Measurements

Mass, Volume, Weight and Density - Conversion of units of mass

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

- Define mass and state its SI unit
- Identify different units of mass
- Convert between different units of mass

In groups, learners are guided to:
- Use balance to measure mass of objects
- Record masses in grams
- Study conversion table for mass units
- Convert between kg, g, mg, tonnes, etc.
- Apply conversions to real situations

How do we convert between different units of mass?

- Master Mathematics Grade 9 pg. 111
- Weighing balances
- Various objects
- Conversion charts
- Calculators

- Observation - Oral questions - Written tests

Measurements

Mass, Volume, Weight and Density - More practice on mass conversions
Mass, Volume, Weight and Density - Relationship between mass and weight

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

- Convert masses to kilograms
- Apply conversions in real-life contexts
- Appreciate the importance of mass measurements

In groups, learners are guided to:
- Convert various masses to kilograms
- Work with large masses (tonnes)
- Work with small masses (milligrams, micrograms)
- Solve practical problems (construction, medicine, shopping)

Why is it important to convert units of mass?

- Master Mathematics Grade 9 pg. 111
- Conversion tables
- Calculators
- Real-world examples
- Reference books
- Spring balances
- Various objects
- Charts

- Observation - Oral questions - Written assignments

Measurements

Mass, Volume, Weight and Density - Calculating mass and gravity

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

- Calculate mass when given weight
- Calculate gravity of different planets
- Apply weight formula in different contexts

In groups, learners are guided to:
- Rearrange formula to find mass: m = W/g
- Rearrange formula to find gravity: g = W/m
- Compare gravity on Earth, Moon, and other planets
- Solve problems involving astronauts on different planets

How do we calculate mass and gravity from weight?

- Master Mathematics Grade 9 pg. 111
- Calculators
- Charts showing planetary data
- Reference materials
- Digital devices

- Observation - Oral questions - Written assignments

Measurements

Mass, Volume, Weight and Density - Introduction to density

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

- Define density
- State units of density
- Relate mass, volume and density

In groups, learners are guided to:
- Weigh empty container
- Measure volume of water using measuring cylinder
- Weigh container with water
- Calculate mass of water
- Divide mass by volume to get density
- Apply formula: Density = Mass/Volume

What is density?

- Master Mathematics Grade 9 pg. 111
- Weighing balances
- Measuring cylinders
- Water
- Containers
- Calculators

- Observation - Oral questions - Written tests

Measurements

Mass, Volume, Weight and Density - Calculating density, mass and volume

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

- Apply density formula to find density
- Calculate mass using density formula
- Calculate volume using density formula

In groups, learners are guided to:
- Apply formula: D = M/V to find density
- Rearrange to find mass: M = D × V
- Rearrange to find volume: V = M/D
- Convert between g/cm³ and kg/m³
- Solve various problems

How do we use the density formula?

- Master Mathematics Grade 9 pg. 111
- Calculators
- Charts with formulas
- Various solid objects
- Reference books

- Observation - Oral questions - Written assignments

Measurements

Mass, Volume, Weight and Density - Applications of density

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

- Apply density to identify materials
- Determine if objects will float or sink
- Solve real-life problems using density

In groups, learners are guided to:
- Compare calculated density with known values
- Identify minerals (e.g., diamond) using density
- Determine if objects float (density < 1 g/cm³)
- Apply to quality control (milk, water)
- Solve problems involving balloons, anchors

How is density used in real life?

- Master Mathematics Grade 9 pg. 111
- Density tables
- Calculators
- Real-world scenarios
- Reference materials

- Observation - Oral questions - Written tests

Measurements

Time, Distance and Speed - Working out speed in km/h and m/s
Time, Distance and Speed - Calculating distance and time from speed

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

- Define speed
- Calculate speed in km/h
- Calculate speed in m/s
- Convert between km/h and m/s

In groups, learners are guided to:
- Go to field and mark two points 100 m apart
- Measure distance between points
- Time a person running between points
- Calculate speed: Speed = Distance/Time
- Calculate speed in m/s using metres and seconds
- Convert distance to kilometers and time to hours
- Calculate speed in km/h
- Convert km/h to m/s (divide by 3.6)
- Convert m/s to km/h (multiply by 3.6)

How do we calculate speed in different units?

