Numbers and Algebra

Real Numbers - Odd and even numbers
Real Numbers - Prime and composite 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
- Mentor Essential Mathematics pg. 3
- Factor charts
- Number cards

- Oral questions - Written exercises - Observation

Numbers and Algebra

Real Numbers - Rational and irrational numbers
Real Numbers - Combined operations on rational numbers
Real Numbers - Combined operations on rational numbers
Real Numbers - Reciprocal of numbers

By the end of the lesson, the learner should be able to:
- Define rational and irrational numbers
- Classify real numbers as rational or irrational
- Relate rational numbers to everyday measurements like prices and quantities

- Use digital devices to search for meaning of rational and irrational numbers
- Classify given numbers as rational or irrational
- Discuss examples of rational numbers in daily transactions

Why are numbers important?

- Mentor Essential Mathematics pg. 5
- Digital devices
- Number charts
- Calculators
- Digital resources
- Mentor Essential Mathematics pg. 7
- Word problem cards
- Mentor Essential Mathematics pg. 8
- Thermometer charts
- Mentor Essential Mathematics pg. 9
- Scientific calculators
- Digital devices

- Oral questions - Written exercises - Observation

Numbers and Algebra

Real Numbers - Application of rational numbers
Indices - Powers and bases
Indices - Expressing numbers in index form
Indices - Multiplication law

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

- Written tests - Portfolio - Class activities

Numbers and Algebra

Indices - Division law
Indices - Power of a power

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
- Mentor Essential Mathematics pg. 17

- Written tests - Class activities - Observation

Numbers and Algebra

Indices - Zero index
Indices - Applying laws of indices
Indices - Applying laws of indices in numerical computations

By the end of the lesson, the learner should be able to:
- State the zero index law
- Apply the zero index to simplify expressions
- Understand why any non-zero number raised to power zero equals one

- Use division law to derive the zero index law
- Simplify expressions involving zero index
- Verify the zero index law using calculators

Why are indices important?

- Mentor Essential Mathematics pg. 18
- Calculators
- Index law charts
- Mentor Essential Mathematics pg. 19
- Digital devices
- Digital resources

- Oral questions - Written exercises - Observation

Numbers and Algebra

Indices - Problem solving with indices
Quadratic Equations - Formation of algebraic expressions
Quadratic Equations - Formation of algebraic expressions from real life

By the end of the lesson, the learner should be able to:
- Apply indices to solve practical problems
- Work collaboratively to solve index problems
- Connect indices to technological applications like data storage

- Work with peers on practical problems involving indices
- Present solutions and discuss different approaches
- Research applications of indices in computer memory and data

Why are indices important?

- Mentor Essential Mathematics pg. 20
- Digital devices
- Calculators
- Mentor Essential Mathematics pg. 21
- Word problem cards
- Charts
- Mentor Essential Mathematics pg. 22

- Portfolio - Observation - Written tests

Numbers and Algebra

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

By the end of the lesson, the learner should be able to:
- Identify quadratic expressions
- Form quadratic expressions by multiplying binomials
- Relate quadratic expressions to calculating areas of rectangles

- Expand products of two binomials
- Identify the structure of quadratic expressions
- Discuss how quadratic expressions represent area problems

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 23
- Rectangular cut-outs
- Charts
- Mentor Essential Mathematics pg. 24
- Diagram charts
- Graph paper

- Oral questions - Written exercises - Observation

Numbers and Algebra

Quadratic Equations - Formation of quadratic equations
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:
- 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
- Mentor Essential Mathematics pg. 26
- Word problem cards
- Mentor Essential Mathematics pg. 27
- Factor pair charts

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Equations - Factorisation by grouping
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 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
- Mentor Essential Mathematics pg. 28
- Factor charts

- Written exercises - Class activities - Oral questions

Numbers and Algebra
Measurements and Geometry

Quadratic Equations - Solving equations with repeated roots
Quadratic Equations - Applications to real life problems
Similarity and Enlargement - Properties of similar figures

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
- Diagram charts
- Calculators
- Mentor Essential Mathematics pg. 31
- Similar objects (containers, shapes)
- Rulers and protractors
- Digital resources

- Oral questions - Written exercises - Observation

Measurements and Geometry

Similarity and Enlargement - Properties of similar figures
Similarity and Enlargement - Centre of enlargement and linear scale factor
Similarity and Enlargement - Linear scale factor
Similarity and Enlargement - Drawing images under enlargement
Similarity and Enlargement - Drawing images on Cartesian plane

By the end of the lesson, the learner should be able to:
- Determine whether given figures are similar
- Calculate ratios of corresponding sides
- Connect similar figures to everyday items like photo frames and tiles

- Work out ratios of corresponding sides of triangles
- Use protractor to measure corresponding angles
- Determine if rectangles are similar by comparing ratios
- Share findings with classmates

What conditions must be met for two figures to be similar?

- Mentor Essential Mathematics pg. 33
- Protractors
- Rulers
- Cut-outs of similar shapes
- Mentor Essential Mathematics pg. 37
- Plain paper
- Pencils
- Mentor Essential Mathematics pg. 38
- Graph paper
- Calculators
- Mentor Essential Mathematics pg. 40
- Geometrical instruments
- Mentor Essential Mathematics pg. 41

- Observation - Oral questions - Written tests

Measurements and Geometry

Similarity and Enlargement - Area scale factor
Similarity and Enlargement - Area scale factor calculations
Similarity and Enlargement - Volume scale factor
Similarity and Enlargement - Relating linear, area and volume scale factors

By the end of the lesson, the learner should be able to:
- Determine the area scale factor of similar figures
- Calculate areas of objects and their images
- Relate area scale factor to land surveying and floor planning

- Draw right-angled triangle and enlarge with scale factor 3
- Calculate areas of object and image
- Determine ratio of areas
- Discuss relationship between linear and area scale factors

What is the relationship between linear scale factor and area scale factor?

