Measurements and Geometry

Area of Polygons - Area of a Triangle given Two Sides and an Included Angle
Area of Polygons - Area of a Triangle using Heron's Formula

By the end of the lesson, the learner should be able to:
- Derive and apply the formula Area = ½bc sin θ for a triangle given two sides and an included angle
- Calculate areas of triangles using the formula when perpendicular height is not given
- Appreciate how trigonometry extends area calculation beyond the standard base-height method

In groups, learners are guided to:
- Derive the formula Area = ½bc sin θ by expressing perpendicular height in terms of sin θ
- Calculate areas of triangles formed by land boundaries and road intersections using the formula
- Verify results using an alternative method where possible

How does knowing two sides and the included angle allow us to find a triangle's area without the perpendicular height?

- Master Essential Mathematics Grade 10 pg. 87
- Scientific calculators
- Reference books
- Master Essential Mathematics Grade 10 pg. 90

- Written exercise - Oral questions - Observation

Measurements and Geometry

Area of Polygons - Area of a Parallelogram
Area of Polygons - Area of a Rhombus

By the end of the lesson, the learner should be able to:
- Derive and apply the formula Area = ab sin θ for a parallelogram given two sides and included angle
- Find unknown angles in a parallelogram given its area and side lengths
- Develop confidence in applying trigonometric area formulas to quadrilaterals

In groups, learners are guided to:
- Derive the parallelogram area formula by substituting h = b sin θ into Area = base × height
- Calculate areas of given parallelograms and find unknown angles where area and sides are known
- Solve real-life problems involving logos, fields and decorative patterns in parallelogram shapes

How does the area formula for a parallelogram change when perpendicular height is replaced by the sine of the included angle?

- Master Essential Mathematics Grade 10 pg. 93
- Scientific calculators
- Reference books
- Master Essential Mathematics Grade 10 pg. 96

- Written exercise - Oral questions - Observation

Measurements and Geometry

Area of Polygons - Area of a Regular Pentagon and Hexagon
Area of Polygons - Area of a Trapezium and Kite

By the end of the lesson, the learner should be able to:
- Calculate the area of a regular hexagon by dividing it into congruent equilateral triangles
- Apply trigonometric area formulas to find areas of regular pentagons and hexagons
- Appreciate how regular polygons are composed of congruent triangular units

In groups, learners are guided to:
- Divide a regular hexagon into 6 equilateral triangles and calculate total area using the triangle formula
- Apply the regular polygon area approach to solve problems involving floor tiles, windows and decorative patterns
- Solve problems involving regular pentagons using the triangle decomposition method

How is the area of a regular polygon calculated by dividing it into congruent triangles?

- Master Essential Mathematics Grade 10 pg. 103
- Scientific calculators
- Reference books
- Master Essential Mathematics Grade 10 pg. 105

- Written exercise - Oral questions - Observation

Measurements and Geometry

Area of Polygons - Application of Area Formulas to Real-Life Contexts
Area of Polygons - Areas of Compound Shapes

By the end of the lesson, the learner should be able to:
- Apply area formulas for triangles, parallelograms, rhombuses, trapeziums and regular polygons to real-life problems
- Select the appropriate formula for a given polygon and justify the choice
- Appreciate the role of polygon area calculations in architecture, design and land surveying

In groups, learners are guided to:
- Solve a mixed set of area problems covering all polygons studied in the sub-strand
- Peer-mark solutions and discuss errors in formula selection or calculation
- Use digital tools to explore areas of compound shapes made up of multiple polygon types

How do we select and apply the correct area formula when given an unfamiliar polygon shape?

