Numbers and Algebra

Quadratic Equations - Factorisation of quadratic expressions
Quadratic Equations - Factorisation by grouping

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

- Identify the coefficients a, b and c in quadratic expressions
- Find factor pairs of ac that sum to b
- Apply factorisation to expressions of the form x² + bx + c

- Factorise quadratic expressions by grouping
- Apply the grouping method to various expressions
- Verify factorisation by expanding the factors

- Identify values of a, b and c in quadratic expressions
- List factor pairs and identify the pair with required sum
- Factorise expressions by splitting the middle term

- Split the middle term into two terms
- Group terms and factorise each group
- Extract the common factor and complete factorisation

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 27
- Factor pair charts
- Calculators

- Mentor Essential Mathematics pg. 27
- Worked examples charts
- Calculators

- Oral questions - Written exercises - Observation
- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Equations - Factorisation of expressions ax² + bx + c

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

- Factorise quadratic expressions where a ≠ 1
- Apply systematic methods to factorise complex expressions
- Connect factorisation to finding dimensions from area expressions

- Find factors of ac and identify the pair summing to b
- Factorise expressions with leading coefficient greater than 1
- Discuss practical applications of factorisation

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 28
- Factor charts
- Calculators

- Written tests - Class activities - Observation

Numbers and Algebra

Quadratic Equations - Solving by factorisation
Quadratic Equations - Solving equations with repeated roots

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

- Apply factorisation to solve quadratic equations
- Find solutions by equating each factor to zero
- Verify solutions by substitution into the original equation

- Factorise the quadratic expression
- Set each factor equal to zero and solve for x
- Check solutions by substituting back into the equation

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 28
- Worked examples charts
- Calculators
- Mentor Essential Mathematics pg. 29
- Calculators
- Worked examples

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Equations - Applications to real life problems

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

- Apply quadratic equations to solve area problems
- Form and solve equations from word problems
- Interpret solutions in real-life contexts like room dimensions and garden sizes

- Form quadratic equations from dimension problems
- Solve and interpret solutions
- Determine dimensions of rooms, carpets and gardens

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 29
- Diagram charts
- Calculators

- Written tests - Portfolio - Class activities

Measurements and Geometry

Reflection - Lines of symmetry in plane figures
Reflection - Lines of symmetry in regular polygons
Reflection - Properties of reflection
Reflection - Drawing images given object and mirror line

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

- Identify lines of symmetry in plane figures
- Determine the number of lines of symmetry in different shapes
- Recognize symmetry in everyday objects like doors, windows and leaves

- Determine the properties of reflection using objects and images
- Compare distances of object and image from mirror line
- Relate reflection properties to how mirrors work in daily life

- Take a walk and collect 2D objects from the environment
- Fold rectangular and square paper cut-outs to find lines of symmetry
- Count number of fold lines that divide shapes into equal parts
- Share findings with other groups

- Observe triangle ABC and its image A'B'C' after reflection
- Compare sizes and shapes of object and image
- Measure and compare distances from mirror line
- Stand at different distances from plane mirror and observe

How do we identify lines of symmetry?
What are the properties of reflection?

- Mentor Essential Mathematics pg. 50
- Paper cut-outs
- Scissors
- Various 2D objects
- Mentor Essential Mathematics pg. 52
- Rulers
- Protractors
- Plain paper
- Mentor Essential Mathematics pg. 53
- Plane mirrors
- Rulers
- Plain paper
- Mentor Essential Mathematics pg. 54
- Plain paper
- Set squares

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection - Reflection along x = 0
Reflection - Reflection along y = 0
Reflection - Reflection along y = x

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

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

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

What happens to coordinates when reflecting along x = 0?

- Mentor Essential Mathematics pg. 56
- Graph paper
- Rulers
- Pencils
- Mentor Essential Mathematics pg. 58
- Calculators
- Mentor Essential Mathematics pg. 57

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection - Drawing mirror line given object and image on plane surface
Reflection - Drawing mirror line on Cartesian plane

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

- Draw the mirror line given an object and its image on a plane surface
- Construct perpendicular bisectors to locate mirror line
- Apply the concept to determining mirror placement in interior design

- Trace objects and their images on plain paper
- Join corresponding points (object to image)
- Construct perpendicular bisector of the line segment
- Verify that perpendicular bisector is the mirror line

How do we find the mirror line given object and image?

