Numbers and Algebra

Indices and Logarithms - Relating index notation to logarithm notation
Indices and Logarithms - Common logarithms from mathematical tables

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

- Relate index notation to logarithm notation to base 10
- Convert between index and logarithm forms
- Connect logarithms to measuring earthquake intensity (Richter scale) and sound (decibels)

- Discuss the relationship between index and logarithm notation
- Convert expressions from index form to logarithm form and vice versa
- Use digital devices to explore logarithms

What is the relationship between indices and logarithms?

- Mentor Core Mathematics Grade 10 pg. 22
- Calculators
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 23
- Mathematical tables
- Calculators

- Oral questions - Written exercises - Observation

Numbers and Algebra

Indices and Logarithms - Logarithms of numbers greater than 10 and less than 1
Indices and Logarithms - Antilogarithms from tables and calculators

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

- Determine logarithms of numbers greater than 10 using standard form
- Determine logarithms of numbers less than 1
- Apply logarithms to express very large or very small quantities in science

- Express numbers in standard form
- Use standard form and tables to find logarithms
- Work with bar notation for negative characteristics

How do we find logarithms of very large or very small numbers?

- Mentor Core Mathematics Grade 10 pg. 25
- Mathematical tables
- Calculators
- Mentor Core Mathematics Grade 10 pg. 29

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices and Logarithms - Application of logarithms in multiplication and division
Indices and Logarithms - Application of logarithms in powers and roots

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

- Apply logarithms in multiplication of numbers
- Apply logarithms in division of numbers
- Use logarithms to simplify complex calculations in business and science

- Use logarithms to multiply numbers by adding logarithms
- Use logarithms to divide numbers by subtracting logarithms
- Work out problems involving multiplication and division

How do logarithms simplify multiplication and division?

- Mentor Core Mathematics Grade 10 pg. 33
- Mathematical tables
- Calculators
- Mentor Core Mathematics Grade 10 pg. 37

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices and Logarithms - Combined operations and problem solving
Quadratic Expressions and Equations - Forming quadratic expressions from statements
Quadratic Expressions and Equations - Forming quadratic expressions from real-life situations
Quadratic Expressions and Equations - Deriving quadratic identities from concept of area

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

- Apply logarithms in combined operations
- Solve complex problems using logarithms
- Use logarithms to solve real-world problems in physics, engineering and finance

- Work out problems involving combined operations
- Use logarithms to evaluate complex expressions
- Apply logarithms to real-life situations

How do we use logarithms to solve complex mathematical problems?

- Mentor Core Mathematics Grade 10 pg. 39
- Mathematical tables
- Calculators
- Mentor Core Mathematics Grade 10 pg. 42
- Graph paper
- Rulers
- Mentor Core Mathematics Grade 10 pg. 43
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 44
- Charts

- Written assignments - Class activities - Oral questions

Numbers and Algebra

Quadratic Expressions and Equations - Deriving more quadratic identities
Quadratic Expressions and Equations - Applying quadratic identities in numerical cases
Quadratic Expressions and Equations - Factorising quadratic expressions (coefficient of x² is 1)
Quadratic Expressions and Equations - Factorising quadratic expressions (coefficient of x² greater than 1)

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

- Derive the identities (a-b)² and (a+b)(a-b) using area concept
- Apply the identities in expanding expressions
- Use quadratic identities to simplify calculations in construction and design

- Use area models to derive identities
- Discuss and verify quadratic identities
- Work out exercises using identities

What are the different quadratic identities and how are they derived?

- Mentor Core Mathematics Grade 10 pg. 45
- Graph paper
- Charts
- Mentor Core Mathematics Grade 10 pg. 47
- Calculators
- Mentor Core Mathematics Grade 10 pg. 48
- Charts
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 49
- Calculators

- Written exercises - Oral questions - Class activities

Numbers and Algebra

Quadratic Expressions and Equations - Forming quadratic equations from given situations
Quadratic Expressions and Equations - Forming quadratic equations from given roots
Quadratic Expressions and Equations - Solving quadratic equations by factorisation

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

- Form quadratic equations from word problems
- Express real-life situations as quadratic equations
- Relate equation formation to modelling practical problems like profit and area calculations

- Read and interpret word problems
- Form quadratic equations from given situations
- Work out exercises involving equation formation

How do we form quadratic equations from real-life situations?

