Measurements and Geometry

Similarity and Enlargement - Centre of enlargement and linear scale factor

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

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

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

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

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

- Observation - Oral questions - Written assignments

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

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

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

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

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Similarity and Enlargement - Relating linear, area and volume scale factors
Similarity and Enlargement - Application of similarity and enlargement to real-life situations

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

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

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

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

- Master Core Mathematics Grade 10 pg. 77
- Calculators
- Models of similar solids
- Digital resources
- Locally available materials
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection and Congruence - Lines of symmetry in plane figures
Reflection and Congruence - Properties of reflection

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

- 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)
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 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
- Master Core Mathematics Grade 10 pg. 88

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection and Congruence - Equation of the mirror line
Reflection and Congruence - Determining and describing mirror line transformations

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

- 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
- Master Core Mathematics Grade 10 pg. 92

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

Where do we use congruence in real life?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Reflection and Congruence - Direct and indirect congruence
Rotation - Properties of rotation

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

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

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

Where do we use congruence in real life?

- Master Core Mathematics Grade 10 pg. 96
- Paper cutouts
- Graph papers
- Rulers
- Master Core Mathematics Grade 10 pg. 100
- Analogue clock or dummy clock
- Pins and cartons

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

How is rotation applied in real-life situations?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

How is rotation applied in real-life situations?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

How is rotation applied in real-life situations?

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Rotation - Axis and order of rotational symmetry in solids
Rotation - Congruence from rotation

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

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

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

How is rotation applied in real-life situations?

- Master Core Mathematics Grade 10 pg. 120
- Models of solids
- Thin wires or straws
- Manila paper
- Master Core Mathematics Grade 10 pg. 122
- Paper cutouts
- Digital resources
- Graph papers

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

What is trigonometry?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

What is trigonometry?

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

How do we use trigonometry in real-life situations?

- Master Core Mathematics Grade 10 pg. 134
- Scientific calculators
- Mathematical tables
- Rulers and geometrical set
- Master Core Mathematics Grade 10 pg. 136
- Rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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 a triangle using Heron's formula
Area of Polygons - Area of parallelograms and rhombus

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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
- Master Core Mathematics Grade 10 pg. 155

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Application of area of polygons to real-life situations
Area of a Part of a Circle - Area of an annulus

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

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

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

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

- Master Core Mathematics Grade 10 pg. 159
- Scientific calculators
- Mathematical tables
- Digital resources
- Master Core Mathematics Grade 10 pg. 161
- Circular objects
- Compasses
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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

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

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

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

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

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

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

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

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

- Master Core Mathematics Grade 10 pg. 167
- Scientific calculators
- Rulers
- Protractors
- Master Core Mathematics Grade 10 pg. 169
- Compasses and protractors
- Rulers and geometrical set
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

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

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
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

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

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Column vectors
Vectors I - Position vectors

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

- Express vectors in column form showing horizontal and vertical components
- Represent column vectors graphically and perform operations on them
- Relate column vectors to real-life movement such as an aircraft moving a given distance east and a given distance upward

- Mark a starting point on a grid and move steps right/left and up/down to form vectors
- Write and represent column vectors graphically
- Perform addition, subtraction and scalar multiplication of column vectors and share work

How do we express a vector in column form?

- Master Core Mathematics Grade 10 pg. 218
- Graph papers
- Rulers
- Grids
- Digital resources
- Master Core Mathematics Grade 10 pg. 221
- Geometrical set
- Calculators

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Magnitude of a vector and midpoint of a vector
Vectors I - Translation 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
- Master Core Mathematics Grade 10 pg. 227
- Paper cutouts
- Geometrical set

- Oral questions - Observation - Written assignments