- Master Mathematics Grade 9 pg. 117
- Stopwatches
- Tape measures
- Open field
- Calculators
- Conversion charts
- Formula charts
- Real-world examples
- Reference materials

- Observation - Oral questions - Written assignments

Measurements

Time, Distance and Speed - Working out average speed

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

- Define average speed
- Calculate average speed for journeys with varying speeds
- Distinguish between speed and average speed
- Solve multi-stage journey problems

In groups, learners are guided to:
- Identify two points with a midpoint
- Run from start to midpoint, walk from midpoint to end
- Calculate speed for each section
- Calculate total distance and total time
- Apply formula: Average speed = Total distance/Total time
- Solve problems on cyclists, buses, motorists
- Work with journeys having different speeds in different sections

What is average speed and how is it different from speed?

- Master Mathematics Grade 9 pg. 117
- Field with marked points
- Stopwatches
- Calculators
- Reference books

- Observation - Oral questions - Written assignments

Measurements

Time, Distance and Speed - Determining velocity

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

- Define velocity
- Distinguish between speed and velocity
- Calculate velocity with direction
- Appreciate the importance of direction in velocity

In groups, learners are guided to:
- Define velocity as speed in a given direction
- Identify that velocity includes direction
- Calculate velocity for objects moving in straight lines
- Understand that velocity can be positive or negative
- Understand that same speed in opposite directions means different velocities
- Apply to real situations involving directional movement

What is the difference between speed and velocity?

- Master Mathematics Grade 9 pg. 117
- Diagrams showing direction
- Calculators
- Charts
- Reference materials

- Observation - Oral questions - Written tests

Measurements

Time, Distance and Speed - Working out acceleration

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

- Define acceleration
- Calculate acceleration from velocity changes
- Apply acceleration formula
- State units of acceleration (m/s²)
- Identify situations involving acceleration

In groups, learners are guided to:
- Walk from one point then run to another point
- Calculate velocity for each section
- Find difference in velocities (change in velocity)
- Define acceleration as rate of change of velocity
- Apply formula: a = (v - u)/t where v=final velocity, u=initial velocity, t=time
- Calculate acceleration when starting from rest (u=0)
- Calculate acceleration with initial velocity
- State that acceleration is measured in m/s²
- Identify real-life examples of acceleration

What is acceleration and how do we calculate it?

- Master Mathematics Grade 9 pg. 117
- Field for activity
- Stopwatches
- Measuring tools
- Calculators
- Formula charts

- Observation - Oral questions - Written assignments

Measurements

Time, Distance and Speed - Deceleration and applications
Time, Distance and Speed - Identifying longitudes on the globe

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

In groups, learners are guided to:
- 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

- Observation - Oral questions - Written tests

Measurements

Time, Distance and Speed - Relating longitudes to time

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

- Explain relationship between longitudes and time
- State that Earth rotates 360° in 24 hours
- Calculate that 1° = 4 minutes
- Understand time zones and GMT

In groups, learners are guided to:
- Understand Earth rotates 360° in 24 hours
- Calculate: 360° = 24 hours = 1440 minutes
- Therefore: 1° = 4 minutes
- Identify time zones on world map
- Understand GMT (Greenwich Mean Time)
- Learn that places East of Greenwich are ahead in time
- Learn that places West of Greenwich are behind in time
- Use digital devices to check time zones

How are longitudes related to time?

- Master Mathematics Grade 9 pg. 117
- Globes
- Time zone maps
- Calculators
- Digital devices

- Observation - Oral questions - Written tests

Measurements

Time, Distance and Speed - Calculating time differences between places

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

- Calculate longitude differences
- Calculate time differences between places
- Apply rules for same side and opposite sides of Greenwich
- Convert time differences to hours and minutes

In groups, learners are guided to:
- Find longitude difference:
• Subtract longitudes if on same side of Greenwich
• Add longitudes if on opposite sides of Greenwich
- Multiply longitude difference by 4 minutes
- Convert minutes to hours and minutes
- Determine if place is ahead or behind GMT
- Solve problems on towns X and Z, Memphis and Kigali
- Complete tables with longitude and time differences

How do we calculate time difference from longitudes?

