Numbers and Algebra

Real Numbers - Odd and even numbers

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

- Identify odd and even numbers
- Classify numbers as odd or even based on the ones place value
- Relate odd and even numbers to real life situations like sharing items equally

- Measure the height of classmates in centimetres and record in a table
- Classify each recorded number as odd or even
- Discuss with peers reasons for classification based on the digit in the ones place value

Why are numbers important?

- Mentor Essential Mathematics pg. 1
- Number cards
- Charts on odd and even numbers

- Oral questions - Written exercises - Observation

Numbers and Algebra

Real Numbers - Prime and composite numbers
Real Numbers - Rational and irrational numbers
Real Numbers - Rational and irrational numbers

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

- Define prime and composite numbers
- Classify numbers as prime or composite by identifying their factors
- Relate prime and composite numbers to grouping items in daily activities

- List factors of given numbers
- Classify numbers based on the number of factors
- Discuss how composite numbers help in dividing items into equal groups

Why are numbers important?

- Mentor Essential Mathematics pg. 3
- Factor charts
- Number cards
- Mentor Essential Mathematics pg. 5
- Digital devices
- Number charts
- Calculators
- Digital resources

- Oral questions - Written exercises - Class activities

Numbers and Algebra

Real Numbers - Combined operations on rational numbers
Real Numbers - Reciprocal of numbers

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

- Perform addition and subtraction of rational numbers
- Apply BODMAS rule in combined operations
- Relate combined operations to budgeting and shopping calculations

- Read and interpret case scenarios involving rational numbers
- Work out combined operations following BODMAS rule
- Discuss real-life situations like calculating total cost of items

Why are numbers important?

- Mentor Essential Mathematics pg. 7
- Calculators
- Word problem cards
- Mentor Essential Mathematics pg. 8
- Thermometer charts
- Mentor Essential Mathematics pg. 9
- Scientific calculators
- Digital devices

- Written exercises - Class activities - Portfolio

Numbers and Algebra

Real Numbers - Application of rational numbers
Indices - Powers and bases

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

- Apply rational numbers in solving real-life problems
- Solve problems involving fractions, decimals and mixed operations
- Connect rational numbers to daily activities like cooking, farming and finance

- Solve problems on sharing resources, measuring ingredients and calculating distances
- Discuss applications in budgeting, farming and construction
- Work with peers on real-life case scenarios

Why are numbers important?

- Mentor Essential Mathematics pg. 11
- Word problem cards
- Calculators
- Mentor Essential Mathematics pg. 13
- Number cards
- Charts on indices

- Written tests - Portfolio - Class activities

Numbers and Algebra

Indices - Expressing numbers in index form
Indices - Multiplication law

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

- Express whole numbers in simplest index form
- Express fractions in index form
- Apply index notation to scientific measurements and data

- Break down numbers into prime factors and express in index form
- Express fractions with numerator and denominator in index form
- Search for population data and express in index form

Why are indices important?

- Mentor Essential Mathematics pg. 14
- Calculators
- Digital resources
- Mentor Essential Mathematics pg. 15
- Index law charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices - Division law

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

- State the division law of indices
- Apply the division law to simplify expressions
- Relate division of indices to sharing and distribution problems

- Divide numbers with the same base by subtracting powers
- Simplify expressions using the division law
- Solve problems on distributing items among groups

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 16
- Index law charts
- Calculators

- Written tests - Class activities - Observation

Numbers and Algebra

Indices - Power of a power
Indices - Zero index

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

- State the power of a power law
- Apply the law to simplify expressions with powers raised to powers
- Apply the law to compound growth calculations

- Expand expressions with powers of powers
- Multiply indices when a power is raised to another power
- Discuss applications in compound interest calculations

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 17
- Index law charts
- Calculators
- Mentor Essential Mathematics pg. 18
- Calculators
- Index law charts

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices - Applying laws of indices

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

- Apply multiple laws of indices in computations
- Simplify complex expressions using combined laws
- Apply indices to scientific notation and large number calculations

- Work out computations requiring multiple index laws
- Simplify expressions with mixed operations
- Use digital resources to explore applications of indices

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 19
- Calculators
- Digital devices

- Written tests - Class activities - Portfolio

Numbers and Algebra

Indices - Applying laws of indices in numerical computations
Indices - Problem solving with indices

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

- Solve complex problems using laws of indices
- Evaluate numerical expressions involving indices
- Apply indices to solve real-world problems in science and technology

- Evaluate expressions combining all laws of indices
- Solve word problems involving indices
- Discuss applications in computing and scientific calculations

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 19
- Calculators
- Digital resources
- Mentor Essential Mathematics pg. 20
- Digital devices
- Calculators

- Written exercises - Class activities - Observation

Numbers and Algebra

Quadratic Equations - Formation of algebraic expressions

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

- Form algebraic expressions from word statements
- Use letters to represent unknown quantities
- Relate algebraic expressions to real situations like shopping and measurements

