Gradient and equations of straight lines

Gradient

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

Find gradient of straight line

Defining
Discussions
Solving problem
Explaining

Apparatus
Books
Videos
Charts

KLB Mathematics
Book Two
Pg 27-29     discovering secondary pg23

Gradient and equations of straight lines

Equation of a line
Linear equation y=mx+c

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

Find equation of a line passing through two points

Defining
Discussions
Solving problem
Explaining

Apparatus
Books
Videos
Charts

KLB Mathematics
Book Two
Pg 34    discovering secondary pg 25

Gradient and equations of straight lines

The y-intercept
The graph of a straight line

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

Find the y-intercept

Defining
Discussions
Solving problem
Explaining

Apparatus
Books
Videos
Charts
Sets

KLB Mathematics
Book Two
Pg 36-37     Discovering secondary pg 27

Gradient and equations of straight lines

Perpendicular lines
Parallel lines

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

Determine the equation of perpendicular lines

Defining
Discussions
Solving problem
Explaining

Apparatus
Books
Videos
Charts

KLB Mathematics
Book Two
Pg 41-42      discovering secondary pg 30

Reflection and congruence

Symmetry
Reflection
Some general deductions using reflection

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

Find the lines of symmetry of shapes

Draw an image under reflection

Defining
Discussions
Solving problem
Explaining

Apparatus
Books
Videos
Charts
Apparatus
Books
Videos
Charts
Sets

KLB Mathematics
Book Two
Pg 46-47   Discovering secondary pg 32
KLB Mathematics
Book Two
Pg 48-50  Discovering secondary pg 33

Reflection and congruence

Some general deductions using reflection
Congruence

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

Deduce some general rules of reflection

Defining
Discussions
Solving problem
Explaining

Apparatus
Books
Videos
Charts

KLB Mathematics
Book Two
Pg 57-59   Discovering secondary pg 37

Reflection and congruence

Congruent triangles

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

State the conditions that satisfy congruent triangles

Defining
Discussions
Solving problem
Explaining

Apparatus
Books
Videos
Charts

KLB Mathematics
Book Two
Pg 63-64  Discovering secondary pg 39

Reflection and congruence

The ambiguous case

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

Determine the two angles that are congruent

Defining
Discussions
Solving problem
Explaining

Apparatus
Books
Videos
Charts

KLB Mathematics
Book Two
Pg 67   Discovering secondary pg 41

Trigonometry 

Pythagoras Theorem
Solutions of problems Using 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
Charts illustrating Pythagoras theorem

KLB BK2 Pg 120   Discovering secondary pg 67

Trigonometry 

Application to real life Situation
Trigonometry Tangent, sine and cosines

By the end of the lesson, the learner should be able to:
Use the formula A = ?s(s-a)(s-b)(s-c) to solve problems in real life

Solving problems in real life using the formula A = ?s(s-a)(s-b)(s-c)

Mathematical table
Charts illustrating tangent, sine and cosine

KLB BK2 Pg 159    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
Establish the relationship of sine and cosine of complimentary angles

Reading trigonometric tables of sines, cosines and tangent
Using established relationship to solve problems

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
KLB BK2 Pg 145

Trigonometry 

Relationship between tangent, sine and cosine

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

KLB BK2 Pg 145

Trigonometry 

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

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

KLB BK2 Pg 146-147

Trigonometry 

Logarithms of Sines
Logarithms of cosines And tangents

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

Solving problems by reading logarithm table of sines

Chalkboard Mathematical tables
Chalkboard Mathematical table

KLB BK2 Pg 149

Trigonometry 

Reading tables of logarithms of sines, cosines and tangents
Application of trigonometry to real life situations

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

KLB BK2 Pg 149-152

Trigonometry 

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:
Calculate the are of a triangle given the base and height

Calculating the area of a triangle given the base and height

Chart illustrating worked problem Chalkboard

KLB BK2 Pg 155

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
Area of a kite

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
Calculate the are of a triangle, square, rectangle, rhombus, parallelogram and trapezium

Deriving the formula ? absinc Using the formula to calculate the area of a triangle given two sides and an included angle
Calculating the area of a triangle, square, rectangle, rhombus, parallelogram and trapezium

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
Model of a kite

KLB BK2 Pg 156
KLB BK2 Pg 161-163

Trigonometry 

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 regular polygon

Calculating the area of a regular polygon

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

KLB BK2 Pg 164

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

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

Finding the area of a minor and a major sector of a circle

Charts illustrating sectors
Chart illustrating a Segment

KLB BK 2 Pg 167

Trigonometry 

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:
Find the area of common region between two circles given the angles ? Education Plus Agencies

Calculating the area of a segment

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

KLB BK 2 Pg 175

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
Finding the surface area of a sphere
Surface area of a Hemispheres

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
Find the surface area of a sphere given the radius of a sphere

