Numbers

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

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

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

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

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

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

- Observation - Oral questions - Written assignments

Numbers

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

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

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

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

How do we work with integers of different signs?

- Master Mathematics Grade 9 pg. 1
- Counters
- Number lines
- Digital devices
- Internet access
- Drawing materials
- Charts showing triangles

- Observation - Oral questions - Written assignments

Numbers

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:

- 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

- Observation - Oral questions - Written assignments - Project work

Numbers

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:

- 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

- Observation - Oral questions - Written assignments

Numbers

Cubes and Cube Roots - Cube roots from mathematical tables

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

- 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

How do we find cube roots using mathematical tables?

- Master Mathematics Grade 9 pg. 12
- Mathematical tables
- Charts
- Reference books

- Observation - Oral questions - Written assignments

Numbers

Cubes and Cube Roots - Using calculators and real-life applications

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

- Observation - Oral questions - Written tests - Project work

Numbers

Indices and Logarithms - Expressing numbers in index form

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

- Observation - Oral questions - Written assignments

Numbers

Indices and Logarithms - Multiplication and division laws of indices

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

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

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

What are the laws of indices?

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

- Observation - Oral questions - Written tests

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

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

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

- 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)

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

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

- Observation - Oral questions - Written assignments

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

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

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

How do we use ratios to solve compound proportion problems?

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

- Observation - Oral questions - Written assignments

Numbers

Compound Proportions and Rates of Work - Compound proportions (continued)

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

- 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

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

- Observation - Oral questions - Written assignments

Numbers

Compound Proportions and Rates of Work - More rate of work problems

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

- Identify different types of rate problems
- Determine resources needed for various tasks
- Appreciate practical applications of mathematics

- Calculate tractors needed for field cultivation
- Determine teachers required for lesson allocation
- Work out lorries needed for transportation
- Solve water pump flow rate problems

How do we apply rates of work to different real-life situations?

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

- Observation - Oral questions - Written tests

Numbers

Compound Proportions and Rates of Work - Applications of rates of work

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

- Observation - Oral questions - Written assignments

Numbers

Compound Proportions and Rates of Work - Using IT and comprehensive applications

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

- 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

- 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 we use technology to solve compound proportion and rate problems?

- Master Mathematics Grade 9 pg. 33
- Digital devices
- Internet access
- Educational games
- Reference materials

- 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

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

- Observation - Oral questions - Written tests

Algebra

Matrices - Determining compatibility for addition and subtraction

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

- Observation - Oral questions - Written assignments

Algebra

Matrices - Addition of matrices

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

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

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

How do we add matrices?

- Master Mathematics Grade 9 pg. 42
- Number cards with matrices
- Charts
- Calculators

- 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

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

- Observation - Oral questions - Written tests

Algebra

Equations of a Straight Line - Determining gradient from two known points

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

- State the formula for gradient from two points
- Determine gradient from two known points on a line
- Appreciate the importance of coordinates

- Plot points on a Cartesian plane
- Count squares to find vertical and horizontal distances
- Use the formula m = (y₂ - y₁)/(x₂ - x₁)
- Work out gradients from given coordinates

How do we find the gradient when given two points?

- Master Mathematics Grade 9 pg. 57
- Graph paper
- Rulers
- Plotting tools
- Digital devices

- Observation - Oral questions - Written assignments

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

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

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

- Observation - Oral questions - Written tests

Algebra

Equations of a Straight Line - Expressing in the form y = mx + c

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

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

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

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

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

- Observation - Oral questions - Written assignments

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

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 - 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

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

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

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

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

- Observation - Oral questions - Written tests

Algebra

Equations of a Straight Line - Finding equations from intercepts

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

- Observation - Oral questions - Written assignments

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

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

- Observation - Oral questions - Written assignments

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

Linear Inequalities - Graphical representation in two unknowns

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

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

How do we represent two-variable inequalities on graphs?

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

- Observation - Oral questions - Written tests

Algebra

Linear Inequalities - Applications to real-life situations

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

- Observation - Oral questions - Written tests - Project work

Measurements

Area - Area of a pentagon

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

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

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

How do we find the area of a pentagon?

- Master Mathematics Grade 9 pg. 85
- Rulers and protractors
- Compasses
- Graph paper
- Charts showing pentagons

- Observation - Oral questions - Written assignments

Measurements

Area - Area of a hexagon

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

- Observation - Oral questions - Written tests

Measurements

Area - Surface area of triangular prisms

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

- Identify triangular prisms
- Sketch nets of triangular prisms
- Calculate surface area of triangular prisms

- Identify differences between triangular and rectangular prisms
- Sketch nets of triangular prisms
- Identify all faces from the net
- Calculate area of each face
- Add all areas to get total surface area

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

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

- Observation - Oral questions - Written assignments

Measurements

Area - Surface area of rectangular prisms

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

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

- Observation - Oral questions - Written assignments

Measurements

Area - Surface area of square and rectangular pyramids

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

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

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

How do we calculate surface area of different pyramids?

- Master Mathematics Grade 9 pg. 85
- Graph paper
- Calculators
- Pyramid models
- Charts

- Observation - Oral questions - Written tests

Measurements

Area - Area of sectors of circles

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

- 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

How do we find the area of a sector?

- Master Mathematics Grade 9 pg. 85
- Compasses and rulers
- Protractors
- Digital devices
- Internet access

- Observation - Oral questions - Written assignments

Measurements

Area - Area of segments of circles

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

- Observation - Oral questions - Written tests

Measurements

Area - Surface area of cones

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

- Define a cone and identify its parts
- Derive the formula for curved surface area
- Calculate surface area of solid cones

- Draw and cut a circle from manila paper
- Divide into two parts and fold to make a cone
- Identify slant height and radius
- Derive formula: πrl for curved surface
- Calculate total surface area: πrl + πr²
- Solve practical problems

How do we find the surface area of a cone?

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

- Observation - Oral questions - Written assignments

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

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

- Observation - Oral questions - Written assignments