Numbers

Integers – Addition of integers

By the end of the lesson, the learner should be able to:
- perform addition of positive and negative integers using a number line;
- apply addition of integers to real-life situations;
- show interest in using integers in daily life.

In groups, learners are guided to:
- Discuss with peers and use number lines to add positive and negative integers
- Play games using number cards to practise addition of integers
- Solve real-life problems involving temperature increases using addition of integers

How do we carry out addition of integers in real-life situations?

- Mentor Mathematics Grade 9 pg. 1–2
- Number lines
- Number cards and charts
- Digital devices

- Oral questions - Observation - Written exercises

Numbers

Integers – Subtraction of integers
Integers – Multiplication of integers
Integers – Division of integers

By the end of the lesson, the learner should be able to:
- perform subtraction of integers using a number line;
- apply subtraction of integers to real-life situations;
- appreciate the role of integers in everyday contexts.

In groups, learners are guided to:
- Use number lines to subtract integers (positive from positive, positive from negative and vice versa)
- Discuss real-life temperature-drop problems and record integer differences
- Solve exercises involving subtraction of integers in groups

How do we apply subtraction of integers in real-life situations?

- Mentor Mathematics Grade 9 pg. 2–3
- Number lines
- Thermometer charts
- Digital devices
- Mentor Mathematics Grade 9 pg. 3–5
- Multiplication tables charts
- Number cards
- Mentor Mathematics Grade 9 pg. 5–6

- Oral questions - Written exercises - Observation

Numbers

Integers – Combined operations on integers
Integers – Real-life applications; use of IT tools

By the end of the lesson, the learner should be able to:
- work out combined operations on integers in the correct order;
- apply order of operations (BODMAS) to evaluate expressions involving integers;
- appreciate the importance of the correct order of operations.

In groups, learners are guided to:
- Work out combined operations using BODMAS with integer values
- Play games involving picking integer cards and performing combined operations in the correct order
- Discuss the effect of changing the order of operations through worked examples

Why is it important to follow the correct order when evaluating combined operations on integers?

- Mentor Mathematics Grade 9 pg. 6–7
- Number cards
- Calculators / digital devices
- Mentor Mathematics Grade 9 pg. 7–8
- Thermometer / temperature charts
- Calculators / digital devices
- Internet access

- Written assignments - Oral questions - Observation

Numbers

Cubes and Cube Roots – Cubes by multiplication
Cubes and Cube Roots – Cubes from mathematical tables
Cubes and Cube Roots – Cube roots by factor method

By the end of the lesson, the learner should be able to:
- work out cubes of numbers by multiplying a number by itself three times;
- apply cubes of numbers to real-life situations such as finding volume;
- appreciate the concept of cubing numbers.

In groups, learners are guided to:
- Use stacks of unit cubes to demonstrate the concept of cubing a number
- Work out cubes of whole numbers and fractions by direct multiplication
- Solve real-life problems involving cubes (e.g. finding the volume of a cubic container)

How do we work out the cube of a number?

- Mentor Mathematics Grade 9 pg. 9–12
- Unit cube models / stacks
- Digital devices
- Mentor Mathematics Grade 9 pg. 12–17
- Mathematical tables (table of cubes)
- Mentor Mathematics Grade 9 pg. 17–18
- Factor tree charts

- Oral questions - Written exercises - Observation

Numbers

Cubes and Cube Roots – Cube roots from mathematical tables

By the end of the lesson, the learner should be able to:
- determine cube roots of numbers from mathematical tables;
- use the ADD column to refine cube root readings using mean differences;
- appreciate the efficiency of mathematical tables in finding cube roots.

In groups, learners are guided to:
- Identify the cube root table and understand its structure (rows, columns, ADD section)
- Follow step-by-step procedures to read cube root values from the table of cubes
- Practise reading cube roots of various numbers, using mean differences where necessary

How do we use mathematical tables to find the cube root of a number?

- Mentor Mathematics Grade 9 pg. 18–19
- Mathematical tables (table of cubes)
- Digital devices

- Written tests - Oral questions - Observation

Numbers

Cubes and Cube Roots – Using a calculator

By the end of the lesson, the learner should be able to:
- use a calculator to find cubes of numbers;
- use a calculator to determine cube roots of numbers;
- appreciate the use of technology in computing cubes and cube roots.

