Measurements and Geometry

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

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

In groups, learners are guided to:
- 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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

By the end of the lesson, the learner should be able to:
- Determine the area of a segment of a circle
- Apply the formula: Area of sector - Area of triangle
- Calculate areas of parking lots, decorations and glass windows

In groups, learners are guided to:
- Draw circle with sector and identify segment
- Calculate area of sector using θ/360 × πr²
- Calculate area of triangle using ½r² sin θ
- Subtract to get area of segment

How do we find the area of a segment?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

In groups, learners are guided to:
- Calculate area of curved paths in school compound
- Work out area of decorations on table cloths
- Solve problems on fanning papers
- Present solutions to class

How are areas of parts of circles applied in design?

- Mentor Essential Mathematics pg. 108
- Calculators
- Rulers
- Digital resources
- Mentor Essential Mathematics pg. 110
- Clocks
- Reference books
- Mentor Essential Mathematics pg. 111
- Exercise books

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area of Solids - Nets of cones
Surface Area of Solids - Surface area of a cone from its net

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Surface Area of Solids - Surface area of cone using formula
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:
- Calculate surface area of cones using πrl + πr²
- Solve problems on surface area of cones
- Use cone surface area in designing Christmas hats, filter papers and decorative cones

In groups, learners are guided to:
- Apply formula: Curved surface area = πrl
- Apply formula: Total surface area = πrl + πr²
- Calculate surface area of Christmas hats
- Solve problems on filter paper cones

How do we calculate surface area of a cone using the formula?

- Mentor Essential Mathematics pg. 114
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 115
- Manila paper
- Scissors
- Rulers
- Mentor Essential Mathematics pg. 116
- Graph paper

- Observation - Oral questions - Written assignments

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
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

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
- 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

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

In groups, learners are guided to:
- 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

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
- Mentor Essential Mathematics pg. 132
- Manila paper
- Sand
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

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

By the end of the lesson, the learner should be able to:
- Calculate volume of cones given dimensions
- Determine capacity of cone-shaped containers
- Apply cone volume to funnel designs and conical flasks in laboratories

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

How do we calculate the capacity of a cone?

- Mentor Essential Mathematics pg. 133
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 134
- Rulers
- Exercise books
- Mentor Essential Mathematics pg. 135
- Pyramid models
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

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

By the end of the lesson, the learner should be able to:
- Solve problems on volume of pyramids
- Calculate capacity of pyramid-shaped containers
- Apply pyramid volume to water tanks and yoghurt packaging boxes

In groups, learners are guided to:
- Calculate volume of underground water tanks
- Work out capacity of pyramid-shaped gift boxes
- Determine dimensions when volume is given
- Share solutions with peers

How is pyramid volume applied in real life?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

By the end of the lesson, the learner should be able to:
- Determine volume of frustum of a pyramid
- Calculate volume by subtracting smaller pyramid from larger pyramid
- Apply to water storage tanks and traditional basket designs

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
Volume and Capacity - Capacity problems

By the end of the lesson, the learner should be able to:
- Calculate volume of composite solids
- Combine volumes of different shapes
- Apply to school podiums, water reservoirs and combined storage structures

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Volume and Capacity - Combined problems
Commercial Arithmetic I - Preparing 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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

In groups, learners are guided to:
- 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

- Observation - Budget presentation - Written tests

Measurements and Geometry

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

By the end of the lesson, the learner should be able to:
- Calculate percentage discount
- Determine selling price after discount
- Compare discounts offered by different shops to make wise purchasing decisions

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

How do we calculate percentage discount?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

In groups, learners are guided to:
- 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

- Observation - Oral questions - Written assignments

Measurements and Geometry
Statistics and Probability

Commercial Arithmetic I - Currency conversion problems
Statistics - Frequency distribution tables for ungrouped data

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
- Mentor Essential Mathematics pg. 166
- Tally charts
- Data collection sheets

- Observation - Oral questions - Written tests

Statistics and Probability

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

By the end of the lesson, the learner should be able to:
- Organize raw data into frequency distribution tables
- Use tally marks to count frequencies accurately
- Apply frequency tables to organize market prices, test scores and survey results

In groups, learners are guided to:
- Organize given data sets into frequency tables
- Practice tallying and counting
- Discuss applications in recording rainfall, temperatures and sales

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

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

- Written exercises - Class activities - Observation

Statistics and Probability

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

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

In groups, learners are guided to:
- 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
- Mentor Essential Mathematics pg. 170
- Calculators
- Data sets

- Oral questions - Written exercises - Observation

Statistics and Probability

Statistics - Bar graphs
Statistics - Line graphs

By the end of the lesson, the learner should be able to:
- Define a bar graph and its components
- Draw bar graphs from frequency tables
- Use bar graphs to display sales data, population figures and survey results

- Choose appropriate scales for axes
- Draw bars of equal width with uniform gaps
- Represent data on fruits sold, learner attendance and vehicle counts

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

- Mentor Essential Mathematics pg. 172
- Graph paper
- Rulers
- Pencils
- Mentor Essential Mathematics pg. 174

- Practical exercises - Observation - Class activities

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
Probability - Range of probability of an event

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
- Mentor Essential Mathematics pg. 201
- Event cards
- Probability scale charts

- Written exercises - Class activities - Oral questions

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

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

- Practical exercises - Observation - Class activities

Statistics and Probability

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:
- 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

In groups, learners are guided to:
- 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
- Mentor Essential Mathematics pg. 206
- Coins
- Dice
- Outcome tables
- Mentor Essential Mathematics pg. 207

- Written exercises - Class activities - Written tests