- Master Mathematics Grade 9 pg. 117
- Atlases
- Calculators
- Time zone charts
- Reference books

- Observation - Oral questions - Written assignments

Measurements

Time, Distance and Speed - Determining local time of places along different longitudes

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

- Calculate local time when given GMT or another place's time
- Add or subtract time differences appropriately
- Account for date changes
- Solve complex time zone problems
- Apply knowledge to real-life situations

In groups, learners are guided to:
- Calculate time difference from longitude difference
- Add time if place is East of reference point (ahead)
- Subtract time if place is West of reference point (behind)
- Account for date changes when crossing midnight
- Solve problems with GMT as reference
- Solve problems with other places as reference
- Apply to phone calls, soccer matches, travel planning
- Work backwards to find longitude from time difference
- Determine whether places are East or West from time relationships

How do we find local time at different longitudes?

- Master Mathematics Grade 9 pg. 117
- World maps
- Calculators
- Time zone references
- Atlases
- Real-world scenarios

- Observation - Oral questions - Written tests - Problem-solving tasks

Measurements

Money - Identifying currencies of different countries
Money - Converting foreign currency to Kenyan shillings

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

- Identify currencies used in different countries
- State the Kenyan currency and its abbreviation
- Match countries with their currencies
- Appreciate diversity in world currencies

In groups, learners are guided to:
- Use digital devices to search for pictures of currencies
- Identify currencies of Britain, Uganda, Tanzania, USA, Rwanda, South Africa
- Make a collage of currencies from African countries
- Complete tables matching countries with their currencies
- Study Kenya shilling and its subdivision into cents
- Discuss the importance of different currencies

What currencies are used in different countries?

- Master Mathematics Grade 9 pg. 131
- Digital devices
- Internet access
- Pictures of currencies
- Atlases
- Reference materials
- Currency conversion tables
- Calculators
- Charts

- Observation - Oral questions - Written assignments - Project work

Measurements

Money - Converting Kenyan shillings to foreign currency and buying/selling rates

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

- Convert Kenyan shillings to foreign currencies
- Distinguish between buying and selling rates
- Apply correct rates when converting currency
- Solve multi-step currency problems

In groups, learners are guided to:
- Convert Ksh to Ugandan shillings, Sterling pounds, Japanese Yen
- Study Table 3.5.2 showing buying and selling rates
- Understand that banks buy at lower rate, sell at higher rate
- Learn when to use buying rate (foreign to Ksh)
- Learn when to use selling rate (Ksh to foreign)
- Solve tourist problems with multiple conversions
- Visit commercial banks or Forex Bureaus

Why do buying and selling rates differ?

- Master Mathematics Grade 9 pg. 131
- Exchange rate tables
- Calculators
- Real-world scenarios
- Reference books

- Observation - Oral questions - Written assignments

Measurements

Money - Export duty on goods

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

- Define export and export duty
- Explain the purpose of export duty
- Calculate product cost and export duty
- Solve problems on exported goods

In groups, learners are guided to:
- Discuss goods Kenya exports to other countries
- Understand how Kenya benefits from exports
- Define product cost and its components
- Apply formula: Product cost = Unit cost × Quantity
- Apply formula: Export duty = Tax rate × Product cost
- Calculate export duty on flowers, tea, coffee, cement
- Discuss importance of increasing exports

What is export duty and why is it charged?

- Master Mathematics Grade 9 pg. 131
- Calculators
- Examples of export goods
- Charts
- Reference materials

- Observation - Oral questions - Written tests

Measurements

Money - Import duty on goods

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

- Define import and import duty
- Calculate customs value of imported goods
- Calculate import duty on goods
- Apply knowledge to real-life situations

In groups, learners are guided to:
- Discuss goods imported into Kenya
- Learn about Kenya Revenue Authority (KRA)
- Calculate customs value: Cost + Insurance + Freight
- Apply formula: Import duty = Tax rate × Customs value
- Solve problems on vehicles, electronics, tractors, phones
- Discuss ways to reduce imports
- Understand importance of local production

What is import duty and how is it calculated?

