Measurements and Geometry

Area of Polygons - Area of triangle given two sides and an included angle
Area of Polygons - Problems on area of triangle

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

- Compute area of a triangle given two sides and an included acute angle
- Apply the formula Area = ½ab sin C
- Calculate areas of triangular flowerbeds, gardens and plots

- Identify triangular shapes from patterns in mats and frames
- Measure two sides and the included angle
- Calculate area using formula ½ab sin C
- Share work with classmates

How do we find the area of a triangle given two sides and an included angle?

- Mentor Essential Mathematics pg. 84
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 85
- Calculators
- Exercise books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Heron's Formula
Area of Polygons - Problems using Heron's Formula

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

- Determine the area of a triangle given three sides using Heron's Formula
- Calculate semi-perimeter of triangles
- Apply Heron's formula to irregular triangular plots and badges

- Draw right-angled triangle with given measurements
- Calculate perimeter and semi-perimeter
- Apply Heron's formula: √[s(s-a)(s-b)(s-c)]
- Compare with area calculated using other methods

How do we find the area of a triangle using Heron's Formula?

- Mentor Essential Mathematics pg. 86
- Calculators
- Rulers
- Scientific calculators
- Mentor Essential Mathematics pg. 87
- Exercise books
- Reference books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of a rhombus
Area of Polygons - Area of rhombus given side and angle

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

- Determine the area of a rhombus given the diagonals
- Apply the formula Area = ½ × d₁ × d₂
- Calculate areas of rhombus-shaped tiles, kites and floor patterns

- Draw rhombus and measure diagonals
- Calculate areas of triangles formed by diagonals
- Add areas to get total area of rhombus
- Verify using formula ½ × d₁ × d₂

How do we find the area of a rhombus?

- Mentor Essential Mathematics pg. 88
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 89
- Calculators
- Protractors

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

- Determine the area of a parallelogram
- Apply the formula Area = base × perpendicular height
- Calculate areas of parallelogram-shaped solar panels and floor plans

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

How do we find the area of a parallelogram?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of a regular pentagon

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

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

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

How do we find the area of a regular pentagon?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Problems on area of pentagon

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

- Solve problems on area of regular pentagons
- Calculate areas of pentagon-shaped objects
- Apply pentagon area to trampoline covers and decorative designs

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

How is area of pentagon applied in real life?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Area of a regular hexagon

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

- Determine the area of a regular hexagon
- Divide hexagon into 6 triangles and calculate total area
- Apply hexagon area to floor tiling and road sign designs

- Draw regular hexagon and divide into 6 triangles
- Measure radius from centre to vertex
- Calculate area of one triangle
- Multiply by 6 to get total area

How do we find the area of a regular hexagon?

- Mentor Essential Mathematics pg. 96
- Rulers
- Protractors
- Calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

How are areas of polygons useful in real life?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

- Calculate area of sector-shaped artisan designs
- Work out angle when area and radius are given
- Determine radius when area and angle are given
- Present solutions to peers

How do we solve problems involving sectors?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

- Solve problems on area of segments
- Calculate areas of segment-shaped objects
- Apply segment area to window decorations and promotional stands

- Calculate area of kitchen garden segments
- Work out area of school logo designs
- Solve problems on triangular glass windows
- Share solutions with classmates

How do we solve problems involving segments?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

- Calculate areas of curved paths and decorations
- Solve problems on sector and segment areas
- Apply concepts to fan blade designs and table cloth decorations

- Calculate area of curved paths in school compound
- Work out area of decorations on table cloths
- Solve problems on fanning papers
- Present solutions to class

How are areas of parts of circles applied in design?

