Numbers

Compound Proportions and Rates of Work - Working out compound proportions using ratio method
Compound Proportions and Rates of Work - Compound proportions (continued)

By the end of the lesson, the learner should be able to:
- Define compound proportion
- Work out compound proportions using the ratio method
- Appreciate proportional relationships

In groups, learners are guided to:
- Measure heights in pictures and compare ratios
- Observe that in compound proportion, quantities change in the same ratio
- Set up and solve proportion equations
- Relate actual measurements to scaled measurements

How do we use ratios to solve compound proportion problems?

- Master Mathematics Grade 9 pg. 33
- Pictures and photos
- Measuring tools
- Charts
- Rectangles and shapes
- Calculators
- Reference materials

- Observation - Oral questions - Written assignments

Numbers

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:
- Define rate of work
- Relate number of workers to time taken
- Appreciate efficient work planning

In groups, learners are guided to:
- Rearrange classroom desks in groups and time the activity
- Compare time taken by different sized groups
- Understand that more workers take less time
- Set up rate of work problems in table format

Why do more workers complete work faster?

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

- Observation - Oral questions - Written assignments

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

In groups, learners are guided to:
- 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

Compound Proportions and Rates of Work - Applications of rates of work
Compound Proportions and Rates of Work - Using IT and comprehensive applications

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

In groups, learners are guided to:
- 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

- Observation - Oral questions - Written assignments

Algebra

Matrices - Identifying a matrix

By the end of the lesson, the learner should be able to:
- Define a matrix and identify rows and columns
- Identify matrices in different situations
- Appreciate the organization of items in rows and columns

- Discuss how items are organised on supermarket shelves
- Observe sitting arrangements of learners in the classroom
- Study tables showing football league standings and calendars
- Identify rows and columns in different arrangements

How do we organize items in rows and columns in real life?

- 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

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

In groups, learners are guided to:
- 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

- Observation - Oral questions - Written tests

Algebra

Matrices - Position of items and equal matrices
Matrices - Determining compatibility for addition and subtraction

By the end of the lesson, the learner should be able to:
- Identify corresponding elements in equal matrices
- Determine values of unknowns in equal matrices
- Appreciate the concept of matrix equality

In groups, learners are guided to:
- Compare elements in matrices with same positions
- Find values of letters in equal matrices
- Study egg trays and other matrix arrangements
- Work out values by equating corresponding elements

How do we compare elements in different matrices?

- Master Mathematics Grade 9 pg. 42
- Number cards
- Matrix charts
- Real objects arranged in matrices
- Charts showing matrix orders
- Classroom arrangement diagrams
- Reference materials

- Observation - Oral questions - Written tests

Algebra

Matrices - Addition of matrices
Matrices - Subtraction of matrices

By the end of the lesson, the learner should be able to:
- Explain the process of adding matrices
- Add compatible matrices accurately
- Show systematic approach to matrix addition

In groups, learners are guided to:
- Identify elements in corresponding positions
- Add matrices by adding corresponding elements
- Work out matrix addition problems
- Verify that resultant matrix has same order as original matrices

How do we add matrices?

- Master Mathematics Grade 9 pg. 42
- Number cards with matrices
- Charts
- Calculators
- Number cards
- Matrix charts
- Reference books

- Observation - Oral questions - Written tests

Algebra

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:
- Identify combined operations on matrices
- Perform combined addition and subtraction of matrices
- Appreciate applications of matrices in real life

In groups, learners are guided to:
- Work out expressions like A + B - C and A - (B + C)
- Apply matrices to basketball scores, shop sales, and stock records
- Solve real-life problems using matrix operations
- Visit supermarkets to observe item arrangements

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

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

- Observation - Oral questions - Written tests - Project work

Algebra

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

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

In groups, learners are guided to:
- 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

- Observation - Oral questions - Written tests

Algebra

Equations of a Straight Line - Types of gradients

By the end of the lesson, the learner should be able to:
- Identify the four types of gradients
- Distinguish between positive, negative, zero and undefined gradients
- Show interest in gradient patterns

In groups, learners are guided to:
- Study lines with positive gradients (rising from left to right)
- Study lines with negative gradients (falling from left to right)
- Identify horizontal lines with zero gradient
- Identify vertical lines with undefined gradient

What are the different types of gradients?

