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

In groups, learners are guided to:

- 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

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

In groups, learners are guided to:

- 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

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices and Logarithms - Application of logarithms in powers and roots
Indices and Logarithms - Combined operations and problem solving

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

- Apply logarithms in evaluating powers of numbers
- Apply logarithms in evaluating roots of numbers
- Use logarithms to solve problems involving compound growth and decay

In groups, learners are guided to:

- Use logarithms to evaluate powers by multiplying logarithms
- Use logarithms to evaluate roots by dividing logarithms
- Work out complex calculations involving powers and roots

How do we use logarithms to evaluate powers and roots?

- Mentor Core Mathematics Grade 10 pg. 37
- Mathematical tables
- Calculators
- Mentor Core Mathematics Grade 10 pg. 39

- Written exercises - Oral questions - Observation

Numbers and Algebra

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
Quadratic Expressions and Equations - Deriving more quadratic identities

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

- Define a quadratic expression
- Form quadratic expressions from given statements
- Relate quadratic expressions to calculating areas of rectangular shapes

In groups, learners are guided to:

- Generate quadratic expressions from given statements
- Draw rectangles and express their areas as quadratic expressions
- Share work with peers

What is a quadratic expression?

- 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
- Mentor Core Mathematics Grade 10 pg. 45
- Charts

- Oral questions - Written exercises - Observation

Numbers and Algebra

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:

- Apply quadratic identities to evaluate numerical expressions
- Use identities to simplify calculations
- Connect quadratic identities to quick mental calculations for large numbers

In groups, learners are guided to:

- Express numerical cases in identity form
- Use identities to evaluate expressions like 99², 101²
- Work out exercises using identities

How do quadratic identities simplify numerical calculations?

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

- Written exercises - Oral questions - Observation

Numbers and Algebra

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

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

In groups, learners are guided to:

- 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

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Expressions and Equations - Solving quadratic equations by factorisation
Quadratic Expressions and Equations - Solving more quadratic equations by factorisation

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

- Solve quadratic equations by factorisation
- Apply the zero product property
- Use solutions of quadratic equations to solve measurement problems

In groups, learners are guided to:

- Factorise quadratic equations
- Apply zero product property to find solutions
- Work out exercises involving solving equations

How do we solve quadratic equations by factorisation?

- Mentor Core Mathematics Grade 10 pg. 53
- Charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra
Measurements and Geometry

Quadratic Expressions and Equations - Problem solving with quadratic equations
Similarity and Enlargement - Determining centre of enlargement

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

In groups, learners are guided to:

- 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. 56
- Graph papers
- Rulers
- Digital devices

- Written assignments - Class activities - Project work

Measurements and Geometry

Similarity and Enlargement - Linear scale factor
Similarity and Enlargement - Constructing images (positive scale factor)
Similarity and Enlargement - Constructing images (negative scale factor)

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

- Determine the linear scale factor from similar figures
- Calculate the ratio of corresponding sides
- Use scale factors in solving problems involving maps and models

In groups, learners are guided to:
- Work out the ratio of lengths of corresponding sides
- Discuss in groups and establish Linear Scale Factor (L.S.F)
- Use digital devices to explore scale factors in maps

What is the relationship between an object and its image under enlargement?

- Mentor Core Mathematics Grade 10 pg. 57
- Graph papers
- Geometrical instruments
- Maps
- Mentor Core Mathematics Grade 10 pg. 61
- Geometrical set
- Rulers
- Mentor Core Mathematics Grade 10 pg. 62
- Cartesian plane grids
- Geometrical instruments

- Written tests - Practical activities - Oral questions

Measurements and Geometry

Similarity and Enlargement - Area scale factor
Similarity and Enlargement - Volume scale factor
Similarity and Enlargement - Relating L.S.F, A.S.F and V.S.F

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

- Determine area scale factor of similar figures
- Establish the relationship between L.S.F and A.S.F
- Apply area scale factor in calculating surface areas of models

In groups, learners are guided to:
- Calculate areas of similar figures
- Work out the ratio of areas
- Discuss relationship A.S.F = (L.S.F)²

How does enlargement affect the area of a figure?

