Numbers and Algebra

Quadratic Equations - Formation of algebraic expressions

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

- Form algebraic expressions from word statements
- Use letters to represent unknown quantities
- Relate algebraic expressions to real situations like shopping and measurements

- Read case scenarios and form algebraic expressions
- Use letters to represent unknown quantities
- Discuss how expressions represent real-life situations

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 21
- Word problem cards
- Charts

- Oral questions - Written exercises - Observation

Numbers and Algebra

Quadratic Equations - Formation of algebraic expressions from real life
Quadratic Equations - Formation of quadratic expressions

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

- Form complex algebraic expressions from multiple quantities
- Simplify algebraic expressions
- Apply algebraic expressions to calculate costs, distances and areas

- Form expressions involving multiple unknown quantities
- Simplify expressions by collecting like terms
- Solve problems on cost, profit and measurements

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 22
- Word problem cards
- Calculators
- Mentor Essential Mathematics pg. 23
- Rectangular cut-outs
- Charts

- Written exercises - Class activities - Portfolio

Numbers and Algebra

Quadratic Equations - Quadratic expressions from real life situations

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

- Form quadratic expressions from real-life contexts
- Interpret word problems to generate quadratic expressions
- Apply quadratic expressions to floor plans, gardens and picture frames

- Read scenarios on area and form quadratic expressions
- Draw diagrams to visualize the problems
- Work out expressions for paths around gardens and margins

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 24
- Diagram charts
- Graph paper

- Written exercises - Class activities - Observation

Numbers and Algebra

Quadratic Equations - Formation of quadratic equations

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

- Distinguish between quadratic expressions and equations
- Form quadratic equations from given conditions
- Apply quadratic equations to problems on area and dimensions

- Form quadratic equations from area problems
- Set up equations where expression equals a given value
- Discuss volleyball pitch and room dimension problems

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 25
- Diagram charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Equations - Quadratic equations from word problems
Quadratic Equations - Factorisation of quadratic expressions

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

- Form quadratic equations from various word problems
- Interpret real-life situations as quadratic equations
- Model age, product and sharing problems using quadratic equations

- Read and interpret word problems
- Form quadratic equations from age and product problems
- Discuss seedbed and carpet area problems

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 26
- Word problem cards
- Calculators
- Mentor Essential Mathematics pg. 27
- Factor pair charts

- Written tests - Class activities - Portfolio

Numbers and Algebra

Quadratic Equations - Factorisation by grouping

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

- Factorise quadratic expressions by grouping
- Apply the grouping method to various expressions
- Verify factorisation by expanding the factors

- Split the middle term into two terms
- Group terms and factorise each group
- Extract the common factor and complete factorisation

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 27
- Worked examples charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Equations - Factorisation of expressions ax² + bx + c

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

- Factorise quadratic expressions where a ≠ 1
- Apply systematic methods to factorise complex expressions
- Connect factorisation to finding dimensions from area expressions

- Find factors of ac and identify the pair summing to b
- Factorise expressions with leading coefficient greater than 1
- Discuss practical applications of factorisation

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 28
- Factor charts
- Calculators

- Written tests - Class activities - Observation

Numbers and Algebra

Quadratic Equations - Solving by factorisation
Quadratic Equations - Solving equations with repeated roots

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

- Apply factorisation to solve quadratic equations
- Find solutions by equating each factor to zero
- Verify solutions by substitution into the original equation

- Factorise the quadratic expression
- Set each factor equal to zero and solve for x
- Check solutions by substituting back into the equation

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 28
- Worked examples charts
- Calculators
- Mentor Essential Mathematics pg. 29
- Calculators
- Worked examples

- Written exercises - Class activities - Oral questions

Numbers and Algebra
Measurements and Geometry

Quadratic Equations - Applications to real life problems
Similarity and Enlargement - Properties of similar figures

