Similarity and enlargement

Similar figures

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

Calculate lengths of objects

Defining
Discussions
Solving problem
Explaining

Apparatus
Books
Videos
Charts

KLB Mathematics
Book Two
Pg 87-88     Discovering secondary pg 52

Similarity and enlargement

Similar figures
Enlargement
Enlarge objects
Linear scale factor

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

Use ratio to calculate the lengths of similar figures

Defining
Discussions
Solving problem
Explaining

Sets
Books
Videos
Charts
Apparatus

KLB Mathematics
Book Two
Pg 88-90    Discovering secondary pg 56

Similarity and enlargement

Linear scale factor
Negative scale factor
Positive and negative linear scale factor
Area scale factor

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

Use the linear scale factor to find lengths

Defining
Discussions
Solving problem
Explaining

Apparatus
Books
Videos
Charts
Sets

KLB Mathematics
Book Two
Pg 100-101   Discovering secondary pg 56

Similarity and enlargement

Area of scale factor
Volume scale factor
Volume scale factor
Area and volume scale factor

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

Use area scale factor to solve problems

Defining
Discussions
Solving problem
Explaining

Apparatus
Books
Videos
Charts

KLB Mathematics
Book Two
Pg 108   Discovering secondary pg 64

Trigonometry 

Pythagoras Theorem
Solutions of problems Using Pythagoras Theorem
Application to real life Situation
Trigonometry Tangent, sine and cosines

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

Deriving Pythagoras Theorem

Chalkboard Charts Illustrating derived theorem
Charts illustrating Pythagoras theorem
Mathematical table
Charts illustrating tangent, sine and cosine

KLB BK2 Pg 120   Discovering secondary pg 67

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

By the end of the lesson, the learner should be able to:
Use trigonometric tables to find the sine, cosine and tangent

Reading trigonometric tables of sines, cosines and tangent

Mathematical table
Mathematical table Charts Chalkboard
Chalkboards
Chalkboard Charts illustrating the relationship of sines and cosines of complimentary angles

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

Trigonometry 

Relationship between tangent, sine and cosine
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:
Relate the three trigonometric ratios, the sine, cosine and tangent

Relating the three trigonometric ratios

Charts showing the three related trigonometric ratio
Charts showing isosceles right angled triangle Charts illustrating Equilateral triangle
Chalkboard
Chalkboard Mathematical tables

KLB BK2 Pg 145

Trigonometry 

Logarithms of cosines And tangents
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 logarithm of cosines and tangents from mathematical tables

Reading logarithms of cosine and tangent from mathematical table

Chalkboard Mathematical table
Mathematical table
Chart illustrating worked problem Chalkboard

KLB BK2 Pg 150-152

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
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 kite

Calculating the area of a Kite

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

KLB BK2 Pg 163

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

KLB BK2 Pg 169-170

Trigonometry 

Area of a square based Pyramid
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 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
Models of a cone
Models of frustrum of a cone and a pyramid

KLB BK 2 Pg 178

Trigonometry 

Finding the surface area of a sphere
Surface area of a Hemispheres
Volume of Solids Volume of prism (triangular based prism)
Volume of prism (hexagonal based prism) given the sides and angle

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
Models of hexagonal based prism

KLB BK 2 Pg 183

Trigonometry 

Volume of a pyramid (square based and rectangular based)
Volume of a cone
Volume of a frustrum of a cone
Volume of a frustrum of a pyramid

By the end of the lesson, the learner should be able to:
Find the volume of a square based pyramid and rectangular based pyramid

Finding the surface area of the base Applying the formula V=?x base area x height to get the volume of the pyramids (square and rectangular based)

Models of square and Rectangular based Pyramids
Model of a cone
Models of a frustrum of a cone
Models of frustrum of a pyramid

KLB BK 2 Pg 189-190

Trigonometry 
Trigonometric Ratios

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

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

Finding the volume of a Sphere

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

KLB BK 2 Pg 195 

Trigonometric Ratios

Tangent of an angle
Using tangents in calculations
Application of tangents
The sine of an angle

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

find the tangent of an angle from 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

The cosine of an angle
Application of sine and cosine
Complementary angles
Special angles

