Numbers and Algebra

Indices and Logarithms - Multiplication law of indices

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

- State the multiplication law of indices
- Simplify expressions by adding indices with the same base during multiplication
- Apply the multiplication law to calculate areas and volumes in real-life contexts such as rooms and swimming pools

- Discuss and derive the multiplication law of indices
- Simplify given expressions using the multiplication law
- Determine areas and volumes of shapes expressed in index form

What happens to the indices when we multiply numbers with the same base?

- Master Core Mathematics Grade 10 pg. 16
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Division law of indices
Indices and Logarithms - Powers, zero index and negative indices

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

- State the division law of indices
- Simplify expressions by subtracting indices with the same base during division
- Use the division law to solve real-life problems such as determining the number of tiles needed to cover a floor

- Discuss and derive the division law of indices
- Simplify given expressions using the division law
- Solve problems involving division of numbers in index form

What happens to the indices when we divide numbers with the same base?

- Master Core Mathematics Grade 10 pg. 17
- Charts
- Master Core Mathematics Grade 10 pg. 19
- Charts
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Fractional indices and application of laws
Indices and Logarithms - Powers of 10 and common logarithms

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

- Express roots of numbers as fractional indices
- Simplify and evaluate expressions involving fractional indices
- Use laws of indices to solve equations and real-life problems involving plant growth and distance calculations

- Discuss and derive the rule for fractional indices
- Simplify expressions involving fractional indices
- Apply all laws of indices to solve equations and evaluate expressions

How do we use fractional indices to represent roots?

- Master Core Mathematics Grade 10 pg. 22
- Calculators
- Master Core Mathematics Grade 10 pg. 26
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

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

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

- Read logarithms of numbers between 1 and 10 from mathematical tables
- Determine logarithms using the main columns and mean difference columns
- Express real-life measurements such as mass and density in the form 10ⁿ using tables

- Discuss the features of the logarithm table
- Read logarithms of numbers with 2, 3, and 4 significant figures from tables
- Express given quantities in the form 10ⁿ

How do we read logarithms of numbers from tables?

- Master Core Mathematics Grade 10 pg. 27
- Mathematical tables
- Master Core Mathematics Grade 10 pg. 29

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Logarithms of numbers less than 1

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

- Determine logarithms of numbers less than 1 using standard form and tables
- Write the bar notation for negative characteristics
- Express real-life quantities such as pipe diameters and pollutant concentrations in the form 10ⁿ

- Express numbers less than 1 in standard form
- Read the logarithm of the number from tables and identify the negative characteristic
- Write logarithms using bar notation for the characteristic

Why do numbers less than 1 have negative characteristics?

- Master Core Mathematics Grade 10 pg. 30
- Mathematical tables

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Antilogarithms using tables

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

- Define antilogarithm as the reverse of a logarithm
- Determine antilogarithms of numbers using tables of antilogarithms
- Use antilogarithms to find actual values from logarithmic results in practical calculations

- Discuss antilogarithm as the reverse process of finding a logarithm
- Use tables of antilogarithms to determine numbers whose logarithms are given
- Determine antilogarithms of numbers with positive and negative (bar) characteristics

How do we use antilogarithm tables to find numbers?

- Master Core Mathematics Grade 10 pg. 31
- Mathematical tables
- Antilogarithm tables

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Logarithms and antilogarithms using calculators

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

- Determine logarithms and antilogarithms of numbers using a calculator
- Use the log and shift-log buttons to find logarithms and antilogarithms
- Compare calculator results with table values to build confidence in using digital tools for computation

- Identify the log button on a scientific calculator
- Determine logarithms and antilogarithms of numbers by keying values into the calculator
- Compare results obtained from calculators with those from tables

How do we use calculators to find logarithms and antilogarithms?

- Master Core Mathematics Grade 10 pg. 33
- Scientific calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Multiplication and division using logarithms

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

- Use logarithms to multiply and divide numbers
- Apply the steps of finding logarithms, adding or subtracting them, and finding the antilogarithm
- Solve real-life multiplication and division problems efficiently using logarithms

- Determine logarithms of numbers, add them to perform multiplication, and find the antilogarithm of the sum
- Determine logarithms, subtract them to perform division, and find the antilogarithm of the difference
- Arrange solutions in a table format

How do logarithms simplify multiplication and division?