- Mentor Essential Mathematics pg. 60
- Plain paper
- Rulers
- Compasses
- Mentor Essential Mathematics pg. 61
- Graph paper

- Observation - Practical work - Written tests

Measurements and Geometry

Reflection - Application in real life situations

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

- Apply reflection in real-life situations
- Solve problems involving reflection
- Use reflection concepts in understanding driving mirrors and road safety

- Discuss uses of reflection in real life
- Solve problems involving town layouts and architectural designs
- Work with peers to apply reflection to practical situations
- Present findings to class

How is reflection used in day-to-day activities?

- Mentor Essential Mathematics pg. 63
- Graph paper
- Rulers
- Digital resources

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Identifying sides of a right-angled triangle
Trigonometry - Tangent ratio
Trigonometry - Applications of tangent ratio
Trigonometry - Sine ratio
Trigonometry - Applications of sine ratio

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

- Identify the sides of a right-angled triangle in relation to a particular angle
- Name the hypotenuse, opposite and adjacent sides
- Recognize right-angled triangles in structures like ladders, ramps and roofs

- Determine the sine of acute angles in a right-angled triangle
- Calculate sine ratios from given measurements
- Connect sine ratio to calculating heights of buildings and trees

- Lean a ladder against classroom wall and identify triangle formed
- Name the type of triangle formed
- Identify hypotenuse, opposite and adjacent sides relative to angle θ
- Discuss real-life examples of right-angled triangles

- Measure opposite side and hypotenuse in similar triangles
- Calculate ratio of opposite to hypotenuse for angle θ
- Observe that the ratio is constant for the same angle
- Work out sine of angles in various triangles

How do we identify the sides of a right-angled triangle?
What is the sine of an angle?

- Mentor Essential Mathematics pg. 65
- Ladders
- Protractors
- Rulers
- Mentor Essential Mathematics pg. 67
- Rulers
- Calculators
- Mentor Essential Mathematics pg. 68
- Calculators
- Reference books
- Mentor Essential Mathematics pg. 69
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 71
- Calculators
- Digital resources

- Observation - Oral questions - Written assignments
- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Cosine ratio
Trigonometry - Applications of cosine ratio

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

- Determine the cosine of acute angles in a right-angled triangle
- Calculate cosine ratios from given measurements
- Apply cosine ratio to navigation and distance calculations

- Measure adjacent side and hypotenuse in similar triangles
- Calculate ratio of adjacent to hypotenuse for angle θ
- Observe that the ratio is constant for the same angle
- Work out cosine of angles in various triangles

What is the cosine of an angle?

- Mentor Essential Mathematics pg. 72
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 74
- Calculators
- Reference books

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Sines and cosines of complementary angles
Trigonometry - Solving equations involving complementary angles

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

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

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

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

- Mentor Essential Mathematics pg. 75
- Scientific calculators
- Reference books
- Digital resources
- Mentor Essential Mathematics pg. 76
- Exercise books
- Reference books

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Making a clinometer

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

- Make a simple clinometer using locally available materials
- Use the clinometer to measure angles
- Apply clinometer skills to measuring heights of buildings and trees

- Gather manila paper, protractor, string and weight
- Trace protractor's curved edge and mark degrees
- Attach straw along straight edge
- Tie string with weight at centre point

How do we make and use a clinometer?

- Mentor Essential Mathematics pg. 77
- Manila paper
- Blackboard protractor
- String and weight

- Observation - Practical work - Oral questions

Measurements and Geometry

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

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

- Apply trigonometric ratios to angles of elevation
- Calculate heights using angles of elevation
- Use angle of elevation in determining heights of flagpoles, trees and buildings

- Solve problems involving angles of elevation
- Apply trigonometric ratios to real-life situations
- Calculate heights of towers, monuments and tall structures

- Use clinometer to measure angle of elevation of tall objects
- Measure horizontal distance from object
- Apply trigonometric ratios to calculate heights
- Compare calculated heights with actual measurements

- Draw sketches from word problems
- Identify given information and required values
- Apply appropriate trigonometric ratios
- Calculate heights and distances

How do we use angles of elevation to find heights?
How do we solve problems on angles of elevation?

- Mentor Essential Mathematics pg. 79
- Clinometers
- Tape measures
- Calculators

- Mentor Essential Mathematics pg. 80
- Calculators
- Rulers
- Exercise books

- Observation - Practical work - Written tests
- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Angle of depression

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

- Apply trigonometric ratios to angles of depression
- Calculate distances using angles of depression
- Use angle of depression in aviation and marine navigation

- Discuss meaning of angle of depression
- Draw diagrams showing angles of depression
- Apply trigonometric ratios to find distances
- Solve problems involving observers on cliffs and buildings

How do we use angles of depression to find distances?

