Numbers

Integers - Addition of positive integers to positive integers
Integers - Addition of negative integers to negative integers

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

- Define integers and identify positive integers
- Add positive integers to positive integers
- Show interest in learning about integers

- Use number cards with positive signs to demonstrate addition of integers
- Draw tables and arrange cards to work out addition
- Discuss real-life scenarios involving addition of positive integers
- Use counters to visualize addition operations

How do we add positive integers in real-life situations?

- Master Mathematics Grade 9 pg. 1
- Number cards
- Counters with positive signs
- Charts
- Number lines
- Number cards with negative signs
- Thermometers

- Observation - Oral questions - Written assignments

Numbers

Integers - Addition of negative to positive integers and subtraction of integers
Integers - Multiplication and division of integers
Integers - Combined operations on integers and applications
Cubes and Cube Roots - Cubes of numbers by multiplication
Cubes and Cube Roots - Cubes of numbers from mathematical tables

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

- Explain addition of integers with different signs
- Add and subtract integers in different situations
- Show interest in integer operations

- Pair positive and negative cards to demonstrate addition
- Work out subtraction using number lines and counters
- Discuss and solve problems involving electricity meters and temperature changes
- Use IT devices to explore integer operations

How do we work with integers of different signs?

- Master Mathematics Grade 9 pg. 1
- Counters
- Number lines
- Digital devices
- Internet access
- Drawing materials
- Charts showing triangles
- Number cards
- Reference books
- Master Mathematics Grade 9 pg. 12
- Dice or cubes
- Charts
- Mathematical tables
- Calculators
- Charts showing sample tables

- Observation - Oral questions - Written assignments

Numbers

Cubes and Cube Roots - Cube roots by factor method
Cubes and Cube Roots - Cube roots from mathematical tables
Cubes and Cube Roots - Using calculators and real-life applications
Indices and Logarithms - Expressing numbers in index form

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

- Identify perfect cubes
- Determine cube roots using the factor method
- Show interest in finding cube roots

- Write numbers in terms of prime factors using factor trees
- Group prime factors into three identical numbers
- Select one factor from each group to find cube roots
- Work out cube roots of algebraic expressions

How do we find cube roots using prime factors?

- Master Mathematics Grade 9 pg. 12
- Number cards
- Charts
- Factor trees diagrams
- Mathematical tables
- Reference books
- Calculators
- Digital devices
- Models of cubes
- Internet access
- Master Mathematics Grade 9 pg. 24
- Factor tree charts
- Drawing materials

- Observation - Oral questions - Written tests

Numbers

Indices and Logarithms - Multiplication and division laws of indices
Indices and Logarithms - Power law and zero indices

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

- State the multiplication and division laws of indices
- Apply the laws to simplify expressions
- Show interest in working with indices

- Use number cards to demonstrate multiplication of indices
- Write numbers in expanded form then in index form
- Discover that when multiplying, indices are added
- Use cards to show that when dividing, indices are subtracted

What are the laws of indices?

- Master Mathematics Grade 9 pg. 24
- Number cards
- Charts
- Mathematical tables
- Calculators
- Reference books

- Observation - Oral questions - Written tests

Numbers

Indices and Logarithms - Negative and fractional indices
Indices and Logarithms - Applications of laws of indices
Indices and Logarithms - Powers of 10 and common logarithms

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

- Define negative and fractional indices
- Apply negative and fractional indices to solve problems
- Show confidence in manipulating indices

- Use factor method to understand negative indices
- Discover that negative index means reciprocal
- Relate fractional indices to square roots and cube roots
- Solve equations involving unknown indices

How do we work with negative and fractional indices?

- Master Mathematics Grade 9 pg. 24
- Mathematical tables
- Calculators
- Charts
- Digital devices
- Internet access
- Reference books

- Observation - Oral questions - Written tests

Numbers

Compound Proportions and Rates of Work - Dividing quantities into proportional parts
Compound Proportions and Rates of Work - Dividing quantities into proportional parts (continued)
Compound Proportions and Rates of Work - Relating different ratios

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

- Define proportion and proportional parts
- Divide quantities into proportional parts accurately
- Appreciate fair sharing of resources

- Discuss the concept of proportion and proportional parts
- Calculate total number of proportional parts
- Share quantities in given ratios
- Solve problems involving sharing profits, land, and resources

What are proportions and how do we share quantities fairly?