- Mentor Core Mathematics Grade 10 pg. 51
- Charts
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 52
- Calculators
- Mentor Core Mathematics Grade 10 pg. 53

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Expressions and Equations - Solving more quadratic equations by factorisation
Quadratic Expressions and Equations - Applying quadratic equations to real-life situations

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

- Solve quadratic equations with leading coefficient greater than 1
- Verify solutions by substitution
- Apply equation solving to find unknown dimensions in practical problems

- Factorise and solve complex quadratic equations
- Verify solutions by substituting back
- Work out various exercises

How do we verify solutions of quadratic equations?

- Mentor Core Mathematics Grade 10 pg. 53
- Charts
- Calculators
- Mentor Core Mathematics Grade 10 pg. 54
- Digital devices

- Written exercises - Oral questions - Observation

Numbers and Algebra
Measurements and Geometry

Quadratic Expressions and Equations - Problem solving with quadratic equations
Reflection and Congruence - Lines of symmetry in plane figures

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

- Solve complex word problems using quadratic equations
- Select appropriate solutions based on context
- Connect quadratic equations to practical applications in business, construction and daily life

- Analyse and solve complex word problems
- Discuss validity of solutions in given contexts
- Search for applications of quadratic equations using digital devices

Why are quadratic equations important in solving real-world problems?

- Mentor Core Mathematics Grade 10 pg. 55
- Digital devices
- Charts
- Mentor Core Mathematics Grade 10 pg. 75
- Paper cut-outs
- Plane mirrors
- Objects from environment

- Written assignments - Class activities - Project work

Measurements and Geometry

Reflection and Congruence - Properties of reflection
Reflection and Congruence - Reflection on plane surface
Reflection and Congruence - Reflection on Cartesian plane (x-axis and y-axis)

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

- Determine properties of reflection
- Use plane mirrors to demonstrate reflection
- Relate reflection to mirror images in daily life

- Use plane mirror to locate image of an object
- Use tracing paper to generate properties of reflection
- Discuss applications in driving mirrors

What are the properties of reflection?

- Mentor Core Mathematics Grade 10 pg. 78
- Plane mirrors
- Tracing paper
- Graph papers
- Mentor Core Mathematics Grade 10 pg. 79
- Plain paper
- Geometrical instruments
- Rulers
- Mentor Core Mathematics Grade 10 pg. 82
- Graph papers
- Geometrical set
- Calculators

- Written assignments - Practical work - Oral questions

Measurements and Geometry

Reflection and Congruence - Reflection along lines y=x and y=-x
Reflection and Congruence - Reflection along other lines

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

- Draw images after reflection along y=x and y=-x
- Determine image coordinates accurately
- Apply knowledge in solving transformation problems

- Draw objects and reflect along y=x
- Reflect along y=-x
- Compare results and establish patterns

What happens to coordinates when reflecting along y=x?

- Mentor Core Mathematics Grade 10 pg. 84
- Graph papers
- Geometrical instruments
- Rulers
- Mentor Core Mathematics Grade 10 pg. 85
- Geometrical set
- Calculators

- Written assignments - Practical work - Observation

Measurements and Geometry

Reflection and Congruence - Determining equation of mirror line
Reflection and Congruence - Congruence tests (SSS and SAS)

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

- Determine equation of mirror line given object and image
- Construct perpendicular bisectors accurately
- Apply knowledge in solving problems

- Join corresponding points and construct perpendicular bisectors
- Determine gradients and y-intercepts
- Form equations of mirror lines

How do we find the equation of a mirror line?

- Mentor Core Mathematics Grade 10 pg. 86
- Graph papers
- Geometrical instruments
- Calculators
- Mentor Core Mathematics Grade 10 pg. 89
- Paper cut-outs
- Rulers

- Written assignments - Practical assessment - Oral questions

Measurements and Geometry

Reflection and Congruence - Congruence tests (ASA and RHS)
Reflection and Congruence - Applications in real life

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

- Carry out congruence tests using ASA and RHS
- Prove triangles are congruent
- Apply congruence in geometric proofs

- Use triangles to establish ASA congruence
- Test for RHS congruence in right-angled triangles
- Solve problems involving congruence

How do we prove triangles are congruent?

- Mentor Core Mathematics Grade 10 pg. 91
- Paper cut-outs
- Protractors
- Rulers
- Mentor Core Mathematics Grade 10 pg. 95
- Plane mirrors
- Digital devices
- Reference materials

- Written assignments - Class exercises - Oral questions

Measurements and Geometry

Rotation - Properties of rotation
Rotation - Rotation on plane surface

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

- Determine properties of rotation
- Demonstrate rotation using a clock
- Relate rotation to movement of clock hands and wheels

- Use an improvised clock to demonstrate rotation
- Discuss movement of minute and hour hands
- Generate properties of rotation

What are the properties of rotation?

