Numbers and Algebra

Quadratic Expressions and Equations - Forming quadratic expressions from statements

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

- Define a quadratic expression
- Form quadratic expressions from given statements
- Relate quadratic expressions to calculating areas of rectangular shapes

- Generate quadratic expressions from given statements
- Draw rectangles and express their areas as quadratic expressions
- Share work with peers

What is a quadratic expression?

- Mentor Core Mathematics Grade 10 pg. 42
- Graph paper
- Rulers

- Oral questions - Written exercises - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Forming quadratic expressions from real-life situations
Quadratic Expressions and Equations - Deriving quadratic identities from concept of area
Quadratic Expressions and Equations - Deriving more quadratic identities
Quadratic Expressions and Equations - Applying quadratic identities in numerical cases

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

- Form quadratic expressions from real-life situations
- Interpret quadratic expressions in context
- Connect quadratic expressions to practical problems like garden design and room carpeting

- Form quadratic expressions from problems involving area
- Work out exercises involving formation of quadratic expressions
- Use digital devices to explore quadratic expressions

How are quadratic expressions formed from real-life situations?

- Mentor Core Mathematics Grade 10 pg. 43
- Graph paper
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 44
- Charts
- Rulers
- Mentor Core Mathematics Grade 10 pg. 45
- Charts
- Mentor Core Mathematics Grade 10 pg. 47
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Expressions and Equations - Factorising quadratic expressions (coefficient of x² is 1)
Quadratic Expressions and Equations - Factorising quadratic expressions (coefficient of x² greater than 1)
Quadratic Expressions and Equations - Forming quadratic equations from given situations
Quadratic Expressions and Equations - Forming quadratic equations from given roots

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

- Factorise quadratic expressions where coefficient of x² is 1
- Identify factors that give required sum and product
- Relate factorisation to finding dimensions of rectangular areas

- Discuss methods of factorising quadratic expressions
- Identify pairs of numbers with required sum and product
- Factorise expressions and verify by expansion

How do we factorise quadratic expressions?

- Mentor Core Mathematics Grade 10 pg. 48
- Charts
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 49
- Calculators
- Mentor Core Mathematics Grade 10 pg. 51
- Mentor Core Mathematics Grade 10 pg. 52

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Expressions and Equations - Solving quadratic equations by factorisation
Quadratic Expressions and Equations - Solving more quadratic equations by factorisation

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

- Solve quadratic equations by factorisation
- Apply the zero product property
- Use solutions of quadratic equations to solve measurement problems

- Factorise quadratic equations
- Apply zero product property to find solutions
- Work out exercises involving solving equations

How do we solve quadratic equations by factorisation?

- Mentor Core Mathematics Grade 10 pg. 53
- Charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Expressions and Equations - Applying quadratic equations to real-life situations
Quadratic Expressions and Equations - Problem solving with quadratic equations

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

- Apply quadratic equations to solve real-life problems
- Interpret solutions in context
- Use quadratic equations to solve problems involving areas, consecutive numbers and profit

- Form and solve quadratic equations from word problems
- Interpret and validate solutions
- Work out real-life application problems

How are quadratic equations applied in real-life situations?

- Mentor Core Mathematics Grade 10 pg. 54
- Charts
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 55
- Digital devices
- Charts

- Written assignments - Class activities - Oral questions

Measurements and Geometry

Similarity and Enlargement - Determining centre of enlargement
Similarity and Enlargement - Linear scale factor
Similarity and Enlargement - Constructing images (positive scale factor)

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
- Mentor Core Mathematics Grade 10 pg. 57
- Geometrical instruments
- Maps
- Mentor Core Mathematics Grade 10 pg. 61
- Geometrical set
- Rulers

- Oral questions - Observation - Written assignments

Measurements and Geometry

Similarity and Enlargement - Constructing images (negative scale factor)
Similarity and Enlargement - Area scale factor
Similarity and Enlargement - Volume scale factor
Similarity and Enlargement - Relating L.S.F, A.S.F and V.S.F

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

- Construct images with negative scale factors
- Draw enlargements on the Cartesian plane
- Connect negative enlargement to real-life applications like projectors

- Draw on Cartesian plane images under enlargement with negative scale factors
- Compare images with positive and negative scale factors
- Discuss how projectors use similar principles

What happens when the scale factor is negative?

- Mentor Core Mathematics Grade 10 pg. 62
- Graph papers
- Cartesian plane grids
- Geometrical instruments
- 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
- Mentor Core Mathematics Grade 10 pg. 68
- Models of solids
- Reference books

- Written tests - Practical work - Oral questions

Measurements and Geometry

Similarity and Enlargement - Real-life applications
Similarity and Enlargement - Project on models
Reflection and Congruence - Lines of symmetry in plane figures

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

- Apply similarity and enlargement to solve real-life problems
- Calculate actual measurements from scale drawings
- Connect concepts to map reading and architectural drawings

- Work out tasks involving similarity in real-life situations
- Solve problems involving maps and models
- Use digital devices to explore applications

Where do we use similarity and enlargement in daily life?