- Master Essential Mathematics Grade 10 pg. 103
- Scientific calculators
- Reference books
- Digital devices
- Master Essential Mathematics Grade 10 pg. 105
- Graph paper

- Written exercise - Portfolio review - Peer assessment

Measurements and Geometry

Area of a Part of a Circle - Area of a Sector of a Circle
Area of a Part of a Circle - Area of a Segment of a Circle

By the end of the lesson, the learner should be able to:
- Derive and apply the formula Area = (θ/360°)πr² to calculate the area of a sector
- Calculate areas of sectors given the radius and angle subtended at the centre
- Appreciate how the sector is a fraction of the full circle corresponding to the angle at the centre

In groups, learners are guided to:
- Identify a sector as the region enclosed by two radii and an arc and derive its area formula as a fraction of the full circle
- Calculate areas of sectors for given radii and angles including sprinklers, sliced fruit and swing gates
- Solve problems requiring sector area and verify units and reasonableness of answers

How does the angle at the centre determine what fraction of the total circle area a sector occupies?

- Master Essential Mathematics Grade 10 pg. 107
- Scientific calculators
- Compass, ruler
- Master Essential Mathematics Grade 10 pg. 110

- Written exercise - Oral questions - Observation

Measurements and Geometry

Area of a Part of a Circle - Arc Length and its Relationship to Sector Area
Area of a Part of a Circle - Application and Mixed Practice

By the end of the lesson, the learner should be able to:
- Calculate the arc length of a sector using Arc length = (θ/360°) × 2πr
- Relate arc length and sector area in solving combined problems
- Show accuracy in calculating arc length and sector area for the same sector

In groups, learners are guided to:
- Derive the arc length formula as a fraction of the full circumference analogous to the sector area formula
- Calculate arc lengths and sector areas for given circles and compare the two results
- Solve problems where both arc length and sector area are needed in the same context

How does the formula for arc length compare to the formula for sector area?

- Master Essential Mathematics Grade 10 pg. 107
- Scientific calculators
- Reference books
- Master Essential Mathematics Grade 10 pg. 110
- Compass, ruler

- Written exercise - Oral questions - Observation

Measurements and Geometry

Surface Area of Solids - Surface Area of a Cone

By the end of the lesson, the learner should be able to:
- Derive the surface area formula for a cone using its net: SA = πrl + πr²
- Calculate the curved surface area and total surface area of a cone given radius and slant height
- Show interest in the connection between the net of a cone and its surface area formula

In groups, learners are guided to:
- Open the curved surface of a cone model to form a sector and derive the curved surface area formula
- Calculate total surface area of open and closed cones given base radius and slant height
- Solve real-life problems involving conical tents, hats and water tanks

How does unfolding the curved surface of a cone into a sector help us derive its surface area formula?

- Master Essential Mathematics Grade 10 pg. 117
- Cone models, ruler
- Scientific calculators

- Written exercise - Oral questions - Observation

Measurements and Geometry

Surface Area of Solids - Surface Area of a Pyramid
Surface Area of Solids - Surface Area of a Sphere and Hemisphere

By the end of the lesson, the learner should be able to:
- Calculate the surface area of a square-based and rectangular-based pyramid using its net
- Apply SA = base area + sum of all triangular face areas correctly
- Develop methodical reasoning in identifying and calculating each face of a pyramid

In groups, learners are guided to:
- Draw the net of square-based and rectangular-based pyramids and label all faces
- Calculate the area of the base and each triangular face then add to get total surface area
- Solve real-life problems involving pyramid-shaped ornaments, monuments and trophies

Why is drawing the net of a pyramid helpful when calculating its total surface area?

- Master Essential Mathematics Grade 10 pg. 120
- Pyramid models, ruler
- Scientific calculators
- Master Essential Mathematics Grade 10 pg. 122
- Spherical objects, ruler, string

- Written assignments - Oral questions - Observation

Measurements and Geometry

Surface Area of Solids - Surface Area of Composite Solids
Surface Area of Solids - Application of Surface Area in Real Life

By the end of the lesson, the learner should be able to:
- Calculate the surface area of composite solids formed by combining two or more standard solids
- Identify which faces are internal and which are external when solids are combined
- Develop spatial reasoning in visualising the surface area of non-standard shapes

In groups, learners are guided to:
- Identify external faces of composite solids such as a cylinder topped with a cone or a cube topped with a pyramid
- Calculate the surface area of each component, subtract shared/internal faces and add to get total external surface area
- Solve real-life problems involving storage tanks and trophy designs made of composite solids

How do we identify which surfaces to include when finding the surface area of a composite solid?

