Numbers and Algebra

Real Numbers - Odd and even numbers
Real Numbers - Prime and composite 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
- Mentor Essential Mathematics pg. 3
- Factor charts
- Number cards

- Oral questions - Written exercises - Observation

Numbers and Algebra

Real Numbers - Rational and irrational numbers
Real Numbers - Combined operations on rational numbers
Real Numbers - Combined operations on rational numbers
Real Numbers - Reciprocal of numbers

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

- Define rational and irrational numbers
- Classify real numbers as rational or irrational
- Relate rational numbers to everyday measurements like prices and quantities

- Use digital devices to search for meaning of rational and irrational numbers
- Classify given numbers as rational or irrational
- Discuss examples of rational numbers in daily transactions

Why are numbers important?

- Mentor Essential Mathematics pg. 5
- Digital devices
- Number charts
- Calculators
- Digital resources
- Mentor Essential Mathematics pg. 7
- Word problem cards
- Mentor Essential Mathematics pg. 8
- Thermometer charts
- Mentor Essential Mathematics pg. 9
- Scientific calculators
- Digital devices

- Oral questions - Written exercises - Observation

Numbers and Algebra

Real Numbers - Application of rational numbers
Indices - Powers and bases
Indices - Expressing numbers in index form

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
- Mentor Essential Mathematics pg. 14
- Calculators
- Digital resources

- Written tests - Portfolio - Class activities

Numbers and Algebra

Indices - Multiplication law
Indices - Division law

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

- State the multiplication law of indices
- Apply the multiplication law to simplify expressions
- Connect the multiplication law to calculating areas and volumes

- Write index numbers in expanded form
- Multiply numbers with the same base and add the powers
- Work out problems on area using index notation

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 15
- Index law charts
- Calculators
- Mentor Essential Mathematics pg. 16

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices - Power of a power
Indices - Zero index
Indices - Applying laws of indices

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
- Mentor Essential Mathematics pg. 19
- Digital devices

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices - Applying laws of indices in numerical computations
Indices - Problem solving with indices

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
- Mentor Essential Mathematics pg. 20
- Digital devices
- Calculators

- Written exercises - Class activities - Observation

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
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:

- 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
- Mentor Essential Mathematics pg. 25
- Calculators

- Oral questions - Written exercises - Observation

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
Quadratic Equations - Factorisation of expressions ax² + bx + c

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
- Mentor Essential Mathematics pg. 28
- Factor charts

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Equations - Solving by factorisation
Quadratic Equations - Solving equations with repeated roots
Quadratic Equations - Applications to real life problems

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
- Diagram charts

- Written exercises - Class activities - Oral questions

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
Similarity and Enlargement - Drawing images under enlargement

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
- Mentor Essential Mathematics pg. 37
- Plain paper
- Pencils
- Mentor Essential Mathematics pg. 38
- Graph paper
- Calculators
- Mentor Essential Mathematics pg. 40
- Geometrical instruments

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Drawing images on Cartesian plane
Similarity and Enlargement - Area scale factor
Similarity and Enlargement - Area scale factor calculations
Similarity and Enlargement - Volume scale factor

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

- Draw images on Cartesian plane given scale factor and centre
- Plot coordinates of image points
- Apply enlargement skills to graphic design and scaling images

- Plot objects on Cartesian plane
- Calculate image coordinates using scale factor
- Draw images under enlargement with different centres
- Verify accuracy of constructions

How do we enlarge figures on the Cartesian plane?

- Mentor Essential Mathematics pg. 41
- Graph paper
- Rulers
- Pencils
- Mentor Essential Mathematics pg. 42
- Calculators
- Rulers
- Mentor Essential Mathematics pg. 44
- Digital resources
- Mentor Essential Mathematics pg. 43
- Similar containers
- Calculators

- Observation - Practical work - Written tests

Measurements and Geometry

Similarity and Enlargement - Relating linear, area and volume scale factors
Similarity and Enlargement - Application to area

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Similarity and Enlargement - Application to volume
Reflection - Lines of symmetry in plane figures
Reflection - Lines of symmetry in regular polygons
Reflection - Properties of reflection
Reflection - Drawing images given object and mirror line

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
- Mentor Essential Mathematics pg. 53
- Plane mirrors
- Mentor Essential Mathematics pg. 54
- Plain paper
- Set squares

- Observation - Project assessment - Written tests

Measurements and Geometry

Reflection - Reflection along x = 0
Reflection - Reflection along y = 0
Reflection - Reflection along y = x
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 an image after reflection along the line x = 0
- Determine coordinates of image points when reflected along y-axis
- Connect reflection to creating symmetric designs and logos

- Plot triangles on Cartesian plane
- Reflect points along line x = 0
- Record coordinates of object and image points
- Observe pattern in coordinates after reflection

What happens to coordinates when reflecting along x = 0?