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

- Apply quadratic equations to solve area problems
- Form and solve equations from word problems
- Interpret solutions in real-life contexts like room dimensions and garden sizes

- Form quadratic equations from dimension problems
- Solve and interpret solutions
- Determine dimensions of rooms, carpets and gardens

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 29
- Diagram charts
- Calculators
- Mentor Essential Mathematics pg. 31
- Similar objects (containers, shapes)
- Rulers and protractors
- Digital resources

- Written tests - Portfolio - Class activities

Measurements and Geometry

Similarity and Enlargement - Properties of similar figures
Similarity and Enlargement - Centre of enlargement and linear scale factor

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

- Determine whether given figures are similar
- Calculate ratios of corresponding sides
- Connect similar figures to everyday items like photo frames and tiles

- Work out ratios of corresponding sides of triangles
- Use protractor to measure corresponding angles
- Determine if rectangles are similar by comparing ratios
- Share findings with classmates

What conditions must be met for two figures to be similar?

- Mentor Essential Mathematics pg. 33
- Protractors
- Rulers
- Cut-outs of similar shapes
- Mentor Essential Mathematics pg. 37
- Plain paper
- Pencils

- Observation - Oral questions - Written tests

Measurements and Geometry

Similarity and Enlargement - Linear scale factor
Similarity and Enlargement - Drawing images under enlargement
Similarity and Enlargement - Drawing images on Cartesian plane

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

- Determine the linear scale factor of similar figures
- Calculate linear scale factor from given measurements
- Apply linear scale factor concepts to map reading and architectural drawings

- Measure distances from centre of enlargement to object and image
- Calculate ratio of image distance to object distance
- Work out linear scale factors for different figures
- Discuss applications of scale factors

What is the relationship between object and image distances?

- Mentor Essential Mathematics pg. 38
- Rulers
- Graph paper
- Calculators
- Mentor Essential Mathematics pg. 40
- Geometrical instruments
- Mentor Essential Mathematics pg. 41
- Pencils

- Observation - Oral questions - Written tests

Measurements and Geometry

Similarity and Enlargement - Area scale factor
Similarity and Enlargement - Area scale factor calculations
Similarity and Enlargement - Volume scale factor

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

- Determine the area scale factor of similar figures
- Calculate areas of objects and their images
- Relate area scale factor to land surveying and floor planning

- Draw right-angled triangle and enlarge with scale factor 3
- Calculate areas of object and image
- Determine ratio of areas
- Discuss relationship between linear and area scale factors

What is the relationship between linear scale factor and area scale factor?

- Mentor Essential Mathematics pg. 42
- Graph paper
- Calculators
- Rulers
- Mentor Essential Mathematics pg. 44
- Rulers
- Digital resources
- Mentor Essential Mathematics pg. 43
- Similar containers
- Calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Relating linear, area and volume scale factors

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

- Relate linear scale factor to area and volume scale factors
- Convert between different scale factors
- Apply scale factor relationships to model making and engineering

- Make similar cylinders of different sizes
- Calculate ratios of heights, areas, and volumes
- Compare the three ratios and establish relationships
- Solve problems involving all three scale factors

How are the three scale factors related?

- Mentor Essential Mathematics pg. 45
- Manila paper
- Calculators
- Scissors

- Observation - Oral questions - Written tests

Measurements and Geometry

Similarity and Enlargement - Application to area

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

- Apply linear scale factor to find areas of similar figures
- Solve problems on area using scale factors
- Connect similarity concepts to architectural blueprints and scale models

- Calculate areas of similar figures using scale factors
- Solve word problems involving area scale factor
- Use digital devices to explore applications
- Present solutions to peers

How do we apply area scale factor to solve problems?

