Numbers and Algebra

Quadratic Expressions and Equations - Formation of quadratic expressions
Quadratic Expressions and Equations - Quadratic identities (a+b)² and (a−b)²

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

- Define a quadratic expression and identify its terms
- Expand and simplify products of two binomials to form quadratic expressions
- Relate quadratic expressions to real-life measurements such as areas of desks, tiles, and rooms

- Measure the sides of a desk and express the area in terms of a variable x
- Expand expressions such as (x+3)(x+5) and (2x−1)(x−3) by multiplying each term
- Identify the quadratic term, linear term, and constant term in the expansion

How do we form quadratic expressions from given factors?

- Master Core Mathematics Grade 10 pg. 40
- Rulers
- Master Core Mathematics Grade 10 pg. 43
- Rulers
- Graph papers

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Difference of two squares identity and numerical applications

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

- Derive the identity (a+b)(a−b) = a²−b² using the concept of area of a rectangle
- Apply quadratic identities to evaluate numerical expressions mentally
- Use identities to quickly calculate areas of ranch lands, gardens, and metal plates

- Draw a rectangle with sides (a+b) and (a−b) and derive the difference of two squares
- Use identities to evaluate numerical squares such as 25², 82², and products like 1024 × 976
- Compare results with calculator answers

How do quadratic identities make numerical calculations easier?

- Master Core Mathematics Grade 10 pg. 44
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Factorisation when coefficient of x² is one
Quadratic Expressions and Equations - Factorisation when coefficient of x² is greater than one

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

- Identify pairs of integers whose sum and product match the linear and constant terms
- Factorise quadratic expressions of the form x²+bx+c by grouping
- Relate factorisation to finding dimensions of rectangular gardens and wooden boards

- Identify the coefficient of the linear term and the constant term
- Find a pair of integers whose sum equals b and product equals c
- Rewrite the middle term and factorise by grouping

How do we factorise quadratic expressions when the coefficient of x² is one?

- Master Core Mathematics Grade 10 pg. 48
- Charts
- Master Core Mathematics Grade 10 pg. 50

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Factorising perfect squares

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

- Identify a perfect square quadratic expression
- Factorise perfect square expressions into identical factors
- Use factorisation of perfect squares to find side lengths of square mats, tiles, and signboards

- Consider expressions and factorise them to observe identical factors
- Factorise expressions of the form a²+2ab+b² and a²−2ab+b²
- Determine the length of sides of square shapes from area expressions

How do we recognise and factorise perfect square expressions?

- Master Core Mathematics Grade 10 pg. 52
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Factorising difference of two squares
Quadratic Expressions and Equations - Formation of quadratic equations from roots

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

- Recognise expressions involving difference of two squares
- Factorise expressions of the form a²−b² into (a+b)(a−b)
- Apply difference of two squares to determine dimensions of rooms, gardens, and concrete slabs

- Rewrite expressions so that both terms are clearly perfect squares
- Factorise in the form (a+b)(a−b)
- Factorise expressions that require extracting a common factor first

How do we factorise expressions that are a difference of two squares?

- Master Core Mathematics Grade 10 pg. 54
- Charts
- Master Core Mathematics Grade 10 pg. 55

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Formation of quadratic equations from real-life situations

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

- Assign variables to unknown quantities in word problems
- Form quadratic equations from statements involving areas, products, and dimensions
- Translate real-life problems involving classrooms, trains, and gardens into quadratic equations

- Measure the length and width of a desk and express the area in terms of x
- Formulate quadratic equations from problems involving consecutive integers, triangles, and rectangular plots
- Form equations from speed, distance, and time relationships

How do we translate real-life problems into quadratic equations?

- Master Core Mathematics Grade 10 pg. 57
- Rulers
- Measuring tapes

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Solving quadratic equations by factorisation

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

- Rearrange a quadratic equation into standard form ax²+bx+c = 0
- Solve quadratic equations by factorising and setting each factor to zero
- Apply factorisation to find dimensions of real objects such as billboards from their area equations

- Write the equation in standard quadratic form
- Factorise the left-hand side of the equation
- Set each factor equal to zero and solve the resulting linear equations

How do we solve quadratic equations using factorisation?