- Mentor Essential Mathematics pg. 56
- Graph paper
- Rulers
- Pencils
- Mentor Essential Mathematics pg. 58
- Calculators
- Mentor Essential Mathematics pg. 57
- Mentor Essential Mathematics pg. 60
- Plain paper
- Compasses
- Mentor Essential Mathematics pg. 61

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection - Application in real life situations
Trigonometry - Identifying sides of a right-angled triangle
Trigonometry - Tangent ratio

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Applications of tangent ratio
Trigonometry - Sine ratio
Trigonometry - Applications of sine ratio
Trigonometry - Cosine ratio
Trigonometry - Applications of cosine 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
- Mentor Essential Mathematics pg. 72
- Mentor Essential Mathematics pg. 74

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Sines and cosines of complementary angles
Trigonometry - Solving equations involving complementary angles
Trigonometry - Making a clinometer

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

- Relate sines and cosines of complementary angles
- Use calculator to find sines and cosines of complementary angles
- Apply complementary angle relationships to solving equations

- Discuss meaning of complementary angles
- Use calculator to complete table of sin θ and cos(90°-θ)
- Observe that sin α = cos(90°-α)
- Verify relationship using different angle pairs

What is the relationship between sine and cosine of complementary angles?

- Mentor Essential Mathematics pg. 75
- Scientific calculators
- Reference books
- Digital resources
- Mentor Essential Mathematics pg. 76
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 77
- Manila paper
- Blackboard protractor
- String and weight

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Angle of elevation
Trigonometry - Problems on angle of elevation
Trigonometry - Angle of depression

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
- Digital resources

- Observation - Practical work - 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
Area of Polygons - Area of rhombus given side and angle
Area of Polygons - Area of a parallelogram

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
- Mentor Essential Mathematics pg. 89
- Protractors
- Mentor Essential Mathematics pg. 92

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of parallelogram using ab sin θ
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:

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

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

How do we apply parallelogram area in real life?

- Mentor Essential Mathematics pg. 94
- Calculators
- Rulers
- Exercise books
- Mentor Essential Mathematics pg. 95
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 97
- 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
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:

- 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
- Mentor Essential Mathematics pg. 101
- Compasses
- Mentor Essential Mathematics pg. 102
- Exercise books

- Observation - Oral questions - Written assignments

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
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:

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

- Observation - Oral questions - Written assignments

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
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:

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Surface Area of Solids - Nets of pyramids
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
Surface Area of Solids - Surface area of a hemisphere

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
- Mentor Essential Mathematics pg. 117
- Mentor Essential Mathematics pg. 120
- Spherical objects
- Rulers
- Calculators
- Mentor Essential Mathematics pg. 121
- Oranges
- Knives

- Observation - Practical work - Written tests

Measurements and Geometry

Surface Area of Solids - Surface area of frustum of a cone
Surface Area of Solids - Problems on 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
- Mentor Essential Mathematics pg. 124
- Calculators
- Exercise books
- Reference books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Surface Area of Solids - Surface area of frustum of a pyramid
Surface Area of Solids - Problems on frustum of a pyramid
Volume and Capacity - Volume of a cone
Volume and Capacity - Problems on volume of cones

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
- Mentor Essential Mathematics pg. 127
- Calculators
- Exercise books
- Digital resources
- Mentor Essential Mathematics pg. 132
- Sand
- Mentor Essential Mathematics pg. 133
- Reference books

- Observation - Practical work - Written assignments

Measurements and Geometry

Volume and Capacity - Volume of cone given slant height
Volume and Capacity - Volume of a pyramid
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:

- Calculate volume of cone given slant height and radius
- Use Pythagoras theorem to find vertical height
- Apply to cone-shaped ornaments and decorative items

- Draw cone with slant height and radius labelled
- Apply Pythagorean relationship to find vertical height
- Calculate volume using V = ⅓πr²h
- Solve problems involving slant heights

How do we find volume when slant height is given?

- Mentor Essential Mathematics pg. 134
- Calculators
- Rulers
- Exercise books
- Mentor Essential Mathematics pg. 135
- Pyramid models
- Calculators
- Mentor Essential Mathematics pg. 136
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 138
- Manila paper
- Scissors
- 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
Volume and Capacity - Volume of composite solids

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

- Observation - Practical work - Written tests

Measurements and Geometry

Volume and Capacity - Capacity problems
Volume and Capacity - Combined problems
Commercial Arithmetic I - Preparing a budget

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

- Create balanced budgets showing income and expenditure
- Allocate funds appropriately including emergency funds
- Use budgeting in planning environmental clean-ups and science fairs

- Decide on club activities and estimate costs
- List all income sources with estimated amounts
- Allocate funds to various expenses
- Ensure total income equals total expenditure
- Present budget to class for peer learning

How do we ensure a budget is balanced?