In groups, learners are guided to:
- Demonstrate how to use the cube (x³) button on a scientific calculator to find cubes
- Demonstrate how to use the shift + x³ button to find cube roots on a calculator
- Solve exercises using a calculator and compare results with mathematical table values

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

- Mentor Mathematics Grade 9 pg. 19–20
- Scientific calculators
- Digital devices / internet access

- Oral questions - Written exercises - Observation

Numbers

Indices and Logarithms – Numbers in index form
Indices and Logarithms – Laws of indices (multiplication law)

By the end of the lesson, the learner should be able to:
- express numbers in index form in different situations;
- identify the base and index (exponent) in a given expression;
- appreciate the use of index notation to represent repeated multiplication.

In groups, learners are guided to:
- Study number cards showing repeated multiplication expressed in index form and identify the base and index
- Express repeated multiplication as indices (e.g. 2×2×2 = 2³)
- Write numbers such as 81, 64, and 125 in their simplest index form

How do we express numbers as powers?

- Mentor Mathematics Grade 9 pg. 20–22
- Number cards / index form charts
- Digital devices
- Mentor Mathematics Grade 9 pg. 22–24
- Index law charts

- Oral questions - Written exercises - Observation

Numbers

Indices and Logarithms – Laws of indices (division law; negative indices; zero index)

By the end of the lesson, the learner should be able to:
- generate and apply the division law of indices (aᵐ ÷ aⁿ = aᵐ⁻ⁿ);
- express numbers with negative indices using positive indices;
- apply the zero index rule (a⁰ = 1).

In groups, learners are guided to:
- Write numbers in expanded form and divide to verify the division law
- Derive the zero index rule from the division law (e.g. 3² ÷ 3² = 3⁰ = 1)
- Derive the rule for negative indices and re-express answers with positive indices

How do we simplify the quotient of powers with the same base?

- Mentor Mathematics Grade 9 pg. 24–26
- Index law charts
- Digital devices

- Written tests - Oral questions - Observation

Numbers

Indices and Logarithms – Laws of indices (power of a power; fractional indices)

By the end of the lesson, the learner should be able to:
- apply the power-of-a-power law ((aᵇ)ʸ = aᵇʸ) to simplify expressions;
- evaluate expressions involving fractional indices;
- appreciate the interconnection of the laws of indices.

In groups, learners are guided to:
- Write numbers raised to a power in expanded form, multiply the indices, and verify the law
- Simplify expressions using the power-of-a-power law
- Evaluate expressions with fractional indices and relate them to roots (e.g. 27^(1/3) = ∛27)

How do we simplify expressions involving a power raised to another power?

- Mentor Mathematics Grade 9 pg. 24–27
- Index law charts
- Digital devices

- Written assignments - Oral questions - Observation

Numbers

Indices and Logarithms – Powers of 10; relating to common logarithms
Indices and Logarithms – Reading logarithms from mathematical tables; using IT tools

By the end of the lesson, the learner should be able to:
- relate powers of 10 to common logarithms;
- express numbers as powers of 10;
- convert between index form and logarithmic notation.

In groups, learners are guided to:
- Study a table of powers of 10 alongside their logarithms and discuss the pattern
- Express numbers as powers of 10 and write the corresponding logarithmic notation
- Convert between index form (10ᵇ = y) and logarithmic notation (log₁₀ y = b)

How do powers of 10 relate to common logarithms?

- Mentor Mathematics Grade 9 pg. 25–27
- Powers-of-10 / logarithm reference table
- Mathematical log tables
- Digital devices
- Mentor Mathematics Grade 9 pg. 27–29
- Scientific calculators
- Digital devices / internet access

- Oral questions - Written exercises - Observation

Numbers

Compound Proportions and Rates of Work – Proportional parts

By the end of the lesson, the learner should be able to:
- divide quantities into proportional parts in real-life situations;
- express each proportional part as a fraction of the whole;
- appreciate the use of proportional parts in fair sharing.

In groups, learners are guided to:
- Cut a strip of manila paper into different equal portions and express each as a fraction of the whole length
- Work out examples of dividing quantities (money, land, goods) into proportional parts using a given ratio
- Solve real-life sharing problems involving two or more people

How do we share quantities fairly using proportional parts?

- Mentor Mathematics Grade 9 pg. 29–31
- Manila paper and scissors
- Counters / cut-out strips
- Digital devices

- Oral questions - Written exercises - Observation

Numbers

Compound Proportions and Rates of Work – Relating ratios

By the end of the lesson, the learner should be able to:
- compare two ratios by expressing them as fractions, percentages, or decimals;
- identify the greater or smaller of two given ratios;
- apply ratio comparison to real-life situations.