- Master Mathematics Grade 9 pg. 33
- Number cards
- Charts
- Reference materials
- Calculators
- Real objects for sharing
- Number lines
- Drawing materials
- Reference books

- Observation - Oral questions - Written assignments

Numbers

Compound Proportions and Rates of Work - Continuous proportion
Compound Proportions and Rates of Work - Working out compound proportions using ratio method

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

- Define continuous proportion
- Determine missing values in continuous proportions
- Show interest in proportional patterns

- Work with four numbers in continuous proportion
- Use the relationship a:b = c:d to solve problems
- Find unknown values in proportional sequences
- Apply continuous proportion to harvest and measurement problems

How do we work with continuous proportions?

- Master Mathematics Grade 9 pg. 33
- Number cards
- Charts
- Calculators
- Pictures and photos
- Measuring tools

- Observation - Oral questions - Written tests

Numbers

Compound Proportions and Rates of Work - Compound proportions (continued)
Compound Proportions and Rates of Work - Introduction to rates of work
Compound Proportions and Rates of Work - Calculating rates of work with two variables

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

- Identify compound proportion problems
- Solve various compound proportion problems
- Show accuracy in calculations

- Work out dimensions of similar rectangles
- Calculate materials needed in construction maintaining ratios
- Solve problems on imports, school enrollment, and harvests
- Discuss consumer awareness in proportional buying

How do we maintain constant ratios in different situations?

- Master Mathematics Grade 9 pg. 33
- Rectangles and shapes
- Calculators
- Reference materials
- Stopwatch or timer
- Classroom furniture
- Charts
- Charts showing worker-day relationships
- Reference books

- Observation - Oral questions - Written tests

Numbers

Compound Proportions and Rates of Work - Rates of work with three variables
Compound Proportions and Rates of Work - More rate of work problems

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

- Explain rate of work with multiple variables
- Apply both increasing and decreasing ratios in one problem
- Show analytical thinking skills

- Set up problems with three variables in table format
- Compare each pair of variables to determine ratio type
- Solve factory, painting, and packing problems
- Multiply ratios to get final answers

How do we solve rate of work problems with multiple variables?

- Master Mathematics Grade 9 pg. 33
- Charts
- Calculators
- Real-world work scenarios
- Charts showing different scenarios
- Reference materials

- Observation - Oral questions - Written assignments

Numbers
Algebra

Compound Proportions and Rates of Work - Applications of rates of work
Compound Proportions and Rates of Work - Using IT and comprehensive applications
Matrices - Identifying a matrix

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

- Explain rates of work in various contexts
- Apply rates of work to land clearing and production
- Show confidence in problem-solving

- Calculate hectares cleared by different numbers of men
- Determine days needed to complete specific work
- Work out production and packing rates
- Discuss efficiency and productivity

How do rates of work help in planning and resource allocation?

- Master Mathematics Grade 9 pg. 33
- Digital devices
- Charts
- Calculators
- Reference books
- Internet access
- Educational games
- Reference materials
- Master Mathematics Grade 9 pg. 42
- Charts showing matrices
- Calendar samples
- Tables and schedules

- Observation - Oral questions - Written assignments

Algebra

Matrices - Determining the order of a matrix
Matrices - Determining the position of items in a matrix
Matrices - Position of items and equal matrices

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

- Define the order of a matrix
- Determine the order of matrices in different situations
- Appreciate the use of matrix notation

- Study parking lot arrangements to determine rows and columns
- Count rows and columns in given matrices
- Write the order of matrices in the form m × n
- Identify row, column, rectangular and square matrices

What is the order of a matrix?

- Master Mathematics Grade 9 pg. 42
- Mathematical tables
- Charts showing different matrix types
- Digital devices
- Classroom seating charts
- Calendar samples
- Football league tables
- Number cards
- Matrix charts
- Real objects arranged in matrices

- Observation - Oral questions - Written tests

Algebra

Matrices - Determining compatibility for addition and subtraction
Matrices - Addition of matrices

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

- Define compatible matrices
- Determine compatibility of matrices for addition and subtraction
- Show understanding of matrix order requirements

- Study classroom stream arrangements with same sitting positions
- Compare orders of different matrices
- Identify matrices that can be added or subtracted
- Determine which matrices have the same order

When can we add or subtract matrices?