- Master Essential Mathematics Grade 10 pg. 122
- Models of composite solids
- Scientific calculators
- Master Essential Mathematics Grade 10 pg. 124
- Reference books
- Digital devices

- Written assignments - Oral questions - Observation

Measurements and Geometry

Surface Area of Solids - Mixed Problems and Consolidation
Volume and Capacity - Volume and Capacity of a Cylinder and Cone

By the end of the lesson, the learner should be able to:
- Compare surface areas of different solid types and relate findings to packaging efficiency
- Solve multi-step surface area problems selecting the correct formula for each solid
- Show confidence and accuracy in a comprehensive surface area consolidation exercise

In groups, learners are guided to:
- Compare surface areas of a cone, pyramid and sphere of similar dimensions and discuss packaging implications
- Solve a comprehensive mixed problem set covering all surface area types studied
- Peer-review solutions and create a personal reference card of all surface area formulas

How do the surface area formulas for a cone, pyramid and sphere each differ from one another?

- Master Essential Mathematics Grade 10 pg. 124
- Scientific calculators
- Reference books
- Master Essential Mathematics Grade 10 pg. 129
- Cylinder and cone models

- Written exercise - Peer assessment - Oral questions

Measurements and Geometry

Volume and Capacity - Volume and Capacity of a Pyramid
Volume and Capacity - Volume and Capacity of a Frustum of a Cone

By the end of the lesson, the learner should be able to:
- Calculate the volume of square-based and rectangular-based pyramids using V = ⅓ × base area × height
- Convert pyramid volumes to capacities and solve for unknown dimensions given the volume
- Show logical reasoning in connecting pyramid and prism volume relationships

In groups, learners are guided to:
- Use V = ⅓ × base area × height to calculate volumes of square-based and rectangular-based pyramids
- Convert volumes to litres and solve for unknown heights or base dimensions given volume
- Solve real-life problems involving pyramid-shaped tents, roofs and storage tanks

How does the volume formula for a pyramid compare to the formula for a prism of the same base and height?

- Master Essential Mathematics Grade 10 pg. 131
- Pyramid models
- Scientific calculators
- Master Essential Mathematics Grade 10 pg. 133
- Frustum models

- Written assignments - Oral questions - Observation

Measurements and Geometry

Volume and Capacity - Volume and Capacity of a Frustum of a Pyramid
Volume and Capacity - Application and Mixed Practice

By the end of the lesson, the learner should be able to:
- Apply the formula V = ⅓h(A₁ + A₂ + √(A₁A₂)) to calculate the volume of a frustum of a pyramid
- Convert volumes to capacities and solve for unknown dimensions
- Show confidence in applying the frustum formula to real-life pyramid-based problems

In groups, learners are guided to:
- Derive the frustum of a pyramid formula by subtracting the volume of the removed pyramid from the original
- Calculate volumes and capacities of frustum-shaped basins, aquariums and display stands
- Solve problems involving rectangular-based pyramid frustums given top and bottom dimensions and height

How is the formula for the volume of a frustum of a pyramid derived from the formula for a complete pyramid?

- Master Essential Mathematics Grade 10 pg. 135
- Scientific calculators
- Reference books
- Master Essential Mathematics Grade 10 pg. 133
- Digital devices

- Written assignments - Oral questions - Observation

Measurements and Geometry

Volume and Capacity - Composite Solid Volume Problems

By the end of the lesson, the learner should be able to:
- Calculate volumes of composite solids by adding or subtracting component volumes
- Solve multi-step real-life problems combining two or more solid types
- Show thoroughness in setting up and solving complex volume problems

In groups, learners are guided to:
- Identify components of composite solids and apply appropriate volume formulas for each part
- Add or subtract component volumes to find total volumes of non-standard solid shapes
- Solve examination-style multi-step volume and capacity problems under timed conditions

How do we find the volume of a composite solid made up of two or more standard solid shapes?