- Master Core Mathematics Grade 10 pg. 58
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Solving quadratic equations with algebraic fractions

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

- Eliminate fractions by multiplying through by the LCM of the denominators
- Solve the resulting quadratic equation by factorisation
- Apply the technique to solve equations arising from rate and proportion problems

- Identify the LCM of the denominators in the equation
- Multiply every term by the LCM to clear fractions
- Rearrange and solve the quadratic equation by factorisation

How do we solve quadratic equations that contain algebraic fractions?

- Master Core Mathematics Grade 10 pg. 61
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Application of quadratic equations to real-life (ages and dimensions)

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

- Formulate quadratic equations from word problems involving ages and dimensions
- Solve the equations and interpret the solutions in context
- Use quadratic equations to determine present ages, lengths of playgrounds, and widths of table mats

- Assign variables to unknowns and form equations from given relationships
- Solve the quadratic equations by factorisation
- Check that solutions are reasonable in the context of the problem

How do we use quadratic equations to solve age and dimension problems?

- Master Core Mathematics Grade 10 pg. 62
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Application of quadratic equations to real-life (ages and dimensions)

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

- Formulate quadratic equations from word problems involving ages and dimensions
- Solve the equations and interpret the solutions in context
- Use quadratic equations to determine present ages, lengths of playgrounds, and widths of table mats

- Assign variables to unknowns and form equations from given relationships
- Solve the quadratic equations by factorisation
- Check that solutions are reasonable in the context of the problem

How do we use quadratic equations to solve age and dimension problems?

- Master Core Mathematics Grade 10 pg. 62
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Application of quadratic equations to real-life (speed, distance and area)

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

- Formulate quadratic equations from problems involving speed, distance, and area
- Solve the equations and select appropriate solutions
- Use quadratic equations to determine cycling speeds, drone heights, and photograph frame widths

- Form equations from speed-distance-time relationships and area problems
- Solve the quadratic equations by factorisation
- Reject solutions that do not make sense in the real-life context

How do we apply quadratic equations to solve speed and area problems?

- Master Core Mathematics Grade 10 pg. 63
- Calculators

- Oral questions - Written assignments - Observation

Measurements and Geometry

Similarity and Enlargement - Centre of enlargement and linear scale factor
Similarity and Enlargement - Image of an object under enlargement (positive scale factor)

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

- Determine the centre of enlargement and the linear scale factor for similar figures
- Draw lines joining corresponding vertices to locate the centre of enlargement
- Relate the concept of enlargement to everyday applications such as photo enlargement and map reading

- Discuss in a group and review the properties of similar figures and enlargement
- Use an object and its image to establish the centre of enlargement and the ratio of the lengths of corresponding sides (Linear Scale Factor)
- Use digital devices to explore enlargement concepts

How are similarity and enlargement applied in day-to-day life?

- Master Core Mathematics Grade 10 pg. 65
- Graph papers
- Rulers and geometrical set
- Digital resources
- Master Core Mathematics Grade 10 pg. 68
- Squared books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Image of an object under enlargement (negative scale factor)

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

- Construct the image of an object under an enlargement given the centre and a negative linear scale factor
- Draw images on the Cartesian plane using a negative scale factor
- Relate negative enlargement to real-life situations such as inverted images in pinhole cameras

- Draw on the Cartesian plane the images of objects under enlargement given the centres and negative linear scale factors
- Discuss the effect of a negative scale factor on the position of the image relative to the centre of enlargement

How are similarity and enlargement applied in day-to-day life?

- Master Core Mathematics Grade 10 pg. 68
- Graph papers
- Rulers and geometrical set

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Area scale factor
Similarity and Enlargement - Volume scale factor

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

- Determine the area scale factor of similar plane figures
- Calculate the ratio of areas of similar figures
- Use area scale factor to solve problems involving tiles, maps and floor plans

- Discuss in a group and establish the Area Scale Factor (A.S.F) from similar plane figures
- Work out the ratio of the area of similar plane figures
- Use grids to compare areas of objects and their images

How are similarity and enlargement applied in day-to-day life?