- Master Mathematics Grade 9 pg. 42
- Charts showing matrix orders
- Classroom arrangement diagrams
- Reference materials
- Number cards with matrices
- Charts
- Calculators

- Observation - Oral questions - Written assignments

Algebra

Matrices - Subtraction of matrices
Matrices - Combined operations and applications
Equations of a Straight Line - Identifying the gradient in real life

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

- Explain the process of subtracting matrices
- Subtract compatible matrices accurately
- Appreciate the importance of corresponding positions

- Identify elements in corresponding positions in matrices
- Subtract matrices by subtracting corresponding elements
- Work out matrix subtraction problems
- Verify compatibility before subtracting

How do we subtract matrices?

- Master Mathematics Grade 9 pg. 42
- Number cards
- Matrix charts
- Reference books
- Digital devices
- Real-world data tables
- Reference materials
- Master Mathematics Grade 9 pg. 57
- Pictures showing slopes
- Internet access
- Charts

- Observation - Oral questions - Written assignments

Algebra

Equations of a Straight Line - Gradient as ratio of rise to run
Equations of a Straight Line - Determining gradient from two known points
Equations of a Straight Line - Types of gradients

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

- Define rise and run in relation to gradient
- Calculate gradient as ratio of vertical to horizontal distance
- Show understanding of positive and negative gradients

- Identify vertical distance (rise) and horizontal distance (run)
- Work out gradient using the formula gradient = rise/run
- Use adjustable ladders to demonstrate different gradients
- Complete tables showing different ladder positions

How do we calculate the slope or gradient?

- Master Mathematics Grade 9 pg. 57
- Ladders or models
- Measuring tools
- Charts
- Reference books
- Graph paper
- Rulers
- Plotting tools
- Digital devices
- Charts showing gradient types
- Internet access

- Observation - Oral questions - Written tests

Algebra

Equations of a Straight Line - Equation given two points
Equations of a Straight Line - More practice on equations from two points

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

- Explain the steps to find equation from two points
- Determine the equation of a line given two points
- Show systematic approach to problem solving

- Calculate gradient using two given points
- Use a general point (x, y) with one of the given points
- Equate the two gradient expressions
- Simplify to get the equation of the line

How do we find the equation of a line from two points?

- Master Mathematics Grade 9 pg. 57
- Graph paper
- Number cards
- Charts
- Reference books
- Plotting tools
- Geometric shapes
- Calculators

- Observation - Oral questions - Written assignments

Algebra

Equations of a Straight Line - Equation from a point and gradient
Equations of a Straight Line - Applications of point-gradient method
Equations of a Straight Line - Expressing in the form y = mx + c

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

- Explain the method for finding equation from point and gradient
- Determine equation given a point and gradient
- Show confidence in using the gradient formula

- Use a given point and a general point (x, y)
- Write expression for gradient using the two points
- Equate the expression to the given gradient value
- Simplify to obtain the equation

How do we find the equation when given a point and gradient?

- Master Mathematics Grade 9 pg. 57
- Number cards
- Graph paper
- Charts
- Reference materials
- Calculators
- Geometric shapes
- Reference books

- Observation - Oral questions - Written assignments

Algebra

Equations of a Straight Line - More practice on y = mx + c form
Equations of a Straight Line - Interpreting y = mx + c
Equations of a Straight Line - Finding gradient and y-intercept from equations

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

- Identify equations that need conversion
- Convert various equations to y = mx + c form
- Appreciate the standard form of linear equations

- Express equations from two points in y = mx + c form
- Express equations from point and gradient in y = mx + c form
- Practice with different types of linear equations
- Verify transformed equations

How do we apply the y = mx + c form to different equations?

- Master Mathematics Grade 9 pg. 57
- Graph paper
- Calculators
- Charts
- Reference books
- Plotting tools
- Digital devices
- Charts with tables
- Reference materials

- Observation - Oral questions - Written tests

Algebra

Equations of a Straight Line - Determining x-intercepts
Equations of a Straight Line - Determining y-intercepts

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

- Define x-intercept of a line
- Determine x-intercepts from equations
- Show understanding that y = 0 at x-intercept

- Observe where lines cross the x-axis on graphs
- Note that y-coordinate is 0 at x-intercept
- Substitute y = 0 in equations to find x-intercept
- Work out x-intercepts from various equations

What is the x-intercept and how do we find it?

