Data Handling and Probability

5.1 Data Presentation and Interpretation - Drawing bar graphs (2)

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

-Draw bar graphs of data
-Appreciate the use of bar graphs in real life situations

-Collect data from their own experiences, e.g., shoe sizes or heights
-Choose a suitable scale to represent the information on a bar graph
-Share work with other learners in class

What are the different ways of representing data?

MENTOR mathematics Learner's Book Grade 8 pg. 233
-Graph paper
-Ruler
MENTOR mathematics Learner's Book Grade 8 pg. 235

-Observation -Written assignments

Data Handling and Probability

5.1 Data Presentation and Interpretation - Interpreting bar graphs (1)
5.1 Data Presentation and Interpretation - Drawing line graphs (2)
5.1 Data Presentation and Interpretation - Drawing line graphs (2)
5.1 Data Presentation and Interpretation - Interpreting line graphs (1)
5.1 Data Presentation and Interpretation - Mode of discrete data (1)
5.1 Data Presentation and Interpretation - Mean of discrete data (2)

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

-Interpret bar graphs of data
-Show interest in analyzing data

-Study given bar graphs
-Interpret data from bar graphs by answering questions
-Share findings with other learners in class

What are the different ways of representing data?

MENTOR mathematics Learner's Book Grade 8 pg. 236
-Bar graphs
MENTOR mathematics Learner's Book Grade 8 pg. 238
-Graph paper
-Ruler
MENTOR mathematics Learner's Book Grade 8 pg. 240
MENTOR mathematics Learner's Book Grade 8 pg. 241
-Line graphs
MENTOR mathematics Learner's Book Grade 8 pg. 243
-Digital devices
MENTOR mathematics Learner's Book Grade 8 pg. 246
-Tape measure

-Observation -Written assignments

Data Handling and Probability

5.1 Data Presentation and Interpretation - Mean of discrete data (2)
5.1 Data Presentation and Interpretation - Median of discrete data (1)
5.2 Probability - Events involving chance (1)
5.2 Probability - Chance experiments (2)
5.2 Probability - Chance experiments (2)

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

-Calculate the mean of a set of discrete data
-Value the use of mean in summarizing data

-Calculate mean of different sets of data
-Share work with other learners in class

How do we determine the mean of data?

MENTOR mathematics Learner's Book Grade 8 pg. 248
-Calculator
MENTOR mathematics Learner's Book Grade 8 pg. 249
-Number cards
-Digital devices
MENTOR mathematics Learner's Book Grade 8 pg. 256
MENTOR mathematics Learner's Book Grade 8 pg. 258
-Coins
MENTOR mathematics Learner's Book Grade 8 pg. 259
-Dice
-Marbles of different colors

-Observation -Written assignments

Data Handling and Probability

5.2 Probability - Experimental probability outcomes (1)
5.2 Probability - Probability outcomes in fractions (1)
5.2 Probability - Probability outcomes in decimals or percentages (2)
5.2 Probability - Probability outcomes in decimals or percentages (2)
5.2 Probability - Probability outcomes in decimals or percentages (2)

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

-Write the experimental probability outcomes
-Show interest in determining chance

-Roll a die multiple times
-Record the number that appears on the top face of the die
-Determine the number of possible outcomes
-State each possible outcome
-Share results with other learners in class

Why is probability important in real life situations?

MENTOR mathematics Learner's Book Grade 8 pg. 260
-Dice
MENTOR mathematics Learner's Book Grade 8 pg. 262
MENTOR mathematics Learner's Book Grade 8 pg. 263
-Coins
MENTOR mathematics Learner's Book Grade 8 pg. 264
-Marbles of different colors

-Observation -Written assignments

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
Integers - Combined operations on integers and applications
Cubes and Cube Roots - Cubes of numbers by multiplication

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

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

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

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

- Master Mathematics Grade 9 pg. 1
- Number cards
- Counters with positive signs
- Charts
- Number lines
- Number cards with negative signs
- Thermometers
- Counters
- Digital devices
- Internet access
- Drawing materials
- Charts showing triangles
- Reference books
- Master Mathematics Grade 9 pg. 12
- Dice or cubes

- Observation - Oral questions - Written assignments

Numbers

Cubes and Cube Roots - Cubes of numbers from mathematical tables
Cubes and Cube Roots - Cube roots by factor method
Cubes and Cube Roots - Cube roots from mathematical tables
Cubes and Cube Roots - Using calculators and real-life applications

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

- Explain how to read mathematical tables for cubes
- Determine cubes of numbers from mathematical tables
- Appreciate the use of mathematical tables

- Study the table of cubes and compare with squares tables
- Locate numbers in rows and columns to read cubes
- Express numbers in the form A × 10ⁿ where needed
- Use the ADD column for more accurate values

How do we use mathematical tables to find cubes of numbers?