- Master Mathematics Grade 9 pg. 57
- Graph paper
- Charts showing gradient types
- Digital devices
- 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

In groups, learners are guided to:
- 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

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

In groups, learners are guided to:
- 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 - Expressing in the form y = mx + c
Equations of a Straight Line - More practice on y = mx + c form

By the end of the lesson, the learner should be able to:
- Define the standard form y = mx + c
- Express linear equations in the form y = mx + c
- Show understanding of equation transformation

In groups, learners are guided to:
- Identify the term with y in given equations
- Take all other terms to the right hand side
- Divide by the coefficient of y to make it equal to 1
- Rewrite equations in standard form

How do we write equations in the form y = mx + c?

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

- Observation - Oral questions - Written assignments

Algebra

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:
- Define m and c in the equation y = mx + c
- Interpret the values of m and c from equations
- Show understanding of gradient and y-intercept

In groups, learners are guided to:
- Draw lines on graph paper and work out their gradients
- Determine equations and express in y = mx + c form
- Compare coefficient of x with calculated gradient
- Identify the y-intercept as the constant c

What do m and c represent in the equation y = mx + c?

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

- Observation - Oral questions - Written assignments

Algebra

Equations of a Straight Line - Determining x-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

In groups, learners are guided to:
- 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

- Observation - Oral questions - Written assignments

Algebra

Equations of a Straight Line - Determining y-intercepts
Equations of a Straight Line - Finding equations from intercepts

By the end of the lesson, the learner should be able to:
- Define y-intercept of a line
- Determine y-intercepts from equations
- Show understanding that x = 0 at y-intercept

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

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

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

- Observation - Oral questions - Written tests

Algebra

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:
- Define linear inequality in one unknown
- Solve linear inequalities involving addition and subtraction
- Show understanding of inequality symbols

In groups, learners are guided to:
- Discuss inequality statements and their meanings
- Substitute integers to test inequality truth
- Solve inequalities by isolating the unknown
- Verify solutions by substitution

How do we solve inequalities with one unknown?

- Master Mathematics Grade 9 pg. 72
- Number cards
- Number lines
- Charts
- Reference books
- Calculators

- Observation - Oral questions - Written tests

Algebra

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

In groups, learners are guided to:
- 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

- Observation - Oral questions - Written tests

Algebra

Linear Inequalities - Graphical representation in two unknowns
Linear Inequalities - Applications to real-life situations

By the end of the lesson, the learner should be able to:
- Explain the steps for graphing two-variable inequalities
- Represent linear inequalities in two unknowns graphically
- Show accuracy in identifying solution regions

In groups, learners are guided to:
- Draw graphs for inequalities like 3x + 5y ≤ 15
- Use continuous or dotted lines appropriately
- Select test points to verify wanted region
- Shade unwanted regions correctly

How do we represent two-variable inequalities on graphs?

- Master Mathematics Grade 9 pg. 72
- Graph paper
- Rulers and plotting tools
- Digital devices
- Reference materials
- Real-world scenarios
- Charts

- Observation - Oral questions - Written tests

Measurements

Area - Area of a pentagon
Area - Area of a hexagon

By the end of the lesson, the learner should be able to:
- Define a regular pentagon
- Draw a regular pentagon and divide it into triangles
- Calculate the area of a regular pentagon

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

How do we find the area of a pentagon?

- Master Mathematics Grade 9 pg. 85
- Rulers and protractors
- Compasses
- Graph paper
- Charts showing pentagons
- Compasses and rulers
- Protractors
- Manila paper
- Digital devices

- Observation - Oral questions - Written assignments

Measurements

Area - Surface area of triangular prisms

By the end of the lesson, the learner should be able to:
- Identify triangular prisms
- Sketch nets of triangular prisms
- Calculate surface area of triangular prisms

In groups, learners are guided to:
- Identify differences between triangular and rectangular prisms
- Sketch nets of triangular prisms
- Identify all faces from the net
- Calculate area of each face
- Add all areas to get total surface area

How do we find the surface area of a triangular prism?

- Master Mathematics Grade 9 pg. 85
- Models of prisms
- Graph paper
- Rulers
- Reference materials

- Observation - Oral questions - Written assignments

Measurements

Area - Surface area of rectangular prisms
Area - Surface area of pyramids

By the end of the lesson, the learner should be able to:
- Identify rectangular prisms (cuboids)
- Sketch nets of cuboids
- Calculate surface area of rectangular prisms

In groups, learners are guided to:
- Sketch nets of rectangular prisms
- Identify pairs of equal rectangular faces
- Calculate area of each face
- Apply formula: 2(lw + lh + wh)
- Solve real-life problems involving cuboids

How do we calculate the surface area of a cuboid?