- Mentor Essential Mathematics pg. 46
- Calculators
- Digital resources
- Reference books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Application to volume
Reflection - Lines of symmetry in plane figures
Reflection - Lines of symmetry in regular polygons

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

- Apply linear scale factor to find volumes of similar objects
- Solve problems on volume using scale factors
- Use similarity in estimating storage capacities and tank volumes

- Calculate volumes of similar solids using scale factors
- Solve word problems involving volume scale factor
- Complete project on making similar containers
- Document processes and take pictures

How do we apply volume scale factor to solve problems?

- Mentor Essential Mathematics pg. 47
- Calculators
- Manila paper
- Locally available materials
- Mentor Essential Mathematics pg. 50
- Paper cut-outs
- Scissors
- Various 2D objects
- Mentor Essential Mathematics pg. 52
- Rulers
- Protractors
- Plain paper

- Observation - Project assessment - Written tests

Measurements and Geometry

Reflection - Properties of reflection
Reflection - Drawing images given object and mirror line

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

- Determine the properties of reflection using objects and images
- Compare distances of object and image from mirror line
- Relate reflection properties to how mirrors work in daily life

- Observe triangle ABC and its image A'B'C' after reflection
- Compare sizes and shapes of object and image
- Measure and compare distances from mirror line
- Stand at different distances from plane mirror and observe

What are the properties of reflection?

- Mentor Essential Mathematics pg. 53
- Plane mirrors
- Rulers
- Plain paper
- Mentor Essential Mathematics pg. 54
- Plain paper
- Set squares

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection - Reflection along x = 0
Reflection - Reflection along y = 0
Reflection - Reflection along y = x

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

- Draw an image after reflection along the line x = 0
- Determine coordinates of image points when reflected along y-axis
- Connect reflection to creating symmetric designs and logos

- Plot triangles on Cartesian plane
- Reflect points along line x = 0
- Record coordinates of object and image points
- Observe pattern in coordinates after reflection

What happens to coordinates when reflecting along x = 0?

- Mentor Essential Mathematics pg. 56
- Graph paper
- Rulers
- Pencils
- Mentor Essential Mathematics pg. 58
- Calculators
- Mentor Essential Mathematics pg. 57

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection - Drawing mirror line given object and image on plane surface
Reflection - Drawing mirror line on Cartesian plane

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

- Draw the mirror line given an object and its image on a plane surface
- Construct perpendicular bisectors to locate mirror line
- Apply the concept to determining mirror placement in interior design

- Trace objects and their images on plain paper
- Join corresponding points (object to image)
- Construct perpendicular bisector of the line segment
- Verify that perpendicular bisector is the mirror line

How do we find the mirror line given object and image?

- Mentor Essential Mathematics pg. 60
- Plain paper
- Rulers
- Compasses
- Mentor Essential Mathematics pg. 61
- Graph paper

- Observation - Practical work - Written tests

Measurements and Geometry

Reflection - Application in real life situations
Trigonometry - Identifying sides of a right-angled triangle

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

- Apply reflection in real-life situations
- Solve problems involving reflection
- Use reflection concepts in understanding driving mirrors and road safety

- Discuss uses of reflection in real life
- Solve problems involving town layouts and architectural designs
- Work with peers to apply reflection to practical situations
- Present findings to class

How is reflection used in day-to-day activities?

- Mentor Essential Mathematics pg. 63
- Graph paper
- Rulers
- Digital resources
- Mentor Essential Mathematics pg. 65
- Ladders
- Protractors
- Rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Tangent ratio
Trigonometry - Applications of tangent ratio
Trigonometry - Sine ratio

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

- Determine the tangent of acute angles in a right-angled triangle
- Calculate tangent ratios from given measurements
- Apply tangent ratio in calculating heights and distances in surveying

- Measure opposite and adjacent sides in similar triangles
- Calculate ratio of opposite to adjacent for angle θ
- Record ratios and observe that they are constant
- Work out tangent of angles in various triangles

What is the tangent of an angle?

