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

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

- Written exercises - Class activities - Portfolio

Numbers and Algebra

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

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

- Identify quadratic expressions
- Form quadratic expressions by multiplying binomials
- Relate quadratic expressions to calculating areas of rectangles

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

- Expand products of two binomials
- Identify the structure of quadratic expressions
- Discuss how quadratic expressions represent area problems

- 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. 23
- Rectangular cut-outs
- Charts

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

- Oral questions - Written exercises - Observation
- 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

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

- Written tests - Class activities - Portfolio

Numbers and Algebra

Quadratic Equations - Quadratic equations from word problems

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

- Written tests - Class activities - Portfolio

Numbers and Algebra

Quadratic Equations - Factorisation of quadratic expressions
Quadratic Equations - Factorisation by grouping

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

- Identify the coefficients a, b and c in quadratic expressions
- Find factor pairs of ac that sum to b
- Apply factorisation to expressions of the form x² + bx + c

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

- Identify values of a, b and c in quadratic expressions
- List factor pairs and identify the pair with required sum
- Factorise expressions by splitting the middle term

- 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
- Factor pair charts
- Calculators

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

- Oral questions - Written exercises - Observation
- 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

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

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Equations - Solving equations with repeated roots

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

- Solve quadratic equations with repeated roots
- Identify perfect square trinomials
- Interpret the meaning of repeated roots in context

- Factorise perfect square trinomials
- Solve equations yielding single solutions
- Discuss what repeated roots mean in area problems

How are quadratic equations applied in real life?

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

- Oral questions - Written exercises - Observation

Numbers and Algebra
Measurements and Geometry

Quadratic Equations - Applications to real life problems
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 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

- Identify lines of symmetry in plane figures
- Determine the number of lines of symmetry in different shapes
- Recognize symmetry in everyday objects like doors, windows and leaves

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

- Take a walk and collect 2D objects from the environment
- Fold rectangular and square paper cut-outs to find lines of symmetry
- Count number of fold lines that divide shapes into equal parts
- Share findings with other groups

How are quadratic equations applied in real life?
How do we identify lines of symmetry?

- Mentor Essential Mathematics pg. 29
- Diagram charts
- Calculators
- Mentor Essential Mathematics pg. 50
- Paper cut-outs
- Scissors
- Various 2D objects
- Mentor Essential Mathematics pg. 52
- Rulers
- Protractors
- Plain paper

- Written tests - Portfolio - Class activities
- Observation - Oral questions - Written assignments

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection - Reflection along y = x
Reflection - Drawing mirror line given object and image on plane surface

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

- Draw an image after reflection along the line y = x
- Determine coordinates of image points when reflected along y = x
- Use reflection in creating tessellations and artistic patterns

- Plot triangles on Cartesian plane
- Draw line y = x and reflect points
- Record and compare coordinates
- Establish the rule for reflection along y = x

What happens to coordinates when reflecting along y = x?

- Mentor Essential Mathematics pg. 57
- Graph paper
- Rulers
- Pencils
- Mentor Essential Mathematics pg. 60
- Plain paper
- Compasses

- Observation - Practical work - Written assignments

Measurements and Geometry

Reflection - Drawing mirror line on Cartesian plane
Reflection - Application in real life situations

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

- Draw the mirror line given an object and its image on Cartesian plane
- Identify the equation of the mirror line
- Connect mirror line concepts to coordinate geometry applications

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

- Plot objects and their images on Cartesian plane
- Join corresponding vertices
- Construct perpendicular bisectors
- Determine equation of mirror line

- 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 do we determine the equation of a mirror line?
How is reflection used in day-to-day activities?

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

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

- Observation - Oral questions - Written assignments
- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Identifying sides of a right-angled triangle
Trigonometry - Tangent ratio

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

- Identify the sides of a right-angled triangle in relation to a particular angle
- Name the hypotenuse, opposite and adjacent sides
- Recognize right-angled triangles in structures like ladders, ramps and roofs

- Lean a ladder against classroom wall and identify triangle formed
- Name the type of triangle formed
- Identify hypotenuse, opposite and adjacent sides relative to angle θ
- Discuss real-life examples of right-angled triangles

How do we identify the sides of a right-angled triangle?