- Master Core Mathematics Grade 10 pg. 71
- Graph papers
- Rulers
- Squared books
- Master Core Mathematics Grade 10 pg. 73
- Models of similar solids
- Rulers

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Relating linear scale factor and area scale factor
Similarity and Enlargement - Relating linear scale factor and volume scale factor

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

- Relate linear scale factor to area scale factor
- Calculate area scale factor from a given linear scale factor
- Apply the relationship between L.S.F and A.S.F to solve problems involving maps and land surveying

- Discuss in a group and establish the relationship between L.S.F and A.S.F using two similar plane figures
- Square the linear scale factor and compare with the area scale factor

How are similarity and enlargement applied in day-to-day life?

- Master Core Mathematics Grade 10 pg. 75
- Graph papers
- Rulers
- Calculators
- Master Core Mathematics Grade 10 pg. 76
- Models of similar solids

- Observation - Oral questions - Written tests

Measurements and Geometry

Similarity and Enlargement - Relating linear, area and volume scale factors

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

- Relate linear scale factor, area scale factor and volume scale factor in enlargements
- Move between the three scale factors using appropriate operations
- Solve real-life problems involving similar containers, tanks and models using all three scale factors

- Discuss in a group and establish the relationship between L.S.F, A.S.F and V.S.F using two similar solids
- Work out tasks involving similarity and enlargements in real-life situations

How are similarity and enlargement applied in day-to-day life?

- Master Core Mathematics Grade 10 pg. 77
- Calculators
- Models of similar solids

- Observation - Oral questions - Written tests

Measurements and Geometry

Similarity and Enlargement - Application of similarity and enlargement to real-life situations
Reflection and Congruence - Lines of symmetry in plane figures

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

- Apply similarity and enlargement to solve real-life problems
- Use scale factors in combined problem-solving situations
- Connect similarity and enlargement to practical situations such as construction of scale models, architectural designs and map interpretation

- Work out tasks involving similarity and enlargements in real-life situations
- Use digital devices and other resources to learn more on the use and application of similarity and enlargement
- Use locally available materials to make models of solids of different sizes using similarity and enlargement

How are similarity and enlargement applied in day-to-day life?

- Master Core Mathematics Grade 10 pg. 77
- Digital resources
- Locally available materials
- Calculators
- Master Core Mathematics Grade 10 pg. 79
- Plane figures
- Rectangular paper
- Rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection and Congruence - Properties of reflection

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

- Determine the properties of reflection
- Use tracing paper and plane mirrors to generate the properties of reflection
- Relate reflection properties to how mirrors and reflective surfaces work in daily life

- Use a plane mirror to locate the image of an object placed at a point in front of the mirror
- Draw a plane figure and a mirror line on tracing paper, fold the paper along the mirror line and trace out the plane figure to generate the properties of reflection

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

- Master Core Mathematics Grade 10 pg. 81
- Plane mirrors
- Tracing paper
- Rulers

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection and Congruence - Drawing an image on a plane surface
Reflection and Congruence - Reflection along a line on the Cartesian plane

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

- Draw an image given an object and a mirror line on a plane surface
- Use the properties of reflection to construct images accurately
- Relate reflection on a plane surface to real-world uses such as fabric pattern design and tiling

- Draw on plain paper a given object and a mirror line and use the properties of reflection to locate the corresponding image
- Use construction methods (arcs) to reflect objects accurately on a plane surface

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

- Master Core Mathematics Grade 10 pg. 82
- Rulers and geometrical set
- Plain paper
- Compasses
- Master Core Mathematics Grade 10 pg. 84
- Graph papers
- Squared books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection and Congruence - Special reflections (x-axis and y-axis)

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

- Reflect objects in the y-axis (line x = 0) and x-axis (line y = 0)
- Determine coordinates of images after reflection in the x-axis and y-axis
- Relate reflection in axes to real-life applications such as mirror images in driving mirrors for road safety