- Mentor Essential Mathematics pg. 108
- Calculators
- Rulers
- Digital resources
- Mentor Essential Mathematics pg. 110
- Clocks
- Reference books

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Combined problems
Surface Area of Solids - Nets of cones

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

- Solve combined problems on sectors and segments
- Apply area of parts of circles in various contexts
- Use concepts in calculating metal sheet areas and flower garden segments

- Calculate area of metal sheet in segment shape
- Work out area of flower segments in circular gardens
- Solve problems on staffroom doors and gates
- Review all concepts on area of parts of circles

Where do we use area of part of a circle in real life?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area of Solids - Surface area of a cone from its net
Surface Area of Solids - Surface area of cone using formula

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

- Determine surface area of cones from nets
- Calculate area of sector and circular base
- Apply cone surface area to calculating material for making party hats and funnels

- Measure angle, radius of sector and radius of circular base
- Calculate area of sector using θ/360 × πr²
- Calculate area of circular base using πr²
- Add to get total surface area

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area of Solids - Nets of pyramids
Surface Area of Solids - Surface area of square-based pyramid

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

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

- Make models of square and rectangular-based pyramids
- Cut and open pyramids along edges to get nets
- Measure edges and slant heights
- Identify base and triangular faces in nets

What shapes make up the net of a pyramid?

- Mentor Essential Mathematics pg. 115
- Manila paper
- Scissors
- Rulers
- Mentor Essential Mathematics pg. 116
- Graph paper
- Calculators

- Observation - Practical work - Written tests

Measurements and Geometry

Surface Area of Solids - Surface area of rectangular-based pyramid
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 rectangular-based pyramids
- Calculate areas of different pairs of triangular faces
- Apply to camping tent designs, monument construction and roof structures

- Draw net of rectangular-based pyramid
- Calculate area of rectangular base
- Work out areas of two pairs of triangular faces
- Add all areas to get total surface area

How do we find surface area of a rectangular-based pyramid?

- Mentor Essential Mathematics pg. 117
- Graph paper
- Calculators
- Rulers
- Mentor Essential Mathematics pg. 120
- Spherical objects
- Rulers
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area of Solids - Surface area of a hemisphere

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

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

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

How do we find the surface area of a hemisphere?

- Mentor Essential Mathematics pg. 121
- Oranges
- Knives
- Calculators

- Observation - Practical work - Written tests

Measurements and Geometry

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

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

- Determine surface area of frustum of a cone
- Identify top radius, bottom radius and slant height
- Apply frustum surface area to bucket designs and lampshade construction

- Make model of cone and cut parallel to base to form frustum
- Identify top radius (r), bottom radius (R) and slant height (L)
- Calculate lateral surface area: πL(R + r)
- Discuss formula for total surface area

How do we find surface area of a frustum of a cone?

- Mentor Essential Mathematics pg. 122
- Manila paper
- Scissors
- Calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Surface Area of Solids - Problems on frustum of a cone

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

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

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

How do we solve problems on frustum surface area?

- Mentor Essential Mathematics pg. 124
- Calculators
- Exercise books
- Reference books

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

- Determine surface area of frustum of a square-based pyramid
- Calculate lateral surface area using ½(P₁ + P₂) × L
- Apply to lampshade designs, water tanks and display stands

- Make model of pyramid and cut parallel to base
- Identify top perimeter (P₁), bottom perimeter (P₂) and slant height (L)
- Calculate lateral surface area: ½(P₁ + P₂) × L
- Add areas of top and bottom to get total surface area

How do we find surface area of a frustum of a pyramid?

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

- Observation - Practical work - Written assignments

Measurements and Geometry

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

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

- Solve problems on surface area of frustums of pyramids
- Calculate surface area of rectangular-based pyramid frustums
- Apply to hollow lampshades, counter designs, statue stands and open water tanks

- Calculate areas of trapezoidal faces for rectangular-based frustums
- Work out surface area of hollow lampshades (lateral only)
- Solve problems on counters and statue stands
- Determine material needed for multiple lampshades

How are frustums of pyramids used in real life?

- Mentor Essential Mathematics pg. 127
- Calculators
- Exercise books
- Digital resources
- Mentor Essential Mathematics pg. 132
- Manila paper
- Sand
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Volume and Capacity - Problems on volume of cones
Volume and Capacity - Volume of cone given slant height

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

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

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

How do we calculate the capacity of a cone?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

- Determine volume of square and rectangular-based pyramids
- Apply the formula V = ⅓ × base area × height
- Calculate volumes of poultry houses and storage structures

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

How do we find the volume of a pyramid?

