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
- Recognize symmetry in nature and art

- Collect objects from environment and identify lines of symmetry
- Fold paper cut-outs to locate lines of symmetry
- Discuss symmetry in nature and architecture

How do we identify lines of symmetry?

- Mentor Core Mathematics Grade 10 pg. 75
- Paper cut-outs
- Plane mirrors
- Objects from environment
- Mentor Core Mathematics Grade 10 pg. 78
- Tracing paper
- Graph papers

- Observation - Oral questions - Practical activities

Measurements and Geometry

Reflection and Congruence - Reflection on plane surface

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

- Draw an image given object and mirror line on plane surface
- Construct perpendicular bisectors accurately
- Apply reflection in creating symmetric designs

- Draw plane figures and mirror lines on paper
- Use properties of reflection to locate images
- Create symmetric patterns using reflection

How do we construct images under reflection?

- Mentor Core Mathematics Grade 10 pg. 79
- Plain paper
- Geometrical instruments
- Rulers

- Practical assessment - Written tests - Observation

Measurements and Geometry

Reflection and Congruence - Reflection on Cartesian plane (x-axis and y-axis)
Reflection and Congruence - Reflection along lines y=x and y=-x

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

- Draw images after reflection along x-axis and y-axis
- State coordinates of images accurately
- Connect coordinate geometry to computer graphics

- Plot objects on Cartesian plane
- Reflect along x-axis and y-axis
- Record coordinates of images

How do coordinates change under reflection along axes?

- Mentor Core Mathematics Grade 10 pg. 82
- Graph papers
- Geometrical set
- Calculators
- Mentor Core Mathematics Grade 10 pg. 84
- Geometrical instruments
- Rulers

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Reflection and Congruence - Reflection along other lines

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

- Draw images reflected along lines like y=2, x=1, y=x+4
- Apply properties of reflection consistently
- Solve complex reflection problems

- Reflect objects along various mirror lines
- Use perpendicular distance method
- Practice with different mirror line equations

How do we reflect along any given line?

- Mentor Core Mathematics Grade 10 pg. 85
- Graph papers
- Geometrical set
- Calculators

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Reflection and Congruence - Determining equation of mirror line
Reflection and Congruence - Congruence tests (SSS and SAS)

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

- Determine equation of mirror line given object and image
- Construct perpendicular bisectors accurately
- Apply knowledge in solving problems

- Join corresponding points and construct perpendicular bisectors
- Determine gradients and y-intercepts
- Form equations of mirror lines

How do we find the equation of a mirror line?

- Mentor Core Mathematics Grade 10 pg. 86
- Graph papers
- Geometrical instruments
- Calculators
- Mentor Core Mathematics Grade 10 pg. 89
- Paper cut-outs
- Rulers

- Written assignments - Practical assessment - Oral questions

Measurements and Geometry

Reflection and Congruence - Congruence tests (ASA and RHS)
Reflection and Congruence - Applications in real life

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

- Carry out congruence tests using ASA and RHS
- Prove triangles are congruent
- Apply congruence in geometric proofs

- Use triangles to establish ASA congruence
- Test for RHS congruence in right-angled triangles
- Solve problems involving congruence

How do we prove triangles are congruent?

- Mentor Core Mathematics Grade 10 pg. 91
- Paper cut-outs
- Protractors
- Rulers
- Mentor Core Mathematics Grade 10 pg. 95
- Plane mirrors
- Digital devices
- Reference materials

- Written assignments - Class exercises - Oral questions

Measurements and Geometry

Rotation - Properties of rotation

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

- Determine properties of rotation
- Demonstrate rotation using a clock
- Relate rotation to movement of clock hands and wheels

- Use an improvised clock to demonstrate rotation
- Discuss movement of minute and hour hands
- Generate properties of rotation

What are the properties of rotation?

- Mentor Core Mathematics Grade 10 pg. 97
- Improvised clock
- Protractors
- Paper cut-outs

- Oral questions - Observation - Written assignments

Measurements and Geometry

Rotation - Rotation on plane surface
Rotation - Rotation through ±90° about origin

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

- Rotate an object given centre and angle on plane surface
- Use protractor and ruler accurately
- Apply rotation in creating patterns and designs

- Draw objects and rotate about given centres
- Measure angles accurately using protractor
- Create rotational patterns

How do we perform rotation on a plane surface?

