Measurements and Geometry

Similarity and Enlargement - Properties of similar figures

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

- Identify properties of similar figures
- Compare corresponding sides and angles of similar figures
- Relate similarity to real life objects like photographs and maps

- Collect objects from the environment and sort similar objects together
- Measure corresponding sides of similar triangles and determine ratios
- Measure corresponding angles of similar figures
- Discuss reasons why objects are considered similar

How do we identify similar figures in our environment?

- Mentor Essential Mathematics pg. 31
- Similar objects (containers, shapes)
- Rulers and protractors
- Digital resources
- Mentor Essential Mathematics pg. 33
- Protractors
- Rulers
- Cut-outs of similar shapes

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Centre of enlargement and linear scale factor
Similarity and Enlargement - Linear scale factor

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

- Determine the centre of enlargement of similar figures
- Locate the centre by joining corresponding vertices
- Recognize how enlargement is used in projectors and magnifying glasses

- Trace objects and images on plain paper
- Join corresponding vertices and extend lines to find centre of enlargement
- Measure distances from centre to object and image
- Discuss findings with peers

How do we locate the centre of enlargement?

- Mentor Essential Mathematics pg. 37
- Plain paper
- Rulers
- Pencils
- Mentor Essential Mathematics pg. 38
- Graph paper
- Calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

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:

- Draw the image of an object given centre and scale factor
- Construct enlarged images accurately
- Connect enlargement to photocopying and image resizing

- Draw objects on Cartesian plane
- Use given centre and scale factor to locate image points
- Construct images under different scale factors
- Compare object and image dimensions

How do we draw an image under enlargement?

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

- Observation - Practical work - Written assignments

Measurements and Geometry

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Volume scale factor

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

- Determine the volume scale factor of similar objects
- Calculate volumes of similar solids
- Apply volume scale factor to container sizing and packaging

- Collect similar containers of different sizes
- Calculate volumes of similar cuboids
- Determine ratio of volumes
- Establish relationship between linear and volume scale factors

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

- Mentor Essential Mathematics pg. 43
- Similar containers
- Rulers
- 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
Reflection - Lines of symmetry in plane figures

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
- Mentor Essential Mathematics pg. 50
- Paper cut-outs
- Scissors
- Various 2D objects

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection - Lines of symmetry in regular polygons
Reflection - Properties of reflection

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

- Determine lines of symmetry in regular polygons
- State that regular polygons have lines of symmetry equal to number of sides
- Connect symmetry to design patterns in fabric and architecture

- Draw regular polygons and identify lines of symmetry
- Trace diagrams and draw lines of symmetry
- State number of lines of symmetry for various alphabets
- Discuss patterns observed

What is the relationship between sides and lines of symmetry in regular polygons?

- Mentor Essential Mathematics pg. 52
- Rulers
- Protractors
- Plain paper
- Mentor Essential Mathematics pg. 53
- Plane mirrors

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection - Drawing images given object and mirror line
Reflection - Reflection along x = 0

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
- Mentor Essential Mathematics pg. 56
- Graph paper
- Pencils

- Observation - Practical work - Written tests

Measurements and Geometry

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 y = 0
- Determine coordinates of image points when reflected along x-axis
- Apply reflection concepts to architectural symmetry and graphic design

- Plot squares and rectangles on Cartesian plane
- Reflect shapes along line y = 0
- Compare coordinates before and after reflection
- Discuss the transformation rule for y = 0 reflection

What happens to coordinates when reflecting along y = 0?

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

- Observation - Oral questions - Written tests

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

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
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

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

- 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

How is cosine ratio applied in real life?

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

- Observation - Oral questions - Written assignments

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 - 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

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
Area of Polygons - Problems using 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
- Mentor Essential Mathematics pg. 87
- Exercise books
- Reference books

- Observation - Oral questions - Written assignments

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

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

- Observation - Oral questions - Written assignments

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 - Application in real life situations
Area of a Part of a Circle - Area of a 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

- Observation - Oral questions - Written tests

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
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

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

- 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

How do we find the surface area of a cone from its net?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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:

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

- Observation - Practical work - Written tests

Measurements and Geometry

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 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

- Observation - Oral questions - Written tests

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

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

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
- Mentor Essential Mathematics pg. 132
- Manila paper
- Sand
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

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:

- Calculate volume of cones given dimensions
- Determine capacity of cone-shaped containers
- Apply cone volume to funnel designs and conical flasks in laboratories

- Calculate volume of cone-shaped containers
- Convert volume to capacity in litres
- Work out radius or height when volume is given
- Solve problems on ice cream cones and funnels

How do we calculate the capacity of a cone?