- Master Essential Mathematics Grade 10 pg. 135
- Scientific calculators
- Reference books

- Written assignments - Oral questions - Observation

Measurements and Geometry

Commercial Arithmetic - Preparing a Budget
Commercial Arithmetic - Discount and Percentage Discount

By the end of the lesson, the learner should be able to:
- Prepare a budget showing income, expenditure and savings or deficit
- Distinguish between savings and deficit and explain their financial implications
- Appreciate the importance of budgeting as a financial planning and management tool

In groups, learners are guided to:
- Discuss the meaning of a budget and the difference between savings and deficit
- Prepare budgets for events such as environmental day celebrations, fundraisers and school activities
- Evaluate whether a given budget results in a surplus or deficit and advise accordingly

Why is it important to prepare a budget before undertaking a financial activity?

- Master Essential Mathematics Grade 10 pg. 142
- Reference books
- Digital devices
- Master Essential Mathematics Grade 10 pg. 147
- Scientific calculators

- Written exercise - Oral questions - Observation

Measurements and Geometry

Commercial Arithmetic - Commission and Percentage Commission
Commercial Arithmetic - Profit and Percentage Profit

By the end of the lesson, the learner should be able to:
- Calculate commission and percentage commission earned on sales
- Solve problems involving tiered commission structures and combined salary and commission earnings
- Appreciate how commission-based income motivates sales and service professionals

In groups, learners are guided to:
- Discuss what commission is and identify occupations where it is earned (sales agents, insurance brokers, real estate agents)
- Calculate commissions on given sales amounts including tiered rates above specified thresholds
- Solve problems involving combined basic salary and commission income

How does a tiered commission structure incentivise higher levels of sales?

- Master Essential Mathematics Grade 10 pg. 149
- Scientific calculators
- Reference books
- Master Essential Mathematics Grade 10 pg. 151

- Written exercise - Oral questions - Observation

Measurements and Geometry

Commercial Arithmetic - Loss and Percentage Loss
Commercial Arithmetic - Mixed Problems on Profit, Loss and Discount

By the end of the lesson, the learner should be able to:
- Calculate loss and percentage loss given cost price and selling price
- Identify situations that lead to a financial loss despite selling above the purchase price
- Show awareness of real-world factors that cause trading losses

In groups, learners are guided to:
- Discuss situations where a trader sells at a loss despite trying to profit (additional costs, spoilage, transport)
- Calculate loss and percentage loss from scenarios involving produce, electronics and second-hand goods
- Solve problems where full cost price includes purchase price plus additional expenses

How can a trader sell at a price above what they paid and still make a loss?

- Master Essential Mathematics Grade 10 pg. 153
- Scientific calculators
- Reference books

- Written exercise - Oral questions - Observation

Measurements and Geometry

Commercial Arithmetic - Foreign Exchange using Mean Rates
Commercial Arithmetic - Buying and Selling Foreign Currency

By the end of the lesson, the learner should be able to:
- Interpret a foreign exchange table showing CBK mean rates
- Convert amounts between local and foreign currencies using mean exchange rates
- Appreciate the role of exchange rates in international trade and travel

In groups, learners are guided to:
- Examine a CBK exchange rate table and discuss what mean rates represent
- Convert amounts from foreign currencies to Kenya shillings and vice versa using mean CBK rates
- Solve real-life problems involving importing goods and calculating equivalent costs in Kenya shillings

Why do exchange rates change and how does this affect the cost of imported goods?