- Master Mathematics Grade 9 pg. 12
- Mathematical tables
- Calculators
- Charts showing sample tables
- Number cards
- Charts
- Factor trees diagrams
- Reference books
- Digital devices
- Models of cubes
- Internet access

- Observation - Oral questions - Written assignments

Numbers

Indices and Logarithms - Expressing numbers in index form
Indices and Logarithms - Multiplication and division laws of indices
Indices and Logarithms - Power law and zero indices

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

- Define base and index
- Express numbers in index form using prime factors
- Appreciate the use of index notation

- Use factor trees to express numbers as products of prime factors
- Count the number of times each prime factor appears
- Express numbers in the form xⁿ where x is the base and n is the index
- Solve for unknown bases or indices

How do we express numbers in powers?

- Master Mathematics Grade 9 pg. 24
- Number cards
- Factor tree charts
- Drawing materials
- Charts
- Mathematical tables
- Calculators
- Reference books

- Observation - Oral questions - Written assignments

Numbers

Indices and Logarithms - Negative and fractional indices
Indices and Logarithms - Applications of laws of indices

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

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

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

How do we work with negative and fractional indices?

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

- Observation - Oral questions - Written tests

Numbers

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

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
- Calculators
- Real objects for sharing

- 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

- 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

How do we determine if ratios are related?

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

- 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
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:

- 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
- Charts
- Real-world work scenarios
- Charts showing different scenarios
- Reference materials

- Observation - Oral questions - Written tests

Numbers
Algebra

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

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

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

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

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

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

- Observation - Oral questions - Written assignments

Algebra

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

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

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

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

What is the order of a matrix?

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

- Observation - Oral questions - Written tests

Algebra

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

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

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

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

When can we add or subtract matrices?

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

- Observation - Oral questions - Written assignments

Algebra

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

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

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

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

How do we subtract matrices?

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

- Observation - Oral questions - Written assignments

Algebra

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

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

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

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

How do we calculate the slope or gradient?

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

- Observation - Oral questions - Written tests

Algebra

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

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

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

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

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

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

- Observation - Oral questions - Written assignments

Algebra

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

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

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

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

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

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

- Observation - Oral questions - Written assignments

Algebra

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

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

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

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

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

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

- Observation - Oral questions - Written tests

Algebra

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

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

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

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

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

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

- Observation - Oral questions - Written assignments

Algebra

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

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

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

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

How do we find the equation from the intercepts?

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

- Observation - Oral questions - Written assignments

Algebra

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

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

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

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

How do we represent inequalities on a graph?

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

- Observation - Oral questions - Written tests

Algebra
Measurements
Measurements

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

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

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

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

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

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

- Observation - Oral questions - Written tests - Project work

Measurements

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

- 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
- Cuboid models
- Manila paper
- Scissors
- Calculators

- Observation - Oral questions - Written assignments

Measurements

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

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

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

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

How do we find the surface area of a pyramid?

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

- Observation - Oral questions - Written assignments

Measurements

Area - Area of segments of circles
Area - Surface area of cones
Area - Surface area of spheres and hemispheres

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

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

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

How do we calculate the area of a segment?

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

- 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
Volume - Volume of rectangular-based pyramids
Volume - Volume of triangular-based pyramids

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

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

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

How do we find the volume of a pyramid?

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

- Observation - Oral questions - Written assignments

Measurements

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

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

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

- 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 is a cone related to a cylinder?

- Master Mathematics Grade 9 pg. 102
- Cone and cylinder models
- Water
- Digital devices
- Internet access
- Cone models
- Calculators
- Graph paper
- Reference materials
- Pyramid models
- Cutting tools
- Rulers

- Observation - Oral questions - Written tests

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

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

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

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

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

How do we calculate the volume of a hemisphere?

- Master Mathematics Grade 9 pg. 102
- Hemisphere models
- Calculators
- Real objects
- Reference materials
- Master Mathematics Grade 9 pg. 111
- Weighing balances
- Various objects
- Conversion charts
- Conversion tables
- 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
Mass, Volume, Weight and Density - Introduction to density

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

- 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
- Weighing balances
- Measuring cylinders
- Water
- Containers

- Observation - Oral questions - Written tests

Measurements

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

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

- Observation - Oral questions - Written assignments

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

- 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
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 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
- Field for activity
- Stopwatches
- Measuring tools
- Formula charts
- Road safety materials

- Observation - Oral questions - Written tests

Measurements

Time, Distance and Speed - Identifying longitudes on the globe
Time, Distance and Speed - Relating longitudes to time
Time, Distance and Speed - Calculating time differences between places

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
- Time zone maps
- Calculators
- Digital devices
- Time zone charts
- Reference books

- Observation - Oral questions - Written assignments

Measurements

Time, Distance and Speed - Determining local time of places along different longitudes
Money - Identifying currencies of different countries

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

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

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

How do we find local time at different longitudes?