- Mentor Essential Mathematics pg. 65
- Ladders
- Protractors
- Rulers
- Mentor Essential Mathematics pg. 67
- Rulers
- Calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Applications of tangent ratio
Trigonometry - Sine ratio

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

- Apply tangent ratio to solve problems
- Calculate tangent from real-life situations
- Use tangent in determining slopes of ramps and roof pitches

- Calculate tangent of angles formed by ladders and walls
- Work out tangent of angles in roof designs
- Solve problems involving ramps and inclined surfaces
- Share solutions with classmates

How is tangent ratio applied in real life?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Applications of sine ratio
Trigonometry - 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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Applications of cosine ratio
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:

- Apply cosine ratio to solve problems
- Calculate cosine from real-life situations
- Use cosine in determining base distances and horizontal measurements

- Solve equations involving sines and cosines of complementary angles
- Apply the relationship sin θ = cos(90°-θ)
- Use complementary angle properties in practical calculations

- Calculate cosine of angles formed by ladders and ground
- Work out cosine of angles in warehouse roof designs
- Solve problems involving ramps and inclined surfaces
- Share solutions with classmates

- Solve equations like sin θ = cos 40°
- Work out problems involving sin(x-55) = cos x
- Apply complementary angle relationships
- Share solutions with peers

How is cosine ratio applied in real life?
How do we solve equations involving complementary angles?

- Mentor Essential Mathematics pg. 74
- Calculators
- Rulers
- Reference books
- Mentor Essential Mathematics pg. 75
- Scientific calculators
- Reference books
- Digital resources

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

- Observation - Oral questions - Written assignments

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

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

- Observation - Practical work - Written tests

Measurements and Geometry

Trigonometry - Problems on angle of elevation

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

- Solve problems involving angles of elevation
- Apply trigonometric ratios to real-life situations
- Calculate heights of towers, monuments and tall structures

- Draw sketches from word problems
- Identify given information and required values
- Apply appropriate trigonometric ratios
- Calculate heights and distances

How do we solve problems on angles of elevation?

- Mentor Essential Mathematics pg. 80
- Calculators
- Rulers
- Exercise books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Angle of depression
Trigonometry - Application in real life situations

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

- 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

- 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

- 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 do we use angles of depression to find distances?
How is trigonometry used in real life?

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

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

- Observation - Oral questions - Written tests
- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of triangle given two sides and an included angle
Area of Polygons - Problems on area of triangle

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

- Compute area of a triangle given two sides and an included acute angle
- Apply the formula Area = ½ab sin C
- Calculate areas of triangular flowerbeds, gardens and plots

- Identify triangular shapes from patterns in mats and frames
- Measure two sides and the included angle
- Calculate area using formula ½ab sin C
- Share work with classmates

How do we find the area of a triangle given two sides and an included angle?

- Mentor Essential Mathematics pg. 84
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 85
- Calculators
- Exercise books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Heron's Formula

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

- Determine the area of a triangle given three sides using Heron's Formula
- Calculate semi-perimeter of triangles
- Apply Heron's formula to irregular triangular plots and badges

- Draw right-angled triangle with given measurements
- Calculate perimeter and semi-perimeter
- Apply Heron's formula: √[s(s-a)(s-b)(s-c)]
- Compare with area calculated using other methods

How do we find the area of a triangle using Heron's Formula?

- Mentor Essential Mathematics pg. 86
- Calculators
- Rulers
- Scientific calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Problems using Heron's Formula
Area of Polygons - Area of a rhombus

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

- Solve problems on area of triangles using Heron's Formula
- Calculate areas of triangles with all three sides given
- Apply Heron's formula to triangular parks, gardens and stool tops

- Calculate areas of triangular cut-outs
- Work out areas of traditional stool tops
- Solve problems on triangular vegetable gardens
- Present solutions to peers

How is Heron's Formula applied in real life?

- Mentor Essential Mathematics pg. 87
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 88
- Rulers
- Protractors
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

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

- Calculate area of rhombus given side and included angle
- Apply the formula Area = a² sin θ
- Use rhombus area calculations for badges, logos and decorations

- Calculate area of parallelogram using ab sin θ
- Solve problems involving parallelograms
- Apply parallelogram area to kitchen floor designs and glass panels

- Draw rhombus-shaped badge with given side and angle
- Calculate lengths of diagonals using trigonometry
- Work out area using ½ × d₁ × d₂
- Verify using formula a² sin θ

- Calculate areas of decorative stones shaped as parallelograms
- Work out areas of kitchen floor plans
- Find angles when area is given
- Share solutions with peers

How do we find area of rhombus given side and angle?
How do we apply parallelogram area in real life?

- Mentor Essential Mathematics pg. 89
- Calculators
- Rulers
- Protractors
- Mentor Essential Mathematics pg. 92
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 94
- Calculators
- Rulers
- Exercise books
- Mentor Essential Mathematics pg. 95
- Protractors
- Calculators

- Observation - Oral questions - Written tests

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Area of a sector
Area of a Part of a Circle - Problems on area of sector
Area of a Part of a Circle - Area of a segment

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

- Determine the area of a sector of a circle
- Apply the formula Area = θ/360 × πr²
- Calculate areas of hand-fans, sprinkler coverage and cake toppings

- Solve problems on area of sectors
- Find radius or angle when area is given
- Apply sector area to garden sprinklers and billboard sections

- Draw circle and mark sector AOB
- Measure radius and angle subtended at centre
- Apply formula θ/360 × πr²
- Share findings with classmates

- Calculate area of sector-shaped artisan designs
- Work out angle when area and radius are given
- Determine radius when area and angle are given
- Present solutions to peers

How do we find the area of a sector?
How do we solve problems involving sectors?