- Master Core Mathematics Grade 10 pg. 35
- Mathematical tables
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Powers and roots using logarithms

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

- Use logarithms to evaluate powers and roots of numbers
- Multiply or divide logarithms by the index to find powers or roots
- Use logarithms to solve real-life problems involving squares, cubes, and roots

- Determine the logarithm of a number and multiply by the power to evaluate squares and cubes
- Divide the logarithm by the root order to evaluate square and cube roots
- Make the bar characteristic exactly divisible when dividing logarithms with bar notation

How do logarithms help in finding powers and roots of numbers?

- Master Core Mathematics Grade 10 pg. 37
- Mathematical tables
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Combined operations using logarithms
Quadratic Expressions and Equations - Formation of quadratic expressions

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

- Use logarithms to evaluate expressions involving combined operations of multiplication, division, powers, and roots
- Organise logarithmic computations systematically in a table format
- Apply logarithms to solve complex real-life calculations involving multiple operations

- Add logarithms of the numerator and denominator separately
- Subtract the sum of denominator logarithms from the sum of numerator logarithms
- Find the antilogarithm of the result to obtain the final answer

How do we use logarithms to evaluate complex expressions?

- Master Core Mathematics Grade 10 pg. 38
- Mathematical tables
- Calculators
- Master Core Mathematics Grade 10 pg. 40
- Rulers

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Quadratic identities (a+b)² and (a−b)²
Quadratic Expressions and Equations - Difference of two squares identity and numerical applications
Quadratic Expressions and Equations - Factorisation when coefficient of x² is one

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

- Derive the quadratic identities (a+b)² = a²+2ab+b² and (a−b)² = a²−2ab+b² using the concept of area
- Expand expressions using the identities
- Relate the identities to calculating areas of square floors, parking lots, and table mats

- Draw a square of side (a+b) and divide it into regions to derive (a+b)²
- Draw a square of side a and cut out regions to derive (a−b)²
- Use the identities to expand given expressions

How do we derive and use the identities (a+b)² and (a−b)²?

- Master Core Mathematics Grade 10 pg. 43
- Rulers
- Graph papers
- Master Core Mathematics Grade 10 pg. 44
- Calculators
- Master Core Mathematics Grade 10 pg. 48
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

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

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

- Identify pairs of integers whose sum equals the coefficient of the linear term and product equals (a × c)
- Factorise quadratic expressions of the form ax²+bx+c where a > 1
- Apply factorisation to determine dimensions of floors and grazing fields from area expressions

- Determine the product of the coefficient of x² and the constant term
- Find a pair of integers whose sum and product match the required values
- Rewrite the linear term using the pair and factorise by grouping

How do we factorise when the coefficient of x² is greater than one?

- Master Core Mathematics Grade 10 pg. 50
- Charts
- Master Core Mathematics Grade 10 pg. 52

- 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
Measurements and Geometry

Quadratic Expressions and Equations - Application of quadratic equations to real-life (speed, distance and area)
Reflection and Congruence - Lines of symmetry in plane figures

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
- Master Core Mathematics Grade 10 pg. 79
- Plane figures
- Rectangular paper
- Rulers

- Oral questions - Written assignments - Observation

Measurements and Geometry

Reflection and Congruence - Properties of reflection
Reflection and Congruence - Drawing an image on a plane surface

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
- Master Core Mathematics Grade 10 pg. 82
- Rulers and geometrical set
- Plain paper
- Compasses

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection and Congruence - Reflection along a line on the Cartesian plane
Reflection and Congruence - Special reflections (x-axis and y-axis)

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

- Draw an image given an object and a mirror line on the Cartesian plane
- Plot objects and their images after reflection on the Cartesian plane
- Connect Cartesian plane reflection to coordinate geometry applications in navigation and design

- Draw on a Cartesian plane given objects and mirror lines, and use the properties of reflection to draw the corresponding images
- Use construction methods to reflect objects on the Cartesian plane

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

- Master Core Mathematics Grade 10 pg. 84
- Graph papers
- Rulers and geometrical set
- Squared books
- Master Core Mathematics Grade 10 pg. 86
- Rulers

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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
- Master Core Mathematics Grade 10 pg. 92

- 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
Rotation - Properties of rotation

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
- Master Core Mathematics Grade 10 pg. 100
- Analogue clock or dummy clock
- Pins and cartons

- Observation - Oral questions - Written tests

Measurements and Geometry

Rotation - Rotation on a plane surface
Rotation - Rotation on the Cartesian plane

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

- Rotate an object given the centre and angle of rotation on a plane surface
- Generate images of objects under rotation on a plain surface
- Connect rotation on a plane to real-life applications such as designing patterns in art and craft

- Generate an image of an object given a centre and angle of rotation on a plane surface
- Use protractors and compasses to carry out rotation accurately on plain paper

How is rotation applied in real-life situations?

