Measurements and Geometry

Trigonometry 1 - Reading tangent from tables
Trigonometry 1 - Reading sine and cosine 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

In groups, learners are guided to:
- 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
- Mentor Core Mathematics Grade 10 pg. 122

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Trigonometry 1 - Using calculators for trigonometric ratios
Trigonometry 1 - Complementary angle relationships

By the end of the lesson, the learner should be able to:
- Determine trigonometric ratios using calculators
- Find angles given trigonometric ratios
- Compare calculator and table values

In groups, learners are guided to:
- Set calculator to degree mode
- Find sin, cos, tan of angles
- Use inverse functions to find angles

How do we use calculators for trigonometric ratios?

- Mentor Core Mathematics Grade 10 pg. 126
- Scientific calculators
- Mathematical tables
- Mentor Core Mathematics Grade 10 pg. 128
- Mathematical tables
- Calculators

- Written tests - Class exercises - Oral questions

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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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
Trigonometry 1 - Angle of elevation

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

In groups, learners are guided to:
- 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
- Mentor Core Mathematics Grade 10 pg. 133
- Clinometer
- Measuring tape

- Written assignments - Oral questions - Class exercises

Measurements and Geometry

Trigonometry 1 - Angle of depression

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

In groups, learners are guided to:
- 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

- Written assignments - Practical work - Observation

Measurements and Geometry

Trigonometry 1 - Applications in real life
Area of Polygons - Deriving area formula

By the end of the lesson, the learner should be able to:
- Apply trigonometric ratios to real-life situations
- Solve problems involving heights and distances
- Connect trigonometry to surveying and aviation

In groups, learners are guided to:
- Solve problems on heights of buildings
- Calculate distances
- Research applications in careers

How do we use trigonometry in daily life?

- Mentor Core Mathematics Grade 10 pg. 136
- Reference books
- Digital devices
- Calculators
- Mentor Core Mathematics Grade 10 pg. 137
- Geometrical instruments

- Written tests - Project work - Oral questions

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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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
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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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
Area of a Part of a Circle - Segment of a circle

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

In groups, learners are guided to:
- 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
- Mentor Core Mathematics Grade 10 pg. 172
- Geometrical instruments
- Calculators

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Area of a Part of a Circle - Problems on segments

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

In groups, learners are guided to:
- 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

- Written tests - Oral questions - Class exercises

Measurements and Geometry

Area of a Part of a Circle - Intersecting circles (introduction)
Area of a Part of a Circle - Calculating common area

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

In groups, learners are guided to:
- 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
- Mentor Core Mathematics Grade 10 pg. 177
- Calculators
- Geometrical instruments

- Observation - Oral questions - Written assignments

Measurements and Geometry

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

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

In groups, learners are guided to:
- 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
- Mentor Core Mathematics Grade 10 pg. 180
- Cardboard
- Beads
- Paints
- Compasses

- Written assignments - Project work - Oral questions

Measurements and Geometry

Area of a Part of a Circle - Review and assessment

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

In groups, learners are guided to:
- 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

- Written tests - Oral questions - Class exercises

Measurements and Geometry

Surface Area and Volume - Rectangular prism
Surface Area and Volume - Triangular and other prisms

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

In groups, learners are guided to:
- 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
- Mentor Core Mathematics Grade 10 pg. 185

- Written assignments - Practical activities - Observation

Measurements and Geometry

Surface Area and Volume - Pyramids

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

In groups, learners are guided to:
- 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

- Written assignments - Practical assessment - Observation

Measurements and Geometry

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

By the end of the lesson, the learner should be able to:
- Calculate surface area of cones
- Use formulas for curved surface and base
- Apply to ice cream cones and funnels

In groups, learners are guided to:
- Make cone models from manila paper
- Calculate curved surface area πrl
- Calculate total surface area

How do we calculate surface area of cones?

- Mentor Core Mathematics Grade 10 pg. 193
- Manila paper
- Compasses
- Calculators
- Mentor Core Mathematics Grade 10 pg. 195
- Cone models
- Scissors

- Written tests - Practical work - Oral questions

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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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
Surface Area and Volume - Volume of prisms and pyramids

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

In groups, learners are guided to:
- 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
- Mentor Core Mathematics Grade 10 pg. 206
- Models of solids

- Written assignments - Practical work - Observation

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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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

In groups, learners are guided to:
- 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
Vectors I - Adding 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

In groups, learners are guided to:
- 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
- Mentor Core Mathematics Grade 10 pg. 225
- Rulers
- Protractors

- Written assignments - Practical work - Observation

Measurements and Geometry

Vectors I - Scalar multiplication

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

In groups, learners are guided to:
- 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

- Written assignments - Class exercises - Observation

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
- Determine horizontal and vertical components
- Add and subtract column vectors

In groups, learners are guided to:
- Determine horizontal and vertical displacements
- Write vectors in column form
- Perform operations on column vectors

How do we express vectors in column form?