In groups, learners are guided to:
- Express ratios as fractions over a common denominator and compare the numerators
- Express ratios as percentages or decimals and compare
- Solve real-life problems involving ratio comparison (e.g. comparing ingredient ratios, student ratios before and after admission)

How do we compare ratios to determine which is greater?

- Mentor Mathematics Grade 9 pg. 31–33
- Ratio comparison charts
- Fraction/percentage tables
- Digital devices

- Written assignments - Oral questions - Observation

Numbers

Compound Proportions and Rates of Work – Compound proportions (concept; four numbers in proportion; continued proportion)
Compound Proportions and Rates of Work – Compound proportions using ratio method (direct variation)

By the end of the lesson, the learner should be able to:
- explain the concept of proportion and continued proportion;
- determine the fourth number when three numbers in a proportion are given;
- find the mean proportional between two numbers.

In groups, learners are guided to:
- Simplify pairs of ratios and determine whether four numbers are in proportion
- Solve for an unknown in a proportion using cross-multiplication
- Find the mean proportional between two numbers and verify through worked examples

How do we determine if four numbers are in proportion?

- Mentor Mathematics Grade 9 pg. 33–35
- Proportion charts
- Digital devices
- Mentor Mathematics Grade 9 pg. 35–36
- Worked example charts

- Oral questions - Written exercises - Observation

Numbers

Compound Proportions and Rates of Work – Compound proportions using ratio method (inverse variation)

By the end of the lesson, the learner should be able to:
- identify quantities that vary inversely in a compound proportion problem;
- correctly reverse the ratio for inverse-variation quantities;
- solve compound proportions involving both direct and inverse variation.

In groups, learners are guided to:
- Identify which quantities vary inversely in multi-variable problems
- Reverse the corresponding ratio for any inverse-variation quantity in the set-up
- Work out compound proportion problems combining both direct and inverse varying quantities

How do we handle inverse variation when solving compound proportions?

- Mentor Mathematics Grade 9 pg. 36–37
- Worked example charts
- Digital devices

- Written tests - Oral questions - Observation

Numbers

Compound Proportions and Rates of Work – Rates of work (concept; single worker or machine)

By the end of the lesson, the learner should be able to:
- define and explain rates of work in real-life situations;
- calculate the rate of work of a single person or machine (work done ÷ time taken);
- appreciate the concept of rates of work.

- Carry out a practical activity filling a basin with water using a jug, recording the rate of work (litres per minute) for each learner
- Work out the rate of work from given data using: rate = work done ÷ time taken
- Solve problems involving a single worker or machine completing a given task

How do we calculate the rate at which a task is completed?

- Mentor Mathematics Grade 9 pg. 37–38
- Water, jugs, and basin (practical)
- Rate-of-work problem cards
- Digital devices

- Oral questions - Observation - Written exercises

Numbers

Compound Proportions and Rates of Work – Rates of work (ratio method; more or fewer workers)
Compound Proportions and Rates of Work – Rates of work (multi-step and multi-variable problems)

By the end of the lesson, the learner should be able to:
- determine the time taken when the number of workers changes, using the ratio method;
- identify whether more or fewer workers leads to more or fewer days;
- apply the ratio method to solve rates-of-work problems efficiently.

In groups, learners are guided to:
- Analyse worked examples showing that more workers reduce the days needed and fewer workers increase it (inverse relationship)
- Set up the ratio method for rates of work, reversing the ratio for the inverse relationship
- Work out exercises involving tractors, men, and machines completing the same task

How does the number of workers affect the time taken to complete a task?

- Mentor Mathematics Grade 9 pg. 38–40
- Rate-of-work problem cards
- Digital devices
- Mentor Mathematics Grade 9 pg. 40–41
- Multi-step problem cards

- Written assignments - Oral questions - Observation

Numbers

Compound Proportions and Rates of Work – Real-life applications (wages, salaries, production output)

By the end of the lesson, the learner should be able to:
- apply compound proportions to solve problems involving wages and production output;
- relate the number of workers, days worked, and wages earned;
- appreciate the relevance of compound proportions in financial and production contexts.

In groups, learners are guided to:
- Work out problems linking number of workers, days worked, and total wages earned
- Solve production problems involving workers, time, and quantity produced
- Discuss and share solutions relating compound proportions to real salary and production scenarios

How do compound proportions help us solve salary and production problems in real life?

- Mentor Mathematics Grade 9 pg. 41–42
- Real-life scenario cards
- Digital devices

- Written assignments - Oral questions - Observation

Numbers
Algebra

Compound Proportions and Rates of Work – Real-life applications (food consumption, construction, mixed contexts)
Matrices — Identifying and representing matrices in different situations

By the end of the lesson, the learner should be able to:
- apply compound proportions to food-consumption and construction problems;
- solve problems involving consumption rates, number of people, and time;
- appreciate the breadth of compound proportion applications in daily life.