- Master Mathematics Grade 9 pg. 131
- Calculators
- Import duty examples
- Charts
- Reference books

- Observation - Oral questions - Written assignments

Measurements

Money - Excise duty and Value Added Tax (VAT)

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

- Define excise duty and VAT
- Identify goods subject to excise duty
- Calculate excise duty and VAT
- Distinguish between the two types of taxes

In groups, learners are guided to:
- Search online for goods subject to excise duty
- Study excise duty rates for different commodities
- Apply formula: Excise duty = Tax rate × Excise value
- Study Electronic Tax Register (ETR) receipts
- Learn that VAT is charged at 16% at multiple stages
- Calculate VAT on purchases
- Apply both taxes to various goods and services

What are excise duty and VAT?

- Master Mathematics Grade 9 pg. 131
- Digital devices
- ETR receipts
- Tax rate tables
- Calculators
- Reference materials

- Observation - Oral questions - Written tests

Measurements

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:

- Calculate multiple taxes on imported goods
- Apply import duty, excise duty, and VAT sequentially
- Solve complex problems involving all taxes
- Appreciate the cumulative effect of taxes

In groups, learners are guided to:
- Calculate import duty first
- Calculate excise value: Customs value + Import duty
- Calculate excise duty on excise value
- Calculate VAT value: Customs value + Import duty + Excise duty
- Calculate VAT on VAT value
- Apply to vehicles, electronics, cement, phones
- Solve comprehensive taxation problems
- Work backwards to find customs value

How do we calculate total taxes on imported goods?

- Master Mathematics Grade 9 pg. 131
- Calculators
- Comprehensive examples
- Charts showing tax flow
- Reference materials
- Master Mathematics Grade 9 pg. 146
- Tape measures
- Various objects to measure
- Containers for capacity

- Observation - Oral questions - Written assignments

Measurements

Approximations and Errors - Determining errors using estimations and actual measurements

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

In groups, learners are guided to:
- 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

- Observation - Oral questions - Written assignments

Measurements

Approximations and Errors - Calculating percentage error

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

- Define percentage error
- Calculate percentage error from approximations
- Express error as a percentage of actual value
- Compare errors using percentages

In groups, learners are guided to:
- Make strides and estimate total distance
- Measure actual distance covered
- Calculate error: Estimated value - Actual value
- Apply formula: Percentage error = (Error/Actual value) × 100%
- Solve problems on pavement width
- Calculate percentage errors in various measurements
- Round answers appropriately

How do we calculate percentage error?

- Master Mathematics Grade 9 pg. 146
- Tape measures
- Calculators
- Open ground for activities
- Reference books

- Observation - Oral questions - Written tests

Measurements

Approximations and Errors - Percentage error in real-life situations

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

- Apply percentage error to real-life situations
- Calculate errors in various contexts
- Analyze significance of errors
- Show integrity when making approximations

In groups, learners are guided to:
- Calculate percentage errors in electoral voting estimates
- Work on football match attendance approximations
- Solve problems on road length estimates
- Apply to temperature recordings
- Calculate errors in land plot sizes
- Work on age recording errors
- Discuss consequences of errors in planning

Why are accurate approximations important in real life?

- Master Mathematics Grade 9 pg. 146
- Calculators
- Real-world scenarios
- Case studies
- Reference materials

- Observation - Oral questions - Written assignments

Measurements
4.0 Geometry
4.0 Geometry

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

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

- Solve complex problems involving percentage errors
- Apply error calculations to budgeting and planning
- Evaluate the impact of errors
- Emphasize honesty and integrity in approximations

In groups, learners are guided to:
- Calculate percentage errors in fuel consumption estimates
- Work on budget estimation errors (school fuel budgets)
- Solve problems on athlete timing and weight
- Apply to construction cost estimates
- Analyze large errors and their consequences
- Discuss ways to minimize errors
- Emphasize ethical considerations in approximations
- Solve comprehensive review problems

How can we minimize errors and ensure accuracy?

