Measurements and Geometry

Similarity and Enlargement - Determining centre of enlargement

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

- Define the terms similar figures and enlargement
- Identify the centre of enlargement from given figures
- Apply knowledge of similarity in identifying objects around them

- Discuss with peers properties of similar figures
- Use an object and its image to locate the centre of enlargement
- Search the internet for real-life examples of similar figures

How do we identify similar figures in our environment?

- Mentor Core Mathematics Grade 10 pg. 56
- Graph papers
- Rulers
- Digital devices

- Oral questions - Observation - Written assignments

Measurements and Geometry

Similarity and Enlargement - Linear scale factor
Similarity and Enlargement - Constructing images (positive scale factor)
Similarity and Enlargement - Constructing images (negative scale factor)

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

- Determine the linear scale factor from similar figures
- Calculate the ratio of corresponding sides
- Use scale factors in solving problems involving maps and models

- Work out the ratio of lengths of corresponding sides
- Discuss in groups and establish Linear Scale Factor (L.S.F)
- Use digital devices to explore scale factors in maps

What is the relationship between an object and its image under enlargement?

- Mentor Core Mathematics Grade 10 pg. 57
- Graph papers
- Geometrical instruments
- Maps
- Mentor Core Mathematics Grade 10 pg. 61
- Geometrical set
- Rulers
- Mentor Core Mathematics Grade 10 pg. 62
- Cartesian plane grids
- Geometrical instruments

- Written tests - Practical activities - Oral questions

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 area scale factor of similar figures
- Establish the relationship between L.S.F and A.S.F
- Apply area scale factor in calculating surface areas of models

- Calculate areas of similar figures
- Work out the ratio of areas
- Discuss relationship A.S.F = (L.S.F)²

How does enlargement affect the area of a figure?

- Mentor Core Mathematics Grade 10 pg. 64
- Similar plane figures
- Calculators
- Manila paper
- Mentor Core Mathematics Grade 10 pg. 66
- Models of similar solids
- Digital devices

- Written assignments - Class exercises - Oral questions

Measurements and Geometry

Similarity and Enlargement - Relating L.S.F, A.S.F and V.S.F
Similarity and Enlargement - Real-life applications
Similarity and Enlargement - Project on models

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

- Relate linear, area and volume scale factors
- Solve problems involving all three scale factors
- Apply relationships to architectural models and designs

- Use two similar solids to establish relationships
- Work out tasks involving L.S.F, A.S.F and V.S.F
- Research applications in architecture

What is the relationship between L.S.F, A.S.F and V.S.F?

- Mentor Core Mathematics Grade 10 pg. 68
- Models of solids
- Calculators
- Reference books
- Mentor Core Mathematics Grade 10 pg. 72
- Maps
- Scale models
- Calculators
- Manila paper
- Cardboard
- Scissors
- Rulers

- Written assignments - Class exercises - Oral questions

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
- 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

- Observation - Oral questions - Practical activities

Measurements and Geometry

Reflection and Congruence - Properties of reflection

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

- Determine properties of reflection
- Use plane mirrors to demonstrate reflection
- Relate reflection to mirror images in daily life

- Use plane mirror to locate image of an object
- Use tracing paper to generate properties of reflection
- Discuss applications in driving mirrors

What are the properties of reflection?

- Mentor Core Mathematics Grade 10 pg. 78
- Plane mirrors
- Tracing paper
- Graph papers

- Written assignments - Practical work - Oral questions

Measurements and Geometry

Reflection and Congruence - Reflection on plane surface
Reflection and Congruence - Reflection on Cartesian plane (x-axis and y-axis)

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

- Practical assessment - Written tests - Observation

Measurements and Geometry

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 y=x and y=-x
- Determine image coordinates accurately
- Apply knowledge in solving transformation problems

- Draw objects and reflect along y=x
- Reflect along y=-x
- Compare results and establish patterns

What happens to coordinates when reflecting along y=x?

