Numbers and Algebra

Real Numbers - Odd and even numbers

By the end of the lesson, the learner should be able to:
- Identify odd and even numbers
- Classify numbers as odd or even based on the ones place value
- Relate odd and even numbers to real life situations like sharing items equally

- Measure the height of classmates in centimetres and record in a table
- Classify each recorded number as odd or even
- Discuss with peers reasons for classification based on the digit in the ones place value

Why are numbers important?

- Mentor Essential Mathematics pg. 1
- Number cards
- Charts on odd and even numbers

- Oral questions - Written exercises - Observation

Numbers and Algebra

Real Numbers - Prime and composite numbers
Real Numbers - Rational and irrational numbers
Real Numbers - Rational and irrational numbers

By the end of the lesson, the learner should be able to:
- Define prime and composite numbers
- Classify numbers as prime or composite by identifying their factors
- Relate prime and composite numbers to grouping items in daily activities

- List factors of given numbers
- Classify numbers based on the number of factors
- Discuss how composite numbers help in dividing items into equal groups

Why are numbers important?

- Mentor Essential Mathematics pg. 3
- Factor charts
- Number cards
- Mentor Essential Mathematics pg. 5
- Digital devices
- Number charts
- Calculators
- Digital resources

- Oral questions - Written exercises - Class activities

Numbers and Algebra

Real Numbers - Combined operations on rational numbers
Real Numbers - Reciprocal of numbers

By the end of the lesson, the learner should be able to:
- Perform addition and subtraction of rational numbers
- Apply BODMAS rule in combined operations
- Relate combined operations to budgeting and shopping calculations

- Read and interpret case scenarios involving rational numbers
- Work out combined operations following BODMAS rule
- Discuss real-life situations like calculating total cost of items

Why are numbers important?

- Mentor Essential Mathematics pg. 7
- Calculators
- Word problem cards
- Mentor Essential Mathematics pg. 8
- Thermometer charts
- Mentor Essential Mathematics pg. 9
- Scientific calculators
- Digital devices

- Written exercises - Class activities - Portfolio

Numbers and Algebra

Real Numbers - Application of rational numbers
Indices - Powers and bases

By the end of the lesson, the learner should be able to:
- Apply rational numbers in solving real-life problems
- Solve problems involving fractions, decimals and mixed operations
- Connect rational numbers to daily activities like cooking, farming and finance

- Solve problems on sharing resources, measuring ingredients and calculating distances
- Discuss applications in budgeting, farming and construction
- Work with peers on real-life case scenarios

Why are numbers important?

- Mentor Essential Mathematics pg. 11
- Word problem cards
- Calculators
- Mentor Essential Mathematics pg. 13
- Number cards
- Charts on indices

- Written tests - Portfolio - Class activities

Numbers and Algebra

Indices - Expressing numbers in index form
Indices - Multiplication law

By the end of the lesson, the learner should be able to:
- Express whole numbers in simplest index form
- Express fractions in index form
- Apply index notation to scientific measurements and data

- Break down numbers into prime factors and express in index form
- Express fractions with numerator and denominator in index form
- Search for population data and express in index form

Why are indices important?

- Mentor Essential Mathematics pg. 14
- Calculators
- Digital resources
- Mentor Essential Mathematics pg. 15
- Index law charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices - Division law

By the end of the lesson, the learner should be able to:
- State the division law of indices
- Apply the division law to simplify expressions
- Relate division of indices to sharing and distribution problems

- Divide numbers with the same base by subtracting powers
- Simplify expressions using the division law
- Solve problems on distributing items among groups

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 16
- Index law charts
- Calculators

- Written tests - Class activities - Observation

Numbers and Algebra

Indices - Power of a power
Indices - Zero index

By the end of the lesson, the learner should be able to:
- State the power of a power law
- Apply the law to simplify expressions with powers raised to powers
- Apply the law to compound growth calculations

- Expand expressions with powers of powers
- Multiply indices when a power is raised to another power
- Discuss applications in compound interest calculations

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 17
- Index law charts
- Calculators
- Mentor Essential Mathematics pg. 18
- Calculators
- Index law charts

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices - Applying laws of indices

By the end of the lesson, the learner should be able to:
- Apply multiple laws of indices in computations
- Simplify complex expressions using combined laws
- Apply indices to scientific notation and large number calculations

- Work out computations requiring multiple index laws
- Simplify expressions with mixed operations
- Use digital resources to explore applications of indices

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 19
- Calculators
- Digital devices

