Numbers and Algebra

Indices and Logarithms - Logarithms of numbers greater than 10 and less than 1

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

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices and Logarithms - Antilogarithms from tables and calculators
Indices and Logarithms - Application of logarithms in multiplication and division

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

- Define antilogarithm as the reverse of logarithm
- Read antilogarithms from tables
- Use antilogarithms to find original values from logarithmic calculations

In groups, learners are guided to:

- Discuss the meaning of antilogarithm
- Read antilogarithms from tables
- Use calculators to find antilogarithms

What is an antilogarithm and how is it determined?

- Mentor Core Mathematics Grade 10 pg. 29
- Mathematical tables
- Calculators
- Mentor Core Mathematics Grade 10 pg. 33

- Written exercises - Oral questions - Observation

Numbers and Algebra

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 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

- Written exercises - Oral questions - Observation

Numbers and Algebra

Indices and Logarithms - Combined operations and problem solving
Quadratic Expressions and Equations - Forming quadratic expressions from statements

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

In groups, learners are guided to:

- 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

- Written assignments - Class activities - Oral questions

Numbers and Algebra

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:

- Form quadratic expressions from real-life situations
- Interpret quadratic expressions in context
- Connect quadratic expressions to practical problems like garden design and room carpeting

In groups, learners are guided to:

- Form quadratic expressions from problems involving area
- Work out exercises involving formation of quadratic expressions
- Use digital devices to explore quadratic expressions

How are quadratic expressions formed from real-life situations?

- Mentor Core Mathematics Grade 10 pg. 43
- Graph paper
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 44
- Charts
- Rulers
- Mentor Core Mathematics Grade 10 pg. 45
- Charts

- Written exercises - Class activities - Oral questions

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

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

Quadratic Expressions and Equations - Solving more quadratic equations by factorisation
Quadratic Expressions and Equations - Problem solving with quadratic equations

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

In groups, learners are guided to:

- 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. 55
- Digital devices
- Charts

- Written exercises - Oral questions - Observation

Measurements and Geometry

Similarity and Enlargement - Determining centre of enlargement
Similarity and Enlargement - Linear scale factor

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

- Define the terms similar figures and enlargement
- Identify the centre of enlargement from given figures
- Apply knowledge of similarity in identifying objects around them

In groups, learners are guided to:
- Discuss with peers properties of similar figures
- Use an object and its image to locate the centre of enlargement
- Search the internet for real-life examples of similar figures

How do we identify similar figures in our environment?

- Mentor Core Mathematics Grade 10 pg. 56
- Graph papers
- Rulers
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 57
- Geometrical instruments
- Maps

- Oral questions - Observation - Written assignments

Measurements and Geometry

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

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

- Construct the image of an object given centre and positive scale factor
- Draw enlargements on a plane surface
- Relate enlargement to photography and photocopying

In groups, learners are guided to:
- Draw on a plane surface the images of objects under enlargement
- Use ruler and compass to construct images
- Discuss applications in photography

How do we construct enlarged images accurately?

- Mentor Core Mathematics Grade 10 pg. 61
- Graph papers
- Geometrical set
- Rulers
- Mentor Core Mathematics Grade 10 pg. 62
- Cartesian plane grids
- Geometrical instruments
- Mentor Core Mathematics Grade 10 pg. 64
- Similar plane figures
- Calculators
- Manila paper

- Observation - Written assignments - Practical assessment

Measurements and Geometry

Similarity and Enlargement - Volume scale factor
Similarity and Enlargement - Relating L.S.F, A.S.F and V.S.F
Similarity and Enlargement - Real-life applications

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

- Determine volume scale factor of similar solids
- Establish the relationship between L.S.F and V.S.F
- Apply volume scale factor to real objects like tanks and containers

In groups, learners are guided to:
- Work out volumes of similar solids
- Establish relationship V.S.F = (L.S.F)³
- Discuss applications in container manufacturing

How does enlargement affect the volume of a solid?