- Mentor Essential Mathematics pg. 67
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 68
- Calculators
- Reference books
- Mentor Essential Mathematics pg. 69

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Applications of sine ratio
Trigonometry - Cosine ratio
Trigonometry - Applications of cosine ratio

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

- Apply sine ratio to solve problems
- Calculate sine from real-life situations
- Use sine in determining heights of slides and inclined structures

- Calculate sine of angles formed by ladders and ground
- Work out sine of angles in roof truss designs
- Solve problems involving playground slides
- Present solutions to peers

How is sine ratio applied in real life?

- Mentor Essential Mathematics pg. 71
- Calculators
- Rulers
- Digital resources
- Mentor Essential Mathematics pg. 72
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 74
- Reference books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Sines and cosines of complementary angles
Trigonometry - Solving equations involving complementary angles

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

- Relate sines and cosines of complementary angles
- Use calculator to find sines and cosines of complementary angles
- Apply complementary angle relationships to solving equations

- Discuss meaning of complementary angles
- Use calculator to complete table of sin θ and cos(90°-θ)
- Observe that sin α = cos(90°-α)
- Verify relationship using different angle pairs

What is the relationship between sine and cosine of complementary angles?

- Mentor Essential Mathematics pg. 75
- Scientific calculators
- Reference books
- Digital resources
- Mentor Essential Mathematics pg. 76
- Exercise books
- Reference books

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Making a clinometer

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

- Make a simple clinometer using locally available materials
- Use the clinometer to measure angles
- Apply clinometer skills to measuring heights of buildings and trees

- Gather manila paper, protractor, string and weight
- Trace protractor's curved edge and mark degrees
- Attach straw along straight edge
- Tie string with weight at centre point

How do we make and use a clinometer?

- Mentor Essential Mathematics pg. 77
- Manila paper
- Blackboard protractor
- String and weight

- Observation - Practical work - Oral questions

Measurements and Geometry

Trigonometry - Angle of elevation
Trigonometry - Problems on angle of elevation

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

- Apply trigonometric ratios to angles of elevation
- Calculate heights using angles of elevation
- Use angle of elevation in determining heights of flagpoles, trees and buildings

- Use clinometer to measure angle of elevation of tall objects
- Measure horizontal distance from object
- Apply trigonometric ratios to calculate heights
- Compare calculated heights with actual measurements

How do we use angles of elevation to find heights?

- Mentor Essential Mathematics pg. 79
- Clinometers
- Tape measures
- Calculators
- Mentor Essential Mathematics pg. 80
- Calculators
- Rulers
- Exercise books

- Observation - Practical work - Written tests

Measurements and Geometry

Trigonometry - Angle of depression

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

- Apply trigonometric ratios to angles of depression
- Calculate distances using angles of depression
- Use angle of depression in aviation and marine navigation

- Discuss meaning of angle of depression
- Draw diagrams showing angles of depression
- Apply trigonometric ratios to find distances
- Solve problems involving observers on cliffs and buildings

How do we use angles of depression to find distances?

- Mentor Essential Mathematics pg. 80
- Calculators
- Rulers
- Digital resources

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Application in real life situations
Area of Polygons - Area of triangle given two sides and an included angle

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

- Solve combined problems on angles of elevation and depression
- Apply trigonometry to various real-life scenarios
- Use trigonometry in determining distances between ships, aircraft heights and building measurements

- Solve problems involving two ships viewed from cliff
- Calculate distances and heights in combined scenarios
- Use digital resources to explore more applications
- Present solutions to class

How is trigonometry used in real life?

- Mentor Essential Mathematics pg. 81
- Calculators
- Digital resources
- Reference books
- Mentor Essential Mathematics pg. 84
- Rulers
- Protractors
- Calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Problems on area of triangle
Area of Polygons - Heron's Formula
Area of Polygons - Problems using Heron's Formula

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

- Solve problems on area of triangles using ½ab sin C
- Find unknown sides or angles given the area
- Apply triangle area calculations to land surveying and construction

- Work out areas of triangular kitchen gardens
- Calculate areas of equilateral triangular seedbeds
- Solve for unknown angles when area is given
- Discuss applications in real life

How do we solve problems involving area of triangles?