- Master Core Mathematics Grade 10 pg. 103
- Rulers and geometrical set
- Protractors
- Plain paper
- Master Core Mathematics Grade 10 pg. 107
- Graph papers
- Protractors

- Observation - Oral questions - Written assignments

Measurements and Geometry

Rotation - Half turn (±180°) about the origin
Rotation - Quarter turns (±90°) about the origin

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

- Rotate objects through ±180° about the origin
- Apply the rule (x, y) → (−x, −y) for half turns about the origin
- Relate half-turn rotation to real-life examples such as inverting objects and U-turns in navigation

- Draw objects and rotate them through +180° and −180° about the origin
- Compare coordinates of the object and image to establish the half-turn rule

How is rotation applied in real-life situations?

- Master Core Mathematics Grade 10 pg. 109
- Graph papers
- Rulers
- Squared books
- Master Core Mathematics Grade 10 pg. 110

- 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
Rotation - Congruence from rotation

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
- Master Core Mathematics Grade 10 pg. 122
- Paper cutouts
- Digital resources
- Graph papers

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Trigonometric ratios from table of tangents
Trigonometry 1 - Trigonometric ratios from table of sines

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

- Determine the tangent of acute angles from mathematical tables
- Read and interpret the table of tangents including main columns and mean difference columns
- Relate the tangent ratio to real-life applications such as determining the slope of a roof or a ramp

- Identify from the immediate environment shapes that make right-angled triangles
- Draw right-angled triangles and use them to define the tangent ratio
- Use mathematical tables to obtain tangent values

What is trigonometry?

- Master Core Mathematics Grade 10 pg. 123
- Mathematical tables
- Rulers and geometrical set
- Calculators
- Master Core Mathematics Grade 10 pg. 127

- 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
Trigonometry 1 - Relationship between sine, cosine and tangent of acute 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
- Master Core Mathematics Grade 10 pg. 136
- Rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Trigonometric ratios of special angles (45°)
Trigonometry 1 - Trigonometric ratios of special angles (30°, 60° and 90°)
Trigonometry 1 - Angles of elevation

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

- Determine trigonometric ratios of 45° using an isosceles right-angled triangle
- Apply Pythagoras' theorem to derive trigonometric ratios of 45°
- Use special angle values to solve problems without tables or calculators

- Draw a square and its diagonal to form an isosceles right-angled triangle
- Use Pythagoras' theorem to calculate the hypotenuse
- Use the triangle to determine the tangent, sine and cosine of 45°

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 138
- Rulers and geometrical set
- Plain paper
- Calculators (for verification)
- Master Core Mathematics Grade 10 pg. 139
- 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
Area of Polygons - Area of trapeziums and kites

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
- Master Core Mathematics Grade 10 pg. 150
- Scientific calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of regular heptagon
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 heptagon 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 heptagon to real-life objects such as road signs, logos and window designs

- Draw a circle and divide the circumference into seven equal parts to form a regular heptagon
- 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. 152
- Rulers, compasses and geometrical set
- Scientific calculators
- Protractors
- Master Core Mathematics Grade 10 pg. 155

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

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
- Master Core Mathematics Grade 10 pg. 161
- Circular objects
- Compasses
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

- Work out the area of a sector of a circle
- Apply the formula Area = (θ/360) × πr²
- Relate the area of a sector to real-life situations such as area swept by a clock hand, paper fans and garden gates

- Work in a group and use paper cutouts to make sectors of circles to determine their areas
- Calculate the area of sectors using the formula

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

- Master Core Mathematics Grade 10 pg. 163
- Compasses and protractors
- Paper cutouts
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 166
- Rulers