- Reflect objects in the y-axis and determine the relationship between coordinates of the object and image
- Reflect objects in the x-axis and determine the relationship between coordinates of the object and image

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

- Master Core Mathematics Grade 10 pg. 86
- Graph papers
- Rulers
- Squared books

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection and Congruence - Special reflections (lines y = x and y = -x)
Reflection and Congruence - Equation of the mirror line

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

- Reflect objects in the lines y = x and y = -x
- Determine coordinates of images after reflection in lines y = x and y = -x
- Use coordinate interchange rules to solve reflection problems efficiently

- Reflect objects in the line y = x and determine the relationship between coordinates of the object and image
- Reflect objects in the line y = -x and determine the relationship between coordinates of the object and image

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

- Master Core Mathematics Grade 10 pg. 88
- Graph papers
- Rulers
- Squared books
- Master Core Mathematics Grade 10 pg. 90
- Rulers and geometrical set
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection and Congruence - Determining and describing mirror line transformations

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

- Determine the equation of the mirror line for various object-image pairs
- Describe fully a reflection transformation by stating the mirror line equation
- Relate mirror line determination to practical applications such as locating the position of a mirror for optimal reflection

- Work out more examples of finding the equation of the mirror line
- Describe single transformations that map objects onto images

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

- Master Core Mathematics Grade 10 pg. 92
- Graph papers
- Rulers and geometrical set
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection and Congruence - Congruence tests for triangles (SSS, SAS, AAS, RHS)

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

- Carry out congruence tests for triangles (SSS, SAS, AAS, RHS)
- Identify congruent triangles using appropriate congruence conditions
- Relate congruence to construction and manufacturing where identical parts are produced

- Work in a group and make paper cutouts of different identical shapes to identify direct and opposite congruent shapes
- Use different triangles to establish the congruence tests: SSS, SAS, AAS and RHS

Where do we use congruence in real life?

- Master Core Mathematics Grade 10 pg. 94
- Paper cutouts
- Rulers and geometrical set
- Protractors

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection and Congruence - Direct and indirect congruence

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

- Distinguish between direct and indirect congruence
- Identify direct congruence from rotation/translation and indirect congruence from reflection
- Connect types of congruence to real-life examples such as matching tiles, stamps and printed patterns

- Use paper cutouts to identify direct and opposite congruent shapes
- Discuss the applications of reflections and congruence on images formed by driving mirrors to enhance road safety

Where do we use congruence in real life?

- Master Core Mathematics Grade 10 pg. 96
- Paper cutouts
- Graph papers
- Rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

Rotation - Properties of rotation
Rotation - Rotation on a plane surface

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

- Determine the properties of rotation
- Demonstrate clockwise and anticlockwise rotation
- Relate rotation to everyday experiences such as the movement of clock hands, wheels and door handles

- Demonstrate rotation using an actual or improvised clock
- Use an object and its image on a plane surface to discuss and generate the properties of rotation
- Discuss and explain the movement of the hour or minute hand

How is rotation applied in real-life situations?

- Master Core Mathematics Grade 10 pg. 100
- Analogue clock or dummy clock
- Paper cutouts
- Pins and cartons
- Master Core Mathematics Grade 10 pg. 103
- Rulers and geometrical set
- Protractors
- Plain paper

- Observation - Oral questions - Written assignments

Measurements and Geometry

Rotation - Rotation on the Cartesian plane
Rotation - Half turn (±180°) about the origin

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

- Rotate an object given the centre and angle of rotation on the Cartesian plane
- Plot objects and their images after rotation on the Cartesian plane
- Apply rotation on the Cartesian plane to solve coordinate geometry problems

- Carry out rotation on a Cartesian plane given the object, centre and angle of rotation
- Determine the coordinates of images after rotation

How is rotation applied in real-life situations?