- Mentor Essential Mathematics pg. 85
- Calculators
- Rulers
- Exercise books
- Mentor Essential Mathematics pg. 86
- Scientific calculators
- Mentor Essential Mathematics pg. 87
- Exercise books
- Reference books

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Area of a rhombus
Area of Polygons - Area of rhombus given side and angle

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

- Determine the area of a rhombus given the diagonals
- Apply the formula Area = ½ × d₁ × d₂
- Calculate areas of rhombus-shaped tiles, kites and floor patterns

- Draw rhombus and measure diagonals
- Calculate areas of triangles formed by diagonals
- Add areas to get total area of rhombus
- Verify using formula ½ × d₁ × d₂

How do we find the area of a rhombus?

- Mentor Essential Mathematics pg. 88
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 89
- Calculators
- Protractors

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of a parallelogram
Area of Polygons - Area of parallelogram using ab sin θ
Area of Polygons - Area of a regular pentagon

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

- Determine the area of a parallelogram
- Apply the formula Area = base × perpendicular height
- Calculate areas of parallelogram-shaped solar panels and floor plans

- Draw parallelogram with given dimensions
- Calculate perpendicular height using trigonometry
- Apply formula: base × perpendicular height
- Work out areas of various parallelograms

How do we find the area of a parallelogram?

- Mentor Essential Mathematics pg. 92
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 94
- Calculators
- Exercise books
- Mentor Essential Mathematics pg. 95

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Problems on area of pentagon

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

- Solve problems on area of regular pentagons
- Calculate areas of pentagon-shaped objects
- Apply pentagon area to trampoline covers and decorative designs

- Calculate area of pentagon-shaped flower beds
- Work out area of pizza box lids
- Solve problems involving pentagon-shaped objects
- Present solutions to class

How is area of pentagon applied in real life?

- Mentor Essential Mathematics pg. 97
- Calculators
- Exercise books
- Digital resources

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Area of a regular hexagon

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

- Determine the area of a regular hexagon
- Divide hexagon into 6 triangles and calculate total area
- Apply hexagon area to floor tiling and road sign designs

- Draw regular hexagon and divide into 6 triangles
- Measure radius from centre to vertex
- Calculate area of one triangle
- Multiply by 6 to get total area

How do we find the area of a regular hexagon?

- Mentor Essential Mathematics pg. 96
- Rulers
- Protractors
- Calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Application in real life situations
Area of a Part of a Circle - Area of a sector
Area of a Part of a Circle - Problems on area of sector

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

- Apply areas of polygons in real-life situations
- Solve combined problems on areas of polygons
- Use polygon areas in calculating material costs and backyard coverage

- Calculate areas of hexagonal tile sections
- Work out total area of backyards covered with hexagonal blocks
- Determine cost of materials for polygon-shaped items
- Discuss applications in day-to-day life

How are areas of polygons useful in real life?

- Mentor Essential Mathematics pg. 98
- Calculators
- Digital resources
- Reference books
- Mentor Essential Mathematics pg. 101
- Compasses
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 102
- Rulers
- Exercise books

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Area of a segment
Area of a Part of a Circle - Problems on area of segment
Area of a Part of a Circle - Area swept by gate

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

- Determine the area of a segment of a circle
- Apply the formula: Area of sector - Area of triangle
- Calculate areas of parking lots, decorations and glass windows

- Draw circle with sector and identify segment
- Calculate area of sector using θ/360 × πr²
- Calculate area of triangle using ½r² sin θ
- Subtract to get area of segment

How do we find the area of a segment?

