Numbers

Integers - Addition of positive integers to positive integers
Integers - Addition of negative integers to negative integers
Integers - Addition of negative to positive integers and subtraction of integers
Integers - Multiplication and division of 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

- Identify negative integers
- Add negative integers to negative integers
- Appreciate the use of negative integers in daily life

- 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
- Use number cards with negative signs to demonstrate addition
- Arrange cards in rows to show addition of negative integers
- Discuss real-life applications involving temperature and borrowing money
- Use number lines to visualize operations

How do we add positive integers in real-life situations?
How do we represent and add negative numbers in everyday situations?

- Master Mathematics Grade 9 pg. 1
- Number cards
- Counters with positive signs
- Charts
- Number lines
- Master Mathematics Grade 9 pg. 1
- Number cards with negative signs
- Number lines
- Thermometers
- Charts
- Counters
- Digital devices
- Internet access
- Drawing materials
- Charts showing triangles

- Observation - Oral questions - Written assignments
- Observation - Oral questions - Written tests

Numbers

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:

- Identify the order of operations for integers
- Perform combined operations on integers following BODMAS
- Show confidence in working with integers

- Work out combined operations following BODMAS rule
- Discuss and solve real-life problems involving temperature and business transactions
- Use digital devices to explore more on integer operations
- Play creative games involving integers

How do we solve problems with multiple integer operations?

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

- Observation - Oral questions - Written assignments - Project work

Numbers

Cubes and Cube Roots - Cube roots by factor method
Cubes and Cube Roots - Cube roots from mathematical tables

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

- Observation - Oral questions - Written tests

Numbers

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 calculator functions for cubes and cube roots
- Use calculators to find cubes and cube roots
- Show confidence in using digital tools

- Key in numbers and use x³ function on calculators
- Use shift and ∛ functions to find cube roots
- Solve problems involving cubic boxes, tanks, and containers
- Calculate lengths of cubes from given volumes

Where do we apply cubes and cube roots in real-life situations?

- Master Mathematics Grade 9 pg. 12
- Calculators
- Digital devices
- Models of cubes
- Internet access
- Master Mathematics Grade 9 pg. 24
- Number cards
- Factor tree charts
- Drawing materials

- Observation - Oral questions - Written tests - Project work

Numbers

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

- Explain the power law for indices
- Apply the power law and zero indices to simplify expressions
- Appreciate the patterns in 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
- Work with indices in brackets and multiply the powers
- Use factor method and division law to discover zero indices
- Use calculators to verify that any number to power zero equals 1
- Simplify expressions combining different laws

What are the laws of indices?
Why does any number to power zero equal one?

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

- Observation - Oral questions - Written tests
- Observation - Oral questions - Written assignments

Numbers

Indices and Logarithms - Applications of laws of indices

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

- Identify equations involving indices
- Solve equations and simultaneous equations with indices
- Appreciate the importance of indices

- Solve for unknowns by equating indices
- Work out simultaneous equations involving indices
- Discuss real-life applications of indices
- Use IT devices to explore more on indices

How do we use indices to solve equations?

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

- Observation - Oral questions - Written assignments

Numbers

Indices and Logarithms - Powers of 10 and common logarithms
Compound Proportions and Rates of Work - Dividing quantities into proportional parts

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

- Define common logarithms
- Relate powers of 10 to common logarithms
- Appreciate the relationship between indices and logarithms

- Study the relationship between numbers and their powers of 10
- Understand that the index is the logarithm when base is 10
- Write expressions in logarithm form and vice versa
- Use digital devices to explore logarithms

How do powers of 10 relate to common logarithms?

- Master Mathematics Grade 9 pg. 24
- Mathematical tables
- Digital devices
- Internet access
- Charts
- Master Mathematics Grade 9 pg. 33
- Number cards
- Reference materials

- Observation - Oral questions - Written tests

Numbers

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

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

- Explain proportional sharing of different quantities
- Work out proportional parts in various contexts
- Show fairness in sharing resources

- Work out proportional sharing of animals, books, and land
- Calculate perimeters using ratios
- Determine attendance using given ratios
- Discuss social justice in resource distribution

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

- Master Mathematics Grade 9 pg. 33
- Calculators
- Real objects for sharing
- Charts

- Observation - Oral questions - Written tests

Numbers

Compound Proportions and Rates of Work - Relating different ratios
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:

- Identify when ratios are related
- Relate two or more ratios accurately
- Appreciate the connections between ratios

- Define compound proportion
- Work out compound proportions using the ratio method
- Appreciate proportional relationships

- Draw number lines to show proportional relationships
- Find distances and relate ratios on number lines
- Identify when numbers are in proportion
- Use cross multiplication to solve proportions
- 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 determine if ratios are related?
How do we use ratios to solve compound proportion problems?