In groups, learners are guided to:
- Work out food-consumption problems involving bags of maize, number of animals or people, and number of days
- Solve construction problems linking workers, days, and materials used
- Compare different real-life scenarios and classify each quantity as direct or inverse

Where else do we encounter compound proportions in daily life?

- Mentor Mathematics Grade 9 pg. 42–44
- Real-life scenario cards
- Digital devices
- Mentor Mathematics Grade 9 pg. 38–40
- Football league tables / travel schedules
- Squared paper

- Written assignments - Oral questions - Observation

Algebra

Matrices — Determining the order of a matrix
Matrices — Determining the position of items in a matrix
Matrices — Determining compatibility of matrices for addition and subtraction

By the end of the lesson, the learner should be able to:
- determine the order of a matrix by counting its rows and columns;
- state the order of a matrix in the form m × n;
- appreciate how the order of a matrix describes its structure.

In groups, learners are guided to:
- Organise objects in rows and columns and state the number of rows and columns
- Determine the order of matrices of different sizes (e.g. 2×3, 3×3, 1×4)
- Write two matrices of a specified order and compare with peers

How do we describe the size of a matrix?

- Mentor Mathematics Grade 9 pg. 40–42
- Squared paper
- Digital devices
- Mentor Mathematics Grade 9 pg. 42–43
- Matrix position charts
- Mentor Mathematics Grade 9 pg. 43–44
- Compatibility charts

- Oral questions - Written exercises - Observation

Algebra

Matrices — Addition of matrices
Matrices — Subtraction of matrices
Matrices — End-of-sub-strand written assessment

By the end of the lesson, the learner should be able to:
- add compatible matrices by adding corresponding elements;
- solve real-life problems involving addition of matrices;
- show interest in using matrices to organise and combine data.

In groups, learners are guided to:
- Represent first-leg and second-leg football results as matrices and add them to get season totals
- Add matrices by adding elements in the same position
- Solve exercises on addition of matrices and find unknowns in matrix addition equations

How do we add matrices to combine real-life data?

- Mentor Mathematics Grade 9 pg. 44–45
- Football league tables
- Digital devices / internet (YouTube link)
- Mentor Mathematics Grade 9 pg. 45–47
- Matrix exercise cards
- Digital devices
- Mentor Mathematics Grade 9 pg. 38–47
- Assessment papers

- Written assignments - Oral questions - Observation

Algebra

Equations of a Straight Line — Identifying gradient; gradient as a measure of steepness

By the end of the lesson, the learner should be able to:
- identify the gradient of a straight line in real-life situations;
- describe gradient as the ratio of vertical distance to horizontal distance;
- appreciate gradient as a measure of steepness in everyday environments.

In groups, learners are guided to:
- Discuss steepness from the immediate environment: ladders, stairs, hills, and ramps
- Use an adjustable ladder inclined at different positions on a wall to demonstrate change in steepness
- Observe and climb stairs or hills and relate the experience to gradient
- Discuss positive, negative, zero, and undefined gradients from real-life examples

How do we use gradient or steepness in our daily activities?

- Mentor Mathematics Grade 9 pg. 48–50
- Adjustable ladder (practical)
- Gradient/slope diagrams
- Digital devices

- Oral questions - Observation - Written exercises

Algebra

Equations of a Straight Line — Calculating the gradient of a line from two known points (m = (y₂−y₁)/(x₂−x₁))
Equations of a Straight Line — Determining the equation of a straight line given two points

By the end of the lesson, the learner should be able to:
- derive and apply the formula m = (y₂ − y₁)/(x₂ − x₁) to calculate gradient;
- calculate the gradient of a line from two given points;
- identify whether the gradient is positive, negative, zero, or undefined.

In groups, learners are guided to:
- Study graphs and count vertical and horizontal steps between two points on a line
- Derive the gradient formula using change in y ÷ change in x
- Calculate gradients from given pairs of coordinates and from graphs
- Classify lines as having positive, negative, zero, or undefined gradients

How do we calculate the gradient of a line passing through two points?