- Mentor Core Mathematics Grade 10 pg. 230
- Graph papers
- Calculators
- Mentor Core Mathematics Grade 10 pg. 234

- Written tests - Oral questions - Class exercises

Measurements and Geometry

Vectors I - Magnitude of a vector
Vectors I - Midpoint 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

In groups, learners are guided to:
- Use formula

v

- Mentor Core Mathematics Grade 10 pg. 238
- Graph papers
- Calculators

How do we calculate the magnitude of a vector?

Measurements and Geometry

Vectors I - Translation as transformation

By the end of the lesson, the learner should be able to:
- Determine translation vector
- Perform translation on objects
- Relate translation to sliding motion

In groups, learners are guided to:
- Demonstrate translation
- Find translation vector from object and image
- Find image given object and translation

What is translation and how is it represented?

- Mentor Core Mathematics Grade 10 pg. 240
- Graph papers
- Geometrical instruments

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Vectors I - Applications and problems
Linear Motion - Basic terms

By the end of the lesson, the learner should be able to:
- Apply vector concepts in solving problems
- Solve mixed problems on vectors
- Connect vectors to physics and engineering

In groups, learners are guided to:
- Solve combined vector problems
- Apply to real-life situations
- Use digital devices to explore applications

Where do we use vectors in real life?

- Mentor Core Mathematics Grade 10 pg. 242
- Calculators
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 244
- Stopwatches
- Measuring tapes

- Written assignments - Project work - Observation

Measurements and Geometry

Linear Motion - Calculating velocity and acceleration
Linear Motion - Drawing displacement-time graphs

By the end of the lesson, the learner should be able to:
- Calculate velocity and acceleration
- Use appropriate formulas
- Apply to vehicle motion and sports

In groups, learners are guided to:
- Participate in races and record time
- Calculate velocity
- Calculate acceleration

How do we calculate velocity and acceleration?

- Mentor Core Mathematics Grade 10 pg. 246
- Stopwatches
- Measuring tapes
- Calculators
- Mentor Core Mathematics Grade 10 pg. 247
- Graph papers
- Rulers

- Written tests - Practical activities - Oral questions

Measurements and Geometry

Linear Motion - Interpreting displacement-time graphs

By the end of the lesson, the learner should be able to:
- Interpret displacement-time graphs
- Calculate velocity from gradient
- Identify periods of rest

In groups, learners are guided to:
- Calculate gradients of graphs
- Identify when object is stationary
- Determine maximum displacement

What information can we get from displacement-time graphs?

- Mentor Core Mathematics Grade 10 pg. 249
- Graph papers
- Calculators

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Linear Motion - Drawing velocity-time graphs
Linear Motion - Interpreting velocity-time graphs

By the end of the lesson, the learner should be able to:
- Draw velocity-time graphs
- Plot data correctly
- Represent different motion types

In groups, learners are guided to:
- Record velocity and time data
- Plot velocity-time graphs
- Draw graphs from given information

How do we draw velocity-time graphs?

- Mentor Core Mathematics Grade 10 pg. 253
- Graph papers
- Rulers
- Calculators
- Mentor Core Mathematics Grade 10 pg. 256

- Written assignments - Practical work - Observation

Measurements and Geometry

Linear Motion - Relative speed (opposite directions)
Linear Motion - Relative speed (same direction)

By the end of the lesson, the learner should be able to:
- Define relative speed
- Calculate relative speed of bodies moving in opposite directions
- Apply to vehicles meeting on roads

In groups, learners are guided to:
- Demonstrate bodies moving towards each other
- Calculate relative speed (sum of speeds)
- Solve problems on meeting times

What is relative speed?

- Mentor Core Mathematics Grade 10 pg. 261
- Digital devices
- Calculators
- Mentor Core Mathematics Grade 10 pg. 263
- Calculators
- Reference materials

- Written assignments - Practical activities - Observation

Measurements and Geometry

Linear Motion - Real-life applications

By the end of the lesson, the learner should be able to:
- Apply linear motion concepts to real-life
- Solve problems involving trains, cars and planes
- Relate to transport and logistics

In groups, learners are guided to:
- Solve real-life problems
- Apply all concepts learned
- Discuss applications in transport

Where do we use linear motion concepts?

- Mentor Core Mathematics Grade 10 pg. 265
- Calculators
- Reference materials
- Digital devices

- Written assignments - Project assessment - Observation