- Master Mathematics Grade 9 pg. 85
- Cuboid models
- Manila paper
- Scissors
- Calculators
- Sticks/straws
- Graph paper
- Protractors
- Reference books

- Observation - Oral questions - Written tests

Measurements

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:
- Distinguish between square and rectangular based pyramids
- Apply Pythagoras theorem to find heights
- Calculate surface area of square and rectangular pyramids

In groups, learners are guided to:
- Sketch nets of square and rectangular pyramids
- Use Pythagoras theorem to find perpendicular heights
- Calculate area of base
- Calculate area of each triangular face
- Apply formula: Base area + sum of triangular faces

How do we calculate surface area of different pyramids?

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

- Observation - Oral questions - Written tests

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

In groups, learners are guided to:
- 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

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

In groups, learners are guided to:
- 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

- Observation - Oral questions - Written tests

Measurements

Volume - Volume of rectangular prisms

By the end of the lesson, the learner should be able to:
- Identify rectangular prisms (cuboids)
- Apply the volume formula for cuboids
- Solve problems involving rectangular prisms

In groups, learners are guided to:
- Identify that cuboids are prisms with rectangular cross-section
- Apply formula: V = l × w × h
- Calculate volumes with different measurements
- Solve real-life problems (water tanks, dump trucks)
- Convert between cubic units

How do we calculate the volume of a cuboid?

- Master Mathematics Grade 9 pg. 102
- Cuboid models
- Calculators
- 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

In groups, learners are guided to:
- 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

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

In groups, learners are guided to:
- 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

- Observation - Oral questions - Written assignments

Measurements

Volume - Calculating volume of cones
Volume - Volume of frustums of pyramids

By the end of the lesson, the learner should be able to:
- Apply the cone volume formula
- Use Pythagoras theorem to find missing dimensions
- Calculate volumes of cones with different measurements

In groups, learners are guided to:
- Apply formula: V = ⅓πr²h
- Use Pythagoras to find radius when given slant height
- Use Pythagoras to find height when given slant height
- Solve practical problems (birthday caps, funnels)

How do we calculate the volume of a cone?

- Master Mathematics Grade 9 pg. 102
- Cone models
- Calculators
- Graph paper
- Reference materials
- Pyramid models
- Cutting tools
- Rulers

- Observation - Oral questions - Written assignments

Measurements

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

By the end of the lesson, the learner should be able to:
- Identify frustums of cones
- Apply the frustum concept to cones
- Calculate volume of frustums of cones

In groups, learners are guided to:
- Identify frustums with circular bases
- Calculate volume of original cone
- Calculate volume of small cone cut off
- Subtract to get volume of frustum
- Solve real-life problems (lampshades, buckets)

How do we calculate the volume of a frustum of a cone?

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

- Observation - Oral questions - Written assignments

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

In groups, learners are guided to:
- 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

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

- Observation - Oral questions - Written assignments

Measurements

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:
- Define weight and state its SI unit
- Distinguish between mass and weight
- Calculate weight from mass using gravity

In groups, learners are guided to:
- Study spring balance showing both mass and weight
- Observe relationship: 1 kg = 10 N
- Apply formula: Weight = mass × gravity
- Calculate weights of various objects
- Understand that mass is constant but weight varies

What is the difference between mass and weight?

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

- Observation - Oral questions - Written tests

Measurements

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

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
- Charts with formulas
- Various solid objects
- Reference books

- Observation - Oral questions - Written tests

Measurements

Mass, Volume, Weight and Density - Applications of density
Time, Distance and Speed - Working out speed in km/h and m/s

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
- Master Mathematics Grade 9 pg. 117
- Stopwatches
- Tape measures
- Open field
- Conversion charts

- Observation - Oral questions - Written tests

Measurements

Time, Distance and Speed - Calculating distance and time from speed
Time, Distance and Speed - Working out average speed

By the end of the lesson, the learner should be able to:
- Rearrange speed formula to find distance
- Rearrange speed formula to find time
- Solve problems involving speed, distance and time
- Apply to real-life situations

In groups, learners are guided to:
- Apply formula: Distance = Speed × Time
- Apply formula: Time = Distance/Speed
- Solve problems with different units
- Apply to journeys, races, train travel
- Work with Madaraka Express train problems
- Calculate distances covered at given speeds
- Calculate time taken for journeys

How do we calculate distance and time from speed?