- Mentor Mathematics Grade 9 pg. 50–52
- Graph paper / Cartesian plane charts
- Digital devices / internet (YouTube link)
- Mentor Mathematics Grade 9 pg. 52–55
- Graph paper
- Worked example charts
- Digital devices

- Written assignments - Oral questions - Observation

Algebra

Equations of a Straight Line — Determining the equation of a straight line from a known point and gradient

By the end of the lesson, the learner should be able to:
- find the equation of a straight line given one point and the gradient;
- set up the gradient equation and simplify to get the line equation;
- show interest in applying the method to different point-gradient combinations.

In groups, learners are guided to:
- Follow step-by-step procedure: use given point B(x₁,y₁) and point C(x,y), form gradient ratio equal to given m, cross-multiply and simplify
- Solve exercises given various points and gradients (including fractional and negative gradients)
- Verify answers by substituting the given point back into the derived equation

How do we find the equation of a line when we know one point and its gradient?

- Mentor Mathematics Grade 9 pg. 55–57
- Worked example charts
- Graph paper
- Digital devices

- Written assignments - Oral questions - Observation

Algebra

Equations of a Straight Line — Expressing the equation of a straight line in the form y = mx + c

By the end of the lesson, the learner should be able to:
- rearrange any linear equation into the form y = mx + c;
- identify the gradient m and y-intercept c directly from the equation;
- appreciate the usefulness of the y = mx + c form in describing a line.

In groups, learners are guided to:
- Rearrange equations step by step: isolate y by moving x-terms to the right and dividing by the coefficient of y
- Identify gradient and y-intercept from equations already in y = mx + c form
- Complete tables matching equations, gradients, and y-intercepts
- Convert equations such as 4y + 3x − 2 = 0 into y = mx + c

How do we rewrite the equation of a straight line in the form y = mx + c?

- Mentor Mathematics Grade 9 pg. 57–59
- Equation rearrangement charts
- Digital devices

- Written tests - Oral questions - Observation

Algebra

Equations of a Straight Line — Interpreting the gradient m and y-intercept c in y = mx + c
Equations of a Straight Line — Determining the x-intercept and y-intercept

By the end of the lesson, the learner should be able to:
- interpret m as the gradient and c as the y-intercept in the equation y = mx + c;
- complete tables of values and draw straight-line graphs from equations;
- recognise the use of equations of straight lines in real-life situations.

In groups, learners are guided to:
- Study the equation y = 2x + 4: discuss the coefficient of x as the gradient and the constant as the y-intercept
- Complete tables of values for given equations and use them to draw lines on a Cartesian plane
- Interpret real-life linear relationships using gradient and intercept
- Use digital devices or other resources to show different hills and relate to gradient

How does the equation y = mx + c describe a straight line?

- Mentor Mathematics Grade 9 pg. 59–61
- Graph paper / Cartesian plane
- Digital devices
- Mentor Mathematics Grade 9 pg. 61–63

- Written assignments - Oral questions - Observation

Algebra

Equations of a Straight Line — End-of-sub-strand written assessment

By the end of the lesson, the learner should be able to:
- demonstrate mastery of all straight-line concepts;
- solve a variety of problems accurately;
- appreciate the application of straight-line equations in everyday contexts.

In groups, learners are guided to:
- Complete assessment exercises covering gradient, equation of a line (two points and point-gradient), y = mx + c form, interpretation, and intercepts
- Correct and discuss solutions as a class

How do we apply equations of straight lines to solve problems?

- Mentor Mathematics Grade 9 pg. 48–64
- Assessment papers
- Graph paper
- Digital devices

- Written assessment - Oral questions - Observation

Algebra

Linear Inequalities — Solving linear inequalities in one unknown

By the end of the lesson, the learner should be able to:
- form linear inequalities from real-life statements;
- solve linear inequalities in one unknown using inverse operations;
- note that dividing or multiplying by a negative number reverses the inequality sign.

In groups, learners are guided to:
- Discuss real-life inequality statements (e.g. "a number multiplied by 4 minus 5 is greater than the number multiplied by 3 plus 2") and form inequalities
- Solve inequalities by adding, subtracting, multiplying, or dividing both sides — noting the sign reversal rule for negatives
- Solve exercises involving fractional and compound inequalities

How do we solve linear inequalities in one unknown?

- Mentor Mathematics Grade 9 pg. 65–67
- Inequality statement cards
- Digital devices / internet (YouTube link)

- Oral questions - Written exercises - Observation

Algebra

Linear Inequalities — Representing linear inequalities in one unknown on a number line and on a Cartesian plane
Linear Inequalities — Representing linear inequalities in two unknowns graphically

By the end of the lesson, the learner should be able to:
- represent linear inequalities in one unknown on a graph;
- use a continuous line for ≤ or ≥ and a broken line for < or >;
- shade the unwanted region to indicate the solution set.