- Mentor Core Mathematics Grade 10 pg. 72
- Maps
- Scale models
- Calculators
- Manila paper
- Cardboard
- Scissors
- Rulers
- Mentor Core Mathematics Grade 10 pg. 75
- Paper cut-outs
- Plane mirrors
- Objects from environment

- Written tests - Project work - Oral questions

Measurements and Geometry

Reflection and Congruence - Properties of reflection
Reflection and Congruence - Reflection on plane surface

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

- Written assignments - Practical work - Oral questions

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
Rotation - Rotation on plane surface

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
- Mentor Core Mathematics Grade 10 pg. 99
- Plain paper
- Rulers
- Compasses

- Oral questions - Observation - Written assignments

Measurements and Geometry

Rotation - Rotation through ±90° about origin
Rotation - Rotation through ±180° 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
- Geometrical instruments

- Written assignments - Class exercises - Oral questions

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
Rotation - Axis and order of rotational symmetry in solids

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
- Mentor Core Mathematics Grade 10 pg. 113
- Models of solids
- Objects from environment

- Oral questions - Practical work - Written assignments

Measurements and Geometry

Rotation - Deducing congruence from rotation
Trigonometry 1 - Reading tangent from tables

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

- Deduce congruence from rotation
- Identify type of congruence in rotation
- Apply rotation and congruence in problem solving

- Use objects and images to identify congruence
- Distinguish direct and indirect congruence
- Solve problems involving rotation and congruence

What type of congruence results from rotation?

- Mentor Core Mathematics Grade 10 pg. 115
- Graph papers
- Geometrical instruments
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 120
- Mathematical tables
- Calculators

- Written assignments - Class exercises - Observation

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
Trigonometry 1 - Angle of depression

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
- Mentor Core Mathematics Grade 10 pg. 134
- Digital devices
- Reference materials

- Practical assessment - Written tests - Oral questions

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

- 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

- 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
Area of Polygons - Area of parallelogram and trapezium

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
- Mentor Core Mathematics Grade 10 pg. 147
- Geometrical instruments

- Written tests - Practical activities - Oral questions

Measurements and Geometry

Area of Polygons - Area of heptagon
Area of Polygons - Area of octagon

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
- Mentor Core Mathematics Grade 10 pg. 156
- Reference materials

- Written tests - Practical work - Oral questions

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
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

- 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

- 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

- 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

- 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
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
Surface Area and Volume - Pyramids

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
- Mentor Core Mathematics Grade 10 pg. 191
- Models of pyramids

- Written tests - Class exercises - Oral questions

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

- 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

- 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
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
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
Surface Area and Volume - Composite solids volume

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

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Vectors I - Introduction to vectors

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

- Oral questions - Written assignments - Observation

Measurements and Geometry

Vectors I - Vector notation
Vectors I - Equivalent vectors

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

- Use vector notations correctly
- Represent vectors as directed line segments
- Write vectors in different forms

- Practice writing vector notations
- Draw vectors on charts
- Use bold letters and arrows

How do we write and represent vectors?

- Mentor Core Mathematics Grade 10 pg. 221
- Charts
- Graph papers
- Rulers
- Mentor Core Mathematics Grade 10 pg. 223
- Geometrical instruments

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Vectors I - Adding vectors
Vectors I - Scalar multiplication

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
- Mentor Core Mathematics Grade 10 pg. 228
- Rulers

- Written tests - Practical assessment - Oral questions

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

- 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

- 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
Vectors I - Applications and problems

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

- Determine translation vector
- Perform translation on objects
- Relate translation to sliding motion

- 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
- Mentor Core Mathematics Grade 10 pg. 242
- Calculators
- Digital devices

- Written tests - Class exercises - Oral questions

Measurements and Geometry

Linear Motion - Basic terms
Linear Motion - Calculating velocity and acceleration

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

- Define distance, displacement, speed, velocity and acceleration
- Distinguish between distance and displacement
- Relate to vehicle motion and athletics

- Demonstrate motion using objects
- Discuss meanings of terms
- Give real-life examples

What is the difference between speed and velocity?

- Mentor Core Mathematics Grade 10 pg. 244
- Stopwatches
- Measuring tapes
- Mentor Core Mathematics Grade 10 pg. 246
- Measuring tapes
- Calculators

- Oral questions - Written assignments - Observation

Measurements and Geometry

Linear Motion - Drawing displacement-time graphs
Linear Motion - Interpreting displacement-time graphs

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

- Draw displacement-time graphs
- Plot data accurately
- Interpret simple graphs

- Collect data on displacement and time
- Plot graphs on Cartesian plane
- Draw graphs from given data

How do we draw displacement-time graphs?

- Mentor Core Mathematics Grade 10 pg. 247
- Graph papers
- Rulers
- Mentor Core Mathematics Grade 10 pg. 249
- Calculators

- Written assignments - Practical assessment - Observation

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

- 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)
Linear Motion - Real-life applications

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

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

- Written assignments - Practical activities - Observation