- Master Essential Mathematics Grade 10 pg. 155
- Scientific calculators
- Reference books
- Digital devices
- Master Essential Mathematics Grade 10 pg. 156

- Written exercise - Oral questions - Observation

Measurements and Geometry
Statistics and Probability
Statistics and Probability

Commercial Arithmetic - Multi-step Foreign Exchange Problems
Statistics - Frequency Distribution Table for Ungrouped Data
Statistics - Constructing and Interpreting Frequency Distribution Tables

By the end of the lesson, the learner should be able to:
- Solve multi-step foreign exchange problems involving two or more currency conversions
- Apply buying and selling rates correctly in complex travel and import/export scenarios
- Appreciate the practical importance of understanding foreign exchange in personal and national finance

In groups, learners are guided to:
- Solve problems involving tourists arriving in Kenya, spending part of their money and converting the balance to a third currency
- Calculate final amounts received after a sequence of conversions using buying and selling rates
- Solve examination-style multi-step foreign exchange problems under timed conditions

How does an understanding of foreign exchange rates help individuals and businesses in international transactions?

- Master Essential Mathematics Grade 10 pg. 156
- Scientific calculators
- Reference books
- Digital devices
- Master Essential Mathematics Grade 10 pg. 160
- Exercise books, ruler

- Written exercise - Portfolio review - Oral questions

Statistics and Probability

Statistics - Mean of Ungrouped Data
Statistics - Mode of Ungrouped Data
Statistics - Median of Ungrouped Data
Statistics - Measures of Central Tendency - Consolidation

By the end of the lesson, the learner should be able to:
- Calculate the mean of ungrouped data using Mean = Σx/n
- Calculate the mean from a frequency distribution table using Mean = Σfx/Σf
- Show accuracy and care when summing values and computing the mean

In groups, learners are guided to:
- Brainstorm the meaning of the term mean and discuss its everyday significance
- Calculate the mean directly from raw data and from frequency distribution tables using Σfx/Σf
- Solve real-life problems involving mean heights, masses, marks and milk production

How does the mean represent a typical value in a data set?

- Master Essential Mathematics Grade 10 pg. 163
- Scientific calculators
- Reference books
- Master Essential Mathematics Grade 10 pg. 167
- Exercise books
- Master Essential Mathematics Grade 10 pg. 170

- Written exercise - Oral questions - Observation

Statistics and Probability

Statistics - Drawing Bar Graphs
Statistics - Interpretation of Data from Bar Graphs
Statistics - Drawing Line Graphs

By the end of the lesson, the learner should be able to:
- Draw accurate bar graphs to represent given data sets using an appropriate scale
- Label axes, bars and titles correctly on a bar graph
- Show neatness and precision in constructing bar graphs to represent data visually

In groups, learners are guided to:
- Recall prior knowledge of bar graphs from Junior School and discuss their features
- Draw bar graphs for given data including school marks, egg production and sports participation using suitable scales
- Review and correct bar graphs drawn by peers for accuracy of scale, labels and spacing

What makes a bar graph an effective tool for displaying and comparing data?

- Master Essential Mathematics Grade 10 pg. 172
- Graph paper, ruler, pencil
- Reference books
- Master Essential Mathematics Grade 10 pg. 175
- Graph paper
- Digital devices
- Master Essential Mathematics Grade 10 pg. 178

- Written exercise - Observation - Oral questions

Statistics and Probability

Statistics - Interpretation of Data from Line Graphs
Statistics - Drawing Pie Charts

By the end of the lesson, the learner should be able to:
- Read and interpret line graphs to extract specific values and identify trends
- Answer questions involving changes, differences and predictions from a line graph
- Appreciate how line graphs reveal trends over time for better planning and forecasting

In groups, learners are guided to:
- Study given line graphs showing town population growth, temperature changes and sales trends
- Answer questions identifying values at specific times, calculating changes between periods and identifying trends
- Discuss how line graph trends are used by businesses, health planners and governments to make decisions

How does the shape of a line graph reveal trends and help in forecasting?

- Master Essential Mathematics Grade 10 pg. 180
- Graph paper
- Reference books
- Digital devices
- Master Essential Mathematics Grade 10 pg. 184
- Compass, protractor, ruler
- Scientific calculators

- Written assignments - Oral questions - Observation

Statistics and Probability

Statistics - Interpretation of Data from Pie Charts
Statistics - Application: Data Collection and Representation Project

By the end of the lesson, the learner should be able to:
- Read and interpret pie charts to answer questions about the data represented
- Calculate actual values from sector angles and percentages in a pie chart
- Appreciate how pie charts enable quick comparison of categories within a whole

- Study given pie charts showing learner career pathways, crop distribution and income expenditure
- Use sector angles and given totals to calculate actual values for each category
- Answer comparison questions including which category is largest, smallest and by how much categories differ

How do we extract actual values from a pie chart when only angles or percentages are given?

