ratios of special angles without using tables

Determining the trigonometric ratios of special angles 30,45,60 and 90 without using tables

Charts showing isosceles right angled triangle Charts illustrating Equilateral triangle
Chalkboard
Chalkboard Mathematical tables

KLB BK2 Pg 146-147

Trigonometry 

Logarithms of cosines And tangents
Reading tables of logarithms of sines, cosines and tangents

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

Reading logarithms of cosine and tangent from mathematical table

Chalkboard Mathematical table

KLB BK2 Pg 150-152

Trigonometry 

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:
Solve problems in real life using trigonometry

Solving problems using trigonometry in real life

Mathematical table
Chart illustrating worked problem Chalkboard

KLB BK2 Pg 153-154

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)

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

KLB BK2 Pg 156

Trigonometry 

Area of Quadrilateral and Polygons Area of a square, rectangle, rhombus, parallelogram and trapezium
Area of a kite

By the end of the lesson, the learner should be able to:
Calculate the are of a triangle, square, rectangle, rhombus, parallelogram and trapezium

Calculating the area of a triangle, square, rectangle, rhombus, parallelogram and trapezium

Charts illustrating formula used in calculating the areas of the quadrilateral
Model of a kite

KLB BK2 Pg 161-163

Trigonometry 

Area of other polygons (regular polygon) e.g. Pentagon
Area of irregular Polygon
Area of part of a circle Area of a sector (minor sector and a major sector)

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

Calculating the area of a regular polygon

Mathematical table Charts illustrating Polygons
Charts illustrating various irregular polygons Polygonal shapes
Charts illustrating sectors

KLB BK2 Pg 164

Trigonometry 

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

By the end of the lesson, the learner should be able to:
- Define what a segment of a circle is - Find the area of a segment of a circle

Finding the area of a segment by first finding the area of a sector less the area of a smaller sector given R and r and angle ?

Chart illustrating a Segment
Charts illustrating common region between the circles Use of a mathematical table during calculation

KLB BK2 Pg 169-170

Trigonometry 

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

By the end of the lesson, the learner should be able to:
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 common region between two intersecting

Charts illustrating common region between two intersecting circles
Models of cylinder, triangular and hexagonal prisms

KLB BK 2 Pg 176

Trigonometry 

Area of a square based Pyramid
Surface area of a Rectangular based Pyramid

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

Finding the surface area of a square based pyramid

Models of a square based pyramid
Models of a Rectangular based pyramid

KLB BK 2 Pg 178

Trigonometry 

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 total surface area of the cone by first finding the area of the circular base and then the area of the curved surface

Finding the area of the circular part Finding the area of the curved part Getting the total surface Area

Models of a cone
Models of frustrum of a cone and a pyramid

KLB BK 2 Pg 181

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)

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

KLB BK 2 Pg 187

Trigonometry 

Volume of a cone
Volume of a frustrum of a cone

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

Finding the volume of a cone

Model of a cone
Models of a frustrum of a cone

KLB BK 2 Pg 191

Trigonometry 

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 Pyramid

Finding volume of a full pyramid Finding volume of cutoff pyramid Find volume of the remaining fig (frustrum) by subtracting i.e. Vf = (V ? v)

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

KLB BK 2 Pg 194

Trigonometry 

Volume of a Hemisphere {(v = ? (4/3?r3)}
Application of area of triangles to real life

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

Working out the volume of a hemisphere

Models of hemisphere
Mathematical table Chart illustrating formula used

Macmillan BK 2 Pg 173

Trigonometric Ratios

Tangent of an angle
Using tangents in calculations

By the end of the lesson, the learner should be able to:
name the sides of a right-angled triangle as opposite, adjacent and hypotenuse. Find the tangent of an angle by calculation

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

Application of tangents
The sine of an angle

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

work out further problems using 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

The cosine of an angle
Application of sine and cosine

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

find the cosine 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

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

Application of Special angles
Logarithms of sines, cosines and tangents

By the end of the lesson, the learner should be able to:
apply the knowledge of special angles to solve problems

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

Relationship between sin, cos and tan
Application to real life situation
Problem solving