In groups, learners are guided to:
- Draw a number line and represent simple inequalities such as x < 4 and x ≥ −3
- Follow steps: treat inequality as an equation, draw the boundary line (broken or continuous), test a point, shade unwanted region
- Solve inequalities and represent the solution on a graph (e.g. 2y − 4 ≤ 2)

How do we represent inequalities in one unknown on a graph?

- Mentor Mathematics Grade 9 pg. 67–70
- Graph paper / Cartesian plane
- Digital devices
- Mentor Mathematics Grade 9 pg. 70–72

- Written assignments - Oral questions - Observation

Algebra

Linear Inequalities — End-of-sub-strand written assessment

By the end of the lesson, the learner should be able to:
- consolidate all linear inequality concepts: solving, one-variable graphs, two-variable graphs, and real-life applications;
- solve a variety of inequality problems accurately;
- appreciate the use of linear inequalities in real-life decision-making.

In groups, learners are guided to:
- Complete mixed exercises: solve inequalities in one unknown, represent on graphs, represent two-unknown inequalities graphically, solve word problems
- Complete a short end-of-sub-strand written assessment
- Correct and discuss solutions as a class

How do we apply linear inequalities to solve and represent real-life situations?

- Mentor Mathematics Grade 9 pg. 65–73
- Assessment papers
- Graph paper
- Digital devices

- Written assessment - Oral questions - Observation

Algebra
Measurements

2.1–2.3 Algebra — Strand 2 consolidation: matrices, equations of a straight line, and linear inequalities
Area — Area of a regular pentagon

By the end of the lesson, the learner should be able to:
- review and consolidate all Strand 2 concepts across the three sub-strands;
- solve mixed problems involving matrices, straight-line equations, and linear inequalities;
- show confidence in applying algebra to solve real-life problems.

In groups, learners are guided to:
- Work through mixed strand revision exercises covering matrices, equations of straight lines, and linear inequalities
- Identify connections between topics: e.g. graphing lines relates to graphing inequalities
- Peer-review solutions and discuss common mistakes
- Use digital devices or graphing tools to verify graphs and equations

How do matrices, equations of straight lines, and linear inequalities connect to real-life problems?

- Mentor Mathematics Grade 9 pg. 38–73 (revision exercises)
- Graph paper
- Revision exercise sheets
- Digital devices
- Mentor Mathematics Grade 9 pg. 73–75
- Cut-outs of pentagons and hexagons
- Ruler and pair of compasses

- Written tests - Oral questions - Peer assessment

Measurements

Area — Area of a regular hexagon
Area — Surface area of rectangular-based prisms (cuboids)
Area — Surface area of triangular-based prisms

By the end of the lesson, the learner should be able to:
- identify the properties of a regular hexagon;
- calculate the area of a regular hexagon by dividing it into six equal triangles from the centre;
- apply area of a hexagon to real-life situations such as tiling.

In groups, learners are guided to:
- Trace and cut out a hexagon, measure the perpendicular height ON of one triangle, and calculate the area of all six triangles
- Derive: Area of hexagon = area of one triangle × 6
- Solve problems involving hexagonal trampolines, tiling areas, and road signs
- Explore ethno-math patterns in fabrics and structures involving hexagons

How do we work out the area of a hexagon?

- Mentor Mathematics Grade 9 pg. 73–76
- Cut-outs of hexagons
- Ruler and pair of compasses
- Digital devices
- Mentor Mathematics Grade 9 pg. 76–79
- Rectangular prism models
- Rulers and scissors
- Mentor Mathematics Grade 9 pg. 79–81
- Triangular prism models
- Digital devices / internet (YouTube link)

- Oral questions - Written exercises - Observation

Measurements

Area — Surface area of square, rectangular, and triangular-based pyramids
Area — Area of a sector; area of a segment of a circle
Area — Surface area of a cone (curved surface and total surface area)

By the end of the lesson, the learner should be able to:
- sketch the net of a pyramid and identify its base and triangular faces;
- calculate the total surface area of square, rectangular, and triangular-based pyramids;
- apply surface area of pyramids to real-life problems.

In groups, learners are guided to:
- Use models of square, rectangular, and triangular pyramids; cut open along edges to get the net
- Measure the faces and calculate area of base + area of all triangular faces
- Solve problems: Great Pyramid of Giza, playing arenas, and cost of painting pyramid-shaped structures

How do we find the total surface area of a pyramid?