- Mentor Core Mathematics Grade 10 pg. 97
- Improvised clock
- Protractors
- Paper cut-outs
- Mentor Core Mathematics Grade 10 pg. 99
- Plain paper
- Rulers
- Compasses

- Oral questions - Observation - Written assignments

Measurements and Geometry

Rotation - Rotation through ±90° about origin
Rotation - Rotation through ±180° about origin
Rotation - Rotation about other centres

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

- Rotate objects through ±90° about the origin
- State coordinates of images correctly
- Recognize patterns in coordinate changes

- Plot objects on Cartesian plane
- Rotate through +90° and -90° about (0,0)
- Record and compare coordinates

How do coordinates change under rotation through 90°?

- Mentor Core Mathematics Grade 10 pg. 103
- Graph papers
- Geometrical set
- Calculators
- Geometrical instruments
- Mentor Core Mathematics Grade 10 pg. 105
- Protractors

- Written assignments - Class exercises - Oral questions

Measurements and Geometry

Rotation - Finding centre and angle of rotation
Rotation - Rotational symmetry of plane figures

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

- Determine centre and angle of rotation given object and image
- Construct perpendicular bisectors accurately
- Apply construction skills in solving problems

- Join corresponding points
- Construct perpendicular bisectors
- Locate centre and measure angle of rotation

How do we find the centre and angle of rotation?

- Mentor Core Mathematics Grade 10 pg. 106
- Graph papers
- Geometrical instruments
- Protractors
- Mentor Core Mathematics Grade 10 pg. 110
- Paper cut-outs
- Pins
- Manila paper

- Written tests - Practical activities - Observation

Measurements and Geometry

Rotation - Axis and order of rotational symmetry in solids
Rotation - Deducing congruence from rotation

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

- Determine axis and order of rotational symmetry in solids
- Identify axes of symmetry in various solids
- Connect rotational symmetry to manufacturing and packaging

- Collect regular solids from environment
- Identify axes of rotational symmetry
- Establish order of rotational symmetry

How do we identify rotational symmetry in solids?

- Mentor Core Mathematics Grade 10 pg. 113
- Models of solids
- Objects from environment
- Mentor Core Mathematics Grade 10 pg. 115
- Graph papers
- Geometrical instruments
- Digital devices

- Observation - Written tests - Oral questions

Measurements and Geometry

Trigonometry 1 - Reading tangent from tables
Trigonometry 1 - Reading sine and cosine from tables

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

- Determine tangent of acute angles from tables
- Read and interpret mathematical tables correctly
- Apply tangent ratios in calculating heights and distances

- Identify angles in table column
- Read tangent values from main columns
- Use mean difference columns for precision

How do we read tangent values from tables?

- Mentor Core Mathematics Grade 10 pg. 120
- Mathematical tables
- Calculators
- Mentor Core Mathematics Grade 10 pg. 122

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Trigonometry 1 - Using calculators for trigonometric ratios
Trigonometry 1 - Complementary angle relationships

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

- Determine trigonometric ratios using calculators
- Find angles given trigonometric ratios
- Compare calculator and table values

- Set calculator to degree mode
- Find sin, cos, tan of angles
- Use inverse functions to find angles

How do we use calculators for trigonometric ratios?

- Mentor Core Mathematics Grade 10 pg. 126
- Scientific calculators
- Mathematical tables
- Mentor Core Mathematics Grade 10 pg. 128
- Mathematical tables
- Calculators

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Trigonometry 1 - Relating sine, cosine and tangent
Trigonometry 1 - Ratios of 45°

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

- Relate sine, cosine and tangent of acute angles
- Prove that tan θ = sin θ/cos θ
- Apply relationships in solving problems

- Use right-angled triangles
- Derive tan θ = sin θ/cos θ
- Solve problems using the relationship

How are sine, cosine and tangent related?

- Mentor Core Mathematics Grade 10 pg. 129
- Mathematical tables
- Calculators
- Mentor Core Mathematics Grade 10 pg. 130
- Geometrical instruments
- Rulers

- Written tests - Oral questions - Class exercises

Measurements and Geometry

Trigonometry 1 - Ratios of 30° and 60°
Trigonometry 1 - Problems involving special angles
Trigonometry 1 - Angle of elevation

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

- Determine trigonometric ratios of 30° and 60°
- Use equilateral triangle to derive ratios
- Solve problems involving special angles

- Draw equilateral triangle of side 2 units
- Calculate perpendicular height
- Derive ratios for 30° and 60°

How do we derive ratios for 30° and 60°?