- Master Mathematics Grade 9 pg. 117
- World maps
- Calculators
- Time zone references
- Atlases
- Real-world scenarios
- Master Mathematics Grade 9 pg. 131
- Digital devices
- Internet access
- Pictures of currencies
- Reference materials

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

Measurements

Money - Converting foreign currency to Kenyan shillings
Money - Converting Kenyan shillings to foreign currency and buying/selling rates
Money - Export duty on goods

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

- Define exchange rate
- Read and interpret exchange rate tables
- Convert foreign currencies to Kenyan shillings
- Apply exchange rates accurately

- Discuss dialogue about using foreign currency in Kenya
- Understand that each country has its own currency
- Learn about exchange rates and their purpose
- Study currency conversion tables (Table 3.5.1)
- Convert US dollars, Euros, and other currencies to Ksh
- Use formula: Ksh amount = Foreign amount × Exchange rate
- Solve practical problems involving conversion

How do we convert foreign currency to Kenya shillings?

- Master Mathematics Grade 9 pg. 131
- Currency conversion tables
- Calculators
- Charts
- Reference materials
- Exchange rate tables
- Real-world scenarios
- Reference books
- Examples of export goods

- Observation - Oral questions - Written tests

Measurements

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

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

What is import duty and how is it calculated?

- Master Mathematics Grade 9 pg. 131
- Calculators
- Import duty examples
- Charts
- Reference books
- Digital devices
- ETR receipts
- Tax rate tables
- Reference materials
- Comprehensive examples
- Charts showing tax flow

- Observation - Oral questions - Written assignments

Measurements

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

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

- 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
- Open ground for activities
- Reference books

- Observation - Oral questions - Practical activities

Measurements
4.0 Geometry

Approximations and Errors - Percentage error in real-life situations
Approximations and Errors - Complex applications and problem-solving
4.1 Coordinates and Graphs - Plotting points on a Cartesian plane

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

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

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

Why are accurate approximations important in real life?

- Master Mathematics Grade 9 pg. 146
- Calculators
- Real-world scenarios
- Case studies
- Reference materials
- Complex scenarios
- Charts
- Reference books
- Real-world case studies
- Master Mathematics Grade 9 pg. 152
- Graph papers/squared books
- Rulers
- Pencils
- Digital devices

- Observation - Oral questions - Written assignments

4.0 Geometry

4.1 Coordinates and Graphs - Drawing straight line graphs given equations
4.1 Coordinates and Graphs - Drawing parallel lines on the Cartesian plane
4.1 Coordinates and Graphs - Relating gradients of parallel lines
4.1 Coordinates and Graphs - Drawing perpendicular lines on the Cartesian plane
4.1 Coordinates and Graphs - Relating gradients of perpendicular lines and applications

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

- Explain the steps for generating a table of values from an equation
- Draw straight line graphs accurately from linear equations
- Appreciate the relationship between equations and graphs

The learner is guided to:
- Generate a table of values for given linear equations
- Plot the points on a Cartesian plane
- Draw straight lines passing through the plotted points
- Share and discuss their working with other members in class

How do we represent linear equations graphically?

- Master Mathematics Grade 9 pg. 154
- Graph papers
- Rulers
- Pencils
- Mathematical tables
- Master Mathematics Grade 9 pg. 156
- Set squares
- Master Mathematics Grade 9 pg. 158
- Calculators
- Digital devices
- Master Mathematics Grade 9 pg. 160
- Protractors
- Master Mathematics Grade 9 pg. 162
- Real-life graph examples

- Observation - Oral questions - Written tests

4.0 Geometry

4.2 Scale Drawing - Compass bearing
4.2 Scale Drawing - True bearings
4.2 Scale Drawing - Determining the bearing of one point from another (1)
4.2 Scale Drawing - Determining the bearing of one point from another (2)
4.2 Scale Drawing - Locating a point using bearing and distance (1)
4.2 Scale Drawing - Locating a point using bearing and distance (2)

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

- Identify the four main and four secondary compass directions
- Measure and express compass bearings correctly
- Develop interest in using compass directions to locate places

The learner is guided to:
- Draw a compass showing N, S, E, W directions
- Show NE, SE, SW, NW on the same compass
- Measure angles between main and secondary directions
- Identify compass bearings of given points

How do we use compass directions to locate places?

- 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
- Graph papers
- Atlas/Maps of Kenya
- Digital devices
- Master Mathematics Grade 9 pg. 173
- Plain papers

- Observation - Oral questions