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

- Written assignments - Practical work - Observation

Measurements and Geometry

Reflection and Congruence - Reflection along other lines
Reflection and Congruence - Determining equation of mirror line

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
- Mentor Core Mathematics Grade 10 pg. 86
- Geometrical instruments

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Reflection and Congruence - Congruence tests (SSS and SAS)

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

- Carry out congruence tests for triangles using SSS and SAS
- Identify directly and indirectly congruent figures
- Apply congruence in construction and engineering

- Make paper cut-outs of identical shapes
- Test for congruence using SSS
- Test for congruence using SAS

When are two triangles congruent?

- Mentor Core Mathematics Grade 10 pg. 89
- Paper cut-outs
- Geometrical instruments
- Rulers

- Written tests - Practical activities - Observation

Measurements and Geometry

Reflection and Congruence - Congruence tests (ASA and RHS)

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

- Written assignments - Class exercises - Oral questions

Measurements and Geometry

Reflection and Congruence - Applications in real life
Rotation - Properties of rotation

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

- Apply reflection and congruence to real-life situations
- Discuss applications in driving mirrors and road safety
- Create designs using reflection

- Discuss applications in driving mirrors
- Create symmetric designs
- Use digital devices to explore applications

How do we use reflection in daily life?

- Mentor Core Mathematics Grade 10 pg. 95
- Plane mirrors
- Digital devices
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 97
- Improvised clock
- Protractors
- Paper cut-outs

- Project work - Written tests - Observation

Measurements and Geometry

Rotation - Rotation on plane surface

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

- Practical assessment - Written tests - Observation

Measurements and Geometry

Rotation - Rotation through ±90° about origin

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

- Rotate objects through ±90° about the origin
- State coordinates of images correctly
- Recognize patterns in coordinate changes

- Plot objects on Cartesian plane
- Rotate through +90° and -90° about (0,0)
- Record and compare coordinates

How do coordinates change under rotation through 90°?

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

- Written assignments - Class exercises - Oral questions

Measurements and Geometry

Rotation - Rotation through ±180° about origin
Rotation - Rotation about other centres

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
- Mentor Core Mathematics Grade 10 pg. 105
- Geometrical set
- Protractors

- Written tests - Practical work - Observation

Measurements and Geometry

Rotation - Finding centre and angle of rotation

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

- Determine centre and angle of rotation given object and image
- Construct perpendicular bisectors accurately
- Apply construction skills in solving problems

- Join corresponding points
- Construct perpendicular bisectors
- Locate centre and measure angle of rotation

How do we find the centre and angle of rotation?

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

- Written tests - Practical activities - Observation

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

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

- Written assignments - Class exercises - Observation

Measurements and Geometry

Trigonometry 1 - Relating sine, cosine and tangent

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

- Relate sine, cosine and tangent of acute angles
- Prove that tan θ = sin θ/cos θ
- Apply relationships in solving problems

- Use right-angled triangles
- Derive tan θ = sin θ/cos θ
- Solve problems using the relationship

How are sine, cosine and tangent related?

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

- Written tests - Oral questions - Class exercises

Measurements and Geometry

Trigonometry 1 - Ratios of 45°
Trigonometry 1 - Ratios of 30° and 60°

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
- Mentor Core Mathematics Grade 10 pg. 131

- Written assignments - Practical work - Oral questions

Measurements and Geometry

Trigonometry 1 - Problems involving special angles

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

- Solve problems using special angle ratios
- Simplify expressions with special angles
- Apply special angles in construction

- Solve problems without tables or calculators
- Simplify trigonometric expressions
- Apply to practical situations

How do we apply special angle ratios?

- Mentor Core Mathematics Grade 10 pg. 132
- Reference materials
- Calculators

- Written assignments - Oral questions - Class exercises

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

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

- Written tests - Oral questions - Class exercises

Measurements and Geometry

Area of Polygons - Heron's formula
Area of Polygons - Area of rhombus

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

- Determine area of triangle using Heron's formula
- Calculate semi-perimeter correctly
- Apply formula to triangles given three sides

- Calculate semi-perimeter
- Apply Heron's formula
- Compare with other methods

How do we use Heron's formula?

