Numbers

Integers - Addition of positive integers to positive integers

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

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

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

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

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

- Observation - Oral questions - Written assignments

Numbers

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

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

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

- 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 represent and add negative numbers in everyday situations?

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

- Observation - Oral questions - Written tests

Numbers

Integers - Multiplication and division of integers
Integers - Combined operations on integers and applications

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

- State the rules for multiplication and division of integers
- Multiply and divide integers accurately
- Appreciate the importance of integer operations

- Draw triangles divided into three parts labeled P and N to show multiplication rules
- Use the same triangle method for division
- Work out problems involving profit and payments
- Watch videos on multiplication and division of integers

What are the rules for multiplying and dividing integers?

- Master Mathematics Grade 9 pg. 1
- Drawing materials
- Charts showing triangles
- Digital devices
- Internet access
- Number cards
- Reference books

- Observation - Oral questions - Written tests

Numbers

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

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

- Define the cube of a number
- Work out cubes of whole numbers, decimals and fractions by multiplication
- Show interest in finding cubes of numbers

- Use stacks of dice to demonstrate the concept of cubes
- Count dice representing length, width, and height
- Multiply numbers three times to find cubes
- Work out cubes of mixed numbers and fractions

How do we work out the cubes of numbers?

- Master Mathematics Grade 9 pg. 12
- Dice or cubes
- Number cards
- Charts
- Drawing materials
- Mathematical tables
- Calculators
- Charts showing sample tables
- Factor trees diagrams

- Observation - Oral questions - Written tests

Numbers

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 the process of reading cube roots from tables
- Determine cube roots from mathematical tables
- Appreciate the use of mathematical tables

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

- Locate numbers in the body of cube tables
- Move horizontally and vertically to find corresponding cube roots
- Express large numbers in the form A × 10ⁿ where n is a multiple of 3
- Use the ADD column for precision
- 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

How do we find cube roots using mathematical tables?
Where do we apply cubes and cube roots in real-life situations?

- Master Mathematics Grade 9 pg. 12
- Mathematical tables
- Charts
- Reference books
- Master Mathematics Grade 9 pg. 12
- Calculators
- Digital devices
- Models of cubes
- Internet access

- Observation - Oral questions - Written assignments
- Observation - Oral questions - Written tests - Project work

Numbers

Indices and Logarithms - Expressing numbers in index form
Indices and Logarithms - Multiplication and division laws of 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

- Observation - Oral questions - Written assignments

Numbers

Indices and Logarithms - Power law and zero indices

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

- Explain the power law for indices
- Apply the power law and zero indices to simplify expressions
- Appreciate the patterns in indices

- 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

Why does any number to power zero equal one?

- Master Mathematics Grade 9 pg. 24
- Calculators
- Charts
- Reference books

- Observation - Oral questions - Written assignments

Numbers

Indices and Logarithms - Negative and fractional 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

- Observation - Oral questions - Written tests

Numbers

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

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

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

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

- 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
- 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 we use indices to solve equations?
How do powers of 10 relate to common logarithms?

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

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

Numbers

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

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

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

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

What are proportions and how do we share quantities fairly?

- Master Mathematics Grade 9 pg. 33
- Number cards
- Charts
- Reference materials

- Observation - Oral questions - Written assignments

Numbers

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

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

- 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
- Number lines
- Drawing materials
- Reference books

- Observation - Oral questions - Written tests

Numbers

Compound Proportions and Rates of Work - Continuous proportion

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

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

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

How do we work with continuous proportions?

- Master Mathematics Grade 9 pg. 33
- Number cards
- Charts
- Calculators

- Observation - Oral questions - Written tests

Numbers

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

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

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

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

- 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
- 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 use ratios to solve compound proportion problems?
How do we maintain constant ratios in different situations?

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

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

Numbers

Compound Proportions and Rates of Work - Introduction to rates of work

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

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

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

Why do more workers complete work faster?

- Master Mathematics Grade 9 pg. 33
- Stopwatch or timer
- Classroom furniture
- Charts

- Observation - Oral questions - Written assignments

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

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

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

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

- 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

- Observation - Oral questions - Written assignments
- Observation - Oral questions - Written tests - Project work

Algebra

Matrices - Identifying a matrix

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

- Define a matrix and identify rows and columns
- Identify matrices in different situations
- Appreciate the organization of items in rows and columns

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

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

- Master Mathematics Grade 9 pg. 42
- Charts showing matrices
- Calendar samples
- Tables and schedules

- Observation - Oral questions - Written assignments

Algebra

Matrices - Determining the order of a matrix

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
Matrices - Addition of matrices