- Master Mathematics Grade 9 pg. 57
- Graph paper
- Plotting tools
- Charts
- Reference books
- Calculators

- Observation - Oral questions - Written assignments

Algebra

Equations of a Straight Line - Finding equations from intercepts
Linear Inequalities - Solving linear inequalities in one unknown
Linear Inequalities - Multiplication and division by negative numbers

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

- Explain how to find equations from x and y intercepts
- Determine equations given both intercepts
- Appreciate the use of intercepts as two points

- Use x-intercept and y-intercept as two points on the line
- Write coordinates as (x-intercept, 0) and (0, y-intercept)
- Calculate gradient from these two points
- Use point-gradient method to find equation

How do we find the equation from the intercepts?

- Master Mathematics Grade 9 pg. 57
- Graph paper
- Number cards
- Charts
- Reference materials
- Master Mathematics Grade 9 pg. 72
- Number lines
- Reference books
- Calculators

- Observation - Oral questions - Written assignments

Algebra

Linear Inequalities - Graphical representation in one unknown
Linear Inequalities - Linear inequalities in two unknowns
Linear Inequalities - Graphical representation in two unknowns

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

- Explain how to represent inequalities graphically
- Represent linear inequalities in one unknown on graphs
- Show understanding of continuous and dotted lines

- Change inequality to equation by replacing inequality sign
- Draw boundary line (continuous for ≤ or ≥, dotted for < or >)
- Choose test points to identify wanted and unwanted regions
- Shade the unwanted region

How do we represent inequalities on a graph?

- Master Mathematics Grade 9 pg. 72
- Graph paper
- Rulers
- Plotting tools
- Charts
- Tables for values
- Calculators
- Rulers and plotting tools
- Digital devices
- Reference materials

- Observation - Oral questions - Written tests

Algebra
Measurements

Linear Inequalities - Applications to real-life situations
Area - Area of a pentagon

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

- Identify real-life situations involving inequalities
- Apply linear inequalities to solve real-life problems
- Appreciate the use of inequalities in planning and budgeting

- Solve problems on wedding planning with budget constraints
- Work on train passenger capacity problems
- Solve worker hiring and payment problems
- Play creative games involving inequalities
- Apply to school trips, tree planting, and other scenarios

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

- Master Mathematics Grade 9 pg. 72
- Digital devices
- Real-world scenarios
- Charts
- Reference materials
- Master Mathematics Grade 9 pg. 85
- Rulers and protractors
- Compasses
- Graph paper
- Charts showing pentagons

- Observation - Oral questions - Written tests - Project work

Measurements

Area - Area of a hexagon
Area - Surface area of triangular prisms
Area - Surface area of rectangular prisms

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

- Define a regular hexagon
- Draw a regular hexagon and identify equilateral triangles
- Calculate the area of a regular hexagon

- Draw a circle of radius 5 cm
- Mark arcs of 5 cm on the circumference to form 6 points
- Join points to form a regular hexagon
- Join vertices to centre to form equilateral triangles
- Calculate area using formula
- Verify using alternative method

How do we find the area of a hexagon?

- Master Mathematics Grade 9 pg. 85
- Compasses and rulers
- Protractors
- Manila paper
- Digital devices
- Models of prisms
- Graph paper
- Rulers
- Reference materials
- Cuboid models
- Scissors
- Calculators

- Observation - Oral questions - Written tests

Measurements

Area - Surface area of pyramids
Area - Surface area of square and rectangular pyramids
Area - Area of sectors of circles

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

- Define different types of pyramids
- Sketch nets of pyramids
- Calculate surface area of triangular-based pyramids

- Make pyramid shapes using sticks or straws
- Count faces of different pyramids
- Sketch nets showing base and triangular faces
- Calculate area of base
- Calculate area of all triangular faces
- Add to get total surface area

How do we find the surface area of a pyramid?