- Master Mathematics Grade 9 pg. 146
- Calculators
- Complex scenarios
- Charts
- Reference books
- 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

- Observation - Oral questions - Written tests - Project work

4.0 Geometry

4.1 Coordinates and Graphs - Drawing parallel lines on the Cartesian plane
4.1 Coordinates and Graphs - Relating gradients of parallel lines

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

- State the properties of parallel lines
- Draw parallel lines accurately on the same Cartesian plane
- Develop interest in identifying parallel lines using graphs

The learner is guided to:
- Generate tables of values for each of the given linear equations
- Plot the points and draw straight line graphs for each equation on the same plane
- Use a set square to determine the distance between the two lines at any point
- Share and discuss findings with other groups

What is the relationship between parallel lines on a graph?

- Master Mathematics Grade 9 pg. 156
- Graph papers
- Rulers
- Set squares
- Pencils
- Master Mathematics Grade 9 pg. 158
- Calculators
- Digital devices

- Class activities - Written tests

4.0 Geometry

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

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

- Explain the meaning of perpendicular lines
- Draw and measure angles between perpendicular lines accurately
- Show interest in recognizing perpendicular lines from their graphs

The learner is guided to:
- Draw straight lines on the same Cartesian plane
- Identify the point where the two lines intersect
- Measure the angle between the two lines at the point of intersection
- Verify that perpendicular lines intersect at 90°

How do we identify perpendicular lines on a graph?

- Master Mathematics Grade 9 pg. 160
- Graph papers
- Protractors
- Rulers
- Set squares
- Master Mathematics Grade 9 pg. 162
- Calculators
- Real-life graph examples
- Master Mathematics Grade 9 pg. 166
- Pair of compasses
- Charts showing compass directions

- Observation - Class activities - Written tests

4.0 Geometry

4.2 Scale Drawing - True bearings
4.2 Scale Drawing - Determining the bearing of one point from another (1)

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

- Explain what true bearings are
- Convert compass bearings to true bearings and measure them accurately
- Appreciate expressing direction using true bearings

The learner is guided to:
- Discuss that true bearings are measured clockwise from North
- Express bearings in three-digit format
- Draw diagrams showing true bearings
- Convert between compass and true bearings

How do we express direction using true bearings?

- Master Mathematics Grade 9 pg. 169
- Protractors
- Rulers
- Compasses
- Map samples
- Master Mathematics Grade 9 pg. 171
- Pencils
- Graph papers

- Written tests - Class activities

4.0 Geometry

4.2 Scale Drawing - Determining the bearing of one point from another (2)

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

- State the bearing of places from maps
- Determine bearings from scale drawings and solve related problems
- Appreciate applying bearing concepts to real-life situations

The learner is guided to:
- Use maps of Kenya to determine bearings of different towns
- Work out bearings of points from given diagrams
- Determine reverse bearings
- Apply bearing concepts to real-life situations

Why is it important to know bearings in real life?

- Master Mathematics Grade 9 pg. 171
- Atlas/Maps of Kenya
- Protractors
- Rulers
- Digital devices

- Class activities - Written tests

4.0 Geometry

4.2 Scale Drawing - Locating a point using bearing and distance (1)

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

- Explain how to choose appropriate scales for scale drawings
- Convert actual distances to scale lengths accurately
- Show interest in representing actual distances on paper

The learner is guided to:
- Draw sketch diagrams showing relative positions
- Choose suitable scales
- Convert actual distances to scale lengths
- Mark North lines and measure angles

How do we represent actual distances on paper?

- Master Mathematics Grade 9 pg. 173
- Rulers
- Protractors
- Compasses
- Plain papers

- Observation - Written assignments

4.0 Geometry

4.2 Scale Drawing - Locating a point using bearing and distance (2)
4.2 Scale Drawing - Identifying angles of elevation (1)

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

- Describe the process of locating points using bearing and distance
- Draw accurate scale diagrams and determine unknown measurements
- Appreciate the accuracy of scale drawings in representing real situations

The learner is guided to:
- Use given bearings and distances to locate points
- Draw accurate scale diagrams
- Measure and determine unknown distances and bearings from diagrams
- Verify accuracy of their drawings

How accurate are scale drawings in representing real situations?