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

- Explain the process of adding matrices
- Add compatible matrices accurately
- Show systematic approach to matrix addition

- 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
- Identify elements in corresponding positions
- Add matrices by adding corresponding elements
- Work out matrix addition problems
- Verify that resultant matrix has same order as original matrices

How do we compare elements in different matrices?
How do we add 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
- Master Mathematics Grade 9 pg. 42
- Number cards with matrices
- Charts
- Calculators

- Observation - Oral questions - Written tests

Algebra

Matrices - Subtraction of matrices

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

- Observation - Oral questions - Written assignments

Algebra

Matrices - Combined operations and applications

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

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

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

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

- Master Mathematics Grade 9 pg. 42
- Digital devices
- Real-world data tables
- Reference materials

- Observation - Oral questions - Written tests - Project work

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
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 the four types of gradients
- Distinguish between positive, negative, zero and undefined gradients
- Show interest in gradient patterns

- 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
- 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

How do we calculate the slope or gradient?
What are the different types of gradients?

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

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

- Observation - Oral questions - Written assignments

Algebra

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

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

- Identify the steps in finding equations from coordinates
- Work out equations of lines passing through two points
- Appreciate the application to geometric shapes

- Find equations of lines through various point pairs
- Determine equations of sides of triangles and parallelograms
- Practice with different types of coordinate pairs
- Verify equations by substitution

How do we apply equations of lines to geometric shapes?

- Master Mathematics Grade 9 pg. 57
- Graph paper
- Plotting tools
- Geometric shapes
- Calculators

- Observation - Oral questions - Written tests

Algebra

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 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

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

- Define the standard form y = mx + c
- Express linear equations in the form y = mx + c
- Show understanding of equation transformation

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

How do we use point-gradient method in different situations?
How do we write equations in the form y = mx + c?

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

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

Algebra

Equations of a Straight Line - Interpreting y = mx + c

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

- Observation - Oral questions - Written assignments

Algebra

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 m and c from equations in standard form
- Determine gradient and y-intercept from various equations
- Appreciate the relationship between equation and graph

- Complete tables showing equations, gradients, and y-intercepts
- Extract m and c values from equations
- Convert equations to y = mx + c form first if needed
- Verify values by graphing

How do we read gradient and y-intercept from equations?

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

- Observation - Oral questions - Written tests

Algebra

Equations of a Straight Line - Determining x-intercepts

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

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

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

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

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

- Observation - Oral questions - Written assignments

Algebra

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

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

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

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

- 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
- 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

What is the y-intercept and how do we find it?
How do we find the equation from the intercepts?

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

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

Algebra

Linear Inequalities - Solving linear inequalities in one unknown
Linear Inequalities - Multiplication and division by negative numbers

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

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

- Discuss inequality statements and their meanings
- Substitute integers to test inequality truth
- Solve inequalities by isolating the unknown
- Verify solutions by substitution

How do we solve inequalities with one unknown?

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

- Observation - Oral questions - Written tests

Algebra

Linear Inequalities - Graphical representation in one unknown

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

- Observation - Oral questions - Written tests

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
Algebra
5.0 Data Handling and Probability

Linear Inequalities - Graphical representation in two unknowns
Linear Inequalities - Applications to real-life situations
5.1 Data Interpretation (Grouped Data) - Determining appropriate class width for grouping data

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

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

- 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
- 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 represent two-variable inequalities on graphs?
How do we use inequalities to solve real-life problems?

- Master Mathematics Grade 9 pg. 72
- Graph paper
- Rulers and plotting tools
- Digital devices
- Reference materials
- Master Mathematics Grade 9 pg. 72
- Digital devices
- Real-world scenarios
- Charts
- Reference materials
- Master Mathematics Grade 9 pg. 224
- Writing materials
- Calculators
- Chart papers

- Observation - Oral questions - Written tests
- Observation - Oral questions - Written tests - Project work

5.0 Data Handling and Probability

5.1 Data Interpretation (Grouped Data) - Drawing frequency distribution tables of grouped data
5.1 Data Interpretation (Grouped Data) - Identifying the modal class of grouped data

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

- Explain the components of a frequency distribution table
- Draw frequency distribution tables for grouped data using tally marks
- Show interest in organizing data systematically

The learner is guided to:
- Discuss suitable class width for given data
- Represent data in each class using tally marks
- Count tally marks and record as frequency
- Complete frequency distribution tables

How do we organize grouped data in tables?