- Mentor Core Mathematics Grade 10 pg. 64
- Similar plane figures
- Calculators
- Manila paper
- Mentor Core Mathematics Grade 10 pg. 66
- Models of similar solids
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 68
- Models of solids
- Reference books

- Written assignments - Class exercises - Oral questions

Measurements and Geometry

Similarity and Enlargement - Real-life applications
Similarity and Enlargement - Project on models

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

- Apply similarity and enlargement to solve real-life problems
- Calculate actual measurements from scale drawings
- Connect concepts to map reading and architectural drawings

In groups, learners are guided to:
- Work out tasks involving similarity in real-life situations
- Solve problems involving maps and models
- Use digital devices to explore applications

Where do we use similarity and enlargement in daily life?

- Mentor Core Mathematics Grade 10 pg. 72
- Maps
- Scale models
- Calculators
- Manila paper
- Cardboard
- Scissors
- Rulers

- Written tests - Project work - Oral questions

Measurements and Geometry

Reflection and Congruence - Lines of symmetry in plane figures
Reflection and Congruence - Properties of reflection

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
- Recognize symmetry in nature and art

In groups, learners are guided to:
- Collect objects from environment and identify lines of symmetry
- Fold paper cut-outs to locate lines of symmetry
- Discuss symmetry in nature and architecture

How do we identify lines of symmetry?

- Mentor Core Mathematics Grade 10 pg. 75
- Paper cut-outs
- Plane mirrors
- Objects from environment
- Mentor Core Mathematics Grade 10 pg. 78
- Tracing paper
- Graph papers

- Observation - Oral questions - Practical activities

Measurements and Geometry

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:

- Draw an image given object and mirror line on plane surface
- Construct perpendicular bisectors accurately
- Apply reflection in creating symmetric designs

In groups, learners are guided to:
- Draw plane figures and mirror lines on paper
- Use properties of reflection to locate images
- Create symmetric patterns using reflection

How do we construct images under reflection?

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

- Practical assessment - Written tests - Observation

Measurements and Geometry

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

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

In groups, learners are guided to:
- 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

- Written assignments - Practical work - Observation

Measurements and Geometry

Reflection and Congruence - Reflection along other lines
Reflection and Congruence - Determining equation of mirror line

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

- Draw images reflected along lines like y=2, x=1, y=x+4
- Apply properties of reflection consistently
- Solve complex reflection problems

In groups, learners are guided to:
- Reflect objects along various mirror lines
- Use perpendicular distance method
- Practice with different mirror line equations

How do we reflect along any given line?

- Mentor Core Mathematics Grade 10 pg. 85
- Graph papers
- Geometrical set
- Calculators
- Mentor Core Mathematics Grade 10 pg. 86
- Geometrical instruments

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Reflection and Congruence - Congruence tests (SSS and SAS)

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

- Carry out congruence tests for triangles using SSS and SAS
- Identify directly and indirectly congruent figures
- Apply congruence in construction and engineering

In groups, learners are guided to:
- Make paper cut-outs of identical shapes
- Test for congruence using SSS
- Test for congruence using SAS

When are two triangles congruent?

- Mentor Core Mathematics Grade 10 pg. 89
- Paper cut-outs
- Geometrical instruments
- Rulers

- Written tests - Practical activities - Observation

Measurements and Geometry

Reflection and Congruence - Congruence tests (ASA and RHS)
Rotation - Properties of rotation

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

In groups, learners are guided to:
- 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. 97
- Improvised clock
- Paper cut-outs

- Written assignments - Class exercises - Oral questions

Measurements and Geometry

Rotation - Rotation on plane surface

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

- Rotate an object given centre and angle on plane surface
- Use protractor and ruler accurately
- Apply rotation in creating patterns and designs

In groups, learners are guided to:
- Draw objects and rotate about given centres
- Measure angles accurately using protractor
- Create rotational patterns

How do we perform rotation on a plane surface?

