Measurements and Geometry

Reflection and Congruence - Lines of symmetry in plane figures

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

- Identify lines of symmetry in plane figures
- Determine the number of lines of symmetry in different shapes
- Recognise symmetry in everyday objects such as letters of the alphabet, leaves and building designs

- Collect and observe different objects from the immediate environment and illustrate the lines and planes of symmetry
- Fold paper to identify lines of symmetry in different plane figures

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Reflection and Congruence - Properties of reflection

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

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

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

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection and Congruence - Special reflections (lines y = x and y = -x)

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection and Congruence - Equation of the mirror line

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

- Determine the equation of the mirror line given an object and its image
- Use midpoints and gradients to derive the equation of the mirror line
- Solve problems involving finding mirror lines in coordinate geometry

- Construct a mirror line given an object and its image on a Cartesian plane
- Work out the equation of the mirror line using midpoint and gradient of perpendicular lines

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection and Congruence - Determining and describing mirror line transformations

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

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

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

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

Where do we use congruence in real life?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection and Congruence - Direct and indirect congruence

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

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

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

Where do we use congruence in real life?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Rotation - Properties of rotation

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Rotation - Rotation on a plane surface

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

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

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

How is rotation applied in real-life situations?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Rotation - Rotation on the Cartesian plane

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

- Rotate an object given the centre and angle of rotation on 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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Rotation - Half turn (±180°) 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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

How is rotation applied in real-life situations?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

How is rotation applied in real-life situations?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Rotation - Axis and order of rotational symmetry in solids

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

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

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

How is rotation applied in real-life situations?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Rotation - Congruence from rotation

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Trigonometric ratios from table of tangents

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

- Observation - Oral questions - Written assignments

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry 1 - Trigonometric ratios from calculators
Trigonometry 1 - Sines and cosines of complementary angles

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

- Determine trigonometric ratios of acute angles using a scientific calculator
- Determine inverse trigonometric ratios using a calculator
- Use calculators to verify results obtained from mathematical tables and solve practical trigonometric problems

- Identify the tan, sin and cos functions on the calculator
- Use the calculator to work out trigonometric ratios and their inverses
- Compare calculator results with table values

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 132
- Scientific calculators
- Mathematical tables
- Master Core Mathematics Grade 10 pg. 134
- Mathematical tables
- Rulers and geometrical set

- Observation - Oral questions - Written assignments

Measurements and Geometry

Trigonometry 1 - Relationship between sine, cosine and tangent of acute angles

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

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

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

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 136
- Scientific calculators
- Mathematical tables
- Rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Trigonometric ratios of special angles (45°)

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)

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

How do we use trigonometry in real-life situations?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Angles of elevation

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

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

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

How do we use trigonometry in real-life situations?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Trigonometry 1 - Angles of 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 - 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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of a triangle using Heron's formula

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

- Determine the area of a triangle using Heron's formula
- Calculate the semi-perimeter and apply it in Heron's formula
- Use Heron's formula to find the area of triangular shapes in real life such as door mats, garden plots and samosa faces

- Work out the perimeter and semi-perimeter of a triangle
- Apply Heron's formula: Area = √[s(s−a)(s−b)(s−c)] to calculate the area of triangles
- Compare results with the ½abSinC formula

How do we work out the area of polygons?

- Master Core Mathematics Grade 10 pg. 148
- Rulers
- Scientific calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of parallelograms and rhombus

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

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

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

How do we work out the area of polygons?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of trapeziums and kites

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

- Observation - Oral questions - Written tests

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Application of area of irregular polygons

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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:

- 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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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:

- 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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Surface area of prisms

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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 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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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 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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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 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

- Observation - Oral questions - Written tests

Measurements and Geometry

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 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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Volume of pyramids

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

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

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

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

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

- 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 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 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

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