- Master Mathematics Grade 9 pg. 85
- Sticks/straws
- Graph paper
- Protractors
- Reference books
- Calculators
- Pyramid models
- Charts
- Compasses and rulers
- Digital devices
- Internet access

- Observation - Oral questions - Written assignments

Measurements

Area - Area of segments of circles
Area - Surface area of cones

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

- Define a segment of a circle
- Distinguish between major and minor segments
- Calculate area of segments

- Draw a circle and mark two points on circumference
- Join points with a chord to form segments
- Calculate area of sector
- Calculate area of triangle
- Apply formula: Area of segment = Area of sector - Area of triangle
- Calculate area of major segments

How do we calculate the area of a segment?

- Master Mathematics Grade 9 pg. 85
- Compasses
- Rulers
- Calculators
- Graph paper
- Manila paper
- Scissors
- Compasses and rulers
- Reference materials

- Observation - Oral questions - Written tests

Measurements

Area - Surface area of spheres and hemispheres
Volume - Volume of triangular prisms
Volume - Volume of rectangular prisms

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

- Define a sphere and hemisphere
- Derive the formula for surface area of a sphere
- Calculate surface area of spheres and hemispheres

- Get a spherical ball and rectangular paper
- Cover ball with paper to form open cylinder
- Measure diameter and compare to height
- Derive formula: 4πr²
- Calculate surface area of hemispheres: 3πr²
- Solve real-life problems

How do we calculate the surface area of a sphere?

- Master Mathematics Grade 9 pg. 85
- Spherical balls
- Rectangular paper
- Rulers
- Calculators
- Master Mathematics Grade 9 pg. 102
- Straws and paper
- Sand or soil
- Measuring tools
- Reference books
- Cuboid models
- Charts
- Reference materials

- Observation - Oral questions - Written tests

Measurements

Volume - Volume of square-based pyramids
Volume - Volume of rectangular-based pyramids

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

- Define a right pyramid
- Relate pyramid volume to cube volume
- Calculate volume of square-based pyramids

- Model a cube and pyramid with same base and height
- Fill pyramid with soil and transfer to cube
- Observe that pyramid is ⅓ of cube
- Apply formula: V = ⅓ × base area × height
- Calculate volumes of square-based pyramids

How do we find the volume of a pyramid?

- Master Mathematics Grade 9 pg. 102
- Modeling materials
- Soil or sand
- Rulers
- Calculators
- Pyramid models
- Graph paper
- Reference books

- Observation - Oral questions - Written assignments

Measurements

Volume - Volume of triangular-based pyramids
Volume - Introduction to volume of cones
Volume - Calculating volume of cones

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

- Calculate area of triangular bases
- Apply Pythagoras theorem where necessary
- Calculate volume of triangular-based pyramids

- Calculate area of triangular base (using ½bh)
- For equilateral triangles, use Pythagoras to find height
- Apply formula: V = ⅓ × (½bh) × H
- Solve problems with different triangular bases

How do we find volume of triangular pyramids?

- Master Mathematics Grade 9 pg. 102
- Triangular pyramid models
- Rulers
- Calculators
- Charts
- Cone and cylinder models
- Water
- Digital devices
- Internet access
- Cone models
- Graph paper
- Reference materials

- Observation - Oral questions - Written assignments

Measurements

Volume - Volume of frustums of pyramids
Volume - Volume of frustums of cones
Volume - Volume of spheres

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

- Define a frustum
- Explain how to obtain a frustum
- Calculate volume of frustums of pyramids

- Model a pyramid and cut it parallel to base
- Identify the frustum formed
- Calculate volume of original pyramid
- Calculate volume of small pyramid cut off
- Apply formula: Volume of frustum = V(large) - V(small)

What is a frustum and how do we find its volume?

- Master Mathematics Grade 9 pg. 102
- Pyramid models
- Cutting tools
- Rulers
- Calculators
- Cone models
- Frustum examples
- Reference books
- Hollow spheres
- Water or soil

- Observation - Oral questions - Written tests

Measurements

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

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

- Define a hemisphere
- Calculate volume of hemispheres
- Solve real-life problems involving volumes

- Apply formula: V = ½ × 4/3πr³ = 2/3πr³
- Calculate volumes of hemispheres
- Solve problems involving spheres and hemispheres
- Apply to real situations (bowls, domes, balls)

How do we calculate the volume of a hemisphere?