- Mentor Core Mathematics Grade 10 pg. 99
- Plain paper
- Protractors
- Rulers
- Compasses

- Practical assessment - Written tests - Observation

Measurements and Geometry

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

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

In groups, learners are guided to:
- 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

- Written assignments - Class exercises - Oral questions

Measurements and Geometry

Rotation - Rotation about other centres

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

- Rotate objects about centres other than origin
- Construct rotations accurately
- Solve rotation problems involving various centres

In groups, learners are guided to:
- Rotate objects about various centres
- Use construction methods
- Practice with different angles and centres

How do we rotate about centres other than origin?

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

- Written assignments - Practical assessment - 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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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

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

In groups, learners are guided to:
- 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

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Trigonometry 1 - Reading sine and cosine from tables
Trigonometry 1 - Using calculators for trigonometric ratios

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

- Determine sine and cosine of acute angles from tables
- Use mean difference correctly
- Apply sine and cosine in solving triangles

In groups, learners are guided to:
- Read sine values from tables
- Read cosine values (subtracting mean difference)
- Practice finding angles given ratios

How do we read sine and cosine from tables?

- Mentor Core Mathematics Grade 10 pg. 122
- Mathematical tables
- Calculators
- Mentor Core Mathematics Grade 10 pg. 126
- Scientific calculators
- Mathematical tables

- Written assignments - Practical work - Observation

Measurements and Geometry

Trigonometry 1 - Complementary angle relationships

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

- Relate sines and cosines of complementary angles
- Prove that sin θ = cos(90°-θ)
- Apply relationships in solving equations

In groups, learners are guided to:
- Generate table of complementary angles
- Compare sines and cosines
- Establish sin θ = cos(90°-θ)

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

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

- Written assignments - Class exercises - Observation

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

In groups, learners are guided to:
- 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°

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

In groups, learners are guided to:
- 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

- Written tests - Class exercises - Observation

Measurements and Geometry

Trigonometry 1 - Problems involving special angles
Trigonometry 1 - Angle of elevation

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

- Solve problems using special angle ratios
- Simplify expressions with special angles
- Apply special angles in construction

In groups, learners are guided to:
- Solve problems without tables or calculators
- Simplify trigonometric expressions
- Apply to practical situations

How do we apply special angle ratios?

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

- Written assignments - Oral questions - Class exercises

Measurements and Geometry

Trigonometry 1 - Angle of depression

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

In groups, learners are guided to:
- 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

- 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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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

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

In groups, learners are guided to:
- 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

- Written assignments - Class exercises - Observation

Measurements and Geometry

Area of Polygons - Area of heptagon
Area of Polygons - Area of octagon

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

- Calculate area of regular heptagon
- Divide heptagon into triangles
- Apply to real objects like road signs

In groups, learners are guided to:
- Divide heptagon into 7 triangles
- Calculate central angle (360°÷7)
- Calculate area of one triangle and multiply

How do we calculate the area of a heptagon?

- Mentor Core Mathematics Grade 10 pg. 152
- Paper cut-outs
- Calculators
- Protractors
- Mentor Core Mathematics Grade 10 pg. 156
- Reference materials

- Written tests - Practical work - Oral questions

Measurements and Geometry

Area of Polygons - Irregular polygons

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

- Determine area of irregular polygons
- Subdivide into regular shapes
- Apply to land surveying and floor plans

In groups, learners are guided to:
- Subdivide irregular polygons into regular shapes
- Calculate area of each shape
- Sum up to get total area

How do we calculate area of irregular polygons?

- Mentor Core Mathematics Grade 10 pg. 159
- Geometrical instruments
- Calculators

- Written tests - Project work - Oral questions