Numbers and Algebra

Indices and Logarithms - Numbers in index form

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

- Identify the base and index of a number in index form
- Express numbers as products of prime factors and write them in index form
- Relate index form to real-life contexts such as expressing large populations and tree planting records

- Discuss how to express numbers in index form
- Express given numbers as products of prime factors and write in power form
- Identify the base and index in given expressions

Why do we write numbers in index form?

- Master Core Mathematics Grade 10 pg. 15
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Multiplication law of indices
Indices and Logarithms - Division 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
- Master Core Mathematics Grade 10 pg. 17

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Powers, zero index and negative indices
Indices and Logarithms - Fractional indices and application of laws

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

- Apply the power of indices rule, zero index rule, and negative index rule
- Simplify expressions involving powers of indices, zero index, and negative indices
- Relate zero and negative indices to real-life contexts such as bacteria growth models and financial processing fees

- Discuss and derive the rules for powers of indices, zero index, and negative indices
- Simplify expressions such as (aᵐ)ⁿ, a⁰, and a⁻ⁿ
- Evaluate expressions involving zero and negative indices

How do we simplify expressions with zero or negative indices?

- Master Core Mathematics Grade 10 pg. 19
- Charts
- Calculators
- Master Core Mathematics Grade 10 pg. 22

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Powers of 10 and common logarithms
Indices and Logarithms - Logarithms of numbers between 1 and 10

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

- Relate index notation to logarithm notation to base 10
- Convert between index form and logarithm form
- Use logarithm notation to express real-life quantities such as vaccination figures and bacteria counts

- Discuss the relationship between powers of 10 and logarithm notation
- Write numbers in logarithm form and convert from logarithm to index form
- Express given numbers in logarithm notation

How are powers of 10 related to common logarithms?

- Master Core Mathematics Grade 10 pg. 26
- Charts
- Master Core Mathematics Grade 10 pg. 27
- Mathematical tables

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Logarithms of numbers greater than 10
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 greater than 10 using standard form and tables
- Identify the characteristic and mantissa of a logarithm
- Express real-life measurements such as diameters and forces in the form 10ⁿ

- Express numbers greater than 10 in standard form (A × 10ⁿ)
- Read the logarithm of A from tables and add the index n
- Identify the characteristic and mantissa parts of logarithms

How do we find logarithms of numbers greater than 10?

- Master Core Mathematics Grade 10 pg. 29
- Mathematical tables
- Master Core Mathematics Grade 10 pg. 30

- 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

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

- 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
Quadratic Expressions and Equations - Factorising difference of two 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
- Master Core Mathematics Grade 10 pg. 54

- Oral questions - Written assignments - Observation

Numbers and Algebra

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

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

- Determine factors of a quadratic equation from given roots
- Form quadratic equations by expanding the product of factors
- Relate the formation of equations to contexts such as determining equations from known dimensions

- Write x−a = 0 and x−b = 0 from given roots x = a and x = b
- Multiply the factors and expand to form the quadratic equation
- Form equations from single roots, opposite roots, and fractional roots

How do we form a quadratic equation when the roots are known?

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

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

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
- Master Core Mathematics Grade 10 pg. 94
- Paper cutouts
- 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
Rotation - Rotation on the Cartesian plane

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
- 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
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:

- 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
- 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
Area of a Part of a Circle - Application of area of a segment

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
- Master Core Mathematics Grade 10 pg. 171
- Scientific calculators
- Protractors

- Observation - Oral questions - Written tests

Measurements and Geometry

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:

- Determine the area of the common region between two intersecting circles
- Identify the common area as the sum of two segments
- Relate intersecting circles to real-life situations such as overlapping lights and water sprinklers

- Draw two circles intersecting at two points
- Join the centres and the points of intersection
- Separate the common region into two segments and calculate the total area

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

- Master Core Mathematics Grade 10 pg. 173
- Compasses and rulers
- Scientific calculators
- Protractors
- Master Core Mathematics Grade 10 pg. 175
- Rulers and geometrical set

- 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
Surface Area and Volume of Solids - Volume of pyramids

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
- Master Core Mathematics Grade 10 pg. 198
- Models of pyramids