- Master Mathematics Grade 9 pg. 226
- Tally sheets
- Rulers
- Data sets
- Pencils
- Master Mathematics Grade 9 pg. 228
- Frequency distribution tables
- Digital devices
- Reference materials

- Class activities - Written tests - Observation

5.0 Data Handling and Probability

5.1 Data Interpretation (Grouped Data) - Calculating the mean of grouped data (1)
5.1 Data Interpretation (Grouped Data) - Calculating the mean of grouped data (2)
5.1 Data Interpretation (Grouped Data) - Determining the median of grouped data (1)

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

- Explain the process of finding mean of grouped data
- Calculate midpoints of classes
- Show interest in organizing data to find the mean

The learner is guided to:
- Group given data into classes
- Add class limits and divide by 2 to get midpoints
- Work out products of midpoints and frequencies (fx)
- Find the sum of fx values

How do we find the mean of grouped data?

- Master Mathematics Grade 9 pg. 230
- Calculators
- Frequency tables
- Writing materials
- Mathematical tables
- Data sets
- Charts
- Master Mathematics Grade 9 pg. 232
- Reference materials
- Digital devices

- Observation - Written tests

5.0 Data Handling and Probability

5.1 Data Interpretation (Grouped Data) - Determining the median of grouped data (2)
5.1 Data Interpretation (Grouped Data) - Determining the median of grouped data (3)

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

- Explain the formula for calculating median of grouped data
- Identify L, N, cf₁, fm and C from given data
- Appreciate the components of the median formula

The learner is guided to:
- Discuss the median formula and its components
- Identify the lower class boundary (L) of median class
- Determine cumulative frequency of class above median class
- Identify frequency of median class and class width

How do we use the median formula?

- Master Mathematics Grade 9 pg. 234
- Calculators
- Formula charts
- Frequency tables
- Master Mathematics Grade 9 pg. 236
- Data sets
- Writing materials
- Practice worksheets

- Class activities - Oral questions - Written assignments

5.0 Data Handling and Probability

5.2 Probability - Experiments involving equally and likely outcomes
5.2 Probability - Range of probability of an event
5.2 Probability - Identifying mutually exclusive events

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

- Define equally likely outcomes
- Perform experiments to determine equally likely outcomes
- Appreciate that equally likely outcomes have equal chances of happening

- State that the sum of all probabilities equals 1
- Determine the range of probability as 0 ≤ P(A) ≤ 1
- Show interest in understanding that P(A) + P(A') = 1

The learner is guided to:
- Toss a coin and note the side facing up
- Predict and observe outcomes of coin tossing
- Discuss whether outcomes are predictable
- Work out probabilities using dice and other objects
The learner is guided to:
- Toss a coin and work out probability of head and tail
- Add probabilities of all outcomes
- Use dice to determine probabilities of all faces
- Discuss that probability ranges from 0 to 1

What are equally likely outcomes?
What is the range of probability?

- Master Mathematics Grade 9 pg. 239
- Coins
- Dice
- Triangular pyramids
- Baskets and pens
- Master Mathematics Grade 9 pg. 241
- Coins
- Dice
- Calculators
- Charts showing probability range
- Master Mathematics Grade 9 pg. 243
- Pictures of referees
- Real-life scenarios
- Charts

- Observation - Oral questions - Practical activities
- Class activities - Written tests - Oral questions

5.0 Data Handling and Probability

5.2 Probability - Experiments of single chance involving mutually exclusive events

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

- Explain the addition law of probability P(A or B) = P(A) + P(B)
- Calculate probabilities of mutually exclusive events
- Show interest in applying the addition law to solve problems

The learner is guided to:
- Pick pens from a closed bag and note colors
- Work out probabilities using the word "OR"
- Apply the formula P(A or B) = P(A) + P(B)
- Solve problems involving mutually exclusive events

How do we calculate probabilities of mutually exclusive events?

- Master Mathematics Grade 9 pg. 244
- Colored pens
- Bags
- Dice
- Number cards
- Calculators

- Class activities - Written tests - Practical exercises

5.0 Data Handling and Probability

5.2 Probability - Experiments involving independent events
5.2 Probability - Drawing tree diagrams for single outcomes

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

- Define independent events
- Apply the multiplication law P(A and B) = P(A) × P(B)
- Appreciate that independent events do not affect each other

The learner is guided to:
- Toss a coin and die together and note outcomes
- Discuss whether coin outcome affects die outcome
- Understand that "and" in probability means multiplication
- Solve problems involving independent events

What are independent events?

- Master Mathematics Grade 9 pg. 246
- Coins
- Dice
- Colored balls
- Baskets
- Calculators
- Master Mathematics Grade 9 pg. 248
- Drawing materials
- Chart papers
- Rulers

- Observation - Written assignments - Written tests