- Mentor Essential Mathematics pg. 103
- Compasses
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 105
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 107
- Tape measures

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of a Part of a Circle - Problems on curved paths and decorations
Area of a Part of a Circle - Clock and sprinkler problems

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

- Calculate areas of curved paths and decorations
- Solve problems on sector and segment areas
- Apply concepts to fan blade designs and table cloth decorations

- Calculate area of curved paths in school compound
- Work out area of decorations on table cloths
- Solve problems on fanning papers
- Present solutions to class

How are areas of parts of circles applied in design?

- Mentor Essential Mathematics pg. 108
- Calculators
- Rulers
- Digital resources
- Mentor Essential Mathematics pg. 110
- Clocks
- Reference books

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Combined problems
Surface Area of Solids - Nets of cones
Surface Area of Solids - Surface area of a cone from its net

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

- Solve combined problems on sectors and segments
- Apply area of parts of circles in various contexts
- Use concepts in calculating metal sheet areas and flower garden segments

- Calculate area of metal sheet in segment shape
- Work out area of flower segments in circular gardens
- Solve problems on staffroom doors and gates
- Review all concepts on area of parts of circles

Where do we use area of part of a circle in real life?

- Mentor Essential Mathematics pg. 111
- Calculators
- Exercise books
- Digital resources
- Mentor Essential Mathematics pg. 112
- Manila paper
- Scissors
- Cone-shaped objects
- Mentor Essential Mathematics pg. 113
- Cone nets
- Protractors
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area of Solids - Surface area of cone using formula
Surface Area of Solids - Nets of pyramids
Surface Area of Solids - Surface area of square-based pyramid

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

- Calculate surface area of cones using πrl + πr²
- Solve problems on surface area of cones
- Use cone surface area in designing Christmas hats, filter papers and decorative cones

- Apply formula: Curved surface area = πrl
- Apply formula: Total surface area = πrl + πr²
- Calculate surface area of Christmas hats
- Solve problems on filter paper cones

How do we calculate surface area of a cone using the formula?

- Mentor Essential Mathematics pg. 114
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 115
- Manila paper
- Scissors
- Rulers
- Mentor Essential Mathematics pg. 116
- Graph paper

- Observation - Oral questions - Written assignments

Measurements and Geometry

Surface Area of Solids - Surface area of rectangular-based pyramid
Surface Area of Solids - Surface area of a sphere

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

- Determine surface area of rectangular-based pyramids
- Calculate areas of different pairs of triangular faces
- Apply to camping tent designs, monument construction and roof structures

- Draw net of rectangular-based pyramid
- Calculate area of rectangular base
- Work out areas of two pairs of triangular faces
- Add all areas to get total surface area

How do we find surface area of a rectangular-based pyramid?

- Mentor Essential Mathematics pg. 117
- Graph paper
- Calculators
- Rulers
- Mentor Essential Mathematics pg. 120
- Spherical objects
- Rulers
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area of Solids - Surface area of a hemisphere
Surface Area of Solids - Surface area of frustum of a cone

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

- Calculate the surface area of a solid hemisphere
- Apply the formula 3πr²
- Use hemisphere surface area in calculating material for bowls, domes and decorative half-spheres

- Cut spherical object (orange) into two equal halves
- Estimate radius of hemisphere
- Calculate curved surface area (2πr²)
- Add circular base area to get total (3πr²)

How do we find the surface area of a hemisphere?

- Mentor Essential Mathematics pg. 121
- Oranges
- Knives
- Calculators
- Mentor Essential Mathematics pg. 122
- Manila paper
- Scissors

- Observation - Practical work - Written tests

Measurements and Geometry

Surface Area of Solids - Problems on frustum of a cone
Surface Area of Solids - Surface area of frustum of a pyramid

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

- Solve problems on surface area of frustums of cones
- Calculate surface areas of open and closed frustums
- Apply to coffee cups, loudspeaker diaphragms and chemical storage buckets

- Calculate total surface area: πL(R+r) + πR² + πr²
- Work out surface area of open-top coffee cups
- Calculate curved surface area of loudspeaker diaphragms
- Solve problems on buckets storing chemicals

How do we solve problems on frustum surface area?

