Numbers and Algebra

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

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

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

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

How do we form quadratic expressions from given factors?

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

- Oral questions - Written assignments - Observation

Numbers and Algebra

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

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

How do quadratic identities make numerical calculations easier?

- Master Core Mathematics Grade 10 pg. 44
- Calculators
- 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)
Similarity and Enlargement - Centre of enlargement and linear scale factor

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. 65
- Graph papers
- Rulers and geometrical set
- Digital resources

- Oral questions - Written assignments - Observation

Measurements and Geometry

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

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

- Construct the image of an object under an enlargement given the centre and a positive linear scale factor
- Draw images on a plane surface and Cartesian plane using the properties of enlargement
- Connect enlargement to real-life uses such as architectural drawings and scale models

- Discuss in a group and draw on a plane surface the images of objects under enlargement given the centres and positive linear scale factors
- Draw on the Cartesian plane the images of objects under enlargement given the centres and linear scale factors

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

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

- Master Core Mathematics Grade 10 pg. 75
- Graph papers
- Rulers
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

- Relate linear scale factor to volume scale factor
- Calculate volume scale factor from a given linear scale factor
- Use the relationship between L.S.F and V.S.F in real-life contexts such as comparing capacities of similar containers

- Discuss in a group and establish the relationship between L.S.F and V.S.F using two similar solids
- Cube the linear scale factor and compare with the volume scale factor

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

- Master Core Mathematics Grade 10 pg. 76
- Models of similar solids
- Calculators
- Master Core Mathematics Grade 10 pg. 77
- Calculators
- Models of similar solids

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection and Congruence - Properties of reflection
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

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

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

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

How is rotation applied in real-life situations?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

How is rotation applied in real-life situations?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Rotation - Quarter turns (±90°) about the origin
Rotation - Determining centre and angle of rotation

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

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

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

How is rotation applied in real-life situations?

- Master Core Mathematics Grade 10 pg. 110
- Graph papers
- Rulers
- Squared books
- Master Core Mathematics Grade 10 pg. 113
- Rulers and geometrical set
- Protractors

- Observation - Oral questions - Written tests

Measurements and Geometry

Rotation - Order of rotational symmetry of plane figures
Rotation - Axis and order of rotational symmetry in solids

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

- Determine the order of rotational symmetry of plane figures
- Use paper cutouts to establish the number of times a figure fits onto itself during a full rotation
- Identify rotational symmetry in everyday objects such as wheel rims, fan blades and logos

- Use paper cutouts of different plane figures to locate points of symmetry and establish the order of rotational symmetry
- Complete figures to show given orders of rotational symmetry

How is rotation applied in real-life situations?

- Master Core Mathematics Grade 10 pg. 117
- Paper cutouts
- Rulers
- Protractors
- Master Core Mathematics Grade 10 pg. 120
- Models of solids
- Thin wires or straws
- Manila paper

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

How is rotation applied in real-life situations?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Trigonometric ratios from table of sines

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

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

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

What is trigonometry?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

What is trigonometry?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry 1 - Sines and cosines of complementary angles
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°)

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Angles of elevation

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

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

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

How do we use trigonometry in real-life situations?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Angles of depression

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

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

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

How do we use trigonometry in real-life situations?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Combined problems on angles of elevation and depression
Area of Polygons - Area of a triangle given two sides and an included angle

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

- Observation - Oral questions - Written tests

 

Measurements and Geometry

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

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

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

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

How do we work out the area of polygons?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Area of regular octagon
Area of Polygons - Area of irregular polygons

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

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

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

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

- Master Core Mathematics Grade 10 pg. 155
- Rulers, compasses and geometrical set
- Scientific calculators
- Protractors
- Master Core Mathematics Grade 10 pg. 158
- Rulers and geometrical set
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

- Solve more complex problems involving irregular polygons
- Work out the area of polygons with multiple component shapes
- Apply the concept of area of irregular polygons to real-life situations such as land surveying and floor plan estimation

- Work out the areas of complex irregular polygons from various real-life contexts
- Research and discuss in a group the use of 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
- Rulers and geometrical set
- Scientific calculators
- Digital resources
- Mathematical tables

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

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

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

- 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

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

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

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

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Common region (finding radii and angles)
Area of a Part of a Circle - Further problems on common region

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

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

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

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

- Master Core Mathematics Grade 10 pg. 175
- Scientific calculators
- Rulers and geometrical set
- Protractors
- Master Core Mathematics Grade 10 pg. 177
- Digital resources
- Rulers and geometrical set

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

- Determine the surface area of prisms (triangular prisms, cuboids, cylinders, hexagonal prisms)
- Draw the net of a prism and calculate the area of each face
- Relate surface area of prisms to real-life applications such as packaging, labelling containers and painting walls

- Cut a prism along the edges and lay out the faces to form a net
- Identify the shapes forming the net and work out the area of each shape
- Add the areas to get the total surface area

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

- Master Core Mathematics Grade 10 pg. 179
- Models of prisms
- Scissors
- Rulers and geometrical set
- Master Core Mathematics Grade 10 pg. 184
- Models of pyramids
- Rulers and geometrical set
- Scientific calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

- Determine the surface area of cones
- Calculate the curved surface area and total surface area of a cone
- Apply surface area of cones to real-life objects such as paper cups, conical hats and tents

- Cut out the circular base and curved surface of a cone to form a net
- Calculate the surface area using Area = πr² + πrl
- Solve problems involving surface area of cones

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

- Master Core Mathematics Grade 10 pg. 186
- Models of cones
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 188
- Models of frustums

- Observation - Oral questions - Written assignments

Measurements and Geometry

Surface Area and Volume of Solids - Surface area of spheres and hemispheres
Surface Area and Volume of Solids - Surface area of composite solids

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

- Determine the surface area of spheres and hemispheres
- Apply the formulae SA = 4πr² (sphere) and SA = 3πr² (hemisphere)
- Relate surface area of spheres to real-life objects such as balls, chocolates and water tanks

- Collect spherical objects and measure their circumference
- Work out the radius and calculate the surface area
- Discuss how to work out the surface area of a hemisphere

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

- Master Core Mathematics Grade 10 pg. 191
- Spherical objects
- String and rulers
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 193
- Models of composite solids
- Rulers and geometrical set

- Observation - Oral questions - Written tests

Measurements and Geometry

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 volume of prisms (triangular, rectangular, cylindrical, hexagonal)
- Apply the formula Volume = Cross-section area × Length
- Relate the volume of prisms to real-life applications such as aquariums, water pipes and metal bars

- Collect different models of prisms and discuss how to determine their volume
- Work out the cross-sectional area and multiply by the length to get the volume

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

- Master Core Mathematics Grade 10 pg. 196
- Models of prisms
- Rulers
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 198
- Models of pyramids
- Rulers and geometrical set

- 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

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

- Observation - Oral questions - Written tests