- Master Mathematics Grade 9 pg. 173
- Rulers
- Protractors
- Compasses
- Graph papers
- Master Mathematics Grade 9 pg. 175
- Pictures showing elevation
- Models

- Class activities - Written tests

4.0 Geometry

4.2 Scale Drawing - Determining angles of elevation (2)

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

- Explain the process of determining angles of elevation
- Draw scale diagrams and measure angles of elevation using protractors
- Appreciate applying concepts to real-life situations

The learner is guided to:
- Draw scale diagrams representing elevation situations
- Use appropriate scales
- Measure angles of elevation from scale drawings
- Solve problems involving heights and distances

How do we calculate angles of elevation?

- Master Mathematics Grade 9 pg. 175
- Protractors
- Rulers
- Graph papers
- Calculators

- Written tests - Class activities

4.0 Geometry

4.2 Scale Drawing - Identifying angles of depression (1)

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

- Define angle of depression
- Identify and sketch situations involving angles of depression
- Show interest in distinguishing between angles of elevation and depression

The learner is guided to:
- Stand at elevated positions and observe objects below
- Identify the angle through which eyes are lowered
- Sketch right-angled triangles formed
- Label the angle of depression correctly

How is angle of depression different from angle of elevation?

- Master Mathematics Grade 9 pg. 178
- Protractors
- Rulers
- Pictures showing depression
- Models

- Observation - Oral questions

4.0 Geometry

4.2 Scale Drawing - Determining angles of depression (2)

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

- Describe the steps for determining angles of depression
- Draw scale diagrams and measure angles of depression accurately
- Appreciate using angles of depression in real life

The learner is guided to:
- Draw scale diagrams representing depression situations
- Use appropriate scales
- Measure angles of depression from scale drawings
- Apply concepts to real-life problems

How do we use angles of depression in real life?

- Master Mathematics Grade 9 pg. 178
- Protractors
- Rulers
- Graph papers
- Calculators

- Written assignments - Written tests

4.0 Geometry

4.2 Scale Drawing - Application in simple surveying - Triangulation (1)

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

- Explain the concept of triangulation in surveying
- Identify baselines and offsets and draw diagrams using triangulation method
- Develop interest in using triangulation for surveying

The learner is guided to:
- Trace irregular shapes to be surveyed
- Enclose the shape with a triangle
- Identify and measure baselines
- Draw perpendicular offsets to the baselines

What is triangulation and how is it used in surveying?

- Master Mathematics Grade 9 pg. 180
- Rulers
- Set squares
- Compasses
- Plain papers

- Observation - Class activities

4.0 Geometry

4.2 Scale Drawing - Application in simple surveying - Triangulation (2)
4.2 Scale Drawing - Application in simple surveying - Transverse survey (1)

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

- Describe how to record measurements in field books
- Draw accurate scale maps using triangulation data
- Appreciate applying triangulation to survey school compound areas

The learner is guided to:
- Measure lengths of offsets
- Record measurements in field book format
- Choose appropriate scales
- Draw accurate scale maps from recorded data

How do we record and use surveying measurements?

- Master Mathematics Grade 9 pg. 180
- Meter rules
- Strings
- Pegs
- Field books
- Rulers
- Set squares
- Plain papers

- Written tests - Practical activities

4.0 Geometry

4.2 Scale Drawing - Application in simple surveying - Transverse survey (2)

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

- Describe the process of completing field books for transverse surveys
- Draw scale maps from transverse survey data
- Appreciate using transverse survey method for road reserves

The learner is guided to:
- Complete field book recordings
- Use appropriate scales to draw maps
- Join offset points to show boundaries
- Compare their work with other members

When do we use transverse survey method?

- Master Mathematics Grade 9 pg. 180
- Rulers
- Pencils
- Graph papers
- Field books

- Written assignments - Practical activities

4.0 Geometry

4.2 Scale Drawing - Surveying using bearings and distances

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

- Explain how to record positions using bearings and distances
- Draw scale maps using bearing and distance data
- Appreciate different surveying methods

The learner is guided to:
- Record bearings and distances from fixed points
- Use ordered pairs to represent positions
- Draw North lines and locate points using bearings
- Join points to show boundaries

How do we survey using bearings and distances?