- Master Mathematics Grade 9 pg. 102
- Hemisphere models
- Calculators
- Real objects
- Reference materials
- Master Mathematics Grade 9 pg. 111
- Weighing balances
- Various objects
- Conversion charts

- Observation - Oral questions - Written assignments

Measurements

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

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

- 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
- Charts showing planetary data
- Reference materials
- Digital devices

- Observation - Oral questions - Written assignments

Measurements

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

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

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

- 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
- Charts with formulas
- Various solid objects
- Reference books
- Density tables
- 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

- 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
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:

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

- 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
- Diagrams showing direction
- Charts
- Reference materials
- Field for activity
- Measuring tools
- Formula charts

- Observation - Oral questions - Written assignments

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

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

- Observation - Oral questions - Written tests

Measurements

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

- 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
- World maps
- Time zone references
- Real-world scenarios

- Observation - Oral questions - Written assignments

Measurements

Money - Identifying currencies of different countries
Money - Converting foreign currency to Kenyan shillings
Money - Converting Kenyan shillings to foreign currency and buying/selling rates

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

- 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
- Exchange rate tables
- Real-world scenarios
- Reference books

- Observation - Oral questions - Written assignments - Project work

Measurements

Money - Export duty on goods
Money - Import duty on goods
Money - Excise duty and Value Added Tax (VAT)

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

- 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
- Import duty examples
- Reference books
- Digital devices
- ETR receipts
- Tax rate tables

- 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

- 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
Approximations and Errors - Calculating percentage error
Approximations and Errors - Percentage error in real-life situations

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

- Observation - Oral questions - Written assignments

Measurements
4.0 Geometry
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
4.1 Coordinates and Graphs - Drawing parallel lines on the Cartesian plane

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

- 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
- Master Mathematics Grade 9 pg. 156
- Set squares

- Observation - Oral questions - Written tests - Project work

4.0 Geometry

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)

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

- Define the gradient of a line
- Calculate and compare gradients of parallel lines
- Appreciate the concept that parallel lines have equal gradients

The learner is guided to:
- Identify two points on each line
- Work out the gradient of the lines
- Compare the gradients of lines identified as parallel
- Express equations in the form y=mx+c and compare gradients

How do gradients help us identify parallel lines?

- Master Mathematics Grade 9 pg. 158
- Graph papers
- Rulers
- Calculators
- Digital devices
- Master Mathematics Grade 9 pg. 160
- Protractors
- Set squares
- 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
- Pencils

- Oral questions - Written assignments

4.0 Geometry

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)

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

- Class activities - Written tests

4.0 Geometry

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)

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
- Calculators

- Class activities - Written tests

4.0 Geometry

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)

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

- Observation - Oral questions

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)
4.2 Scale Drawing - Surveying using bearings and distances
4.3 Similarity and Enlargement - Similar figures

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

- Written assignments - Practical activities

4.0 Geometry

4.3 Similarity and Enlargement - Properties of similar figures (1)
4.3 Similarity and Enlargement - Properties of similar figures (2)
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
- Protractors
- Practice worksheets
- Master Mathematics Grade 9 pg. 189
- Compasses
- Plain papers

- Class activities - Written assignments

4.0 Geometry

4.3 Similarity and Enlargement - Determining properties of enlargement
4.3 Similarity and Enlargement - Positive scale factor (1)

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

- Class activities - Written assignments

4.0 Geometry

4.3 Similarity and Enlargement - Positive scale factor (2)
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:

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

- Class activities - Written assignments

4.0 Geometry

4.3 Similarity and Enlargement - Enlargement on the Cartesian plane (1)
4.3 Similarity and Enlargement - Enlargement on the Cartesian plane (2)

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
- Digital devices

- Observation - Written assignments

4.0 Geometry

4.3 Similarity and Enlargement - Linear scale factor of similar figures (1)
4.3 Similarity and Enlargement - Linear scale factor of similar figures (2)
4.4 Trigonometry - Angles and sides of right-angled triangles

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
- Maps
- Scale models
- Real objects
- Master Mathematics Grade 9 pg. 205
- Set squares
- Models of triangles
- Charts

- Observation - Oral questions

4.0 Geometry

4.4 Trigonometry - Tangent ratio and tables of tangents
4.4 Trigonometry - Sine and cosine ratios, tables of sines and cosines
4.4 Trigonometry - Using calculators and applications of trigonometric ratios

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

- Define tangent of an angle as opposite/adjacent
- Calculate tangent ratios from right-angled triangles and read from tables
- Appreciate that tangent ratio is constant for a given angle

The learner is guided to:
- Work out ratios of opposite to adjacent sides
- Recognize that the ratio is constant for a given angle
- Define tangent as opposite/adjacent
- Read tangent values from tables

What is the tangent of an angle?