- Master Essential Mathematics Grade 10 pg. 187
- Compass, protractor, ruler
- Scientific calculators
- Master Essential Mathematics Grade 10 pg. 188
- Graph paper, compass, protractor
- Digital devices
- Reference books

- Written assignments - Oral questions - Observation

Statistics and Probability

Statistics - Mixed Practice and Consolidation

By the end of the lesson, the learner should be able to:
- Solve a comprehensive set of problems covering all Statistics (I) topics including frequency tables, measures of central tendency and graphical representation
- Identify and correct errors in data organisation and graph construction
- Show confidence and accuracy in a full sub-strand revision exercise

In groups, learners are guided to:
- Work through a timed mixed revision exercise covering all topics in Statistics (I)
- Peer-mark solutions and discuss common errors in frequency tables, mean calculation and graph construction
- Discuss how statistical skills are applied in real-world professions such as healthcare, business and government

What statistical skills are most important for making informed decisions in everyday life?

- Master Essential Mathematics Grade 10 pg. 184
- Scientific calculators
- Graph paper
- Reference books

- Written exercise - Peer assessment - Oral questions

Statistics and Probability

Statistics - Extended Mixed Problems on Statistics (I)
Statistics - Further Mixed Practice on Graphs and Charts

By the end of the lesson, the learner should be able to:
- Solve multi-step problems that combine data organisation, measures of central tendency and graphical representation
- Interpret data presented in different formats and draw meaningful conclusions
- Appreciate the value of statistical thinking in processing and communicating information

In groups, learners are guided to:
- Solve integrated problems that involve constructing a frequency table, computing mean and mode and drawing an appropriate graph from the same data set
- Discuss how data misrepresentation can mislead and why accuracy in statistics is important
- Present solutions in full showing all working clearly and logically

How can the same data set be represented and interpreted in multiple ways using different statistical tools?

- Master Essential Mathematics Grade 10 pg. 163
- Scientific calculators
- Graph paper
- Digital devices
- Master Essential Mathematics Grade 10 pg. 178
- Graph paper, compass, protractor

- Written assignments - Oral questions - Portfolio review

Statistics and Probability

Statistics - Solving Mixed Statistics Problems from Real-Life Contexts
Probability - Experiments Involving Equally Likely Outcomes

By the end of the lesson, the learner should be able to:
- Apply all Statistics (I) skills to analyse and interpret data drawn from real school and community contexts
- Compute mean, mode and median and represent findings graphically for a real data set
- Appreciate how statistics underpins evidence-based decision-making in everyday life

In groups, learners are guided to:
- Collect a fresh small data set from the school environment and compute mean, mode and median
- Represent the same data set on a bar graph and a pie chart
- Discuss the implications of the findings and present conclusions to the class

How do different statistical tools together give a more complete picture of a data set?

- Master Essential Mathematics Grade 10 pg. 167
- Scientific calculators
- Graph paper, compass
- Digital devices
- Master Essential Mathematics Grade 10 pg. 191
- Coins, dice, spinners, cards
- Reference books

- Written assignments - Oral presentation - Portfolio review

Statistics and Probability

Probability - Computing Probability of Equally Likely Outcomes
Probability - Range of Probability and Complementary Events

By the end of the lesson, the learner should be able to:
- Apply the formula P(event) = number of favourable outcomes / total number of possible outcomes
- Calculate the probability of simple events in experiments with equally likely outcomes
- Show accuracy in listing outcomes and computing probabilities as fractions

In groups, learners are guided to:
- Use the probability formula to compute probabilities for events involving coins, dice, coloured balls and labelled cards
- List sample spaces for given experiments and identify favourable outcomes for stated events
- Solve real-life probability problems involving equally likely outcomes

How is the probability of an event calculated when all outcomes are equally likely?