- Mentor Essential Mathematics pg. 124
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 125
- Manila paper
- Scissors
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area of Solids - Problems on frustum of a pyramid

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

- Solve problems on surface area of frustums of pyramids
- Calculate surface area of rectangular-based pyramid frustums
- Apply to hollow lampshades, counter designs, statue stands and open water tanks

- Calculate areas of trapezoidal faces for rectangular-based frustums
- Work out surface area of hollow lampshades (lateral only)
- Solve problems on counters and statue stands
- Determine material needed for multiple lampshades

How are frustums of pyramids used in real life?

- Mentor Essential Mathematics pg. 127
- Calculators
- Exercise books
- Digital resources

- Observation - Oral questions - Written tests

Measurements and Geometry

Volume and Capacity - Volume of a cone
Volume and Capacity - Problems on volume of cones
Volume and Capacity - Volume of cone given slant height

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

- Determine the volume of a cone
- Apply the formula V = ⅓πr²h
- Relate cone volume to measuring ingredients and ice cream scoops

- Make models of cone and cylinder with equal base radius and height
- Fill cone with sand and empty into cylinder
- Count number of cones needed to fill cylinder
- Establish relationship between cone and cylinder volumes

What is the relationship between volume of a cone and cylinder?

- Mentor Essential Mathematics pg. 132
- Manila paper
- Sand
- Calculators
- Mentor Essential Mathematics pg. 133
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 134
- Rulers
- Exercise books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Volume and Capacity - Volume of a pyramid
Volume and Capacity - Problems on volume of pyramids
Volume and Capacity - Volume of frustum of a cone

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

- Determine volume of square and rectangular-based pyramids
- Apply the formula V = ⅓ × base area × height
- Calculate volumes of poultry houses and storage structures

- Collect objects in shape of pyramids
- Measure vertical height, base length and width
- Calculate volume using V = ⅓ × base area × h
- Compare volumes of different pyramids

How do we find the volume of a pyramid?

- Mentor Essential Mathematics pg. 135
- Pyramid models
- Rulers
- Calculators
- Mentor Essential Mathematics pg. 136
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 138
- Manila paper
- Scissors

- Observation - Oral questions - Written tests

Measurements and Geometry

Volume and Capacity - Problems on frustum of a cone
Volume and Capacity - Volume of frustum of a pyramid

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

- Solve problems on volume of frustum of a cone
- Calculate capacity of frustum-shaped containers
- Apply to traditional cooking pots, water collection containers and metallic buckets

- Calculate volume of rainwater collection containers
- Work out capacity of traditional cooking pots
- Determine volume of frustum-shaped drinking water buckets
- Convert volumes to litres and millilitres

How do we calculate capacity of frustum-shaped containers?

- Mentor Essential Mathematics pg. 140
- Calculators
- Exercise books
- Digital resources
- Mentor Essential Mathematics pg. 142
- Manila paper
- Scissors
- Calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Volume and Capacity - Problems on frustum of a pyramid
Volume and Capacity - Volume of composite solids

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

- Solve problems on volume of frustum of a pyramid
- Calculate capacity of pyramid frustum containers
- Apply to water troughs, flower vases and lunch boxes

- Calculate volume of water troughs cut from pyramids
- Work out capacity of traditional woven baskets
- Determine volume of flower vases and lunch boxes
- Convert to litres and millilitres

How is frustum of pyramid volume applied?

- Mentor Essential Mathematics pg. 144
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 145
- Models of solids
- Digital resources

- Observation - Oral questions - Written assignments

Measurements and Geometry

Volume and Capacity - Capacity problems

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

- Convert between volume and capacity units
- Solve problems involving litres and millilitres
- Apply to water storage, milk packaging and fuel tank capacities

- Convert cubic metres to litres
- Convert cubic centimetres to millilitres
- Calculate capacity of various containers
- Solve real-life problems on water and fuel storage

Why is the knowledge of volume and capacity useful?