- Written tests - Class activities - Portfolio

Numbers and Algebra

Indices - Applying laws of indices in numerical computations

By the end of the lesson, the learner should be able to:
- Solve complex problems using laws of indices
- Evaluate numerical expressions involving indices
- Apply indices to solve real-world problems in science and technology

- Evaluate expressions combining all laws of indices
- Solve word problems involving indices
- Discuss applications in computing and scientific calculations

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 19
- Calculators
- Digital resources

- Written exercises - Class activities - Observation

Numbers and Algebra

Indices - Problem solving with indices
Quadratic Equations - Formation of algebraic expressions

By the end of the lesson, the learner should be able to:
- Apply indices to solve practical problems
- Work collaboratively to solve index problems
- Connect indices to technological applications like data storage

- Work with peers on practical problems involving indices
- Present solutions and discuss different approaches
- Research applications of indices in computer memory and data

Why are indices important?

- Mentor Essential Mathematics pg. 20
- Digital devices
- Calculators
- Mentor Essential Mathematics pg. 21
- Word problem cards
- Charts

- Portfolio - Observation - Written tests

Numbers and Algebra

Quadratic Equations - Formation of algebraic expressions from real life

By the end of the lesson, the learner should be able to:
- Form complex algebraic expressions from multiple quantities
- Simplify algebraic expressions
- Apply algebraic expressions to calculate costs, distances and areas

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

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 22
- Word problem cards
- Calculators

- Written exercises - Class activities - Portfolio

Numbers and Algebra

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

By the end of the lesson, the learner should be able to:
- Identify quadratic expressions
- Form quadratic expressions by multiplying binomials
- Relate quadratic expressions to calculating areas of rectangles

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

- Oral questions - Written exercises - Observation

Numbers and Algebra

Quadratic Equations - Formation of quadratic equations

By the end of the lesson, the learner should be able to:
- Distinguish between quadratic expressions and equations
- Form quadratic equations from given conditions
- Apply quadratic equations to problems on area and dimensions

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

How are quadratic equations applied in real life?

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

- Written exercises - Class activities - Oral questions

Numbers and Algebra

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

By the end of the lesson, the learner should be able to:
- Form quadratic equations from various word problems
- Interpret real-life situations as quadratic equations
- Model age, product and sharing problems using quadratic equations

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

How are quadratic equations applied in real life?

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

- Written tests - Class activities - Portfolio

Numbers and Algebra

Quadratic Equations - Factorisation by grouping

By the end of the lesson, the learner should be able to:
- Factorise quadratic expressions by grouping
- Apply the grouping method to various expressions
- Verify factorisation by expanding the factors

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

How are quadratic equations applied in real life?

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

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Equations - Factorisation of expressions ax² + bx + c
Quadratic Equations - Solving by factorisation

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
- Worked examples charts

- Written tests - Class activities - Observation

Numbers and Algebra

Quadratic Equations - Solving equations with repeated roots

By the end of the lesson, the learner should be able to:
- Solve quadratic equations with repeated roots
- Identify perfect square trinomials
- Interpret the meaning of repeated roots in context

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

How are quadratic equations applied in real life?

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

- Oral questions - Written exercises - Observation

Numbers and Algebra
Measurements and Geometry
Measurements and Geometry

Quadratic Equations - Applications to real life problems
Trigonometry - Identifying sides of a right-angled triangle
Trigonometry - Tangent ratio

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

- Written tests - Portfolio - Class activities

Measurements and Geometry

Trigonometry - Applications of tangent ratio
Trigonometry - Sine ratio
Trigonometry - Applications of 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
- Mentor Essential Mathematics pg. 71
- Digital resources

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Cosine ratio
Trigonometry - Applications of cosine ratio
Trigonometry - Sines and cosines of complementary angles

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
- 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
Trigonometry - Making a clinometer

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Angle of elevation

By the end of the lesson, the learner should be able to:
- Apply trigonometric ratios to angles of elevation
- Calculate heights using angles of elevation
- Use angle of elevation in determining heights of flagpoles, trees and buildings

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

How do we use angles of elevation to find heights?

- Mentor Essential Mathematics pg. 79
- Clinometers
- Tape measures
- Calculators

- Observation - Practical work - Written tests

Measurements and Geometry

Trigonometry - Problems on angle of elevation

By the end of the lesson, the learner should be able to:
- Solve problems involving angles of elevation
- Apply trigonometric ratios to real-life situations
- Calculate heights of towers, monuments and tall structures

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

How do we solve problems on angles of elevation?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

By the end of the lesson, the learner should be able to:
- Apply trigonometric ratios to angles of depression
- Calculate distances using angles of depression
- Use angle of depression in aviation and marine navigation

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Area of triangle given two sides and an included angle
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:
- 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
- Mentor Essential Mathematics pg. 86
- Scientific calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Problems using Heron's Formula
Area of Polygons - Area of a rhombus
Area of Polygons - Area of rhombus given side and angle

By the end of the lesson, the learner should be able to:
- Solve problems on area of triangles using Heron's Formula
- Calculate areas of triangles with all three sides given
- Apply Heron's formula to triangular parks, gardens and stool tops

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

How is Heron's Formula applied in real life?