- Mentor Essential Mathematics pg. 135
- Pyramid models
- Rulers
- Calculators
- Mentor Essential Mathematics pg. 136
- Calculators
- Exercise books
- Reference books

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

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

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

- Observation - Practical work - Written tests

Measurements and Geometry

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

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

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

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

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

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

- Observation - Practical work - Written tests

Measurements and Geometry

Volume and Capacity - Volume of composite solids

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

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

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

How do we find volume of composite solids?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Volume and Capacity - Capacity problems

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

- Convert between volume and capacity units
- Solve problems involving litres and millilitres
- Apply to water storage, milk packaging and fuel tank capacities

- Convert cubic metres to litres
- Convert cubic centimetres to millilitres
- Calculate capacity of various containers
- Solve real-life problems on water and fuel storage

Why is the knowledge of volume and capacity useful?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Volume and Capacity - Combined problems

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

- Solve combined problems on volume and capacity
- Apply volume concepts to various real-life situations
- Use volume and capacity in water trough designs for livestock and reservoir planning

- Solve mixed problems on cones, pyramids and frustums
- Calculate capacity of mugs, buckets and tanks
- Work out dimensions when capacity is given
- Review all concepts on volume and capacity

How do we apply volume and capacity in daily life?

- Mentor Essential Mathematics pg. 147
- Calculators
- Digital resources
- Reference books

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

Why do we need a budget?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

What is a discount and how is it calculated?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

- Calculate commission earned on sales
- Determine commission as percentage of total sales
- Apply commission calculations to sales jobs and real estate transactions

- Brainstorm jobs where people earn commission
- Role-play sales scenarios where commission is earned
- Calculate commission using: Commission = Rate × Total sales
- Discuss advantages of commission to companies and employees

Why do companies offer commission?

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

- Observation - Role play - Written assignments

Measurements and Geometry

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

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

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

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

How do we determine profit in business?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Commercial Arithmetic I - Currency exchange rates

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

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

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

How do exchange rates help travellers?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Commercial Arithmetic I - Currency conversion problems

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

- Convert foreign currencies to Kenyan shillings
- Solve problems involving buying and selling rates
- Apply currency conversion to international trade, remittances and travel budgeting

- Convert US dollars, Euros and Yen to Kenya shillings
- Use buying rate when bank buys foreign currency
- Use selling rate when bank sells foreign currency
- Calculate amount received after currency exchange round trips

How do we convert currencies using exchange rates?

- Mentor Essential Mathematics pg. 162
- Currency exchange tables
- Calculators
- Exercise books

- Observation - Oral questions - Written tests

Statistics and Probability

Statistics - Frequency distribution tables for ungrouped data
Statistics - Constructing frequency distribution tables

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

- Oral questions - Observation - Practical exercises

Statistics and Probability

Statistics - Mean of ungrouped data
Statistics - Mean from frequency distribution tables

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

- Define the mean of a data set
- Calculate the mean of ungrouped data
- Connect mean to finding average scores, prices and measurements in daily life

- Collect data on number of children in families
- Calculate the sum of all values and divide by count
- Discuss average marks, heights and incomes

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

- Mentor Essential Mathematics pg. 167
- Calculators
- Data collection sheets
- Mentor Essential Mathematics pg. 168
- Frequency table templates

- Oral questions - Written exercises - Class activities

Statistics and Probability

Statistics - Mode of ungrouped data
Statistics - Median of ungrouped data

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

- Define the mode of a data set
- Identify the mode from raw data and frequency tables
- Relate mode to finding most popular items like favourite colours, foods or transport means

- Identify the most frequently occurring value in data sets
- Determine mode from frequency distribution tables
- Discuss applications in market research and voting

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

- Mentor Essential Mathematics pg. 169
- Data sets
- Frequency tables
- Calculators

- Oral questions - Written exercises - Observation

Statistics and Probability

Statistics - Comparing mean, mode and median
Statistics - Bar graphs

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

- Calculate mean, mode and median from the same data set
- Compare the three measures of central tendency
- Choose appropriate measures for analyzing cattle masses, learner ages and product prices

- Calculate all three measures from given data
- Compare and discuss which measure best represents the data
- Solve problems involving all three measures