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

Application of Special angles
Logarithms of sines, cosines and tangents
Relationship between sin, cos and tan

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
Area of A Triangle
Area of A Triangle

Application to real life situation
Problem solving
Area =
Solve problems involving =

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

apply the knowledge of trigonometry to real life situations

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 of Quadrilaterals
Area of Quadrilaterals

A =?s(s-a) (s-b) (s-c)
Problem solving
Area of parallelogram
Area of Rhombus

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
Parallelograms
Trapeziums
Polygons
Squares/rectangles

KLB Maths Bk2 Pg. 155-157

Area of Quadrilaterals
Area of Part of a Circle

Area of trapezium and kite
Area of regular polygons
Problem solving
Area of a sector

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
Circles
Chart illustrating the area of a sector

KLB Maths Bk2 Pg. 162-163

Area of Part of a Circle

Area of a segment
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 area of a segment

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
Surface area of frustrum with circular base

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
Chart illustrating the surface area of a frustrum

KLB Maths Bk2 Pg. 177

Surface Area of Solids

Surface area of frustrum with square base
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 square base

Drawing cones/frustums
Making cones/frustums
Measuring lengths/
angles
Discussions Learners find the surface area

Chart illustrating frustrum with a square base
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
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 prism

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

Prism
Pyramid
Cone
Sphere

KLB Maths Bk2 Pg. 186-188

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
Quadratic Expressions and Equations

Application to real life situation
Problem solving
Expansion of Algebraic Expressions
Quadratic identities

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

Application of identities
Factorise the Identities
Factorise other quadratic expressions
Factorisation of expressions of the form k2-9y2

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
Chart illustrating factorization of a quadratic expression

KLB Maths Bk2 Pg. 204-205

Quadratic Expressions and Equations

Simplification of an expression by factorisation
Solving quadratic equations
The formation of quadratic equations
Formation and solving of quadratic equations from word problems

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
Linear Inequalities
Linear Inequalities

Solving on quadratic equations
Forming quadratic equations from the roots
Inequalities symbols
Number line

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

Discussions
Multiplying numbers
Dividing numbers
Adding numbers
Subtracting numbers
Exercises

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

KLB Maths Bk2 Pg. 208-210

Linear Inequalities

Inequalities in one unknown
Graphical representation
Graphical solutions of simultaneous linear inequalities
Graphical solutions of simultaneous linear inequalities

By the end of the lesson, the learner should be able to:
solve linear inequalities in one unknown and state the integral values

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
Linear Motion

Area of the wanted region
Inequalities from inequality graphs
Problem solving.
Displacement, velocity, speed and acceleration

By the end of the lesson, the learner should be able to:
calculate the area of the wanted region

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
Interpret the velocity time graph

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
Drawn graphs

KLB Maths Bk2 Pg. 228-238

Linear Motion
Statistics

Interpreting graphs
Relative speed (objects moving in the same direction)
Problem solving
Definition

By the end of the lesson, the learner should be able to:
interpret graphs of linear motion

Learners interpret graphs

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.334

Statistics

Collection and organization of data
Frequency tables
Grouped data

By the end of the lesson, the learner should be able to:
collect and organize data

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

Mean of ungrouped data
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 mean of ungrouped data

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
Histograms

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

Frequency polygons
Histograms with uneven distribution
Interpretation of data
Problem solving

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

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

Histograms drawn. Data
Data with uneven classes
Real life situations
Past paper questions

KLB Maths Bk2 Pg. 241-252

Angle Properties of a Circle

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:
identify an arc, chord and segment

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

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. 264-278

Angle Properties of a Circle

Cyclic quadrilateral
Exterior angle property
Problem solving

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
different parts Past paper questions

KLB Maths Bk2 Pg. 264-278

Angle Properties of a Circle
Vectors
Vectors
Vectors

Problem solving
Definition and Representation of vectors
Equivalent vectors
Addition of vectors

By the end of the lesson, the learner should be able to:
state all the properties and use them selectively to solve missing angles.

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

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

KLB Maths Bk2 Pg. 264-278

Vectors

Multiplication of 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:
multiply a vector and a scalar

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. 290