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

- Solve more problems involving the area of an annular sector
- Apply the concept to various real-life contexts
- Use annular sector area in practical problems such as assembly grounds, brake pads and dart boards

- Work out more examples involving area of annular sectors
- Solve problems related to annular sectors from real-life situations

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

- Master Core Mathematics Grade 10 pg. 167
- Scientific calculators
- Rulers
- Protractors
- 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
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:

- 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
- Master Core Mathematics Grade 10 pg. 175

- 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
Surface Area and Volume of Solids - Surface area of prisms

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
- Master Core Mathematics Grade 10 pg. 179
- Models of prisms
- Scissors
- Rulers and geometrical set

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Surface area of pyramids
Surface Area and Volume of Solids - Surface area of cones

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

- Determine the surface area of pyramids (square-based, rectangular-based, hexagonal-based)
- Draw the nets of pyramids and calculate the area of each face
- Apply surface area of pyramids to real-life objects such as tents, roofs and monuments

- Determine the number of faces of each pyramid
- Draw the nets of the pyramids and calculate areas using Heron's formula and other methods
- Add the base area and the triangular face areas

Why do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 184
- Models of pyramids
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 186
- Models of cones

- Observation - Oral questions - Written assignments

Measurements and Geometry

Surface Area and Volume of Solids - Surface area of frustums
Surface Area and Volume of Solids - Surface area of spheres and hemispheres

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

- Determine the surface area of frustums of cones and pyramids
- Extend slant heights to obtain the original solid and subtract the cut-off part
- Apply surface area of frustums to real-life objects such as lamp shades, buckets and flower vases

- Extend the slant heights of a frustum to obtain the original solid
- Calculate the curved surface area of the original solid and the small solid cut off
- Subtract and add the top area to get the frustum's surface area

How do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 188
- Models of frustums
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 191
- Spherical objects
- String and rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Surface area of composite solids
Surface Area and Volume of Solids - Volume of prisms

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

- Calculate the surface area of composite solids
- Identify the component shapes of a composite solid and calculate individual surface areas
- Relate composite solids to real-life objects such as storage containers, flasks and trophies

- Identify all the shapes that form a composite solid
- Work out the surface area of each exposed shape
- Add the individual surface areas to get the total surface area

Why do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 193
- Models of composite solids
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 196
- Models of prisms
- Rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Volume of pyramids
Surface Area and Volume of Solids - Volume of cones

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

- Calculate the volume of pyramids (square-based, rectangular-based, pentagonal, hexagonal)
- Apply the formula Volume = ⅓ × Base area × Height
- Relate volume of pyramids to real-life objects such as roofs, monuments and milk packets

- Collect different models of pyramids and discuss how to work out the volume
- Calculate the base area and perpendicular height to determine the volume

Why do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 198
- Models of pyramids
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 200
- Models of cones and cylinders
- Sand or water

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Volume of frustums

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

- Calculate the volume of frustums of cones and pyramids
- Extend slant heights to form the original solid and subtract the volume of the cut-off part
- Apply the volume of frustums to real-life objects such as buckets, water tanks and washing sinks

- Extend the slant heights of a frustum to obtain the original solid
- Calculate the volume of the original solid and the small solid cut off
- Subtract to get the volume of the frustum

How do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 201
- Models of frustums
- Rulers
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Volume of spheres and hemispheres

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

- Calculate the volume of spheres and hemispheres
- Apply the formulae V = ⁴⁄₃πr³ (sphere) and V = ²⁄₃πr³ (hemisphere)
- Relate volume of spheres to real-life objects such as balls, ornaments, bowls and water tanks

- Collect spherical objects and measure their circumference
- Work out the radius and calculate the volume
- Discuss and work out the volume of hemispheres

Why do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 204
- Spherical objects
- String and rulers
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Volume of composite solids
Surface Area and Volume of Solids - Application to real-life situations

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

- Determine the volume of composite solids
- Identify the component shapes, calculate individual volumes and sum them
- Relate composite solids to real-life objects such as LPG tanks, silos and trophies

- Collect a model of a composite solid and identify all the basic shapes
- Work out the volume of each shape and add the volumes
- Solve problems involving composite solids

Why do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 206
- Models of composite solids
- Rulers
- Scientific calculators
- Containers from the local environment
- Scientific calculators
- Digital resources

- Observation - Oral questions - Written tests