- Mentor Core Mathematics Grade 10 pg. 139
- Calculators
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 143
- Models of rhombus
- Calculators

- Written assignments - Class exercises - Observation

Measurements and Geometry

Area of Polygons - Area of parallelogram and trapezium

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

- Written assignments - Class exercises - Observation

Measurements and Geometry

Area of Polygons - Area of heptagon

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

- Calculate area of regular heptagon
- Divide heptagon into triangles
- Apply to real objects like road signs

- Divide heptagon into 7 triangles
- Calculate central angle (360°÷7)
- Calculate area of one triangle and multiply

How do we calculate the area of a heptagon?

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

- Written tests - Practical work - Oral questions

Measurements and Geometry

Area of Polygons - Area of octagon
Area of Polygons - Irregular polygons

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
- Mentor Core Mathematics Grade 10 pg. 159
- Geometrical instruments
- Calculators

- Written assignments - Class exercises - Observation

Measurements and Geometry

Area of Polygons - Real-life applications

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

- Apply area of polygons to real-life situations
- Solve problems involving land and flooring
- Relate to careers in architecture and surveying

- Solve real-life problems
- Calculate areas of compound shapes
- Discuss applications in various careers

Where do we use area of polygons in real life?

- Mentor Core Mathematics Grade 10 pg. 163
- Reference materials
- Digital devices

- Written assignments - Project assessment - Observation

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

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

- Written assignments - Practical assessment - Observation

Measurements and Geometry

Area of a Part of a Circle - Problems on segments
Area of a Part of a Circle - Intersecting circles (introduction)

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

- Solve complex problems involving segments
- Apply to church windows and architectural designs
- Calculate missing elements

- Solve various segment problems
- Apply to real-life contexts
- Calculate angles given area

How do we apply segment area in solving problems?

- Mentor Core Mathematics Grade 10 pg. 174
- Calculators
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 176
- Compasses
- Rulers
- Graph papers

- Written tests - Oral questions - Class exercises

Measurements and Geometry

Area of a Part of a Circle - Calculating common area

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

- Written tests - Class exercises - Observation

Measurements and Geometry

Area of a Part of a Circle - Complex problems

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

- Solve complex problems on intersecting circles
- Calculate shaded regions
- Apply to decorative patterns and designs

- Solve problems involving common regions
- Calculate shaded areas
- Research applications in design

Where do we use intersecting circles in real life?

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

- Written assignments - Project work - Oral questions

Measurements and Geometry

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

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
- Mentor Core Mathematics Grade 10 pg. 181
- Calculators
- Past papers

- Project assessment - Peer evaluation - Observation

Measurements and Geometry

Surface Area and Volume - Rectangular prism

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

- Determine surface area of rectangular prisms
- Draw nets of rectangular prisms
- Apply to packaging and construction

- Collect models of rectangular prisms
- Sketch nets
- Calculate surface area

How do we calculate surface area of rectangular prisms?

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

- Written assignments - Practical activities - Observation

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

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

- Written assignments - Practical assessment - Observation

Measurements and Geometry

Surface Area and Volume - Frustum of pyramid
Surface Area and Volume - Spheres and hemispheres

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

- Calculate surface area of frustum of a pyramid
- Apply similar figure properties
- Connect to kitchen worktops and counters

- Sketch original pyramid
- Use similar figures to find dimensions
- Calculate surface area

How do we find surface area of pyramid frustum?

- Mentor Core Mathematics Grade 10 pg. 197
- Models
- Calculators
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 200
- Spherical objects
- Calculators

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Surface Area and Volume - Composite solids

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

- Written tests - Project work - Oral questions

Measurements and Geometry

Surface Area and Volume - Volume of cones

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

- Calculate volume of cones using ⅓πr²h
- Relate cone and cylinder volumes
- Apply to storage containers

- Compare cone and cylinder volumes
- Establish cone volume = ⅓ cylinder volume
- Solve practical problems

What is the relationship between cone and cylinder volumes?