- Master Core Mathematics Grade 10 pg. 107
- Graph papers
- Rulers and geometrical set
- Protractors
- Master Core Mathematics Grade 10 pg. 109
- Rulers
- Squared books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Rotation - Quarter turns (±90°) about the origin

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

- Rotate objects through −90° and +90° about the origin
- Apply the rules (x, y) → (y, −x) for −90° and (x, y) → (−y, x) for +90°
- Use quarter-turn rules to solve rotation problems involving game design and robotics

- Draw objects and rotate them through −90° (clockwise) and +90° (anticlockwise) about the origin
- Compare coordinates of the object and image to establish the quarter-turn rules

How is rotation applied in real-life situations?

- Master Core Mathematics Grade 10 pg. 110
- Graph papers
- Rulers
- Squared books

- Observation - Oral questions - Written tests

Measurements and Geometry

Rotation - Determining centre and angle of rotation
Rotation - Order of rotational symmetry of plane figures

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

- Determine the centre of rotation given an object and its image
- Determine the angle of rotation given an object and its image
- Use construction (perpendicular bisectors) to locate the centre of rotation

- In a group, use construction to find the centre and angle of rotation given the object and its image on a plane surface and the Cartesian plane
- Bisect lines joining corresponding vertices to locate the centre of rotation

How is rotation applied in real-life situations?

- Master Core Mathematics Grade 10 pg. 113
- Graph papers
- Rulers and geometrical set
- Protractors
- Master Core Mathematics Grade 10 pg. 117
- Paper cutouts
- Rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

Rotation - Axis and order of rotational symmetry in solids

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

- Determine the axis and order of rotational symmetry in solids
- Identify axes of symmetry in common solids such as pyramids, prisms and cylinders
- Relate rotational symmetry in solids to real objects such as bolts, nuts and decorative items

- Collect regular solids such as pyramids, triangular prisms, cones, tetrahedrons from the immediate environment and identify the axis to establish the order of rotational symmetry
- Insert thin wires through models to demonstrate axes of symmetry

How is rotation applied in real-life situations?

- Master Core Mathematics Grade 10 pg. 120
- Models of solids
- Thin wires or straws
- Manila paper

- Observation - Oral questions - Written tests

Measurements and Geometry

Rotation - Congruence from rotation
Trigonometry 1 - Trigonometric ratios from table of tangents

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

- Deduce congruence from rotation
- Identify that rotation always results in direct congruence
- Relate rotation and congruence to real-life manufacturing processes where identical rotated parts are produced

- Use different objects and their images to identify the type of congruence in rotation
- Use digital devices and other resources to learn more on rotation of plane figures and solids

How is rotation applied in real-life situations?

- Master Core Mathematics Grade 10 pg. 122
- Paper cutouts
- Digital resources
- Graph papers
- Master Core Mathematics Grade 10 pg. 123
- Mathematical tables
- Rulers and geometrical set
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Trigonometric ratios from table of sines

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

- Determine the sine of acute angles from mathematical tables
- Read and interpret the table of sines including main columns and mean difference columns
- Connect the sine ratio to practical problems such as determining the height reached by a ladder against a wall

- Use mathematical tables to read and obtain sines of acute angles
- Determine angles whose sine values are given using tables
- Solve problems involving the sine ratio in right-angled triangles

What is trigonometry?

- Master Core Mathematics Grade 10 pg. 127
- Mathematical tables
- Rulers and geometrical set
- Calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry 1 - Trigonometric ratios from table of cosines
Trigonometry 1 - Trigonometric ratios from calculators

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

- Determine the cosine of acute angles from mathematical tables
- Read and interpret the table of cosines, noting that mean differences are subtracted
- Apply the cosine ratio to solve problems such as finding horizontal distances in construction

- Use mathematical tables to read and obtain cosines of acute angles
- Determine angles whose cosine values are given using tables
- Note the difference between tables of cosines and tables of sines/tangents

What is trigonometry?

