Measurements and Geometry

Surface Area of Solids - Nets of cones

By the end of the lesson, the learner should be able to:
- Identify the net of a cone
- Recognize parts of a cone net (sector and circular base)
- Relate cone shapes to everyday objects like ice cream cones and traffic cones

In groups, learners are guided to:
- Collect common solids with cone shapes from the environment
- Make model of closed cone using manila paper
- Open the cone along its slant to get net
- Identify sector and circular base in the net

What shapes make up the net of a cone?

- 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

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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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
Surface Area of Solids - Surface area of a hemisphere

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

In groups, learners are guided to:
- 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
- Mentor Essential Mathematics pg. 121
- Oranges
- Knives

- Observation - Oral questions - 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

In groups, learners are guided to:
- 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
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

In groups, learners are guided to:
- 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

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

In groups, learners are guided to:
- 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

- Observation - Oral questions - Written tests

Measurements and Geometry

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 the volume of a cone
- Apply the formula V = ⅓πr²h
- Relate cone volume to measuring ingredients and ice cream scoops

In groups, learners are guided to:
- Make models of cone and cylinder with equal base radius and height
- Fill cone with sand and empty into cylinder
- Count number of cones needed to fill cylinder
- Establish relationship between cone and cylinder volumes

What is the relationship between volume of a cone and cylinder?

- Mentor Essential Mathematics pg. 132
- Manila paper
- Sand
- Calculators
- Mentor Essential Mathematics pg. 133
- Calculators
- Exercise books
- Reference books

- Observation - Oral questions - 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

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

In groups, learners are guided to:
- 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

- Observation - Oral questions - Written assignments

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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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
Commercial Arithmetic I - Preparing a budget
Commercial Arithmetic I - Balancing a budget

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

In groups, learners are guided to:
- 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
- Mentor Essential Mathematics pg. 148
- Sample budgets
- Exercise books
- Calculators
- Mentor Essential Mathematics pg. 149
- Chart paper

- Observation - Oral questions - Written tests

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

In groups, learners are guided to:
- 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
Commercial Arithmetic I - Profit and percentage profit

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

In groups, learners are guided to:
- 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
- Mentor Essential Mathematics pg. 155

- Observation - Role play - Written assignments

Measurements and Geometry

Commercial Arithmetic I - Loss and percentage loss
Commercial Arithmetic I - Currency exchange rates

By the end of the lesson, the learner should be able to:
- Determine loss incurred in sale of goods
- Calculate percentage loss
- Apply loss calculations to perishable goods like fruits and vegetables

In groups, learners are guided to:
- Discuss situations where businesses make losses
- Calculate loss: Cost price - Selling price
- Work out percentage loss: (Loss/Cost price) × 100%
- Discuss how to avoid losses in business

How do we calculate loss in business?

- Mentor Essential Mathematics pg. 157
- Calculators
- Exercise books
- Case studies
- Mentor Essential Mathematics pg. 160
- Currency exchange tables
- Digital resources

- Observation - Oral questions - Written tests

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

In groups, learners are guided to:
- 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
Statistics - Mean 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

In groups, learners are guided to:
- 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

- Oral questions - Observation - Practical exercises

Statistics and Probability

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

By the end of the lesson, the learner should be able to:
- Calculate the mean using frequency distribution tables
- Apply the formula: Mean = Σfx/Σf
- Use mean to analyze average wages, temperatures and production outputs

In groups, learners are guided to:
- Construct frequency tables with fx column
- Calculate mean using the formula
- Solve problems on average mass, height and scores

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

- Mentor Essential Mathematics pg. 168
- Calculators
- Frequency table templates
- Mentor Essential Mathematics pg. 169
- Data sets
- Frequency tables

- Written exercises - Class activities - Written tests

Statistics and Probability

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

In groups, learners are guided to:
- 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

- Written exercises - Class activities - Oral questions

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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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
Statistics - Interpreting line graphs and pie charts

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

In groups, learners are guided to:
- 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
- Mentor Essential Mathematics pg. 185
- Sample graphs and charts
- Calculators
- Protractors

- Oral questions - Written exercises - Class activities

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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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
Probability - Calculating probability of 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

In groups, learners are guided to:
- 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

- Practical exercises - Observation - Class activities

Statistics and Probability

Probability - Independent events
Probability - Calculating probability of 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

In groups, learners are guided to:
- 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
- Mentor Essential Mathematics pg. 207
- Calculators
- Probability problem cards

- Practical exercises - Observation - Oral questions