- Master Mathematics Grade 9 pg. 180
- Protractors
- Compasses
- Rulers
- Field books

- Class activities - Written tests

4.0 Geometry

4.3 Similarity and Enlargement - Similar figures

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

- Define similar figures
- Identify and sort similar figures from collections of objects
- Show interest in recognizing similar figures in the environment

The learner is guided to:
- Collect different objects from the environment
- Sort objects according to similarity
- Discuss criteria used for sorting
- Identify pairs of similar figures from given diagrams

What makes two figures similar?

- Master Mathematics Grade 9 pg. 185
- Various objects
- Cut-outs of shapes
- Charts
- Models

- Observation - Oral questions

4.0 Geometry

4.3 Similarity and Enlargement - Properties of similar figures (1)
4.3 Similarity and Enlargement - Drawing similar figures

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

- State the properties of similar figures
- Measure corresponding sides and determine ratios accurately
- Appreciate that ratios of corresponding sides are constant

The learner is guided to:
- Trace similar triangles
- Measure lengths of corresponding sides
- Determine ratios of corresponding sides
- Observe that the ratios are equal

What is the relationship between sides of similar figures?

- Master Mathematics Grade 9 pg. 186
- Rulers
- Tracing papers
- Calculators
- Pencils
- Master Mathematics Grade 9 pg. 189
- Compasses
- Protractors
- Plain papers

- Class activities - Written assignments

4.0 Geometry

4.3 Similarity and Enlargement - Determining properties of enlargement

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

- Define centre of enlargement and scale factor
- Locate the centre of enlargement and determine scale factor
- Appreciate that enlargements produce similar figures

The learner is guided to:
- Join corresponding points of objects and images
- Locate the centre where lines meet
- Measure distances from centre to object and image
- Calculate the scale factor

What is the relationship between object and image in enlargement?

- Master Mathematics Grade 9 pg. 190
- Rulers
- Compasses
- Tracing papers
- Models

- Class activities - Written assignments

4.0 Geometry

4.3 Similarity and Enlargement - Positive scale factor (1)

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

- Explain what happens when scale factor is greater than 1
- Draw enlargements with scale factors greater than 1 accurately
- Develop interest in observing that images are larger when scale factor > 1

The learner is guided to:
- Draw lines from centre to object vertices
- Multiply distances by scale factor
- Locate image points along extended lines
- Observe that object and image are on same side of centre

What happens when the scale factor is greater than 1?

- Master Mathematics Grade 9 pg. 192
- Rulers
- Compasses
- Graph papers
- Pencils

- Observation - Written tests

4.0 Geometry

4.3 Similarity and Enlargement - Positive scale factor (2)

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

- Describe what happens when scale factor is between 0 and 1
- Draw enlargements with fractional scale factors accurately
- Appreciate comparing enlargements with different positive scale factors

The learner is guided to:
- Draw enlargements with fractional scale factors
- Observe that images are smaller than objects
- Note that object and image remain upright
- Practice with various positive scale factors

What happens when the scale factor is between 0 and 1?

- Master Mathematics Grade 9 pg. 192
- Rulers
- Compasses
- Plain papers
- Models

- Class activities - Written assignments

4.0 Geometry

4.3 Similarity and Enlargement - Negative scale factor (1)
4.3 Similarity and Enlargement - Negative scale factor (2)

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

- State the properties of enlargement with negative scale factors
- Draw enlargements with negative scale factors and position images correctly
- Show interest in recognizing that images are inverted with negative scale factors

The learner is guided to:
- Observe objects and images with negative scale factors
- Note that they are on opposite sides of centre
- Draw enlargements with negative scale factors
- Observe that images are inverted

What is special about negative scale factors?

- Master Mathematics Grade 9 pg. 196
- Rulers
- Compasses
- Graph papers
- Tracing papers
- Plain papers
- Calculators

- Observation - Oral questions

4.0 Geometry

4.3 Similarity and Enlargement - Enlargement on the Cartesian plane (1)

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

- State the rule (x,y) → (kx, ky) for enlargement with centre at origin
- Plot and enlarge figures accurately with centre at origin
- Develop interest in applying enlargement rules on coordinate axes

The learner is guided to:
- Plot given points on Cartesian plane
- Apply scale factor to coordinates
- Plot image points and join them
- Verify using measurement from origin

How do we enlarge figures on coordinate axes?