- Mentor Essential Mathematics pg. 133
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 134
- Rulers
- Exercise books

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

- Determine volume of frustum of a cone
- Calculate volume by subtracting smaller cone from larger cone
- Apply to bucket designs and lampshade constructions

- Make model of cone and cut parallel to base
- Measure radii and heights of both cones
- Calculate volumes of original and cut-off cones
- Subtract to get volume of frustum

How do we find volume of a frustum of a cone?

- Mentor Essential Mathematics pg. 138
- Manila paper
- Scissors
- Calculators
- Mentor Essential Mathematics pg. 140
- Calculators
- Exercise books
- Digital resources

- Observation - Practical work - Written tests

Measurements and Geometry

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

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

- Determine volume of frustum of a pyramid
- Calculate volume by subtracting smaller pyramid from larger pyramid
- Apply to water storage tanks and traditional basket designs

- Make model of pyramid and cut parallel to base
- Measure dimensions of original and cut-off pyramids
- Calculate volumes of both pyramids
- Subtract to get volume of frustum

How do we find volume of a frustum of a pyramid?

- Mentor Essential Mathematics pg. 142
- Manila paper
- Scissors
- Calculators
- Mentor Essential Mathematics pg. 144
- Calculators
- Exercise books
- Reference books

- Observation - Practical work - Written tests

Measurements and Geometry

Volume and Capacity - Volume of composite solids

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

- Calculate volume of composite solids
- Combine volumes of different shapes
- Apply to school podiums, water reservoirs and combined storage structures

- Identify composite solids made of frustums and other shapes
- Break down into simpler shapes
- Calculate volume of each part
- Add to get total volume

How do we find volume of composite solids?

- Mentor Essential Mathematics pg. 145
- Calculators
- Models of solids
- Digital resources

- Observation - Oral questions - Written tests

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Commercial Arithmetic I - Preparing a budget
Commercial Arithmetic I - Balancing a budget

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

- Prepare a budget for clubs or societies
- Identify sources of income and expenditure
- Apply budgeting skills to planning school events and fundraising activities

- Study sample budget presentation for drama club
- Discuss sources of income and fund allocation
- Brainstorm creative ways to raise funds for clubs
- Discuss what happens if expenses exceed income

Why do we need a budget?

- Mentor Essential Mathematics pg. 148
- Sample budgets
- Exercise books
- Calculators
- Mentor Essential Mathematics pg. 149
- Calculators
- Chart paper

- Observation - Oral questions - Written assignments

Measurements and Geometry

Commercial Arithmetic I - Calculating discounts
Commercial Arithmetic I - Percentage discount

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

- Calculate discount given marked price and selling price
- Understand the meaning of discount in trading
- Apply discount calculations to shopping and back-to-school promotions

- Study posters showing discounted prices at supermarkets
- Calculate discount as: Marked price - Selling price
- Role-play shopping scenarios with discounts
- Share experiences on discounts seen in shops

What is a discount and how is it calculated?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Commercial Arithmetic I - Calculating commission
Commercial Arithmetic I - Percentage commission and tiered rates

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

- Observation - Role play - Written assignments

Measurements and Geometry

Commercial Arithmetic I - Profit and percentage profit
Commercial Arithmetic I - Loss and percentage loss

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

- Determine profit made in sale of goods
- Calculate percentage profit
- Apply profit calculations to small businesses like mandazi selling and craft making

- Discuss meaning of cost price and selling price
- Calculate profit: Selling price - Cost price
- Work out percentage profit: (Profit/Cost price) × 100%
- Solve problems on businesses making profits

How do we determine profit in business?

- Mentor Essential Mathematics pg. 155
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 157
- Case studies

- Observation - Oral questions - Written assignments

Measurements and Geometry

Commercial Arithmetic I - Currency exchange rates

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

- Read and interpret currency exchange rate tables
- Convert Kenyan shillings to foreign currencies
- Apply currency conversion when travelling abroad or importing goods

- Study exchange rate tables from Central Bank
- Discuss meaning of buying and selling rates
- Convert Kenya shillings to US dollars, Euros and Pounds
- Convert to East African currencies (Uganda, Tanzania, Rwanda)

How do exchange rates help travellers?

- Mentor Essential Mathematics pg. 160
- Currency exchange tables
- Calculators
- Digital resources

- Observation - Oral questions - Written assignments

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