- Mentor Essential Mathematics pg. 87
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 88
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 89
- Protractors

- Observation - Oral questions - Written tests

Measurements and Geometry

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

By the end of the lesson, the learner should be able to:
- Determine the area of a parallelogram
- Apply the formula Area = base × perpendicular height
- Calculate areas of parallelogram-shaped solar panels and floor plans

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

How do we find the area of a parallelogram?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Problems on area of pentagon

By the end of the lesson, the learner should be able to:
- Solve problems on area of regular pentagons
- Calculate areas of pentagon-shaped objects
- Apply pentagon area to trampoline covers and decorative designs

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

How is area of pentagon applied in real life?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Area of a regular hexagon
Area of Polygons - Application in real life situations

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
- Mentor Essential Mathematics pg. 98
- Calculators
- Digital resources
- Reference books

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

By the end of the lesson, the learner should be able to:
- Determine the area of a sector of a circle
- Apply the formula Area = θ/360 × πr²
- Calculate areas of hand-fans, sprinkler coverage and cake toppings

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

- Observation - Oral questions - Written assignments

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

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
- Mentor Essential Mathematics pg. 108
- Rulers
- Digital resources

- Observation - Oral questions - Written tests

Measurements and Geometry

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:
- Solve problems involving clock hands and sprinklers
- Calculate area covered by minute and hour hands
- Apply sector area to irrigation system design and garden planning

- Calculate area swept by minute hand of clock
- Work out area covered by hour hand moving through 180°
- Determine area watered by rotating sprinklers
- Discuss efficient irrigation systems

How do we apply sector area to clocks and sprinklers?

- Mentor Essential Mathematics pg. 110
- Calculators
- Clocks
- Reference books
- Mentor Essential Mathematics pg. 111
- Exercise books
- Digital resources
- Mentor Essential Mathematics pg. 112
- Manila paper
- Scissors
- Cone-shaped objects

- Observation - Oral questions - Written assignments

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

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
Volume and Capacity - Volume of frustum of a cone

By the end of the lesson, the learner should be able to:
- Determine volume of square and rectangular-based pyramids
- Apply the formula V = ⅓ × base area × height
- Calculate volumes of poultry houses and storage structures

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

How do we find the volume of a pyramid?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

By the end of the lesson, the learner should be able to:
- Solve problems on volume of frustum of a cone
- Calculate capacity of frustum-shaped containers
- Apply to traditional cooking pots, water collection containers and metallic buckets

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

How do we calculate capacity of frustum-shaped containers?

- Mentor Essential Mathematics pg. 140
- Calculators
- Exercise books
- Digital resources
- Mentor Essential Mathematics pg. 142
- Manila paper
- Scissors
- Calculators
- Mentor Essential Mathematics pg. 144
- Reference books

- Observation - Oral questions - Written assignments

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
Volume and Capacity - Combined 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
- Mentor Essential Mathematics pg. 147
- Digital resources
- Reference books

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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
- Mentor Essential Mathematics pg. 150
- Price lists
- Shopping receipts

- Observation - Oral questions - Written assignments

Measurements and Geometry

Commercial Arithmetic I - Percentage discount
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 percentage discount
- Determine selling price after discount
- Compare discounts offered by different shops to make wise purchasing decisions

- Calculate percentage discount using formula: (Discount/Marked price) × 100%
- Work out selling price when percentage discount is given
- Compare prices at different shops offering different discounts
- Determine which shop offers better value

How do we calculate percentage discount?

- Mentor Essential Mathematics pg. 151
- Calculators
- Price catalogues
- Exercise books
- Mentor Essential Mathematics pg. 153
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 154
- Digital resources

- Observation - Oral questions - Written tests

Measurements and Geometry

Commercial Arithmetic I - Profit and percentage profit
Commercial Arithmetic I - Loss and percentage loss
Commercial Arithmetic I - Currency exchange rates
Commercial Arithmetic I - Currency conversion problems

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
- Mentor Essential Mathematics pg. 160
- Currency exchange tables
- Digital resources
- Mentor Essential Mathematics pg. 162
- Exercise books

- Observation - Oral questions - Written assignments