- Mentor Core Mathematics Grade 10 pg. 131
- Geometrical instruments
- Rulers
- Mentor Core Mathematics Grade 10 pg. 132
- Reference materials
- Calculators
- Mentor Core Mathematics Grade 10 pg. 133
- Clinometer
- Measuring tape

- Written tests - Class exercises - Observation

Measurements and Geometry

Trigonometry 1 - Angle of depression
Trigonometry 1 - Applications in real life

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

- Define angle of depression
- Solve problems involving angles of depression
- Apply to navigation and surveying

- Demonstrate angles of depression
- Sketch diagrams correctly
- Solve problems involving depression

What is angle of depression?

- Mentor Core Mathematics Grade 10 pg. 134
- Clinometer
- Digital devices
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 136
- Reference books
- Calculators

- Written assignments - Practical work - Observation

Measurements and Geometry

Area of Polygons - Deriving area formula
Area of Polygons - Calculating area using Area = ½abSinC

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

- Derive formula for area of triangle given two sides and included angle
- Use trigonometric ratios in derivation
- Apply formula Area = ½abSinC

- Use trigonometric ratios to derive formula
- Discuss in groups and generate formula
- Practice using the formula

How do we derive the area formula using trigonometry?

- Mentor Core Mathematics Grade 10 pg. 137
- Geometrical instruments
- Calculators
- Mentor Core Mathematics Grade 10 pg. 138
- Calculators
- Mathematical tables

- Written assignments - Class exercises - Observation

Measurements and Geometry

Area of Polygons - Heron's formula
Area of Polygons - Area of rhombus

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

- Determine area of triangle using Heron's formula
- Calculate semi-perimeter correctly
- Apply formula to triangles given three sides

- Calculate semi-perimeter
- Apply Heron's formula
- Compare with other methods

How do we use Heron's formula?

- Mentor Core Mathematics Grade 10 pg. 139
- Calculators
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 143
- Models of rhombus
- Calculators

- Written assignments - Class exercises - Observation

Measurements and Geometry

Area of Polygons - Area of parallelogram and trapezium
Area of Polygons - Area of heptagon

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

- Calculate area of parallelogram using base × height
- Calculate area of trapezium
- Apply formulas to practical situations

- Calculate areas of parallelograms
- Calculate areas of trapeziums
- Identify shapes in environment

How do we calculate areas of parallelograms and trapeziums?

- Mentor Core Mathematics Grade 10 pg. 147
- Geometrical instruments
- Calculators
- Mentor Core Mathematics Grade 10 pg. 152
- Paper cut-outs
- Calculators
- Protractors

- Written assignments - Class exercises - Observation

Measurements and Geometry

Area of Polygons - Area of octagon
Area of Polygons - Irregular polygons
Area of Polygons - Real-life applications

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

- Calculate area of regular octagon
- Use formula involving central angles
- Connect to real objects like stop signs

- Divide octagon into 8 triangles
- Calculate central angle (45°)
- Calculate total area

How do we calculate the area of an octagon?

- Mentor Core Mathematics Grade 10 pg. 156
- Paper cut-outs
- Calculators
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 159
- Geometrical instruments
- Calculators
- Mentor Core Mathematics Grade 10 pg. 163
- Reference materials
- Digital devices

- Written assignments - Class exercises - Observation

Measurements and Geometry

Area of a Part of a Circle - Annulus
Area of a Part of a Circle - Area of sector

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

- Define annulus and its components
- Calculate area of annulus
- Apply to circular paths and rings

- Draw concentric circles
- Calculate area of annulus using πR² - πr²
- Solve practical problems

What is an annulus and how do we calculate its area?

- Mentor Core Mathematics Grade 10 pg. 166
- Compasses
- Calculators
- Mentor Core Mathematics Grade 10 pg. 167
- Paper
- Scissors

- Written tests - Practical activities - Oral questions

Measurements and Geometry

Area of a Part of a Circle - Annular sector
Area of a Part of a Circle - Segment of a circle

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

- Calculate area of annular sector
- Apply to windscreen wipers and fan blades
- Solve practical problems

- Illustrate annular sectors
- Calculate area using sector formula
- Relate to car windscreen wipers

How do we calculate area of an annular sector?

- Mentor Core Mathematics Grade 10 pg. 170
- Diagrams
- Calculators
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 172
- Geometrical instruments
- Calculators

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Area of a Part of a Circle - Problems on segments
Area of a Part of a Circle - Intersecting circles (introduction)

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

- Solve complex problems involving segments
- Apply to church windows and architectural designs
- Calculate missing elements

- Solve various segment problems
- Apply to real-life contexts
- Calculate angles given area

How do we apply segment area in solving problems?