- Mentor Mathematics Grade 9 pg. 81–85
- Pyramid models
- Rulers and scissors
- Digital devices
- Mentor Mathematics Grade 9 pg. 85–91
- Circle cut-outs with sectors and segments
- Pair of compasses and ruler
- Mentor Mathematics Grade 9 pg. 91–93
- Card paper and scissors
- Pair of compasses
- Scientific calculators

- Written assignments - Oral questions - Observation

Measurements

Volume of Solids — Volume of triangular-based prisms

By the end of the lesson, the learner should be able to:
- identify the cross-sectional area of a triangular prism;
- calculate the volume of a triangular prism using V = cross-sectional area × length;
- apply volume of triangular prisms to real-life problems such as greenhouses and concrete blocks.

In groups, learners are guided to:
- Collect prism-shaped objects; identify and discuss features of triangular prisms
- Calculate height of the triangular face using Pythagoras, find cross-sectional area, then multiply by length
- Solve problems: greenhouse volumes, concrete blocks, and loading company loaders

How do we determine the volume of different solids?

- Mentor Mathematics Grade 9 pg. 98–101
- Triangular prism models
- Rulers
- Digital devices

- Oral questions - Written exercises - Observation

Measurements

Volume of Solids — Volume of rectangular-based prisms (cuboids)
Volume of Solids — Volume of square, rectangular, and triangular-based pyramids

By the end of the lesson, the learner should be able to:
- calculate the volume of a rectangular prism using V = l × w × h;
- determine height or base area when volume is given;
- apply volume of rectangular prisms to real-life situations such as storage tanks, sandboxes, and water tanks.

In groups, learners are guided to:
- Collect rectangular containers from the locality; measure length, width, and height; calculate base area then multiply by height
- Solve problems: movie theatre popcorn containers, rectangular water tanks, and soap containers
- Determine height from given volume and base area

How do we use the volume of solids in real-life situations?

- Mentor Mathematics Grade 9 pg. 101–105
- Rectangular prism containers
- Rulers
- Digital devices
- Mentor Mathematics Grade 9 pg. 105–109
- Pyramid models
- Digital devices / internet

- Written assignments - Oral questions - Observation

Measurements

Volume of Solids — Volume of a cone

By the end of the lesson, the learner should be able to:
- calculate the volume of a cone using V = ⅓πr²h;
- find a missing dimension (radius or height) when the volume is given;
- apply volume of a cone to real-life situations such as ice cream cups and party hats.

In groups, learners are guided to:
- Use digital resources to explore the formula for volume of a cone
- Apply V = ⅓πr²h to calculate volumes; rearrange to find radius or height
- Solve problems: ice cream vendor cones, hourglasses made of two identical cones, yoghurt cups, and birthday party hats

How do we work out the volume of a cone?

- Mentor Mathematics Grade 9 pg. 109–111
- Cone models
- Scientific calculators
- Digital devices

- Written tests - Oral questions - Observation

Measurements

Volume of Solids — Volume of a frustum (cone-based and pyramid-based)

By the end of the lesson, the learner should be able to:
- identify a frustum as the solid formed when the top of a cone or pyramid is cut off horizontally;
- calculate the volume of a frustum using: V = volume of big solid − volume of small solid;
- apply volume of frustum to real-life situations such as lampshades and water troughs.

In groups, learners are guided to:
- Use a model pyramid or cone; cut horizontally to form a frustum and a smaller solid
- Apply: Volume of frustum = volume of big cone/pyramid − volume of small cone/pyramid
- Solve problems: cone-shaped water containers, lampshades, and water troughs cut from a pyramid

How do we determine the volume of a frustum?

- Mentor Mathematics Grade 9 pg. 111–114
- Cone and pyramid models
- Scissors
- Digital devices

- Written assignments - Oral questions - Observation

Measurements

Mass, Volume, Weight and Density — Converting units of mass
Mass, Volume, Weight and Density — Relationship between mass and weight; W = mg

By the end of the lesson, the learner should be able to:
- identify and state the units of mass and their abbreviations;
- convert units of mass from one form to another (g, kg, mg, Hg, Dg, dg, cg, μg, Mg, tonnes);
- appreciate the importance of accurate mass measurement in everyday life.

In groups, learners are guided to:
- Discuss different instruments used in weighing: beam balance, electronic weighing machine, spring balance
- Take a walk outside class, collect objects of different sizes, weigh them, and express masses in kilograms
- Convert masses between units and record findings in a table

How do you weigh materials and objects?