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

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

- Written tests - Class activities - Portfolio

Statistics and Probability

Statistics - Line graphs

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

- Define a line graph and its uses
- Draw line graphs from given data
- Apply line graphs to show temperature changes, sales trends and growth patterns

- Plot points on a Cartesian plane
- Join points with straight lines
- Draw line graphs for temperature, rainfall and production data

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

- Mentor Essential Mathematics pg. 174
- Graph paper
- Rulers
- Pencils

- Practical exercises - Observation - Written exercises

Statistics and Probability

Statistics - Pie charts

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

- Practical exercises - Observation - Class activities

Statistics and Probability

Statistics - Interpreting bar graphs

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

- Read and interpret information from bar graphs
- Answer questions based on bar graph data
- Extract information from graphs showing rainfall, sports attendance and hospital discharges

- Identify scales used on axes
- Read values from bars accurately
- Calculate totals, differences and comparisons from bar graphs

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

- Mentor Essential Mathematics pg. 181
- Sample bar graphs
- Calculators

- Oral questions - Written exercises - Class activities

Statistics and Probability

Statistics - Interpreting line graphs and pie charts

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

- Written tests - Class activities - Portfolio

Statistics and Probability

Probability - Equally likely outcomes

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

- Define probability and equally likely outcomes
- Perform experiments with coins and dice
- Relate probability to games of chance and weather prediction

- Toss coins and record outcomes
- Roll dice and list possible outcomes
- Discuss probability spaces for simple experiments

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

- Mentor Essential Mathematics pg. 198
- Coins
- Dice
- Spinners

- Practical exercises - Observation - Oral questions

Statistics and Probability

Probability - Calculating probability of equally likely outcomes

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

- State the probability formula
- Calculate probability of equally likely outcomes
- Apply probability to picking cards, selecting items and drawing balls from bags

- Calculate probability using P(E) = n(E)/n(S)
- Solve problems on picking coloured balls, numbered cards
- Discuss probability of events in sports and games

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

- Mentor Essential Mathematics pg. 199
- Coloured balls
- Number cards
- Calculators

- Written exercises - Class activities - Oral questions

Statistics and Probability

Probability - Range of probability of an event

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

- Oral questions - Written exercises - Observation

Statistics and Probability

Probability - Mutually exclusive events

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

- Define mutually exclusive events
- Identify mutually exclusive events in real situations
- Relate mutually exclusive events to choices like selecting one job from two offers at the same time

- Use digital resources to research mutually exclusive events
- Classify given events as mutually exclusive or not
- Discuss examples in elections, travel choices and course selection

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

- Mentor Essential Mathematics pg. 202
- Digital devices
- Event scenario cards

- Written exercises - Class activities - Oral questions

Statistics and Probability

Probability - Performing experiments on mutually exclusive 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

- Practical exercises - Observation - Class activities

Statistics and Probability

Probability - Calculating probability of mutually exclusive events

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

- Calculate probability of mutually exclusive events
- Apply the addition rule: P(A or B) = P(A) + P(B)
- Solve problems on selecting items, choosing colours and picking numbers

- Calculate probability of one event or another occurring
- Solve problems involving picking pens, balls of different colours
- Discuss probability of rolling different numbers on a die

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

- Mentor Essential Mathematics pg. 204
- Calculators
- Probability problem cards

- Written exercises - Class activities - Written tests

Statistics and Probability

Probability - Independent events

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

- Define independent events
- Perform experiments involving independent events
- Relate independent events to tossing coins while rolling dice or weather on different days

- Toss a coin and roll a die simultaneously
- List all possible combined outcomes
- Discuss why outcome of one event doesn't affect the other

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

- Mentor Essential Mathematics pg. 206
- Coins
- Dice
- Outcome tables

- Practical exercises - Observation - Oral questions

Statistics and Probability

Probability - Calculating probability of independent events

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

- Calculate probability of independent events
- Apply the multiplication rule: P(A and B) = P(A) × P(B)
- Solve problems on passing exams, hitting targets and machine breakdowns

- Calculate probability of both events occurring
- Solve problems involving learners passing tests, machines working
- Discuss probability in archery, darts and sports predictions

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

- Mentor Essential Mathematics pg. 207
- Calculators
- Probability problem cards

- Written tests - Class activities - Portfolio