- Observation - Oral questions - Written tests

Measurements and Geometry

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 cones
- Apply the formula Volume = ⅓πr²h
- Relate volume of cones to real-life objects such as cupcakes, grain silos and ice cream dispensers

- Collect a model of a cone and measure the base radius and slanting height
- Work out the height using Pythagoras' theorem and determine the volume
- Use models of a cone and a cylinder to demonstrate that the volume of a cone is a third of the volume of the cylinder

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

- Master Core Mathematics Grade 10 pg. 200
- Models of cones and cylinders
- Sand or water
- Scientific calculators

- 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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Application to real-life situations
Vectors I - Vector and scalar quantities

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

- Apply surface area and volume of solids to solve mixed real-life problems
- Combine different formulae to solve problems involving various solids
- Use the concepts of surface area and volume in practical situations such as determining quantities of materials for construction, painting and storage capacity

- Use appropriate containers from the local environment to work out the volume and capacity
- Use digital devices and other resources to work out the surface area and volume of solids
- Solve combined problems involving surface area and volume

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

- Master Core Mathematics Grade 10 pg. 206
- Containers from the local environment
- Scientific calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 208
- Measuring tape
- Magnetic compass
- Stopwatch

- Observation - Oral questions - Written tests

Measurements and Geometry

Vectors I - Vector notation
Vectors I - Representation of vectors

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

- Write vectors using correct notation in print and handwriting
- Practise writing vector notations using bold letters, arrows and wavy lines on charts
- Relate vector notation to real-life directional signs such as road arrows and signposts that guide movement

- Use digital devices or other resources to search for vector notations
- Practise writing vector notations using charts
- Compare different ways of denoting vectors in print and handwriting and share work with peers

How do we write and identify vectors using correct notation?

- Master Core Mathematics Grade 10 pg. 209
- Charts
- Rulers
- Digital resources
- Master Core Mathematics Grade 10 pg. 210
- Graph papers

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Equivalent vectors
Vectors I - Addition of vectors using head-to-tail method

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

- Define equivalent vectors and state their properties
- Identify equivalent vectors from grids and plane figures such as cuboids
- Relate equivalent vectors to parallel lanes on a highway where vehicles move the same distance in the same direction

- Brainstorm on the meaning of equivalent vectors
- Draw different pairs of vectors with the same magnitude and direction on a graph
- Identify equivalent vectors from cuboids and grids and discuss real-life examples

When are two vectors said to be equivalent?

- Master Core Mathematics Grade 10 pg. 211
- Graph papers
- Rulers
- Charts showing cuboids
- Digital resources
- Master Core Mathematics Grade 10 pg. 213
- Geometrical set

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Addition of vectors using parallelogram method
Vectors I - Multiplication of vectors by scalar
Vectors I - Column vectors

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

- Add vectors using the parallelogram method
- Draw the resultant vector as the diagonal of a completed parallelogram
- Relate the parallelogram method to real-life scenarios such as a boat crossing a river while being pushed by a current from a different direction

- Draw two vectors from a common point on a grid
- Complete the parallelogram and draw the diagonal as the resultant vector
- Solve problems on addition and subtraction of vectors and share work with peers

How is the parallelogram method used to add vectors?

- Master Core Mathematics Grade 10 pg. 214
- Graph papers
- Rulers
- Geometrical set
- Digital resources
- Master Core Mathematics Grade 10 pg. 216
- Charts
- Master Core Mathematics Grade 10 pg. 218
- Grids

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Position vectors

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

- Define and determine position vectors of points on a Cartesian plane
- Express vectors between two points using position vectors
- Relate position vectors to real-life mapping such as locating buildings on a town plan or GPS coordinates

- Plot points on a Cartesian plane and draw position vectors from the origin
- Write position vectors as column vectors
- Determine vectors between two points using the formula AB = OB − OA and share work

How do we describe the position of a point using vectors?