- Read case scenarios and form algebraic expressions
- Use letters to represent unknown quantities
- Discuss how expressions represent real-life situations

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 21
- Word problem cards
- Charts

- Oral questions - Written exercises - Observation

Numbers and Algebra

Quadratic Equations - Formation of algebraic expressions from real life
Quadratic Equations - Formation of quadratic expressions

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

- Form complex algebraic expressions from multiple quantities
- Simplify algebraic expressions
- Apply algebraic expressions to calculate costs, distances and areas

- Form expressions involving multiple unknown quantities
- Simplify expressions by collecting like terms
- Solve problems on cost, profit and measurements

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 22
- Word problem cards
- Calculators
- Mentor Essential Mathematics pg. 23
- Rectangular cut-outs
- Charts

- Written exercises - Class activities - Portfolio

Numbers and Algebra

Quadratic Equations - Quadratic expressions from real life situations

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

- Form quadratic expressions from real-life contexts
- Interpret word problems to generate quadratic expressions
- Apply quadratic expressions to floor plans, gardens and picture frames

- Read scenarios on area and form quadratic expressions
- Draw diagrams to visualize the problems
- Work out expressions for paths around gardens and margins

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 24
- Diagram charts
- Graph paper

- Written exercises - Class activities - Observation

Numbers and Algebra

Quadratic Equations - Formation of quadratic equations

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

- Distinguish between quadratic expressions and equations
- Form quadratic equations from given conditions
- Apply quadratic equations to problems on area and dimensions

- Form quadratic equations from area problems
- Set up equations where expression equals a given value
- Discuss volleyball pitch and room dimension problems

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 25
- Diagram charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Equations - Quadratic equations from word problems
Quadratic Equations - Factorisation of quadratic expressions

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

- Form quadratic equations from various word problems
- Interpret real-life situations as quadratic equations
- Model age, product and sharing problems using quadratic equations

- Read and interpret word problems
- Form quadratic equations from age and product problems
- Discuss seedbed and carpet area problems

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 26
- Word problem cards
- Calculators
- Mentor Essential Mathematics pg. 27
- Factor pair charts

- Written tests - Class activities - Portfolio

Numbers and Algebra

Quadratic Equations - Factorisation by grouping

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

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

- 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
- Worked examples charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Equations - Factorisation of expressions ax² + bx + c
Quadratic Equations - Solving by factorisation

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
- Worked examples charts

- Written tests - Class activities - Observation

Numbers and Algebra

Quadratic Equations - Solving equations with repeated roots

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

- Solve quadratic equations with repeated roots
- Identify perfect square trinomials
- Interpret the meaning of repeated roots in context

- Factorise perfect square trinomials
- Solve equations yielding single solutions
- Discuss what repeated roots mean in area problems

How are quadratic equations applied in real life?

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

- Oral questions - Written exercises - Observation

Numbers and Algebra
Measurements and Geometry
Measurements and Geometry

Quadratic Equations - Applications to real life problems
Reflection - Lines of symmetry in plane figures
Reflection - Lines of symmetry in regular polygons

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
- Mentor Essential Mathematics pg. 50
- Paper cut-outs
- Scissors
- Various 2D objects
- Mentor Essential Mathematics pg. 52
- Rulers
- Protractors
- Plain paper

- Written tests - Portfolio - Class activities

Measurements and Geometry

Reflection - Properties of reflection
Reflection - Drawing images given object and mirror line
Reflection - Reflection along x = 0

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

- 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

- 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

What are the properties of reflection?

- Mentor Essential Mathematics pg. 53
- Plane mirrors
- Rulers
- Plain paper
- Mentor Essential Mathematics pg. 54
- Plain paper
- Set squares
- Mentor Essential Mathematics pg. 56
- Graph paper
- Pencils

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection - Reflection along y = 0
Reflection - Reflection along y = x
Reflection - Drawing mirror line given object and image on plane surface

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

- Draw an image after reflection along the line y = 0
- Determine coordinates of image points when reflected along x-axis
- Apply reflection concepts to architectural symmetry and graphic design

- Plot squares and rectangles on Cartesian plane
- Reflect shapes along line y = 0
- Compare coordinates before and after reflection
- Discuss the transformation rule for y = 0 reflection

What happens to coordinates when reflecting along y = 0?

- Mentor Essential Mathematics pg. 58
- Graph paper
- Rulers
- Calculators
- Mentor Essential Mathematics pg. 57
- Pencils
- Mentor Essential Mathematics pg. 60
- Plain paper
- Compasses

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection - Drawing mirror line on Cartesian plane
Reflection - Application in real life situations

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

- Draw the mirror line given an object and its image on Cartesian plane
- Identify the equation of the mirror line
- Connect mirror line concepts to coordinate geometry applications

- Plot objects and their images on Cartesian plane
- Join corresponding vertices
- Construct perpendicular bisectors
- Determine equation of mirror line

How do we determine the equation of a mirror line?

