Measurements and Geometry

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:

- 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

- 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 do we identify lines of symmetry?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection - Properties of reflection

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection - Drawing images given object and mirror line

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

- Draw an image given an object and mirror line on a plane surface
- Construct perpendicular lines to locate image points
- Apply reflection skills to understanding kaleidoscopes and periscopes

- Trace figures and mirror lines on plain paper
- Construct perpendicular lines from vertices to mirror line
- Measure equal distances on opposite side of mirror line
- Join image points to form reflected image

How do we draw the image of an object after reflection?

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

- Observation - Practical work - Written tests

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

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

- Observation - Practical work - Written assignments

Measurements and Geometry

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

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

- Observation - Practical work - Written tests

Measurements and Geometry

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 Cartesian plane
- Identify the equation of the mirror line
- Connect mirror line concepts to coordinate geometry applications

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

How do we determine the equation of a mirror line?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection - Application in real life situations

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Identifying sides of a right-angled triangle

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Tangent ratio
Trigonometry - Applications of tangent 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

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Sine ratio

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

- Determine the sine of acute angles in a right-angled triangle
- Calculate sine ratios from given measurements
- Connect sine ratio to calculating heights of buildings and trees

- Measure opposite side and hypotenuse in similar triangles
- Calculate ratio of opposite to hypotenuse for angle θ
- Observe that the ratio is constant for the same angle
- Work out sine of angles in various triangles

What is the sine of an angle?

- Mentor Essential Mathematics pg. 69
- Rulers
- Protractors
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Applications of sine 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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Cosine ratio
Trigonometry - Applications of cosine ratio

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

- Determine the cosine of acute angles in a right-angled triangle
- Calculate cosine ratios from given measurements
- Apply cosine ratio to navigation and distance calculations

- Measure adjacent side and hypotenuse in similar triangles
- Calculate ratio of adjacent to hypotenuse for angle θ
- Observe that the ratio is constant for the same angle
- Work out cosine of angles in various triangles

What is the cosine of an angle?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Sines and cosines of 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

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Solving equations involving complementary angles

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

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

- 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 do we solve equations involving complementary angles?

- 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 - 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

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Application in real life situations

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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:

- 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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Problems on area of triangle
Area of Polygons - 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

- Observation - Oral questions - Written tests

Measurements and Geometry

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 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

- 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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of parallelogram using ab sin θ

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

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

- 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 apply parallelogram area in real life?

- Mentor Essential Mathematics pg. 94
- Calculators
- Rulers
- Exercise books

- Observation - Oral questions - Written tests

Measurements and Geometry

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 regular pentagon
- Divide pentagon into triangles and calculate total area
- Apply pentagon area to flower bed designs and pizza box lids

- Draw regular pentagon and divide into 5 triangles
- Measure radius from centre to vertex
- Calculate area of one triangle
- Multiply by 5 to get total area

How do we find the area of a regular pentagon?

- Mentor Essential Mathematics pg. 95
- Rulers
- Protractors
- Calculators

- 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 - 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

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

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

How do we find the area of a sector?

- Mentor Essential Mathematics pg. 101
- Compasses
- Protractors
- Calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

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:

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

- 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 solve problems involving sectors?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Area swept by gate

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

- Apply area of sector to find area swept by rotating objects
- Calculate area covered by opening gates and doors
- Use sector area in clock hand problems and fan blade designs

- Observe area covered by gate when it opens
- Measure angle of rotation and length of gate
- Calculate area swept using sector formula
- Discuss other applications

How do we calculate area swept by rotating objects?

- Mentor Essential Mathematics pg. 107
- Tape measures
- Protractors
- Calculators

- Observation - Practical work - 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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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:

- Identify the net of a cone
- Recognize parts of a cone net (sector and circular base)
- Relate cone shapes to everyday objects like ice cream cones and traffic cones

- Collect common solids with cone shapes from the environment
- Make model of closed cone using manila paper
- Open the cone along its slant to get net
- Identify sector and circular base in the net

What shapes make up the net of a cone?

- Mentor Essential Mathematics pg. 112
- Manila paper
- Scissors
- Cone-shaped objects
- Mentor Essential Mathematics pg. 113
- Cone nets
- Protractors
- Calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Surface Area of Solids - Surface area of cone using formula

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Surface Area of Solids - Nets of pyramids

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

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

- 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

What shapes make up the net of a pyramid?

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

- 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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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 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

- Observation - Practical work - Written tests

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

- 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

- 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 find surface area of a frustum of a pyramid?

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

- Observation - Practical work - Written assignments

Measurements and Geometry

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

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

- 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

- 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 find surface area of a frustum of a pyramid?

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

- 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