- Master Core Mathematics Grade 10 pg. 130
- Mathematical tables
- Rulers and geometrical set
- Calculators
- Master Core Mathematics Grade 10 pg. 132
- Scientific calculators
- Mathematical tables

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry 1 - Sines and cosines of complementary angles

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

- Relate sines and cosines of complementary angles
- Apply the relationships sin θ = cos(90° − θ) and cos θ = sin(90° − θ)
- Use complementary angle relationships to simplify trigonometric problems in surveying and engineering

- Draw a right-angled triangle and determine the sine and cosine of complementary angles
- Generate a table of angles and their complements and determine their sines and cosines to establish the relationships

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 134
- Scientific calculators
- Mathematical tables
- Rulers and geometrical set

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Relationship between sine, cosine and tangent of acute angles
Trigonometry 1 - Trigonometric ratios of special angles (45°)

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

- Relate the sine, cosine and tangent of acute angles using tan θ = sin θ / cos θ
- Determine one trigonometric ratio given the other two
- Apply the relationship to solve problems involving right-angled triangles in practical contexts

- Work in a group and using different acute angles, generate a table of the ratios of sine, cosine and tangents to establish the relationship
- Use a right-angled triangle to derive the relationship tan θ = sin θ / cos θ

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 136
- Scientific calculators
- Mathematical tables
- Rulers
- Master Core Mathematics Grade 10 pg. 138
- Rulers and geometrical set
- Plain paper
- Calculators (for verification)

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Trigonometric ratios of special angles (30°, 60° and 90°)

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

- Determine trigonometric ratios of 30°, 60° and 90° using an equilateral triangle
- Summarise trigonometric ratios of all special angles in a table
- Evaluate expressions involving special angles without tables or calculators in contexts such as construction and design

- Draw an equilateral triangle of sides 2 units and draw a perpendicular from a vertex to the base
- Use Pythagoras' theorem to calculate the height
- Determine the trigonometric ratios of 30°, 60° and 90°

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 139
- Rulers and geometrical set
- Plain paper
- Calculators (for verification)

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Angles of elevation

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

- Apply trigonometric ratios to solve problems involving angles of elevation
- Draw sketches and use trigonometric ratios to determine unknown heights and distances
- Relate angles of elevation to practical situations such as measuring the height of buildings, trees and towers

- Identify a tall object within the school compound
- Use a protractor or clinometer to estimate the angle of elevation to the top of the object
- Use trigonometric ratios to determine the height of the object

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 141
- Protractors or clinometers
- Measuring tapes
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Angles of elevation

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

- Apply trigonometric ratios to solve problems involving angles of elevation
- Draw sketches and use trigonometric ratios to determine unknown heights and distances
- Relate angles of elevation to practical situations such as measuring the height of buildings, trees and towers

- Identify a tall object within the school compound
- Use a protractor or clinometer to estimate the angle of elevation to the top of the object
- Use trigonometric ratios to determine the height of the object

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 141
- Protractors or clinometers
- Measuring tapes
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Angles of elevation

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

- Apply trigonometric ratios to solve problems involving angles of elevation
- Draw sketches and use trigonometric ratios to determine unknown heights and distances
- Relate angles of elevation to practical situations such as measuring the height of buildings, trees and towers

- Identify a tall object within the school compound
- Use a protractor or clinometer to estimate the angle of elevation to the top of the object
- Use trigonometric ratios to determine the height of the object

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 141
- Protractors or clinometers
- Measuring tapes
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Angles of elevation

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

- Apply trigonometric ratios to solve problems involving angles of elevation
- Draw sketches and use trigonometric ratios to determine unknown heights and distances
- Relate angles of elevation to practical situations such as measuring the height of buildings, trees and towers

- Identify a tall object within the school compound
- Use a protractor or clinometer to estimate the angle of elevation to the top of the object
- Use trigonometric ratios to determine the height of the object

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 141
- Protractors or clinometers
- Measuring tapes
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Angles of elevation

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

- Apply trigonometric ratios to solve problems involving angles of elevation
- Draw sketches and use trigonometric ratios to determine unknown heights and distances
- Relate angles of elevation to practical situations such as measuring the height of buildings, trees and towers

- Identify a tall object within the school compound
- Use a protractor or clinometer to estimate the angle of elevation to the top of the object
- Use trigonometric ratios to determine the height of the object