- Mentor Essential Mathematics pg. 61
- Graph paper
- Rulers
- Compasses
- Mentor Essential Mathematics pg. 63
- Digital resources

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

- 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

How do we identify the sides of a right-angled triangle?

- Mentor Essential Mathematics pg. 65
- Ladders
- Protractors
- Rulers
- Mentor Essential Mathematics pg. 67
- Rulers
- Calculators
- Mentor Essential Mathematics pg. 68
- Calculators
- Reference books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Sine ratio
Trigonometry - Applications of sine ratio
Trigonometry - Cosine ratio

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

- 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

- 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

What is the sine of an angle?

- Mentor Essential Mathematics pg. 69
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 71
- Calculators
- Digital resources
- Mentor Essential Mathematics pg. 72

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry - Applications of cosine ratio
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:

- Apply cosine ratio to solve problems
- Calculate cosine from real-life situations
- Use cosine in determining base distances and horizontal measurements

- Calculate cosine of angles formed by ladders and ground
- Work out cosine of angles in warehouse roof designs
- Solve problems involving ramps and inclined surfaces
- Share solutions with classmates

How is cosine ratio applied in real life?

- Mentor Essential Mathematics pg. 74
- Calculators
- Rulers
- Reference books
- Mentor Essential Mathematics pg. 75
- Scientific calculators
- Reference books
- Digital resources
- Mentor Essential Mathematics pg. 76
- Exercise books

- Observation - Oral questions - Written assignments

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

- 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

How do we use angles of elevation to find heights?

- Mentor Essential Mathematics pg. 79
- Clinometers
- Tape measures
- Calculators
- Mentor Essential Mathematics pg. 80
- Calculators
- Rulers
- Exercise books

- Observation - Practical work - Written tests

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
Area of Polygons - Area of a rhombus

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
- Mentor Essential Mathematics pg. 88
- Protractors
- Calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

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:

- Calculate area of rhombus given side and included angle
- Apply the formula Area = a² sin θ
- Use rhombus area calculations for badges, logos and decorations

- Draw rhombus-shaped badge with given side and angle
- Calculate lengths of diagonals using trigonometry
- Work out area using ½ × d₁ × d₂
- Verify using formula a² sin θ

How do we find area of rhombus given side and angle?

- Mentor Essential Mathematics pg. 89
- Calculators
- Rulers
- Protractors
- Mentor Essential Mathematics pg. 92
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 94
- Exercise books

- Observation - Oral questions - Written tests

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

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

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

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

How are areas of polygons useful in real life?

- Mentor Essential Mathematics pg. 98
- Calculators
- Digital resources
- Reference books
- Mentor Essential Mathematics pg. 101
- Compasses
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 102
- 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

- 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

- 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
Surface Area of Solids - Surface area of cone using formula

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

- 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
- Mentor Essential Mathematics pg. 114
- Calculators
- Exercise books
- Reference books

- Observation - Oral questions - Written assignments

Measurements and Geometry

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:

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

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

What shapes make up the net of a pyramid?

- Mentor Essential Mathematics pg. 115
- Manila paper
- Scissors
- Rulers
- Mentor Essential Mathematics pg. 116
- Graph paper
- Calculators
- Mentor Essential Mathematics pg. 117

- Observation - Practical work - Written tests

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
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

- 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

- 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
Statistics and Probability
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

- 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. 166
- Tally charts
- Data collection sheets
- Mentor Essential Mathematics pg. 167
- Data sets
- Tally charts

- Observation - Oral questions - Written tests

Statistics and Probability

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

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

- Oral questions - Written exercises - Class activities

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

- 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
Statistics - Pie charts

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

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

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

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

- Mentor Essential Mathematics pg. 174
- Graph paper
- Rulers
- Pencils
- Mentor Essential Mathematics pg. 176
- Protractors
- Compasses
- Calculators

- Practical exercises - Observation - Written exercises

Statistics and Probability

Statistics - Interpreting bar graphs

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

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

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

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

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

- Oral questions - Written exercises - Class activities

Statistics and Probability

Statistics - Interpreting line graphs and pie charts
Probability - Equally likely outcomes

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

- Written tests - Class activities - Portfolio

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

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

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

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

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

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

- Oral questions - Written exercises - Observation

Statistics and Probability

Probability - Performing experiments on mutually exclusive events

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

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

- Spin colour wheels and record outcomes
- Pick cards from a deck and note results
- Discuss why two mutually exclusive events cannot occur together

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

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

- Practical exercises - Observation - Class activities

Statistics and Probability

Probability - Calculating probability of mutually exclusive events
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

- 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