- Master Mathematics Grade 9 pg. 33
- Number lines
- Drawing materials
- Charts
- Reference books
- Number cards
- Calculators
- Master Mathematics Grade 9 pg. 33
- Pictures and photos
- Measuring tools
- Charts

- Observation - Oral questions - Written assignments

Numbers

Compound Proportions and Rates of Work - Compound proportions (continued)
Compound Proportions and Rates of Work - Introduction to rates of work

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

- Observation - Oral questions - Written tests

Numbers

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 increasing and decreasing ratios
- Calculate workers needed for specific time periods
- Show systematic problem-solving skills

- Solve problems involving men and days
- Determine when to use increasing and decreasing ratios
- Calculate additional workers needed
- Practice with work completion scenarios

How do we calculate the number of workers needed to complete work in a given time?

- Master Mathematics Grade 9 pg. 33
- Charts showing worker-day relationships
- Calculators
- 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
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

- Identify IT tools for solving rate problems
- Use IT devices to work on rates of work
- Appreciate the use of compound proportions and rates in real life

- 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
- Use digital devices to solve rate problems
- Play creative games on rates and proportions
- Review and consolidate all concepts covered
- Discuss careers involving proportions and rates

How do rates of work help in planning and resource allocation?
How do we use technology to solve compound proportion and rate problems?

- Master Mathematics Grade 9 pg. 33
- Digital devices
- Charts
- Calculators
- Reference books
- Master Mathematics Grade 9 pg. 33
- Digital devices
- 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
- Observation - Oral questions - Written tests - Project work

Algebra

Matrices - Determining the order of 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

- 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

- Observation - Oral questions - Written tests

Algebra

Matrices - Determining the position of items in a matrix

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

- Explain how to identify position of elements in a matrix
- Determine the position of items in terms of rows and columns
- Show accuracy in identifying matrix elements

- Study classroom sitting arrangements in matrix form
- Describe positions using row and column notation
- Identify elements using subscript notation
- Work with calendars and football league tables

How do we locate specific items in a matrix?

- Master Mathematics Grade 9 pg. 42
- Classroom seating charts
- Calendar samples
- Football league tables

- Observation - Oral questions - Written assignments

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

- 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
Matrices - Combined operations and applications

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

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

- 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
- 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 add matrices?
How do we subtract matrices?

- Master Mathematics Grade 9 pg. 42
- Number cards with matrices
- Charts
- Calculators
- Master Mathematics Grade 9 pg. 42
- Number cards
- Matrix charts
- Reference books
- Digital devices
- Real-world data tables
- Reference materials

- Observation - Oral questions - Written tests
- Observation - Oral questions - Written assignments

Algebra

Equations of a Straight Line - Identifying the gradient in real life

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

- Define gradient and slope
- Identify gradients in real-life situations
- Appreciate the concept of steepness

- Search for the meaning of gradient using digital devices
- Identify slopes in pictures of hills, roofs, stairs, and ramps
- Discuss steepness in different structures
- Observe slopes in the immediate environment

What is a gradient and where do we see it in real life?

- Master Mathematics Grade 9 pg. 57
- Pictures showing slopes
- Digital devices
- 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

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

- 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

- 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
Equations of a Straight Line - Equation from a point and gradient

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

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

- 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
- 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 of a line from two points?
How do we find the equation when given a point and gradient?

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

- Observation - Oral questions - Written assignments

Algebra

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:

- Identify problems involving point and gradient
- Apply the point-gradient method to various situations
- Appreciate practical applications of linear equations

- Work out equations of lines with different gradients and points
- Solve problems involving edges of squares and sides of triangles
- Find unknown coordinates using equations
- Determine missing values in linear relationships

How do we use point-gradient method in different situations?

