Numbers and Algebra

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

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
- Mentor Essential Mathematics pg. 22
- Calculators

- Oral questions - Written exercises - Observation

Numbers and Algebra

Quadratic Equations - Formation of quadratic expressions

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

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

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 23
- Rectangular cut-outs
- Charts

- Oral questions - Written exercises - Observation

Numbers and Algebra

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

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

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

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

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 24
- Diagram charts
- Graph paper
- Mentor Essential Mathematics pg. 25
- Calculators

- Written exercises - Class activities - Observation

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

- 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

How are quadratic equations applied in real life?

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

- Oral questions - Written exercises - Observation

Numbers and Algebra

Quadratic Equations - Factorisation of expressions ax² + bx + c

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

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

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

How are quadratic equations applied in real life?

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

- Written tests - Class activities - Observation

Numbers and Algebra

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

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

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

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

How are quadratic equations applied in real life?

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

- Written exercises - Class activities - Oral questions

Numbers and Algebra
Measurements and Geometry

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

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

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

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

How are quadratic equations applied in real life?

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

- Written tests - Portfolio - Class activities

Measurements and Geometry

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

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

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

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

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

- Mentor Essential Mathematics pg. 33
- Protractors
- Rulers
- Cut-outs of similar shapes
- Mentor Essential Mathematics pg. 37
- Plain paper
- Pencils
- Mentor Essential Mathematics pg. 38
- Graph paper
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Similarity and Enlargement - Drawing images under enlargement
Similarity and Enlargement - Drawing images on Cartesian plane
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:

- 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
- Mentor Essential Mathematics pg. 42
- Calculators
- Rulers
- Mentor Essential Mathematics pg. 44
- Digital resources

- Observation - Practical work - Written assignments

Measurements and Geometry

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Application to area

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

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

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

How do we apply area scale factor to solve problems?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

How do we apply volume scale factor to solve problems?

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

- Observation - Project assessment - Written tests

Measurements and Geometry

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection - Reflection along y = 0
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 = 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
- Mentor Essential Mathematics pg. 60
- Plain paper
- Compasses

- Observation - Oral questions - Written tests

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

- 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
- Mentor Essential Mathematics pg. 63
- Digital resources

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Identifying sides of a right-angled triangle
Trigonometry - Tangent ratio
Trigonometry - Applications of 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
- Mentor Essential Mathematics pg. 68
- Calculators
- Reference books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Sine ratio
Trigonometry - Applications of sine ratio
Trigonometry - Cosine 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
- Mentor Essential Mathematics pg. 71
- Calculators
- Digital resources
- Mentor Essential Mathematics pg. 72

- Observation - Oral questions - Written tests

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

- 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
- Mentor Essential Mathematics pg. 76
- Exercise 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
Trigonometry - Problems on angle of elevation

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

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

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

How do we use angles of elevation to find heights?

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

- Observation - Practical work - Written tests

Measurements and Geometry

Trigonometry - Angle of depression

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

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

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

How do we use angles of depression to find distances?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

How is trigonometry used in real life?

- Mentor Essential Mathematics pg. 81
- Calculators
- Digital resources
- Reference books
- Mentor Essential Mathematics pg. 84
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 85
- Exercise books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Heron's Formula
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:

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

- Observation - Oral questions - Written assignments

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

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

- 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

How do we find area of rhombus given side and angle?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Area of a regular pentagon
Area of Polygons - Problems on area of 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
- Mentor Essential Mathematics pg. 97
- Calculators
- Exercise books
- Digital resources

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

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

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

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

How are areas of polygons useful in real life?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

How do we find the area of a segment?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

- 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
- Mentor Essential Mathematics pg. 111
- Exercise books
- 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

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

- Observation - Oral questions - 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
Surface Area of Solids - Surface area of a sphere

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

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

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

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

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

How do we find the surface area of a hemisphere?

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

- Observation - Practical work - Written tests

Measurements and Geometry

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

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

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

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

How do we solve problems on frustum surface area?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area of Solids - Problems on frustum of a pyramid
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
Volume and Capacity - Volume of a pyramid

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
- Mentor Essential Mathematics pg. 135
- Pyramid models
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Volume and Capacity - Problems on volume of pyramids
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:

- Solve problems on volume of pyramids
- Calculate capacity of pyramid-shaped containers
- Apply pyramid volume to water tanks and yoghurt packaging boxes

- Calculate volume of underground water tanks
- Work out capacity of pyramid-shaped gift boxes
- Determine dimensions when volume is given
- Share solutions with peers

How is pyramid volume applied in real life?

- Mentor Essential Mathematics pg. 136
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 138
- Manila paper
- Scissors
- Calculators
- Mentor Essential Mathematics pg. 140
- Digital resources

- Observation - Oral questions - Written assignments

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
Volume and Capacity - Capacity problems

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

- Observation - Oral questions - Written tests

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