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 141
- Protractors or clinometers
- Measuring tapes
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Angles of depression

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

- Apply trigonometric ratios to solve problems involving angles of depression
- Draw sketches and use trigonometric ratios to determine unknown distances from elevated positions
- Apply angles of depression to real-life problems such as navigation, CCTV camera positioning and lighthouse observations

- Choose an elevated position and measure the angle of depression of an object on the ground
- Use trigonometric ratios to determine distances involving angles of depression

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 142
- Protractors or clinometers
- Measuring tapes
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Combined problems on angles of elevation and depression

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

- Solve combined problems involving both angles of elevation and depression
- Draw accurate diagrams for combined elevation and depression problems
- Apply trigonometric problem-solving to real-life scenarios such as determining distances between ships from a control tower or heights of flagpoles on buildings

- Work out combined problems involving two or more angles of elevation and depression
- Use digital devices and other resources such as books, manuals and journals to learn more about trigonometric ratios

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 143
- Scientific calculators
- Mathematical tables
- Rulers and geometrical set

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Area of a triangle given two sides and an included angle
Area of Polygons - Area of a triangle using Heron's formula

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

- Derive the formula for the area of a triangle given two sides and an included angle
- Work out the area of a triangle given two sides and an included angle
- Apply the formula to real-life problems such as calculating the area of triangular plots, fields and gardens

- Discuss in groups and use trigonometric ratios to generate the formula for the area of a triangle given two sides and an included angle (Area = ½abSinC)
- Use the formula to calculate the area of different triangular shapes

How do we work out the area of polygons?

- Master Core Mathematics Grade 10 pg. 145
- Rulers and geometrical set
- Scientific calculators
- Mathematical tables
- Master Core Mathematics Grade 10 pg. 148
- Rulers
- Scientific calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of parallelograms and rhombus

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

- Determine the area of parallelograms using A = ab sin θ
- Determine the area of a rhombus using A = a² sin θ
- Apply the formulae to real-life objects such as cloth pieces, tiles and parking lots

- Consider a parallelogram divided into two equal triangles and derive the area formula
- Work out the area of parallelograms and rhombuses using the sine of included angles

How do we work out the area of polygons?

- Master Core Mathematics Grade 10 pg. 149
- Rulers and geometrical set
- Scientific calculators
- Mathematical tables

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of trapeziums and kites
Area of Polygons - Area of regular heptagon

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

- Determine the area of trapeziums using trigonometric methods
- Determine the area of kites by dividing into triangles
- Relate the area of trapeziums and kites to practical applications such as bridge supports and shutters

- Work out the area of trapeziums by finding the height using trigonometric ratios
- Divide kites into triangles and calculate the total area
- Solve problems involving real-life trapezoidal and kite shapes

How do we work out the area of polygons?

- Master Core Mathematics Grade 10 pg. 150
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 152
- Rulers, compasses and geometrical set
- Scientific calculators
- Protractors

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Area of regular octagon

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

- Work out the area of a regular octagon by dividing it into triangles from the centre
- Calculate the central angle and use the sine formula for triangles
- Apply the area of a regular octagon to real-life objects such as nut openers, bolt heads and floor tile patterns

- Draw a circle and divide the circumference into eight equal parts to form a regular octagon
- Join the vertices to the centre and calculate the area of each triangle formed
- Use the formula for area of a regular polygon

How do we apply the concept of the area of polygons in real-life situations?

- Master Core Mathematics Grade 10 pg. 155
- Rulers, compasses and geometrical set
- Scientific calculators
- Protractors

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Area of irregular polygons
Area of Polygons - Application of area of irregular polygons

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

- Determine the area of irregular polygons by dividing into regular shapes
- Calculate the area of each component shape and sum them up
- Solve real-life problems involving irregular polygons such as farm plots, camping tent outlines and village boundaries

- Identify objects with shapes of irregular polygons in the environment
- Divide irregular polygons into trapeziums, rectangles and triangles and calculate total area

How do we apply the concept of the area of polygons in real-life situations?