- Mentor Essential Mathematics pg. 146
- Calculators
- Containers
- Exercise books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Volume and Capacity - Combined problems
Commercial Arithmetic I - Preparing a budget

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

- Solve combined problems on volume and capacity
- Apply volume concepts to various real-life situations
- Use volume and capacity in water trough designs for livestock and reservoir planning

- Solve mixed problems on cones, pyramids and frustums
- Calculate capacity of mugs, buckets and tanks
- Work out dimensions when capacity is given
- Review all concepts on volume and capacity

How do we apply volume and capacity in daily life?

- Mentor Essential Mathematics pg. 147
- Calculators
- Digital resources
- Reference books
- Mentor Essential Mathematics pg. 148
- Sample budgets
- Exercise books
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Commercial Arithmetic I - Balancing a budget
Commercial Arithmetic I - Calculating discounts
Commercial Arithmetic I - Percentage discount

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

- Create balanced budgets showing income and expenditure
- Allocate funds appropriately including emergency funds
- Use budgeting in planning environmental clean-ups and science fairs

- Decide on club activities and estimate costs
- List all income sources with estimated amounts
- Allocate funds to various expenses
- Ensure total income equals total expenditure
- Present budget to class for peer learning

How do we ensure a budget is balanced?

- Mentor Essential Mathematics pg. 149
- Calculators
- Exercise books
- Chart paper
- Mentor Essential Mathematics pg. 150
- Price lists
- Shopping receipts
- Mentor Essential Mathematics pg. 151
- Price catalogues
- Exercise books

- Observation - Budget presentation - Written tests

Measurements and Geometry

Commercial Arithmetic I - Calculating commission
Commercial Arithmetic I - Percentage commission and tiered rates
Commercial Arithmetic I - Profit and percentage profit

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

- Calculate commission earned on sales
- Determine commission as percentage of total sales
- Apply commission calculations to sales jobs and real estate transactions

- Brainstorm jobs where people earn commission
- Role-play sales scenarios where commission is earned
- Calculate commission using: Commission = Rate × Total sales
- Discuss advantages of commission to companies and employees

Why do companies offer commission?

- Mentor Essential Mathematics pg. 153
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 154
- Digital resources
- Mentor Essential Mathematics pg. 155

- Observation - Role play - Written assignments

Measurements and Geometry

Commercial Arithmetic I - Loss and percentage loss
Commercial Arithmetic I - Currency exchange rates

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

- Determine loss incurred in sale of goods
- Calculate percentage loss
- Apply loss calculations to perishable goods like fruits and vegetables

- Discuss situations where businesses make losses
- Calculate loss: Cost price - Selling price
- Work out percentage loss: (Loss/Cost price) × 100%
- Discuss how to avoid losses in business

How do we calculate loss in business?

- Mentor Essential Mathematics pg. 157
- Calculators
- Exercise books
- Case studies
- Mentor Essential Mathematics pg. 160
- Currency exchange tables
- Digital resources

- Observation - Oral questions - Written tests

Measurements and Geometry

Commercial Arithmetic I - Currency conversion problems

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

- Convert foreign currencies to Kenyan shillings
- Solve problems involving buying and selling rates
- Apply currency conversion to international trade, remittances and travel budgeting

- Convert US dollars, Euros and Yen to Kenya shillings
- Use buying rate when bank buys foreign currency
- Use selling rate when bank sells foreign currency
- Calculate amount received after currency exchange round trips

How do we convert currencies using exchange rates?

- Mentor Essential Mathematics pg. 162
- Currency exchange tables
- Calculators
- Exercise books

- Observation - Oral questions - Written tests