- Mentor Core Mathematics Grade 10 pg. 174
- Calculators
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 176
- Compasses
- Rulers
- Graph papers

- Written tests - Oral questions - Class exercises

Measurements and Geometry

Area of a Part of a Circle - Calculating common area
Area of a Part of a Circle - Complex problems

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

- Calculate area of common region
- Sum areas of two segments
- Solve problems involving intersecting circles

- Calculate area of each segment
- Sum to get common area
- Solve practical problems

How do we calculate the common area?

- Mentor Core Mathematics Grade 10 pg. 177
- Calculators
- Geometrical instruments
- Mentor Core Mathematics Grade 10 pg. 179
- Reference materials
- Digital devices
- Calculators

- Written tests - Class exercises - Observation

Measurements and Geometry

Area of a Part of a Circle - Making dartboard and necklaces
Area of a Part of a Circle - Review and assessment

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

- Make dartboard using concentric circles
- Create beaded necklaces using annular sectors
- Apply concepts creatively

- Make dartboard from available materials
- Create necklaces using beading techniques
- Present projects

How do we apply area concepts in creating designs?

- Mentor Core Mathematics Grade 10 pg. 180
- Cardboard
- Beads
- Paints
- Compasses
- Mentor Core Mathematics Grade 10 pg. 181
- Calculators
- Past papers

- Project assessment - Peer evaluation - Observation

Measurements and Geometry

Surface Area and Volume - Rectangular prism
Surface Area and Volume - Triangular and other prisms
Surface Area and Volume - Pyramids

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

- Determine surface area of rectangular prisms
- Draw nets of rectangular prisms
- Apply to packaging and construction

- Collect models of rectangular prisms
- Sketch nets
- Calculate surface area

How do we calculate surface area of rectangular prisms?

- Mentor Core Mathematics Grade 10 pg. 182
- Models of prisms
- Nets
- Calculators
- Mentor Core Mathematics Grade 10 pg. 185
- Mentor Core Mathematics Grade 10 pg. 191
- Models of pyramids

- Written assignments - Practical activities - Observation

Measurements and Geometry

Surface Area and Volume - Cones
Surface Area and Volume - Frustum of cone

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

- Calculate surface area of cones
- Use formulas for curved surface and base
- Apply to ice cream cones and funnels

- Make cone models from manila paper
- Calculate curved surface area πrl
- Calculate total surface area

How do we calculate surface area of cones?

- Mentor Core Mathematics Grade 10 pg. 193
- Manila paper
- Compasses
- Calculators
- Mentor Core Mathematics Grade 10 pg. 195
- Cone models
- Scissors

- Written tests - Practical work - Oral questions

Measurements and Geometry

Surface Area and Volume - Frustum of pyramid
Surface Area and Volume - Spheres and hemispheres

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

- Calculate surface area of frustum of a pyramid
- Apply similar figure properties
- Connect to kitchen worktops and counters

- Sketch original pyramid
- Use similar figures to find dimensions
- Calculate surface area

How do we find surface area of pyramid frustum?

- Mentor Core Mathematics Grade 10 pg. 197
- Models
- Calculators
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 200
- Spherical objects
- Calculators

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Surface Area and Volume - Composite solids
Surface Area and Volume - Volume of cones

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

- Calculate surface area of composite solids
- Identify component solids
- Apply to real structures and objects

- Identify components of composite solids
- Calculate surface area of each component
- Combine appropriately

How do we find surface area of composite solids?

- Mentor Core Mathematics Grade 10 pg. 202
- Models of composite solids
- Calculators
- Mentor Core Mathematics Grade 10 pg. 205
- Cone and cylinder models
- Sand/water

- Written tests - Project work - Oral questions

Measurements and Geometry

Surface Area and Volume - Volume of prisms and pyramids
Surface Area and Volume - Volume of spheres and hemispheres
Surface Area and Volume - Volume of frustums
Surface Area and Volume - Composite solids volume

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

- Calculate volume of various prisms
- Calculate volume of pyramids using ⅓Bh
- Apply to buildings and storage

- Calculate volumes of prisms
- Apply pyramid volume formula
- Solve real-life problems

How do we calculate volumes of prisms and pyramids?

- Mentor Core Mathematics Grade 10 pg. 206
- Models of solids
- Calculators
- Mentor Core Mathematics Grade 10 pg. 210
- Spherical objects
- Mentor Core Mathematics Grade 10 pg. 212
- Models
- Calculators
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 216
- Models of composite solids

- Written tests - Class exercises - Oral questions