- Mentor Core Mathematics Grade 10 pg. 205
- Cone and cylinder models
- Sand/water
- Calculators

- Written assignments - Practical work - Observation

Measurements and Geometry

Surface Area and Volume - Volume of prisms and pyramids
Surface Area and Volume - Volume of spheres and hemispheres

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
- Mentor Core Mathematics Grade 10 pg. 210
- Spherical objects

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Surface Area and Volume - Volume of frustums

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

- Calculate volume of frustum of cone and pyramid
- Use similar figure relationships
- Apply to buckets, lampshades and pots

- Calculate volume of original solid
- Subtract volume of cut-off part
- Solve problems involving frustums

How do we calculate volume of a frustum?

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

- Written tests - Class exercises - Oral questions

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

Measurements and Geometry

Vectors I - Introduction to vectors
Vectors I - Vector notation

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

- Distinguish vector and scalar quantities
- Give examples of vectors and scalars
- Relate vectors to displacement and force

- Brainstorm meanings of vector and scalar
- Give examples from daily life
- Discuss arrows on roads as vector indicators

What are vector and scalar quantities?

- Mentor Core Mathematics Grade 10 pg. 220
- Charts
- Reference materials
- Mentor Core Mathematics Grade 10 pg. 221
- Graph papers
- Rulers

- Oral questions - Written assignments - Observation

Measurements and Geometry

Vectors I - Equivalent vectors

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

- Identify equivalent vectors
- Determine conditions for equivalent vectors
- Find equivalent vectors in shapes

- Identify vectors with same magnitude and direction
- Use grids to compare vectors
- Identify equivalent vectors in solids

When are two vectors equivalent?

- Mentor Core Mathematics Grade 10 pg. 223
- Graph papers
- Geometrical instruments

- Written assignments - Practical work - Observation

Measurements and Geometry

Vectors I - Adding vectors

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

- Add vectors graphically
- Determine resultant vector
- Apply to finding net force or displacement

- Draw vectors head to tail
- Determine resultant vector
- Practice with multiple vectors

How do we add vectors?

- Mentor Core Mathematics Grade 10 pg. 225
- Graph papers
- Rulers
- Protractors

- Written tests - Practical assessment - Oral questions

Measurements and Geometry

Vectors I - Scalar multiplication
Vectors I - Column vectors

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

- Multiply vectors by scalars
- Understand effect of positive and negative scalars
- Apply in solving problems

- Multiply vectors by positive scalars
- Multiply by negative scalars
- Observe effect on magnitude and direction

What happens when we multiply a vector by a scalar?

- Mentor Core Mathematics Grade 10 pg. 228
- Graph papers
- Rulers
- Mentor Core Mathematics Grade 10 pg. 230
- Calculators

- Written assignments - Class exercises - Observation

Measurements and Geometry

Vectors I - Position vectors

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

- Determine position vectors
- Express vectors in terms of position vectors
- Use position vectors in calculations

- Define position vectors from origin
- Calculate vectors using a⃗ = OB⃗ - OA⃗
- Solve problems using position vectors

What are position vectors?

- Mentor Core Mathematics Grade 10 pg. 234
- Graph papers
- Calculators

- Written assignments - Practical work - Observation

Measurements and Geometry

Vectors I - Magnitude of a vector

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

- Calculate magnitude of vectors
- Use Pythagoras theorem
- Apply magnitude in solving problems

- Use formula

v

How do we calculate the magnitude of a vector?

Measurements and Geometry

Vectors I - Midpoint of a vector
Vectors I - Translation as transformation
Vectors I - Applications and problems

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

- Determine midpoint of a vector
- Use midpoint formula
- Apply in geometry problems

- Calculate midpoint coordinates
- Use formula (x₁+x₂)/2, (y₁+y₂)/2
- Solve problems involving midpoints

How do we find the midpoint of a vector?

- Mentor Core Mathematics Grade 10 pg. 238
- Graph papers
- Calculators
- Mentor Core Mathematics Grade 10 pg. 240
- Geometrical instruments
- Mentor Core Mathematics Grade 10 pg. 242
- Calculators
- Digital devices

- Written assignments - Practical assessment - Observation