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

Models of a cone
Models of frustrum of a cone and a pyramid
Models of a sphere Charts illustrating formula for finding the surface area of a sphere
Models of a hemisphere

KLB BK 2 Pg 181
KLB BK 2 Pg 183

Trigonometry 

Volume of Solids Volume of prism (triangular based prism)

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

Finding the volume of a triangular based prism

Models of a triangular based prism

KLB BK 2 Pg 186

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)}

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

Macmillan BK 2 Pg 173

Trigonometry 
Trigonometric Ratios

Application of area of triangles to real life
Tangent of an angle
Tangent of an angle
Using tangents in calculations

By the end of the lesson, the learner should be able to:
Use the knowledge of the area of triangles in solving problems in real life situation

find the tangent of an angle from tables

Solving problems in real life using the knowledge of the area of triangle
Measuring lengths/angles
Dividing numbers
Drawing right angles
Reading mathematical tables

Mathematical table Chart illustrating formula used
Protractor
Ruler
Right corners
Mathematical tables

KLB BK 2 Pg 159
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

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

Special angles
Application of Special angles

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

find the sine, cos, and tan of 300,600,450,00,900, without using 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

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

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

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

derive the formula Area =

Measuring lengths/angles
Dividing numbers
Drawing right angles
Reading mathematical tables
Discussions
Drawing triangles
Measuring lengths/angles
Calculating area

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 119-122

KLB Maths Bk2 Pg. 155-157

Area of A Triangle

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

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 A Triangle
Area of Quadrilaterals

Problem solving
Area of parallelogram

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

solve problems on 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 Rhombus
Area of trapezium and kite

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

find the area of a regular polygon.

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

Parallelograms
Trapeziums
Polygons
Squares/rectangles
Mathematical tables

KLB Maths Bk2 Pg. 161

Area of Quadrilaterals

Area of regular polygons
Problem solving

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

find the area of a regular polygon by using the formula A=

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

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

KLB Maths Bk2 Pg. 119-122

Area of Part of a Circle

Area of a sector

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

find area of a sector

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

Circles
Chart illustrating the area of a sector

KLB Maths Bk2 Pg. 167-169

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

find the area of the common region between two circles and solve problems related to that

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

Circles
Chart illustrating the area of a minor segment
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

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

KLB Maths Bk2 Pg. 177

Surface Area of Solids

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 cone

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

Cone
Chart illustrating the surface area of a frustrum

KLB Maths Bk2 Pg. 180
KLBMathematics Bk2
Discovering Secondary Mathematics Bk2

Surface Area of Solids

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 square base

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

Chart illustrating frustrum with a square base

KLB Maths Bk2 Pg. 181-183

Surface Area of Solids

Surface area of frustrum with rectangular base
Surface area of spheres

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

KLB Maths Bk2 Pg. 181-183

Surface Area of Solids
Volume of Solids

Problem solving
Volume of prism

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

solve problems on surface area of solids

Learners solve problems

Past paper questions
Prism

KLB Maths Bk2 Pg. 183

Volume of Solids

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 pyramid

find the volume of a sphere

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

Pyramid
Cone
Sphere

KLB Maths Bk2 Pg. 189-190

KLB Maths Bk2 Pg. 195

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

Problem solving
Expansion of Algebraic Expressions

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

Quadratic identities
Application of 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 the Identities

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

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

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

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

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

KLB Maths Bk2 Pg. 205-208

Quadratic Expressions and 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:
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

Quadratic Expressions and Equations

Solving on quadratic equations
Forming quadratic equations from the roots

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

KLB Maths Bk2 Pg. 208-210

Linear Inequalities

Inequalities symbols

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

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

Number line
Inequalities in one unknown

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

KLB Maths Bk2 Pg. 213-224

Linear Inequalities

Graphical representation
Graphical solutions of simultaneous linear inequalities

By the end of the lesson, the learner should be able to:
represent linear inequalities in one unknown 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
Number lines
Graph papers

KLB Maths Bk2 Pg. 213-224

Linear Inequalities

Graphical solutions of simultaneous linear inequalities
Area of the wanted region
Inequalities from inequality graphs

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

KLB Maths Bk2 Pg. 213-224

Linear Inequalities
Linear Motion

Problem solving.
Displacement, velocity, speed and acceleration

By the end of the lesson, the learner should be able to:
solve problems on linear inequalities

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

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

Distance time graphs
Interpret the velocity time graph

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

plot and draw the distance time graphs

Plotting graphs
Drawing graphs

Graph papers
Stones
Pieces of paper
Drawn graphs

KLB Maths Bk2 Pg. 228-238

Linear Motion

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

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

KLB
Maths Bk2
Pg.334

Linear Motion

Problem solving

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

solve problems on linear motion

Question answer method

Past paper questions

KLB
Maths Bk2
Pg.330