- Master Mathematics Grade 9 pg. 207
- Mathematical tables
- Rulers
- Calculators
- Right-angled triangles
- Master Mathematics Grade 9 pg. 211
- Models
- Master Mathematics Grade 9 pg. 217
- Scientific calculators
- Protractors
- Real-life problem scenarios

- Class activities - Written tests

5.0 Data Handling and Probability

5.1 Data Interpretation (Grouped Data) - Determining appropriate class width for grouping data
5.1 Data Interpretation (Grouped Data) - Drawing frequency distribution tables of grouped data
5.1 Data Interpretation (Grouped Data) - Identifying the modal class of grouped data
5.1 Data Interpretation (Grouped Data) - Calculating the mean of grouped data (1)
5.1 Data Interpretation (Grouped Data) - Calculating the mean of grouped data (2)

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

- Define class and class width
- Determine appropriate class width from given range of data
- Appreciate the importance of grouping data with many values

The learner is guided to:
- Choose numbers between 1 and 100 and find the range
- Divide the range into equal intervals or classes
- Discuss the width of classes selected
- Compare class widths with other groups

How do we group data with many values?

- Master Mathematics Grade 9 pg. 224
- Writing materials
- Calculators
- Chart papers
- Digital devices
- Master Mathematics Grade 9 pg. 226
- Tally sheets
- Rulers
- Data sets
- Pencils
- Master Mathematics Grade 9 pg. 228
- Frequency distribution tables
- Reference materials
- Master Mathematics Grade 9 pg. 230
- Frequency tables
- Mathematical tables
- Charts

- Observation - Oral questions - Written assignments

5.0 Data Handling and Probability

5.1 Data Interpretation (Grouped Data) - Determining the median of grouped data (1)
5.1 Data Interpretation (Grouped Data) - Determining the median of grouped data (2)
5.1 Data Interpretation (Grouped Data) - Determining the median of grouped data (3)
5.2 Probability - Experiments involving equally and likely outcomes
5.2 Probability - Range of probability of an event

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

- Define cumulative frequency
- Determine cumulative frequencies from frequency tables
- Show interest in understanding the median class

The learner is guided to:
- Search for the meaning of cumulative frequency
- Transfer first frequency to cumulative frequency column
- Add frequencies cumulatively in ascending order
- Identify the median class by finding N/2

What is cumulative frequency?

- Master Mathematics Grade 9 pg. 232
- Frequency tables
- Calculators
- Reference materials
- Digital devices
- Master Mathematics Grade 9 pg. 234
- Formula charts
- Master Mathematics Grade 9 pg. 236
- Data sets
- Writing materials
- Practice worksheets
- Master Mathematics Grade 9 pg. 239
- Coins
- Dice
- Triangular pyramids
- Baskets and pens
- Master Mathematics Grade 9 pg. 241
- Charts showing probability range

- Observation - Written tests

5.0 Data Handling and Probability

5.2 Probability - Identifying mutually exclusive events
5.2 Probability - Experiments of single chance involving mutually exclusive events
5.2 Probability - Experiments involving independent events
5.2 Probability - Drawing tree diagrams for single outcomes

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

- Define mutually exclusive events
- Identify mutually exclusive events from given situations
- Appreciate that mutually exclusive events cannot occur simultaneously

The learner is guided to:
- Observe a coin toss and note that both sides cannot face up
- Discuss what the referee does before a football match
- Identify events that exclude each other
- Give examples of mutually exclusive events from daily life

What are mutually exclusive events?

- Master Mathematics Grade 9 pg. 243
- Coins
- Pictures of referees
- Real-life scenarios
- Charts
- Master Mathematics Grade 9 pg. 244
- Colored pens
- Bags
- Dice
- Number cards
- Calculators
- Master Mathematics Grade 9 pg. 246
- Colored balls
- Baskets
- Master Mathematics Grade 9 pg. 248
- Drawing materials
- Chart papers
- Rulers

- Observation - Oral questions - Written assignments