- Mentor Core Mathematics Grade 10 pg. 99
- Plain paper
- Protractors
- Rulers
- Compasses
- Mentor Core Mathematics Grade 10 pg. 103
- Graph papers
- Geometrical set
- Calculators

- Practical assessment - Written tests - Observation

Measurements and Geometry

Rotation - Rotation through ±180° about origin

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

- Rotate objects through ±180° about the origin
- Determine image coordinates accurately
- Connect half-turn to reflection through a point

- Plot objects and rotate through 180°
- Compare results with -180° rotation
- Establish coordinate patterns

What is the effect of a half-turn on coordinates?

- Mentor Core Mathematics Grade 10 pg. 103
- Graph papers
- Geometrical instruments
- Calculators

- Written tests - Practical work - Observation

Measurements and Geometry

Rotation - Rotation about other centres
Rotation - Finding centre and angle of rotation

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

- Rotate objects about centres other than origin
- Construct rotations accurately
- Solve rotation problems involving various centres

- Rotate objects about various centres
- Use construction methods
- Practice with different angles and centres

How do we rotate about centres other than origin?

- Mentor Core Mathematics Grade 10 pg. 105
- Graph papers
- Geometrical set
- Protractors
- Mentor Core Mathematics Grade 10 pg. 106
- Geometrical instruments

- Written assignments - Practical assessment - Oral questions

Measurements and Geometry

Rotation - Rotational symmetry of plane figures

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

- Determine order of rotational symmetry of plane figures
- Use paper cut-outs to demonstrate rotational symmetry
- Identify rotational symmetry in logos and designs

- Use paper cut-outs to locate points of symmetry
- Establish order of rotational symmetry
- Discuss symmetry in logos and patterns

What is the order of rotational symmetry?

- Mentor Core Mathematics Grade 10 pg. 110
- Paper cut-outs
- Pins
- Manila paper

- Oral questions - Practical work - Written assignments

Measurements and Geometry

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

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

- Determine axis and order of rotational symmetry in solids
- Identify axes of symmetry in various solids
- Connect rotational symmetry to manufacturing and packaging

- Collect regular solids from environment
- Identify axes of rotational symmetry
- Establish order of rotational symmetry

How do we identify rotational symmetry in solids?

- Mentor Core Mathematics Grade 10 pg. 113
- Models of solids
- Objects from environment
- Mentor Core Mathematics Grade 10 pg. 115
- Graph papers
- Geometrical instruments
- Digital devices

- Observation - Written tests - Oral questions

Measurements and Geometry

Trigonometry 1 - Reading tangent from tables

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

- Determine tangent of acute angles from tables
- Read and interpret mathematical tables correctly
- Apply tangent ratios in calculating heights and distances

- Identify angles in table column
- Read tangent values from main columns
- Use mean difference columns for precision

How do we read tangent values from tables?

- Mentor Core Mathematics Grade 10 pg. 120
- Mathematical tables
- Calculators

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Trigonometry 1 - Reading sine and cosine from tables
Trigonometry 1 - Using calculators for trigonometric ratios

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

- Determine sine and cosine of acute angles from tables
- Use mean difference correctly
- Apply sine and cosine in solving triangles

- Read sine values from tables
- Read cosine values (subtracting mean difference)
- Practice finding angles given ratios

How do we read sine and cosine from tables?

- Mentor Core Mathematics Grade 10 pg. 122
- Mathematical tables
- Calculators
- Mentor Core Mathematics Grade 10 pg. 126
- Scientific calculators
- Mathematical tables

- Written assignments - Practical work - Observation

Measurements and Geometry

Trigonometry 1 - Complementary angle relationships
Trigonometry 1 - Relating sine, cosine and tangent

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

- Relate sines and cosines of complementary angles
- Prove that sin θ = cos(90°-θ)
- Apply relationships in solving equations

- Generate table of complementary angles
- Compare sines and cosines
- Establish sin θ = cos(90°-θ)

What is the relationship between sine and cosine of complementary angles?

- Mentor Core Mathematics Grade 10 pg. 128
- Mathematical tables
- Calculators
- Mentor Core Mathematics Grade 10 pg. 129

- Written assignments - Class exercises - Observation

Measurements and Geometry

Trigonometry 1 - Ratios of 45°

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

- Determine trigonometric ratios of 45° using triangles
- Derive exact values without tables
- Apply in solving problems with exact values

- Draw isosceles right-angled triangle
- Calculate hypotenuse using Pythagoras
- Derive sin 45°, cos 45°, tan 45°

How do we find exact values of trigonometric ratios?