- Mentor Essential Mathematics pg. 42
- Graph paper
- Calculators
- Rulers
- Mentor Essential Mathematics pg. 44
- Rulers
- Digital resources
- Mentor Essential Mathematics pg. 43
- Similar containers
- Calculators
- Mentor Essential Mathematics pg. 45
- Manila paper
- Scissors

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Application to area
Similarity and Enlargement - Application to volume
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 linear scale factor to find areas of similar figures
- Solve problems on area using scale factors
- Connect similarity concepts to architectural blueprints and scale models

- Calculate areas of similar figures using scale factors
- Solve word problems involving area scale factor
- Use digital devices to explore applications
- Present solutions to peers

How do we apply area scale factor to solve problems?

- Mentor Essential Mathematics pg. 46
- Calculators
- Digital resources
- Reference books
- Mentor Essential Mathematics pg. 47
- Manila paper
- Locally available materials
- Mentor Essential Mathematics pg. 50
- Paper cut-outs
- Scissors
- Various 2D objects
- Mentor Essential Mathematics pg. 52
- Rulers
- Protractors
- Plain paper

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection - Properties of reflection
Reflection - Drawing images given object and mirror line
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:
- 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
- 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
Reflection - Application in real life situations
Trigonometry - Identifying sides of a right-angled triangle
Trigonometry - Tangent ratio

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
- Mentor Essential Mathematics pg. 63
- Digital resources
- Mentor Essential Mathematics pg. 65
- Ladders
- Protractors
- Rulers
- Mentor Essential Mathematics pg. 67
- Calculators

- Observation - Practical work - Written tests

Measurements and Geometry

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

By the end of the lesson, the learner should be able to:
- Apply tangent ratio to solve problems
- Calculate tangent from real-life situations
- Use tangent in determining slopes of ramps and roof pitches

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

How is tangent ratio applied in real life?

- Mentor Essential Mathematics pg. 68
- Calculators
- Rulers
- Reference books
- Mentor Essential Mathematics pg. 69
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 71
- Digital resources
- Mentor Essential Mathematics pg. 72
- Mentor Essential Mathematics pg. 74

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry - Sines and cosines of complementary angles
Trigonometry - Solving equations involving complementary angles
Trigonometry - Making a clinometer

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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
- Digital resources

- Observation - Practical work - 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
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:
- 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
- Mentor Essential Mathematics pg. 86
- Scientific calculators
- Mentor Essential Mathematics pg. 87
- Exercise 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
Area of Polygons - Area of a regular pentagon

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

- 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

How do we find the area of a rhombus?

- Mentor Essential Mathematics pg. 88
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 89
- Calculators
- Protractors
- Mentor Essential Mathematics pg. 92
- Mentor Essential Mathematics pg. 94
- Exercise books
- Mentor Essential Mathematics pg. 95

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Problems on area of pentagon
Area of Polygons - Area of a regular hexagon
Area of Polygons - Application in real life situations

By the end of the lesson, the learner should be able to:
- Solve problems on area of regular pentagons
- Calculate areas of pentagon-shaped objects
- Apply pentagon area to trampoline covers and decorative designs

- Calculate area of pentagon-shaped flower beds
- Work out area of pizza box lids
- Solve problems involving pentagon-shaped objects
- Present solutions to class

How is area of pentagon applied in real life?

- Mentor Essential Mathematics pg. 97
- Calculators
- Exercise books
- Digital resources
- Mentor Essential Mathematics pg. 96
- Rulers
- Protractors
- Calculators
- Mentor Essential Mathematics pg. 98
- 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

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

How do we find the area of a sector?

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

By the end of the lesson, the learner should be able to:
- 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
- Mentor Essential Mathematics pg. 112
- Manila paper
- Scissors
- Cone-shaped objects
- Mentor Essential Mathematics pg. 113
- Cone nets
- Protractors
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area of Solids - Surface area of cone using formula
Surface Area of Solids - Nets of pyramids
Surface Area of Solids - Surface area of square-based pyramid
Surface Area of Solids - Surface area of rectangular-based pyramid
Surface Area of Solids - Surface area of a sphere
Surface Area of Solids - Surface area of a hemisphere

By the end of the lesson, the learner should be able to:
- Calculate surface area of cones using πrl + πr²
- Solve problems on surface area of cones
- Use cone surface area in designing Christmas hats, filter papers and decorative cones

- Apply formula: Curved surface area = πrl
- Apply formula: Total surface area = πrl + πr²
- Calculate surface area of Christmas hats
- Solve problems on filter paper cones

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

- Mentor Essential Mathematics pg. 114
- Calculators
- Exercise books
- Reference books
- Mentor Essential Mathematics pg. 115
- Manila paper
- Scissors
- Rulers
- Mentor Essential Mathematics pg. 116
- Graph paper
- Mentor Essential Mathematics pg. 117
- 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
Surface Area of Solids - Surface area of frustum of a pyramid
Surface Area of Solids - Problems on frustum of a pyramid
Volume and Capacity - Problems on volume of pyramids

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
- Mentor Essential Mathematics pg. 125
- Mentor Essential Mathematics pg. 127
- Digital resources
- Mentor Essential Mathematics pg. 136

- Observation - Oral questions - Written assignments