- Master Core Mathematics Grade 10 pg. 158
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 159
- Scientific calculators
- Digital resources

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Application of area of polygons to real-life situations

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

- Apply the concept of area of polygons to solve mixed real-life problems
- Combine different formulae to solve problems involving various polygons
- Relate area of polygons to practical applications such as landscaping, painting surfaces and material estimation

- Work out the area of various polygons from combined real-life contexts
- Use digital devices and other resources to explore more on the area of polygons in real-life situations

How do we apply the concept of the area of polygons in real-life situations?

- Master Core Mathematics Grade 10 pg. 159
- Scientific calculators
- Mathematical tables
- Digital resources

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Area of an annulus
Area of a Part of a Circle - Area of a sector of a circle

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

- Determine the area of an annulus in different situations
- Calculate the area of the region between two concentric circles
- Apply the area of an annulus to real-life objects such as swimming pool pavements, roundabouts and car tyres

- Use circular shapes or objects to identify concentric rings formed by inner and outer space
- Work out the area of an annulus as the difference between the area of the outer circle and the inner circle

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 161
- Circular objects
- Compasses
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 163
- Compasses and protractors
- Paper cutouts

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of a Part of a Circle - Area of an annular sector
Area of a Part of a Circle - Application of area of an annular sector

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

- Determine the area of an annular sector
- Apply the formula Area = (θ/360) × π(R² − r²)
- Connect the area of an annular sector to real-life objects such as car wiper blade sweeps and javelin landing sectors

- Draw two concentric circles and a sector to illustrate the annular sector
- Calculate the area of the annular sector as the difference between the outer and inner sectors

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 166
- Compasses and protractors
- Rulers
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 167
- Scientific calculators
- Protractors

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of a Part of a Circle - Area of a segment of a circle

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

- Work out the area of a segment of a circle
- Apply the formula: Area of segment = Area of sector − Area of triangle
- Relate the area of a segment to real-life shapes such as the top part of an arched door or a crescent moon drawing

- Draw different segments of a circle and calculate their area
- Use the perpendicular from the centre to bisect the chord and determine the angle

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 169
- Compasses and protractors
- Rulers and geometrical set
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Application of area of a segment
Area of a Part of a Circle - Area of common region between two intersecting circles

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

- Solve more complex problems involving the area of a segment
- Work out the area of segments when the chord length and radius are given
- Apply segment area calculations to greenhouse cross-sections, door arches and other curved structures

- Calculate the area of segments given different sets of information
- Work out problems involving segments from real-life contexts

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 171
- Scientific calculators
- Rulers and geometrical set
- Protractors
- Master Core Mathematics Grade 10 pg. 173
- Compasses and rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Common region (finding radii and angles)

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

- Calculate the area of the common region when radii need to be determined first
- Use trigonometric ratios and simultaneous equations to find missing dimensions
- Apply the concept to problems involving overlapping umbrella shadows, intersecting street lights and coat of arms designs

- Work out more complex problems involving the common area between two intersecting circles
- Use tangent and cosine ratios to determine unknown radii and angles

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 175
- Scientific calculators
- Rulers and geometrical set
- Protractors

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Further problems on common region

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

- Solve further problems involving the area of the common region between two intersecting circles
- Work out problems involving overlapping circles with different radii
- Use the area of intersecting circles to solve practical problems such as planning water sprinkler coverage and designing logos

- Work out further problems on the area of the common region
- Use digital devices and other resources to learn more about the area of a part of a circle

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 177
- Scientific calculators
- Digital resources
- Rulers and geometrical set

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Application to real-life situations

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

- Apply the area of a part of a circle to solve mixed real-life problems
- Combine different concepts (annulus, sector, annular sector, segment, common region)
- Relate the area of a part of a circle to practical projects such as making dartboards and beaded necklaces

- Relate and work out the area of a part of a circle in real-life situations
- Make a dartboard of different numbers of concentric circles from locally available materials
- Discuss and create rules for scoring the game

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 177
- Locally available materials
- Scientific calculators
- Digital resources

- Observation - Oral questions - Written tests