- Mentor Core Mathematics Grade 10 pg. 130
- Geometrical instruments
- Rulers

- Written assignments - Practical work - Oral questions

Measurements and Geometry

Trigonometry 1 - Ratios of 30° and 60°
Trigonometry 1 - Problems involving special angles

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

- Determine trigonometric ratios of 30° and 60°
- Use equilateral triangle to derive ratios
- Solve problems involving special angles

- Draw equilateral triangle of side 2 units
- Calculate perpendicular height
- Derive ratios for 30° and 60°

How do we derive ratios for 30° and 60°?

- Mentor Core Mathematics Grade 10 pg. 131
- Geometrical instruments
- Rulers
- Mentor Core Mathematics Grade 10 pg. 132
- Reference materials
- Calculators

- Written tests - Class exercises - Observation

Measurements and Geometry

Trigonometry 1 - Angle of elevation

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

- Define angle of elevation
- Use clinometer to measure angles of elevation
- Calculate heights of buildings, trees and towers

- Use clinometer to measure angles
- Sketch diagrams showing angles of elevation
- Calculate unknown heights

What is angle of elevation and how do we use it?

- Mentor Core Mathematics Grade 10 pg. 133
- Clinometer
- Measuring tape
- Calculators

- Practical assessment - Written tests - Oral questions

Measurements and Geometry

Trigonometry 1 - Angle of depression
Trigonometry 1 - Applications in real life

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

- Define angle of depression
- Solve problems involving angles of depression
- Apply to navigation and surveying

- Demonstrate angles of depression
- Sketch diagrams correctly
- Solve problems involving depression

What is angle of depression?

- Mentor Core Mathematics Grade 10 pg. 134
- Clinometer
- Digital devices
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 136
- Reference books
- Calculators

- Written assignments - Practical work - Observation

Measurements and Geometry

Area of Polygons - Deriving area formula

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

- Derive formula for area of triangle given two sides and included angle
- Use trigonometric ratios in derivation
- Apply formula Area = ½abSinC

- Use trigonometric ratios to derive formula
- Discuss in groups and generate formula
- Practice using the formula

How do we derive the area formula using trigonometry?

- Mentor Core Mathematics Grade 10 pg. 137
- Geometrical instruments
- Calculators

- Written assignments - Class exercises - Observation

Measurements and Geometry

Area of Polygons - Calculating area using Area = ½abSinC
Area of Polygons - Heron's formula

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

- Calculate area of triangle given two sides and included angle
- Find missing sides or angles given area
- Apply to practical problems

- Calculate areas of various triangles
- Find missing elements given area
- Solve practical problems

How do we calculate area using trigonometry?

- Mentor Core Mathematics Grade 10 pg. 138
- Calculators
- Mathematical tables
- Mentor Core Mathematics Grade 10 pg. 139
- Reference materials

- Written tests - Oral questions - Class exercises

Measurements and Geometry

Area of Polygons - Area of rhombus

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

- Calculate area of rhombus using diagonals
- Calculate area using base and height
- Apply to real-life situations like floor tiles

- Identify rhombuses in environment
- Calculate areas using Area = ½d₁d₂
- Solve practical problems

How do we calculate the area of a rhombus?

- Mentor Core Mathematics Grade 10 pg. 143
- Models of rhombus
- Calculators

- Written tests - Practical activities - Oral questions

Measurements and Geometry

Area of Polygons - Area of parallelogram and trapezium
Area of Polygons - Area of heptagon

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

- Calculate area of parallelogram using base × height
- Calculate area of trapezium
- Apply formulas to practical situations

- Calculate areas of parallelograms
- Calculate areas of trapeziums
- Identify shapes in environment

How do we calculate areas of parallelograms and trapeziums?

- Mentor Core Mathematics Grade 10 pg. 147
- Geometrical instruments
- Calculators
- Mentor Core Mathematics Grade 10 pg. 152
- Paper cut-outs
- Calculators
- Protractors

- Written assignments - Class exercises - Observation

Measurements and Geometry

Area of Polygons - Area of octagon

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

- Calculate area of regular octagon
- Use formula involving central angles
- Connect to real objects like stop signs

- Divide octagon into 8 triangles
- Calculate central angle (45°)
- Calculate total area

How do we calculate the area of an octagon?