- Master Mathematics Grade 9 pg. 198
- Graph papers
- Rulers
- Calculators
- Pencils

- Observation - Written assignments

4.0 Geometry

4.3 Similarity and Enlargement - Enlargement on the Cartesian plane (2)

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

- Describe the process of enlarging figures with centre not at origin
- Determine coordinates of images after enlargement and solve related problems
- Appreciate applying both positive and negative scale factors on Cartesian plane

The learner is guided to:
- Plot figures with given vertices
- Enlarge with centres at various points
- Determine image coordinates
- Apply both positive and negative scale factors

What happens when the centre is not at the origin?

- Master Mathematics Grade 9 pg. 198
- Graph papers
- Rulers
- Calculators
- Digital devices

- Written tests - Class activities

4.0 Geometry

4.3 Similarity and Enlargement - Linear scale factor of similar figures (1)

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

- Define linear scale factor
- Calculate linear scale factor from similar figures and use it to find unknown lengths
- Show interest in applying linear scale factor to practical situations

The learner is guided to:
- Measure corresponding sides of similar figures
- Calculate ratios to find linear scale factor
- Use scale factor to determine unknown dimensions
- Apply to practical situations

What is linear scale factor?

- Master Mathematics Grade 9 pg. 200
- Rulers
- Similar objects
- Calculators
- Models

- Observation - Oral questions

4.0 Geometry

4.3 Similarity and Enlargement - Linear scale factor of similar figures (2)

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

- Explain applications of linear scale factor in real-life situations
- Solve problems involving scale models and drawings
- Appreciate use of similarity in architecture and mapping

The learner is guided to:
- Work with scale drawings and models
- Determine actual dimensions from scale drawings
- Calculate linear scale factors from given information
- Discuss applications in architecture and mapping

How is linear scale factor used in real life?

- Master Mathematics Grade 9 pg. 200
- Maps
- Scale models
- Calculators
- Real objects

- Written assignments - Written tests

4.0 Geometry

4.4 Trigonometry - Angles and sides of right-angled triangles
4.4 Trigonometry - Tangent ratio and tables of tangents

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

- Define hypotenuse, opposite and adjacent sides
- Identify and name sides with reference to given angles
- Show interest in recognizing right-angled triangles in real situations

The learner is guided to:
- Draw right-angled triangles
- Identify the hypotenuse
- Label opposite and adjacent sides for given angles
- Practice with different orientations of triangles

How do we identify sides of a right-angled triangle?

- Master Mathematics Grade 9 pg. 205
- Rulers
- Set squares
- Models of triangles
- Charts
- Master Mathematics Grade 9 pg. 207
- Mathematical tables
- Calculators
- Right-angled triangles

- Observation - Oral questions

4.0 Geometry

4.4 Trigonometry - Sine and cosine ratios, tables of sines and cosines

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

- Define sine and cosine of an angle
- Calculate sine and cosine ratios and read values from mathematical tables
- Develop interest in observing that cosine values decrease as angles increase

The learner is guided to:
- Work out ratios of opposite to hypotenuse (sine)
- Work out ratios of adjacent to hypotenuse (cosine)
- Read values from tables of sines and cosines
- Observe that values in cosine tables are subtracted

How are sine and cosine different from tangent?

- Master Mathematics Grade 9 pg. 211
- Mathematical tables
- Rulers
- Calculators
- Models

- Observation - Written assignments

4.0 Geometry

4.4 Trigonometry - Using calculators and applications of trigonometric ratios

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

- Explain how to use calculators to find trigonometric ratios
- Apply trigonometric ratios to calculate unknown sides and angles
- Appreciate using trigonometry to solve real-life problems

The learner is guided to:
- Use calculator buttons for sin, cos, tan
- Find inverse trigonometric ratios
- Calculate unknown lengths in right-angled triangles
- Solve problems involving heights, distances and angles

How do we use trigonometry to solve real-life problems?

- Master Mathematics Grade 9 pg. 217
- Scientific calculators
- Rulers
- Protractors
- Real-life problem scenarios

- Written tests - Practical activities