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

- Observation - Oral questions - Written tests

Algebra

Equations of a Straight Line - More practice on y = mx + c form

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

- Observation - Oral questions - Written tests

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

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

- Define y-intercept of a line
- Determine y-intercepts from equations
- Show understanding that x = 0 at y-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
- 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 x-intercept and how do we find it?
What is the y-intercept and how do we find it?

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

- Observation - Oral questions - Written assignments
- Observation - Oral questions - Written tests

Algebra

Linear Inequalities - Solving linear inequalities in one unknown

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

- 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

- Observation - Oral questions - Written tests

Algebra

Linear Inequalities - Multiplication and division by negative numbers
Linear Inequalities - Graphical representation in one unknown

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

- Explain the effect of multiplying/dividing by negative numbers
- Solve inequalities involving multiplication and division
- Appreciate that inequality sign reverses with negative operations

- Solve inequalities and test with integer substitution
- Observe that inequality sign reverses when multiplying/dividing by negative
- Compare solutions with and without sign reversal
- Work out various inequality problems

What happens to the inequality sign when we multiply or divide by a negative number?

- Master Mathematics Grade 9 pg. 72
- Number lines
- Number cards
- Charts
- Calculators
- Graph paper
- Rulers
- Plotting tools

- Observation - Oral questions - Written assignments

Algebra

Linear Inequalities - Linear inequalities in two unknowns

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

- Identify linear inequalities in two unknowns
- Solve linear inequalities with two variables
- Appreciate the relationship between equations and inequalities

- Generate tables of values for linear equations
- Change inequalities to equations
- Plot points and draw boundary lines
- Test points to determine correct regions

How do we work with inequalities that have two unknowns?

- Master Mathematics Grade 9 pg. 72
- Graph paper
- Plotting tools
- Tables for values
- Calculators

- Observation - Oral questions - Written assignments

Algebra
Measurements

Linear Inequalities - Graphical representation in two unknowns
Linear Inequalities - Applications to real-life situations
Area - Area of a pentagon

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

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

- 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
- 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 represent two-variable inequalities on graphs?
How do we find the area of a pentagon?

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

- Observation - Oral questions - Written tests
- Observation - Oral questions - Written assignments

Measurements

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

- Observation - Oral questions - Written tests

Measurements

Area - Surface area of rectangular prisms

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

- 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

- Observation - Oral questions - Written tests

Measurements

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

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

- Define 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

- Observation - Oral questions - Written assignments

Measurements

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

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

- Draw a circle and mark a clock face
- Identify sectors formed by clock hands
- Derive formula: Area = (θ/360) × πr²
- Calculate areas of sectors with different angles
- Use digital devices to watch videos on sectors
- 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 find the area of a sector?
How do we calculate the area of a segment?

- Master Mathematics Grade 9 pg. 85
- Compasses and rulers
- Protractors
- Digital devices
- Internet access
- Master Mathematics Grade 9 pg. 85
- Compasses
- Rulers
- Calculators
- Graph paper
- Manila paper
- Scissors
- Compasses and rulers
- Reference materials

- Observation - Oral questions - Written assignments
- Observation - Oral questions - Written tests

Measurements

Area - Surface area of spheres and hemispheres

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

- Observation - Oral questions - Written tests

Measurements

Volume - Volume of triangular prisms
Volume - Volume of rectangular prisms

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

- Define a prism
- Identify uniform cross-sections
- Calculate volume of triangular prisms

- Make a triangular prism using locally available materials
- Place prism vertically and fill with sand
- Identify the cross-section
- Apply formula: V = Area of cross-section × length
- Calculate area of triangular cross-section
- Multiply by length to get volume

How do we find the volume of a prism?

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

- Observation - Oral questions - Written assignments

Measurements

Volume - Volume of square-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

- Observation - Oral questions - Written assignments

Measurements

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

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

- Apply volume formula to rectangular-based pyramids
- Calculate base area of rectangles
- Solve problems involving rectangular pyramids

- Define a cone as a circular-based pyramid
- Relate cone volume to cylinder volume
- Derive the volume formula for cones

- Calculate area of rectangular base
- Apply formula: V = ⅓ × (l × w) × h
- Work out volumes with different dimensions
- Solve real-life problems (roofs, monuments)
- Model a cylinder and cone with same radius and height
- Fill cone with water and transfer to cylinder
- Observe that cone is ⅓ of cylinder
- Derive formula: V = ⅓πr²h
- Use digital devices to watch videos

How do we calculate volume of rectangular pyramids?
How is a cone related to a cylinder?

