Measurements

Area - Area of a pentagon
Area - Area of a hexagon
Area - Surface area of triangular prisms
Area - Surface area of rectangular prisms
Area - Surface area of pyramids
Area - Surface area of square and rectangular pyramids

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

- Define a regular pentagon
- Draw a regular pentagon and divide it into triangles
- Calculate the area of a regular pentagon

- Draw a regular pentagon of sides 4 cm using protractor (108° angles)
- Join vertices to the centre to form triangles
- Determine the height of one triangle
- Calculate area of one triangle then multiply by number of triangles
- Use alternative formula: ½ × perimeter × perpendicular height

How do we find the area of a pentagon?

- Master Mathematics Grade 9 pg. 85
- Rulers and protractors
- Compasses
- Graph paper
- Charts showing pentagons
- Compasses and rulers
- Protractors
- Manila paper
- Digital devices
- Models of prisms
- Rulers
- Reference materials
- Cuboid models
- Scissors
- Calculators
- Sticks/straws
- Reference books
- Pyramid models
- Charts

- Observation - Oral questions - Written assignments

Measurements

Area - Area of sectors of circles
Area - Area of segments of circles
Area - Surface area of cones
Area - Surface area of spheres and hemispheres
Volume - Volume of triangular prisms
Volume - Volume of rectangular prisms
Volume - Volume of square-based pyramids
Volume - Volume of rectangular-based pyramids
Volume - Volume of triangular-based pyramids
Volume - Introduction to volume of cones
Volume - Calculating volume of cones
Volume - Volume of frustums of pyramids
Volume - Volume of frustums of cones

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

- Define a sector of a circle
- Distinguish between major and minor sectors
- Calculate area of sectors using the formula

- Draw a circle and mark a clock face
- Identify sectors formed by clock hands
- Derive formula: Area = (θ/360) × πr²
- Calculate areas of sectors with different angles
- Use digital devices to watch videos on sectors

How do we find the area of a sector?

- Master Mathematics Grade 9 pg. 85
- Compasses and rulers
- Protractors
- Digital devices
- Internet access
- Compasses
- Rulers
- Calculators
- Graph paper
- Manila paper
- Scissors
- Reference materials
- Spherical balls
- Rectangular paper
- Master Mathematics Grade 9 pg. 102
- Straws and paper
- Sand or soil
- Measuring tools
- Reference books
- Cuboid models
- Charts
- Modeling materials
- Soil or sand
- Pyramid models
- Triangular pyramid models
- Cone and cylinder models
- Water
- Cone models
- Cutting tools
- Frustum examples

- Observation - Oral questions - Written assignments

Measurements

Volume - Volume of spheres
Volume - Volume of hemispheres and applications
Mass, Volume, Weight and Density - Conversion of units of mass
Mass, Volume, Weight and Density - More practice on mass conversions
Mass, Volume, Weight and Density - Relationship between mass and weight
Mass, Volume, Weight and Density - Calculating mass and gravity
Mass, Volume, Weight and Density - Introduction to density
Mass, Volume, Weight and Density - Calculating density, mass and volume
Mass, Volume, Weight and Density - Applications of density
Time, Distance and Speed - Working out speed in km/h and m/s
Time, Distance and Speed - Calculating distance and time from speed
Time, Distance and Speed - Working out average speed
Time, Distance and Speed - Determining velocity
Time, Distance and Speed - Working out acceleration

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

- Relate sphere volume to cone volume
- Derive the formula for volume of a sphere
- Calculate volumes of spheres

- Select hollow spherical object
- Model cone with same radius and height 2r
- Fill cone and transfer to sphere
- Observe that 2 cones fill the sphere
- Derive formula: V = 4/3πr³
- Calculate volumes with different radii

How do we find the volume of a sphere?

- Master Mathematics Grade 9 pg. 102
- Hollow spheres
- Cone models
- Water or soil
- Calculators
- Hemisphere models
- Real objects
- Reference materials
- Master Mathematics Grade 9 pg. 111
- Weighing balances
- Various objects
- Conversion charts
- Conversion tables
- Real-world examples
- Reference books
- Spring balances
- Charts
- Charts showing planetary data
- Digital devices
- Measuring cylinders
- Water
- Containers
- Charts with formulas
- Various solid objects
- Density tables
- Real-world scenarios
- Master Mathematics Grade 9 pg. 117
- Stopwatches
- Tape measures
- Open field
- Formula charts
- Field with marked points
- Diagrams showing direction
- Field for activity
- Measuring tools

- Observation - Oral questions - Written tests

Measurements

Time, Distance and Speed - Deceleration and applications
Time, Distance and Speed - Identifying longitudes on the globe
Time, Distance and Speed - Relating longitudes to time
Time, Distance and Speed - Calculating time differences between places
Time, Distance and Speed - Determining local time of places along different longitudes
Money - Identifying currencies of different countries
Money - Converting foreign currency to Kenyan shillings
Money - Converting Kenyan shillings to foreign currency and buying/selling rates
Money - Export duty on goods
Money - Import duty on goods
Money - Excise duty and Value Added Tax (VAT)
Money - Combined duties and taxes on imported goods
Approximations and Errors - Approximating quantities in measurements

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

- Define deceleration (retardation)
- Calculate deceleration
- Distinguish between acceleration and deceleration
- Solve problems involving both acceleration and deceleration
- Appreciate safety implications

- Define deceleration as negative acceleration
- Calculate when final velocity is less than initial velocity
- Apply to vehicles slowing down, braking
- Apply to matatus crossing speed bumps
- Understand safety implications of deceleration
- Calculate final velocity given acceleration and time
- Solve problems on cars, buses, gazelles
- Discuss importance of controlled deceleration for safety

What is deceleration and why is it important for safety?