- Master Mathematics Grade 9 pg. 117
- Calculators
- Formula charts
- Real-world examples
- Reference materials
- Field with marked points
- Stopwatches
- Reference books

- Observation - Oral questions - Written tests

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
Time, Distance and Speed - Deceleration and applications

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
- Road safety materials
- Charts
- Reference materials

- Observation - Oral questions - Written assignments

Measurements

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:
- Identify longitudes on a globe
- Distinguish between latitudes and longitudes
- Use atlas to find longitudes of places
- State longitudes of various towns and cities

In groups, learners are guided to:
- Study globe showing longitudes and latitudes
- Identify that longitudes run North to South (meridians)
- Identify that latitudes run East to West
- Identify Greenwich Meridian (0°)
- Use atlas to find longitudes of various places
- Distinguish between East and West longitudes
- Find longitudes of towns in Kenya, Africa, and world map
- Identify islands at specific longitudes

What are longitudes and how do we identify them?

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

- Observation - Oral questions - Written assignments

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

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
- 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

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
Money - Import 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
- Import duty examples
- Reference books

- Observation - Oral questions - Written tests

Measurements

Money - Excise duty and Value Added Tax (VAT)
Money - Combined duties and taxes on imported goods

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
- Comprehensive examples
- Charts showing tax flow

- Observation - Oral questions - Written tests

Measurements

Approximations and Errors - Approximating quantities in measurements
Approximations and Errors - Determining errors using estimations and actual measurements

By the end of the lesson, the learner should be able to:
- Define approximation
- Approximate quantities using arbitrary units
- Use estimation in various contexts
- Appreciate the use of approximations in daily life

In groups, learners are guided to:
- Estimate length of teacher's table using palm length
- Estimate height of classroom door in metres
- Estimate width of textbook using palm
- Approximate distance using strides
- Approximate weight, capacity, temperature, time
- Use arbitrary units like strides and palm lengths
- Understand that approximations are not accurate
- Apply approximations in budgeting and planning

What is approximation and when do we use it?

- Master Mathematics Grade 9 pg. 146
- Tape measures
- Various objects to measure
- Containers for capacity
- Reference materials
- Measuring cylinders
- Water bottles
- Weighing scales
- Calculators

- Observation - Oral questions - Practical activities

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 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
- Real-world scenarios
- Case studies
- Reference materials

- Observation - Oral questions - Written tests

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
4.1 Coordinates and Graphs - Drawing perpendicular lines on the Cartesian plane

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
- Master Mathematics Grade 9 pg. 160
- Protractors

- Class activities - Written tests

4.0 Geometry

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:
- State the relationship between gradients of perpendicular lines
- Apply the relationship m₁ × m₂ = -1 to solve problems
- Appreciate solving real-life problems involving graphs of straight lines

The learner is guided to:
- Work out the gradient of each perpendicular line
- Multiply the gradients of two perpendicular lines
- Apply the concept to determine equations of perpendicular lines
- Interpret graphs representing real-life situations

What is the relationship between gradients of perpendicular lines?

- Master Mathematics Grade 9 pg. 162
- Graph papers
- Calculators
- Real-life graph examples
- Master Mathematics Grade 9 pg. 166
- Pair of compasses
- Protractors
- Rulers
- Charts showing compass directions
- Master Mathematics Grade 9 pg. 169
- Compasses
- Map samples
- Master Mathematics Grade 9 pg. 171
- Pencils

- Written assignments - Class activities

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)

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

- Class activities - Written tests

4.0 Geometry

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:
- Define angle of elevation
- Identify and sketch right-angled triangles showing angles of elevation
- Develop interest in recognizing situations involving angles of elevation

The learner is guided to:
- Observe objects above eye level
- Identify the angle through which eyes are raised
- Sketch right-angled triangles formed
- Label the angle of elevation correctly

What is an angle of elevation?

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

- Observation - Oral questions

4.0 Geometry

4.2 Scale Drawing - Identifying angles of depression (1)
4.2 Scale Drawing - Determining angles of depression (2)

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

- Observation - Oral questions

4.0 Geometry

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

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
- Meter rules
- Strings
- Pegs
- Field books

- Observation - Class activities

4.0 Geometry

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

By the end of the lesson, the learner should be able to:
- Explain transverse survey method
- Identify baselines and draw offsets on either side accurately
- Show interest in understanding different surveying methods

The learner is guided to:
- Draw baselines at the middle of areas to be surveyed
- Draw offsets perpendicular to baselines on both sides
- Measure lengths of offsets from baselines
- Record measurements in tables

How is transverse survey different from triangulation?

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

- Observation - Oral questions

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