- Mentor Essential Mathematics pg. 101
- Compasses
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 102
- Calculators
- Rulers
- Exercise books
- Mentor Essential Mathematics pg. 103
- Compasses
- Protractors
- Calculators

- Observation - Oral questions - Written assignments
- Observation - Oral questions - Written tests

Measurements and Geometry

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:

- Solve problems on area of segments
- Calculate areas of segment-shaped objects
- Apply segment area to window decorations and promotional stands

- Calculate area of kitchen garden segments
- Work out area of school logo designs
- Solve problems on triangular glass windows
- Share solutions with classmates

How do we solve problems involving segments?

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

- Observation - Oral questions - Written tests

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area of Solids - Surface area of a cone from its net
Surface Area of Solids - Surface area of cone using formula
Surface Area of Solids - Nets of pyramids

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

- Determine surface area of cones from nets
- Calculate area of sector and circular base
- Apply cone surface area to calculating material for making party hats and funnels

- Identify nets of square and rectangular-based pyramids
- Draw nets of pyramids
- Connect pyramid shapes to monuments, roof structures and tent designs

- Measure angle, radius of sector and radius of circular base
- Calculate area of sector using θ/360 × πr²
- Calculate area of circular base using πr²
- Add to get total surface area

- Make models of square and rectangular-based pyramids
- Cut and open pyramids along edges to get nets
- Measure edges and slant heights
- Identify base and triangular faces in nets

How do we find the surface area of a cone from its net?
What shapes make up the net of a pyramid?

- Mentor Essential Mathematics pg. 113
- Cone nets
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 114
- Calculators
- Exercise books
- Reference books

- Mentor Essential Mathematics pg. 115
- Manila paper
- Scissors
- Rulers

- Observation - Oral questions - Written tests
- Observation - Practical work - Written tests

Measurements and Geometry

Surface Area of Solids - Surface area of square-based pyramid
Surface Area of Solids - Surface area of rectangular-based pyramid

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

- Determine surface area of square-based pyramids from nets
- Calculate area of square base and triangular faces
- Apply to gift box designs, glass covers for skylights and decorative items

- Sketch net of square-based pyramid
- Calculate area of square base
- Calculate area of four identical triangular faces
- Add to get total surface area

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

- Mentor Essential Mathematics pg. 116
- Graph paper
- Calculators
- Rulers
- Mentor Essential Mathematics pg. 117

- Observation - Oral questions - Written assignments

Measurements and Geometry

Surface Area of Solids - Surface area of a sphere
Surface Area of Solids - Surface area of a hemisphere

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

- Calculate the surface area of a sphere
- Apply the formula 4πr²
- Use sphere surface area in calculating material for balls, globes and decorative spheres

- Collect spherical objects (soccer balls, marbles, oranges)
- Estimate and record radius of each object
- Calculate surface area using formula 4πr²
- Share work with other groups

How do we find the surface area of a sphere?

- Mentor Essential Mathematics pg. 120
- Spherical objects
- Rulers
- Calculators
- Mentor Essential Mathematics pg. 121
- Oranges
- Knives

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

- Determine surface area of frustum of a cone
- Identify top radius, bottom radius and slant height
- Apply frustum surface area to bucket designs and lampshade construction

- Make model of cone and cut parallel to base to form frustum
- Identify top radius (r), bottom radius (R) and slant height (L)
- Calculate lateral surface area: πL(R + r)
- Discuss formula for total surface area

How do we find surface area of a frustum of a cone?

- Mentor Essential Mathematics pg. 122
- Manila paper
- Scissors
- Calculators

- Observation - Oral questions - Written assignments

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

- Determine surface area of frustum of a square-based pyramid
- Calculate lateral surface area using ½(P₁ + P₂) × L
- Apply to lampshade designs, water tanks and display stands

- 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

- Make model of pyramid and cut parallel to base
- Identify top perimeter (P₁), bottom perimeter (P₂) and slant height (L)
- Calculate lateral surface area: ½(P₁ + P₂) × L
- Add areas of top and bottom to get total surface area

How do we solve problems on frustum surface area?
How do we find surface area of a frustum of a pyramid?

- Mentor Essential Mathematics pg. 124
- Calculators
- Exercise books
- Reference books

- Mentor Essential Mathematics pg. 125
- Manila paper
- Scissors
- Calculators

- Observation - Oral questions - Written tests
- Observation - Practical work - Written assignments

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