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

relate sin, cos and tan that is tan?=sin?
cos?
Solve problems using the relationship

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

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 119-122

Area of A Triangle

Area =
Solve problems involving =

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

derive the formula Area =

Discussions
Drawing triangles
Measuring lengths/angles
Calculating area

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 155-157

Area of A Triangle

A =?s(s-a) (s-b) (s-c)
Problem solving

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

find the area of a triangle given the three sides

Discussions
Drawing triangles
Measuring lengths/angles
Calculating area

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 155-157

Area of Quadrilaterals

Area of parallelogram
Area of Rhombus

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

find the area of quadrilaterals like trapeziums, parallelogram etc. by dividing the shape of triangles

Drawing trapeziums/polygons
Measuring lengths/angles
Reading mathematical tables
Discussions

Parallelograms
Trapeziums
Polygons
Squares/rectangles
Mathematical tables

KLB Maths Bk2 Pg. 160

Area of Quadrilaterals

Area of trapezium and kite
Area of regular polygons

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

solve problems on the area of a regular polygon

Drawing trapeziums/polygons
Measuring lengths/angles
Reading mathematical tables
Discussions

Parallelograms
Trapeziums
Polygons
Squares/rectangles
Mathematical tables
Mathematical tables Chalkboard illustrations

KLB Maths Bk2 Pg. 162-163

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

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

KLB Maths Bk2 Pg. 167-169

Area of Part of a Circle
Surface Area of Solids

Problem solving
Surface area of prisms

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

solve problems involving the area of part of a circle

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

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

KLB Maths Bk2 Pg. 167-169

Surface Area of Solids

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 pyramid

Drawing pyramids
Measuring lengths/
angles
Opening pyramids to
form nets
Discussions
Calculating area

Pyramids with square base, rectangular base, triangular base
Cone

KLB Maths Bk2 Pg. 178

Surface Area of Solids

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

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

Surface Area of Solids

Surface area of frustrum with rectangular base
Surface area of spheres
Problem solving

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

find the surface area of frustrum with rectangular base

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

Chart illustrating frustrum with a rectangular base
Chalkboard illustrations
Past paper questions

KLB Maths Bk2 Pg. 181-183

Volume of Solids

Volume of prism
Volume of pyramid

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

find the volume of a prism

Identifying prisms
Identifying the cross-sectional area
Drawing/sketching prisms

Prism
Pyramid

KLB Maths Bk2 Pg. 186-188

Volume of Solids

Volume of a cone
Volume of a sphere

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

find the volume of a cone

Making cones/frustums
Opening cones/frustums
to form nets

Cone
Sphere

KLB Maths Bk2 Pg. 191

Volume of Solids

Volume of frustrum
Volume of frustrum with a square 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

KLB Maths Bk2 Pg. 192-193

Volume of Solids

Volume of frustrum with a rectangular base
Application to real life situation

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

find the volume of a frustrum with a rectangular base

Making cones/frustums
Opening cones/frustums
to form nets

Frustrum with rectangular base
Models of pyramids, prism, cones and spheres

KLB Maths Bk2 Pg. 192-193

Volume of Solids
Quadratic Expressions and Equations
Quadratic Expressions and Equations

Problem solving
Expansion of Algebraic Expressions
Quadratic identities

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

solve problems on volume of solids

Making cones/frustums
Opening cones/frustums
to form nets

Past paper questions
Real-life experiences
Worked out
expressions

KLB Maths Bk2 Pg. 196

Quadratic Expressions and Equations

Application of identities
Factorise the Identities

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

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

Simplification of an expression by factorisation
Solving quadratic equations

By the end of the lesson, the learner should be able to:
simplify a quadratic expression by factorisation

Discussions
Multiplying numbers
Dividing numbers
Adding numbers
Subtracting numbers
Exercises

Real-life experiences
Worked out
expressions

KLB Maths Bk2 Pg. 205-208

Quadratic Expressions and 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

By the end of the lesson, the learner should be able to:
form quadratic equations from information

Discussions
Multiplying numbers
Dividing numbers
Adding numbers
Subtracting numbers
Exercises

Real-life experiences
Worked out
expressions

KLB Maths Bk2 Pg. 208