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

- Observation - Oral questions - Written tests

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

- 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

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

- 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

- Observation - Oral questions - Written assignments

Measurements

Volume - Volume of spheres
Volume - Volume of hemispheres and applications

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

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

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

How do we find the volume of a sphere?

- Master Mathematics Grade 9 pg. 102
- Hollow spheres
- Cone models
- Water or soil
- Calculators
- Hemisphere models
- Real objects
- Reference materials

- Observation - Oral questions - Written tests

Measurements

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

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

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

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

- Use balance to measure mass of objects
- Record masses in grams
- Study conversion table for mass units
- Convert between kg, g, mg, tonnes, etc.
- Apply conversions to real situations
- Convert various masses to kilograms
- Work with large masses (tonnes)
- Work with small masses (milligrams, micrograms)
- Solve practical problems (construction, medicine, shopping)

How do we convert between different units of mass?
Why is it important to convert units of mass?

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

- Observation - Oral questions - Written tests
- Observation - Oral questions - Written assignments

Measurements

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

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

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

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

How do we calculate mass and gravity from weight?

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

- Observation - Oral questions - Written assignments

Measurements

Mass, Volume, Weight and Density - Introduction to density

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

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

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

What is density?

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

- Observation - Oral questions - Written tests

Measurements

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

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

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

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

How do we use the density formula?

- Master Mathematics Grade 9 pg. 111
- Calculators
- Charts with formulas
- Various solid objects
- Reference books
- Density tables
- Real-world scenarios
- Reference materials

- Observation - Oral questions - Written assignments

Measurements

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

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

- Rearrange speed formula to find distance
- Rearrange speed formula to find time
- Solve problems involving speed, distance and time
- Apply to real-life situations

- 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)
- 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 speed in different units?
How do we calculate distance and time from speed?

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

- 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

- 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

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

- 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

- Observation - Oral questions - Written assignments

Measurements

Time, Distance and Speed - Relating longitudes to time
Time, Distance and Speed - Calculating time differences between places
Time, Distance and Speed - Determining local time of places along different longitudes

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

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

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

- Understand Earth rotates 360° in 24 hours
- Calculate: 360° = 24 hours = 1440 minutes
- Therefore: 1° = 4 minutes
- Identify time zones on world map
- Understand GMT (Greenwich Mean Time)
- Learn that places East of Greenwich are ahead in time
- Learn that places West of Greenwich are behind in time
- Use digital devices to check time zones
- Calculate time difference from longitude difference
- Add time if place is East of reference point (ahead)
- Subtract time if place is West of reference point (behind)
- Account for date changes when crossing midnight
- Solve problems with GMT as reference
- Solve problems with other places as reference
- Apply to phone calls, soccer matches, travel planning
- Work backwards to find longitude from time difference
- Determine whether places are East or West from time relationships

How are longitudes related to time?
How do we find local time at different longitudes?

- Master Mathematics Grade 9 pg. 117
- Globes
- Time zone maps
- Calculators
- Digital devices
- Atlases
- Time zone charts
- Reference books
- Master Mathematics Grade 9 pg. 117
- World maps
- Calculators
- Time zone references
- Atlases
- Real-world scenarios

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

Measurements

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

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

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

- 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

- 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

- 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
Approximations and Errors - Approximating quantities in measurements

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

- 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

- 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
- 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

What are excise duty and VAT?
How do we calculate total taxes on imported goods?

- Master Mathematics Grade 9 pg. 131
- Digital devices
- ETR receipts
- Tax rate tables
- Calculators
- Reference materials
- 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 tests
- Observation - Oral questions - Written assignments

Measurements

Approximations and Errors - Determining errors using estimations and actual measurements

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

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

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

What is error and how do we calculate it?

- Master Mathematics Grade 9 pg. 146
- Measuring cylinders
- Water bottles
- Weighing scales
- Calculators
- Reference materials

- Observation - Oral questions - Written assignments

Measurements

Approximations and Errors - Calculating percentage error
Approximations and Errors - Percentage error in real-life situations
Approximations and Errors - Complex applications and problem-solving

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

- 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
- Complex scenarios
- Charts
- Real-world case studies

- Observation - Oral questions - Written tests