- Master Core Mathematics Grade 10 pg. 221
- Graph papers
- Rulers
- Geometrical set
- Calculators
- Digital resources

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Magnitude of a vector and midpoint of a vector

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

- Determine the magnitude of a vector using the Pythagorean theorem
- Calculate the midpoint of a vector given coordinates of two points
- Relate magnitude and midpoint to real-life applications such as finding the straight-line distance between two towns or the halfway point of a journey

- Draw a right-angled triangle from a vector on a grid and use Pythagoras' theorem to find the magnitude
- Calculate magnitude of different vectors and determine midpoints of given vectors
- Solve problems involving magnitude and midpoint and share work with peers

How do we determine the length of a vector and the midpoint between two points?

- Master Core Mathematics Grade 10 pg. 224
- Graph papers
- Rulers
- Calculators
- Digital resources

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Translation vector
Linear Motion - Distance, displacement, speed, velocity and acceleration

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

- Define and determine translation vectors as a transformation
- Find the image of a point or shape under a given translation
- Relate translation vectors to real-life movements such as sliding furniture across a room or shifting objects on a conveyor belt without rotating them

- Draw a Cartesian plane and place a triangular paper cutout, then slide it and record new coordinates
- Express the movement as a column vector and determine images of points under translation
- Draw objects and their images under translation on the same axes and share work

How do we use vectors to describe the movement of objects without turning?

- Master Core Mathematics Grade 10 pg. 227
- Graph papers
- Rulers
- Paper cutouts
- Geometrical set
- Digital resources
- Master Core Mathematics Grade 10 pg. 231
- Measuring tape
- Stopwatch

- Oral questions - Observation - Written assignments

Measurements and Geometry

Linear Motion - Velocity
Linear Motion - Acceleration and deceleration

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

- Calculate velocity given displacement and time
- Convert velocity between m/s and km/h
- Connect velocity calculations to real-life scenarios such as determining how fast an athlete runs a race or a helicopter flies between two towns

- Make an inclined plane and release a toy car or marble, timing its motion to calculate average velocity
- Work out velocity problems involving athletes, vehicles and ships
- Convert units between m/s and km/h and share work with peers

How do we calculate and use velocity in real-life situations?

- Master Core Mathematics Grade 10 pg. 232
- Rulers
- Stopwatch
- Toy car or marble
- Wooden plank
- Digital resources
- Master Core Mathematics Grade 10 pg. 234
- Measuring tape
- Ball
- Ramp
- Calculators

- Oral questions - Observation - Written assignments

Measurements and Geometry

Linear Motion - Displacement-time graph
Linear Motion - Interpreting displacement-time graph

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

- Draw displacement-time graphs from given data tables
- Select suitable scales for axes when plotting graphs
- Connect displacement-time graphs to real-life journeys such as plotting an athlete's race or a cyclist's trip between towns

- Mark a straight track and walk at a steady pace, recording displacement at intervals
- Use data tables to plot displacement-time graphs on graph paper
- Draw displacement-time graphs for journeys involving stops and return trips and share work

How do we represent a journey using a displacement-time graph?

- Master Core Mathematics Grade 10 pg. 236
- Graph papers
- Rulers
- Stopwatch
- Measuring tape
- Calculators
- Master Core Mathematics Grade 10 pg. 238
- Calculators
- Digital resources

- Oral questions - Observation - Written assignments

Measurements and Geometry

Linear Motion - Velocity-time graph
Linear Motion - Interpreting velocity-time graph
Linear Motion - Relative speed of bodies moving in opposite and same directions
Linear Motion - Relative speed involving delayed departure and passing lengths

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

- Draw velocity-time graphs from given data tables and descriptions
- Select suitable scales and plot velocity against time accurately
- Connect velocity-time graphs to real-life scenarios such as recording a car's changing speed along a highway or a cyclist accelerating then braking

- Roll a ball along a track, calculate velocity at each interval and record in a table
- Use data tables to draw velocity-time graphs on graph paper
- Draw velocity-time graphs for motions involving acceleration, constant velocity and deceleration and share work

How do we represent changing velocity on a graph?

- Master Core Mathematics Grade 10 pg. 241
- Graph papers
- Rulers
- Stopwatch
- Ball
- Tape measure
- Calculators
- Master Core Mathematics Grade 10 pg. 244
- Calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 248
- Balls
- Master Core Mathematics Grade 10 pg. 250

- Oral questions - Observation - Written assignments