- Mentor Essential Mathematics pg. 149
- Calculators
- Exercise books
- Chart paper
- Mentor Essential Mathematics pg. 150
- Price lists
- Shopping receipts
- Mentor Essential Mathematics pg. 151
- Price catalogues
- Exercise books
- Mentor Essential Mathematics pg. 153
- Reference books
- Mentor Essential Mathematics pg. 154
- Digital resources

- Observation - Budget presentation - 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

Statistics and Probability

Statistics - Frequency distribution tables for ungrouped data
Statistics - Constructing frequency distribution tables
Statistics - Mean of ungrouped data
Statistics - Mean from frequency distribution tables
Statistics - Mode of ungrouped data

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

- Define frequency and frequency distribution
- Collect and record data from the immediate environment
- Relate data collection to real-life surveys like shoe sizes and heights

- Collect data on shoe sizes of classmates
- Record data using tally marks
- Construct a frequency distribution table from collected data

How do we use statistics in day-to-day life?

- Mentor Essential Mathematics pg. 166
- Tally charts
- Data collection sheets
- Mentor Essential Mathematics pg. 167
- Data sets
- Tally charts
- Calculators
- Mentor Essential Mathematics pg. 168
- Frequency table templates
- Mentor Essential Mathematics pg. 169
- Frequency tables

- Oral questions - Observation - Practical exercises

Statistics and Probability

Statistics - Median of ungrouped data
Statistics - Comparing mean, mode and median
Statistics - Bar graphs
Statistics - Line graphs

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

- Define the median of a data set
- Determine the median by arranging data in order
- Apply median to find middle values in income distributions and test scores

- Arrange data in ascending or descending order
- Identify the middle value for odd number of items
- Calculate median for even number of items

How do we use statistics in day-to-day life?

- Mentor Essential Mathematics pg. 169
- Data sets
- Calculators
- Mentor Essential Mathematics pg. 170
- Calculators
- Data sets
- Mentor Essential Mathematics pg. 172
- Graph paper
- Rulers
- Pencils
- Mentor Essential Mathematics pg. 174

- Written exercises - Class activities - Oral questions

Statistics and Probability

Statistics - Pie charts
Statistics - Interpreting bar graphs

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

- Define a pie chart and calculate sector angles
- Draw pie charts from frequency tables
- Use pie charts to display budget allocations, time spent on activities and crop distributions

- Calculate angles for each category (value/total × 360°)
- Use protractor to draw sectors accurately
- Represent salary budgets, fruit sales and land use data

How do we use statistics in day-to-day life?

- Mentor Essential Mathematics pg. 176
- Protractors
- Compasses
- Calculators
- Mentor Essential Mathematics pg. 181
- Sample bar graphs

- Practical exercises - Observation - Class activities

Statistics and Probability

Statistics - Interpreting line graphs and pie charts
Probability - Equally likely outcomes
Probability - Calculating probability of equally likely outcomes

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

- Interpret data from line graphs and pie charts
- Draw conclusions from graphical representations
- Analyze trends in book sales, sleep patterns and company profits from graphs

- Read values and identify trends from line graphs
- Calculate actual values from pie chart sectors
- Compare data across different categories

How do we use statistics in day-to-day life?

- Mentor Essential Mathematics pg. 185
- Sample graphs and charts
- Calculators
- Protractors
- Mentor Essential Mathematics pg. 198
- Coins
- Dice
- Spinners
- Mentor Essential Mathematics pg. 199
- Coloured balls
- Number cards
- Calculators

- Written tests - Class activities - Portfolio

Statistics and Probability

Probability - Range of probability of an event
Probability - Mutually exclusive events

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

- State the range of probability (0 to 1)
- Identify certain and impossible events
- Relate probability range to everyday certainties like sunrise and impossibilities like flying unaided

- Discuss events that are certain (probability = 1)
- Identify impossible events (probability = 0)
- Calculate probability and verify it falls within 0 to 1

How do we apply probability in day-to-day life?

- Mentor Essential Mathematics pg. 201
- Event cards
- Probability scale charts
- Mentor Essential Mathematics pg. 202
- Digital devices
- Event scenario cards

- Oral questions - Written exercises - Observation

Statistics and Probability

Probability - Performing experiments on mutually exclusive events
Probability - Calculating probability of mutually exclusive events
Probability - Independent events
Probability - Calculating probability of independent events

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

- Perform experiments involving mutually exclusive events
- Record and analyze outcomes
- Apply experiments to spinning wheels, drawing cards and rolling dice

- Spin colour wheels and record outcomes
- Pick cards from a deck and note results
- Discuss why two mutually exclusive events cannot occur together

How do we apply probability in day-to-day life?

- Mentor Essential Mathematics pg. 203
- Spinners
- Dice
- Coloured cards
- Mentor Essential Mathematics pg. 204
- Calculators
- Probability problem cards
- Mentor Essential Mathematics pg. 206
- Coins
- Outcome tables
- Mentor Essential Mathematics pg. 207

- Practical exercises - Observation - Class activities