- Mentor Core Mathematics Grade 10 pg. 66
- Models of similar solids
- Calculators
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 68
- Models of solids
- Reference books
- Mentor Core Mathematics Grade 10 pg. 72
- Maps
- Scale models
- Calculators

- Written tests - Practical activities - Observation

Measurements and Geometry

Similarity and Enlargement - Project on models

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

- Make models of solids using similarity and enlargement
- Present projects on similar figures
- Relate model-making to careers in engineering and design

In groups, learners are guided to:
- Use locally available materials to make models
- Present and discuss models made
- Explore careers using similarity concepts

How can we use similarity concepts in creating models?

- Mentor Core Mathematics Grade 10 pg. 72
- Manila paper
- Cardboard
- Scissors
- Rulers

- Project assessment - Peer evaluation - Observation

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

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

- Practical assessment - Written tests - Observation

Measurements and Geometry

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 images after reflection along x-axis and y-axis
- State coordinates of images accurately
- Connect coordinate geometry to computer graphics

In groups, learners are guided to:
- Plot objects on Cartesian plane
- Reflect along x-axis and y-axis
- Record coordinates of images

How do coordinates change under reflection along axes?

- Mentor Core Mathematics Grade 10 pg. 82
- Graph papers
- Geometrical set
- Calculators

- Written tests - Class exercises - 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

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
- 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

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

In groups, learners are guided to:
- 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

- Written assignments - Practical assessment - 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

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

- Written assignments - Class exercises - Oral questions

Measurements and Geometry

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 ±180° about the origin
- Determine image coordinates accurately
- Connect half-turn to reflection through a point

In groups, learners are guided to:
- Plot objects and rotate through 180°
- Compare results with -180° rotation
- Establish coordinate patterns

What is the effect of a half-turn on coordinates?

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

- Written tests - Practical work - Observation

Measurements and Geometry

Rotation - Finding centre and angle of rotation

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

- Written tests - Practical activities - Observation

Measurements and Geometry

Rotation - Rotational symmetry of plane figures

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

- Determine order of rotational symmetry of plane figures
- Use paper cut-outs to demonstrate rotational symmetry
- Identify rotational symmetry in logos and designs

In groups, learners are guided to:
- Use paper cut-outs to locate points of symmetry
- Establish order of rotational symmetry
- Discuss symmetry in logos and patterns

What is the order of rotational symmetry?

- Mentor Core Mathematics Grade 10 pg. 110
- Paper cut-outs
- Pins
- Manila paper

- Oral questions - Practical work - Written assignments

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

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

- Written assignments - Practical work - Observation

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

In groups, learners are guided to:
- 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

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

- Written tests - Oral questions - Class exercises

Measurements and Geometry

Trigonometry 1 - Ratios of 45°

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

- Determine trigonometric ratios of 45° using triangles
- Derive exact values without tables
- Apply in solving problems with exact values

In groups, learners are guided to:
- Draw isosceles right-angled triangle
- Calculate hypotenuse using Pythagoras
- Derive sin 45°, cos 45°, tan 45°

How do we find exact values of trigonometric ratios?

- Mentor Core Mathematics Grade 10 pg. 130
- Geometrical instruments
- Rulers

- Written assignments - Practical work - Oral questions

Measurements and Geometry

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

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
- Mentor Core Mathematics Grade 10 pg. 132
- Reference materials
- Calculators

- Written tests - Class exercises - Observation

Measurements and Geometry

Trigonometry 1 - Angle of elevation

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

- Define angle of elevation
- Use clinometer to measure angles of elevation
- Calculate heights of buildings, trees and towers

In groups, learners are guided to:
- Use clinometer to measure angles
- Sketch diagrams showing angles of elevation
- Calculate unknown heights

What is angle of elevation and how do we use it?

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

- Practical assessment - Written tests - Oral questions

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