- Master Essential Mathematics Grade 10 pg. 192
- Coins, dice, coloured balls
- Scientific calculators
- Master Essential Mathematics Grade 10 pg. 193
- Coloured marbles, coins, dice

- Written exercise - Oral questions - Observation

Statistics and Probability

Probability - Application of the Complementary Rule
Probability - Mutually Exclusive Events

By the end of the lesson, the learner should be able to:
- Apply P(A') = 1 − P(A) confidently to solve multi-step probability problems
- Interpret given probability values in context and use them to find unknown probabilities
- Show logical reasoning in working backwards from a complementary probability

In groups, learners are guided to:
- Solve problems where the probability of an event not happening is given and the probability of it happening must be found
- Apply the complementary rule to events involving spinners, dice, cards and real-life scenarios such as weather and defective goods
- Verify answers by checking that all probabilities in a sample space sum to 1

How does the complementary rule simplify the calculation of probability in complex situations?

- Master Essential Mathematics Grade 10 pg. 193
- Scientific calculators
- Reference books
- Master Essential Mathematics Grade 10 pg. 195
- Spinners, coins, dice

- Written exercise - Oral questions - Observation

Statistics and Probability

Probability - Probability of Single Chance Mutually Exclusive Events
Probability - Experiments Involving Independent Events

By the end of the lesson, the learner should be able to:
- Calculate the probability of one event from a set of mutually exclusive events given the probabilities of the others
- Apply the rule that the sum of all mutually exclusive probabilities equals 1
- Show logical reasoning in finding an unknown probability using the complement of known probabilities

In groups, learners are guided to:
- Use the rule ΣP(all outcomes) = 1 to find missing probabilities in a set of mutually exclusive events
- Solve problems involving planting choices, spinner sections and road routing where probabilities of all but one event are given
- Verify solutions by checking that all computed probabilities sum to 1

How do we find the probability of one event when the probabilities of all other mutually exclusive events are known?

- Master Essential Mathematics Grade 10 pg. 197
- Scientific calculators
- Reference books
- Master Essential Mathematics Grade 10 pg. 199
- Coins, dice, cards

- Written assignments - Oral questions - Observation

Statistics and Probability

Probability - Computing Probability of Independent Events
Probability - Further Problems on Independent Events

By the end of the lesson, the learner should be able to:
- Apply the multiplication rule P(A and B) = P(A) × P(B) for independent events
- Calculate the probability that both, neither or one of two independent events occurs
- Appreciate that "and" implies multiplication while "or" implies addition in probability

In groups, learners are guided to:
- State and apply the rule P(A and B) = P(A) × P(B) using examples involving rain and reading, coins and dice
- Calculate probabilities that two independent events both occur, one occurs and the other does not, and neither occurs
- Solve real-life problems involving independent events such as homework submission and quiz occurrence

Why does the multiplication rule apply to independent events and what does "and" mean in probability?

- Master Essential Mathematics Grade 10 pg. 200
- Scientific calculators
- Reference books

- Written exercise - Oral questions - Observation

Statistics and Probability

Probability - Application and Mixed Practice

By the end of the lesson, the learner should be able to:
- Solve a mixed set of problems covering equally likely outcomes, complementary events, mutually exclusive events and independent events
- Select the appropriate probability rule for each problem type and justify the choice
- Appreciate the role of probability in making predictions and informing decisions in everyday life

In groups, learners are guided to:
- Solve a comprehensive mixed practice exercise covering all Probability (I) topics under timed conditions
- Peer-mark solutions and discuss errors in identifying event types and applying probability rules
- Discuss how probability is applied in insurance, weather forecasting, medicine and games of chance

How does understanding probability help us make better predictions and decisions in daily life?

- Master Essential Mathematics Grade 10 pg. 195
- Scientific calculators
- Reference books
- Digital devices

- Written exercise - Peer assessment - Portfolio review