- Mentor Essential Mathematics pg. 80
- Calculators
- Rulers
- Digital resources

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Application in real life situations
Area of Polygons - Area of triangle given two sides and an included angle
Area of Polygons - Problems on area of triangle

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

- Solve combined problems on angles of elevation and depression
- Apply trigonometry to various real-life scenarios
- Use trigonometry in determining distances between ships, aircraft heights and building measurements

- Solve problems involving two ships viewed from cliff
- Calculate distances and heights in combined scenarios
- Use digital resources to explore more applications
- Present solutions to class

How is trigonometry used in real life?

- Mentor Essential Mathematics pg. 81
- Calculators
- Digital resources
- Reference books
- Mentor Essential Mathematics pg. 84
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 85
- Exercise books

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

- 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

- 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 rhombus?
How do we find the area of a parallelogram?

- Mentor Essential Mathematics pg. 88
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 89
- Calculators
- Protractors
- 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
Area of Polygons - Problems on area of 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
- Mentor Essential Mathematics pg. 97
- Calculators
- Exercise books
- Digital resources

- Observation - Oral questions - Written assignments

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Area of a sector
Area of a Part of a Circle - Problems on area of sector
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 sector of a circle
- Apply the formula Area = θ/360 × πr²
- Calculate areas of hand-fans, sprinkler coverage and cake toppings

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

- Draw circle and mark sector AOB
- Measure radius and angle subtended at centre
- Apply formula θ/360 × πr²
- Share findings with classmates

- 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 find the area of a sector?
How do we solve problems involving segments?

- Mentor Essential Mathematics pg. 101
- Compasses
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 102
- Calculators
- Rulers
- Exercise books
- Mentor Essential Mathematics pg. 103
- Mentor Essential Mathematics pg. 105
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 107
- Tape measures
- Protractors
- Calculators

- Observation - Oral questions - Written assignments
- 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
Surface Area of Solids - Nets of pyramids
Surface Area of Solids - Surface area of square-based pyramid
Surface Area of Solids - Surface area of rectangular-based pyramid

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

- Determine surface area of square-based pyramids from nets
- Calculate area of square base and triangular faces
- Apply to gift box designs, glass covers for skylights and decorative items

- 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

- Sketch net of square-based pyramid
- Calculate area of square base
- Calculate area of four identical triangular faces
- Add to get total surface area

How do we find the surface area of a cone from its net?
How do we find surface area of a square-based pyramid?

- Mentor Essential Mathematics pg. 113
- Cone nets
- Protractors
- Calculators
- 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
- Calculators
- Rulers
- Mentor Essential Mathematics pg. 117

- Observation - Oral questions - Written tests
- Observation - Oral questions - Written assignments

Measurements and Geometry

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:

- Calculate the surface area of a sphere
- Apply the formula 4πr²
- Use sphere surface area in calculating material for balls, globes and decorative spheres

- Collect spherical objects (soccer balls, marbles, oranges)
- Estimate and record radius of each object
- Calculate surface area using formula 4πr²
- Share work with other groups

How do we find the surface area of a sphere?

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

- Observation - Oral questions - Written assignments

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
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

- 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
Statistics and Probability

Surface Area of Solids - Problems on frustum of a pyramid
Statistics - Frequency distribution tables for ungrouped data
Statistics - Constructing frequency distribution tables

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

- 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

- 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

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

How are frustums of pyramids used in real life?
How do we use statistics in day-to-day life?

- Mentor Essential Mathematics pg. 127
- Calculators
- Exercise books
- Digital resources
- Mentor Essential Mathematics pg. 166
- Tally charts
- Data collection sheets
- Mentor Essential Mathematics pg. 167
- Data sets
- Tally charts

- Observation - Oral questions - Written tests
- 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
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

- 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
Statistics - Interpreting bar graphs

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

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

- 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

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

- 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. 176
- Protractors
- Compasses
- Calculators

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

- Practical exercises - Observation - Class activities
- 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
Probability - Mutually exclusive events
Probability - Performing experiments on mutually exclusive events

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

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

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

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

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

- Mentor Essential Mathematics pg. 203
- Spinners
- Dice
- Coloured cards

- Oral questions - Written exercises - Observation
- 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