- Mentor Core Mathematics Grade 10 pg. 156
- Paper cut-outs
- Calculators
- Reference materials

- Written assignments - Class exercises - Observation

Measurements and Geometry

Area of Polygons - Irregular polygons
Area of Polygons - Real-life applications

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

- Determine area of irregular polygons
- Subdivide into regular shapes
- Apply to land surveying and floor plans

- Subdivide irregular polygons into regular shapes
- Calculate area of each shape
- Sum up to get total area

How do we calculate area of irregular polygons?

- Mentor Core Mathematics Grade 10 pg. 159
- Geometrical instruments
- Calculators
- Mentor Core Mathematics Grade 10 pg. 163
- Reference materials
- Digital devices

- Written tests - Project work - Oral questions

Measurements and Geometry

Area of a Part of a Circle - Annulus
Area of a Part of a Circle - Area of sector

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

- Define annulus and its components
- Calculate area of annulus
- Apply to circular paths and rings

- Draw concentric circles
- Calculate area of annulus using πR² - πr²
- Solve practical problems

What is an annulus and how do we calculate its area?

- Mentor Core Mathematics Grade 10 pg. 166
- Compasses
- Calculators
- Mentor Core Mathematics Grade 10 pg. 167
- Paper
- Scissors

- Written tests - Practical activities - Oral questions

Measurements and Geometry

Area of a Part of a Circle - Annular sector

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

- Calculate area of annular sector
- Apply to windscreen wipers and fan blades
- Solve practical problems

- Illustrate annular sectors
- Calculate area using sector formula
- Relate to car windscreen wipers

How do we calculate area of an annular sector?

- Mentor Core Mathematics Grade 10 pg. 170
- Diagrams
- Calculators
- Reference materials

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Area of a Part of a Circle - Segment of a circle
Area of a Part of a Circle - Problems on segments

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

- Define segment of a circle
- Calculate area of segment
- Apply formula: Area of sector - Area of triangle

- Draw segments of circles
- Calculate area of sector
- Subtract area of triangle

How do we calculate the area of a segment?

- Mentor Core Mathematics Grade 10 pg. 172
- Geometrical instruments
- Calculators
- Mentor Core Mathematics Grade 10 pg. 174
- Calculators
- Reference materials

- Written assignments - Practical assessment - Observation

Measurements and Geometry

Area of a Part of a Circle - Intersecting circles (introduction)

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

- Identify common region between two intersecting circles
- Understand components of common region
- Connect to Venn diagrams and logos

- Draw two intersecting circles
- Identify common region
- Discuss structure of common area

What is the common region between two intersecting circles?

- Mentor Core Mathematics Grade 10 pg. 176
- Compasses
- Rulers
- Graph papers

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of a Part of a Circle - Calculating common area
Area of a Part of a Circle - Complex problems

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

- Calculate area of common region
- Sum areas of two segments
- Solve problems involving intersecting circles

- Calculate area of each segment
- Sum to get common area
- Solve practical problems

How do we calculate the common area?

- Mentor Core Mathematics Grade 10 pg. 177
- Calculators
- Geometrical instruments
- Mentor Core Mathematics Grade 10 pg. 179
- Reference materials
- Digital devices
- Calculators

- Written tests - Class exercises - Observation

Measurements and Geometry

Area of a Part of a Circle - Making dartboard and necklaces

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

- Make dartboard using concentric circles
- Create beaded necklaces using annular sectors
- Apply concepts creatively

- Make dartboard from available materials
- Create necklaces using beading techniques
- Present projects

How do we apply area concepts in creating designs?

- Mentor Core Mathematics Grade 10 pg. 180
- Cardboard
- Beads
- Paints
- Compasses

- Project assessment - Peer evaluation - Observation

Measurements and Geometry

Area of a Part of a Circle - Review and assessment
Surface Area and Volume - Rectangular prism

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

- Solve mixed problems on area of parts of a circle
- Apply all concepts learned
- Evaluate understanding of the sub-strand

- Review all concepts
- Solve mixed problems
- Assess understanding

How well can we apply area concepts?