- Master Mathematics Grade 9 pg. 117
- Calculators
- Road safety materials
- Charts
- Reference materials
- Globes
- Atlases
- World maps
- Time zone maps
- Digital devices
- Time zone charts
- Reference books
- Time zone references
- Real-world scenarios
- Master Mathematics Grade 9 pg. 131
- Internet access
- Pictures of currencies
- Currency conversion tables
- Exchange rate tables
- Examples of export goods
- Import duty examples
- ETR receipts
- Tax rate tables
- Comprehensive examples
- Charts showing tax flow
- Master Mathematics Grade 9 pg. 146
- Tape measures
- Various objects to measure
- Containers for capacity

- Observation - Oral questions - Written tests

Measurements
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry
4.0 Geometry

Approximations and Errors - Determining errors using estimations and actual measurements
Approximations and Errors - Calculating percentage error
Approximations and Errors - Percentage error in real-life situations
Approximations and Errors - Complex applications and problem-solving
4.1 Coordinates and Graphs - Plotting points on a Cartesian plane
4.1 Coordinates and Graphs - Drawing straight line graphs given equations
4.1 Coordinates and Graphs - Drawing parallel lines on the Cartesian plane
4.1 Coordinates and Graphs - Relating gradients of parallel lines
4.1 Coordinates and Graphs - Drawing perpendicular lines on the Cartesian plane
4.1 Coordinates and Graphs - Relating gradients of perpendicular lines and applications
4.2 Scale Drawing - Compass bearing
4.2 Scale Drawing - True bearings
4.2 Scale Drawing - Determining the bearing of one point from another (1)
4.2 Scale Drawing - Determining the bearing of one point from another (2)
4.2 Scale Drawing - Locating a point using bearing and distance (1)
4.2 Scale Drawing - Locating a point using bearing and distance (2)
4.2 Scale Drawing - Identifying angles of elevation (1)
4.2 Scale Drawing - Determining angles of elevation (2)
4.2 Scale Drawing - Identifying angles of depression (1)
4.2 Scale Drawing - Determining angles of depression (2)
4.2 Scale Drawing - Application in simple surveying - Triangulation (1)
4.2 Scale Drawing - Application in simple surveying - Triangulation (2)
4.2 Scale Drawing - Application in simple surveying - Transverse survey (1)
4.2 Scale Drawing - Application in simple surveying - Transverse survey (2)
4.2 Scale Drawing - Surveying using bearings and distances

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

- Define error in measurement
- Calculate error using approximated and actual values
- Distinguish between positive and negative errors
- Appreciate the importance of accuracy

- Fill 500 ml bottle and measure actual volume
- Calculate difference between labeled and actual values
- Apply formula: Error = Approximated value - Actual value
- Work with errors in mass, length, volume, time
- Complete tables showing actual, estimated values and errors
- Apply to bread packages, water bottles, cement bags
- Discuss integrity in measurements

What is error and how do we calculate it?

- Master Mathematics Grade 9 pg. 146
- Measuring cylinders
- Water bottles
- Weighing scales
- Calculators
- Reference materials
- Tape measures
- Open ground for activities
- Reference books
- Real-world scenarios
- Case studies
- Complex scenarios
- Charts
- Real-world case studies
- Master Mathematics Grade 9 pg. 152
- Graph papers/squared books
- Rulers
- Pencils
- Digital devices
- Master Mathematics Grade 9 pg. 154
- Graph papers
- Mathematical tables
- Master Mathematics Grade 9 pg. 156
- Set squares
- Master Mathematics Grade 9 pg. 158
- Master Mathematics Grade 9 pg. 160
- Protractors
- Master Mathematics Grade 9 pg. 162
- Real-life graph examples
- Master Mathematics Grade 9 pg. 166
- Pair of compasses
- Charts showing compass directions
- Master Mathematics Grade 9 pg. 169
- Compasses
- Map samples
- Master Mathematics Grade 9 pg. 171
- Atlas/Maps of Kenya
- Master Mathematics Grade 9 pg. 173
- Plain papers
- Master Mathematics Grade 9 pg. 175
- Pictures showing elevation
- Models
- Master Mathematics Grade 9 pg. 178
- Pictures showing depression
- Master Mathematics Grade 9 pg. 180
- Meter rules
- Strings
- Pegs
- Field books

- Observation - Oral questions - Written assignments