- Mentor Core Mathematics Grade 10 pg. 181
- Calculators
- Past papers
- Mentor Core Mathematics Grade 10 pg. 182
- Models of prisms
- Nets
- Calculators

- Written tests - Oral questions - Class exercises

Measurements and Geometry

Surface Area and Volume - Triangular and other prisms

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

- Calculate surface area of triangular prisms
- Calculate surface area of other prisms
- Apply to tents and buildings

- Draw nets of triangular prisms
- Calculate surface areas
- Solve practical problems

How do we find surface area of triangular prisms?

- Mentor Core Mathematics Grade 10 pg. 185
- Models of prisms
- Calculators

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Surface Area and Volume - Pyramids
Surface Area and Volume - Cones

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

- Determine surface area of pyramids
- Draw nets of pyramids
- Apply to structures like Egyptian pyramids

- Measure edges of pyramid models
- Cut and open to get nets
- Calculate surface area

How do we calculate surface area of pyramids?

- Mentor Core Mathematics Grade 10 pg. 191
- Models of pyramids
- Calculators
- Mentor Core Mathematics Grade 10 pg. 193
- Manila paper
- Compasses

- Written assignments - Practical assessment - Observation

Measurements and Geometry

Surface Area and Volume - Frustum of cone
Surface Area and Volume - Frustum of pyramid

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

- Calculate surface area of frustum of a cone
- Use similar cone properties
- Apply to lampshades and buckets

- Make frustum by cutting cone
- Calculate surfaces of original and cut-off cone
- Find surface area of frustum

How do we calculate surface area of a frustum?

- Mentor Core Mathematics Grade 10 pg. 195
- Cone models
- Scissors
- Calculators
- Mentor Core Mathematics Grade 10 pg. 197
- Models
- Calculators
- Reference materials

- Written assignments - Practical assessment - Observation

Measurements and Geometry

Surface Area and Volume - Spheres and hemispheres

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

- Calculate surface area of spheres using 4πr²
- Calculate surface area of hemispheres
- Apply to balls, domes and bowls

- Brainstorm on spheres
- Apply formula 4πr²
- Calculate hemisphere surface area (3πr²)

How do we calculate surface area of spheres?

- Mentor Core Mathematics Grade 10 pg. 200
- Spherical objects
- Calculators

- Written assignments - Practical activities - Observation

Measurements and Geometry

Surface Area and Volume - Composite solids
Surface Area and Volume - Volume of cones

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

- Calculate surface area of composite solids
- Identify component solids
- Apply to real structures and objects

- Identify components of composite solids
- Calculate surface area of each component
- Combine appropriately

How do we find surface area of composite solids?

- Mentor Core Mathematics Grade 10 pg. 202
- Models of composite solids
- Calculators
- Mentor Core Mathematics Grade 10 pg. 205
- Cone and cylinder models
- Sand/water

- Written tests - Project work - Oral questions

Measurements and Geometry

Surface Area and Volume - Volume of prisms and pyramids

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

- Calculate volume of various prisms
- Calculate volume of pyramids using ⅓Bh
- Apply to buildings and storage

- Calculate volumes of prisms
- Apply pyramid volume formula
- Solve real-life problems

How do we calculate volumes of prisms and pyramids?

- Mentor Core Mathematics Grade 10 pg. 206
- Models of solids
- Calculators

- Written tests - Class exercises - Oral questions

Measurements and Geometry

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

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

- Calculate volume of spheres using (4/3)πr³
- Calculate volume of hemispheres
- Apply to balls, tanks and containers

- Apply sphere volume formula
- Calculate hemisphere volumes
- Solve practical problems

How do we calculate volume of spheres?

- Mentor Core Mathematics Grade 10 pg. 210
- Spherical objects
- Calculators
- Mentor Core Mathematics Grade 10 pg. 212
- Models
- Calculators
- Reference materials

- Written assignments - Practical activities - Observation

Measurements and Geometry

Surface Area and Volume - Composite solids volume

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

- Calculate volume of composite solids
- Identify and separate components
- Apply to real objects like test tubes and tanks

- Identify composite solid components
- Calculate volume of each part
- Sum up total volume

How do we find volume of composite solids?

- Mentor Core Mathematics Grade 10 pg. 216
- Models of composite solids
- Calculators

- Written assignments - Project assessment - Observation