- Mentor Mathematics Grade 9 pg. 115–117
- Beam balance / electronic weighing machine
- Objects of different sizes
- Digital devices
- Mentor Mathematics Grade 9 pg. 117–119
- Beam balance and spring balance
- Stones of different sizes

- Oral questions - Written exercises - Observation

Measurements
Geometry

Mass, Volume, Weight and Density — Density: concept, formula, and calculations (D = M/V)
Coordinates and Graphs — Plotting points on a Cartesian plane

By the end of the lesson, the learner should be able to:
- define density as mass per unit volume;
- calculate density, mass, or volume using the formula D = M/V;
- convert density between g/cm³ and kg/m³ and apply to real-life situations.

In groups, learners are guided to:
- Use a 100 cm³ container and a beam balance; fill with different substances (sand, water, gravel, soil), measure mass, and calculate mass ÷ volume
- Derive: Density = Mass ÷ Volume; rearrange to find mass or volume
- Convert: 1 g/cm³ = 1 000 kg/m³; solve problems using oil, paraffin, copper, mercury, and petrol densities

How do we determine the density of a substance?

- Mentor Mathematics Grade 9 pg. 119–122
- 100 cm³ containers
- Beam balance / electronic scale
- Sand, water, gravel, and soil
- Digital devices
- Mentor Mathematics Grade 9 pg. 166–168
- Graph paper
- Ruler and pencil

- Written assignments - Oral questions - Observation

Geometry

Coordinates and Graphs — Drawing straight line graphs by generating tables of values
Coordinates and Graphs — Drawing parallel lines; establishing that parallel lines have equal gradients

By the end of the lesson, the learner should be able to:
- generate a table of values for a given linear equation;
- plot the points and join them to draw a straight line graph;
- determine the equation of a straight line from a given graph.

In groups, learners are guided to:
- Generate a table of values for y = 3x – 3 by substituting chosen x-values; plot the points and join them
- Draw straight line graphs for equations such as y = 2x + 4, y + 2x = 3, y = –2x + 3, x + y = 5, and 3y = 9x – 12
- Read equations from given straight line graphs drawn on a Cartesian plane

How do we interpret graphs of straight lines?

- Mentor Mathematics Grade 9 pg. 168–170
- Graph paper
- Ruler and pencil
- Digital devices
- Mentor Mathematics Grade 9 pg. 170–174
- Ruler
- Digital devices / internet (YouTube link)

- Written assignments - Oral questions - Observation

Geometry

Coordinates and Graphs — Drawing perpendicular lines; establishing that m₁ × m₂ = –1
Coordinates and Graphs — Applying straight-line graphs, parallel and perpendicular lines to real-life and mixed problems
Scale Drawing — Compass bearings (Nθ°E/W, Sθ°E/W) and true bearings (3-digit clockwise notation)

By the end of the lesson, the learner should be able to:
- draw perpendicular line pairs on the same Cartesian plane;
- verify that the product of gradients of perpendicular lines equals –1;
- find the equation of a line perpendicular to a given line and passing through a given point.

In groups, learners are guided to:
- Draw y = –2x + 2 and y = ½x + 2; use a protractor to confirm the 90° angle; verify: (–2) × (½) = –1
- Draw y = ¼x + 5 and y = –4x – 2; confirm perpendicularity by measuring the angle
- Find gradient of line w perpendicular to m (y = ¾x – 4) at Q(4,–1); write the equation of w; solve exercises finding perpendicular line equations through given points

How do we use gradients to identify perpendicular lines?

- Mentor Mathematics Grade 9 pg. 174–179
- Graph paper
- Ruler and protractor
- Digital devices
- Mentor Mathematics Grade 9 pg. 166–179 (revision)
- Revision exercise sheets
- Mentor Mathematics Grade 9 pg. 180–183
- Protractors and rulers
- Compass direction diagrams
- Graph paper

- Written assignments - Oral questions - Observation

Geometry

Scale Drawing — Determining compass and true bearings of one point from another using a protractor; back bearings
Scale Drawing — Making scale drawings from bearing-and-distance data involving 2–3 points
Scale Drawing — Complex scale drawing problems involving 3–4 bearing-and-distance points

By the end of the lesson, the learner should be able to:
- determine the compass and true bearing of one point from another using a protractor;
- determine back bearings from given forward bearings;
- solve problems involving bearings of multiple points from a single reference location.

In groups, learners are guided to:
- Study a map of Hekima village; use a protractor to determine the compass and true bearing of the dispensary, quarry, mosque, market, and school from the tower
- Determine: if bearing of Q from P = 120°, bearing of P from Q = 300°; practise finding back bearings for various cases
- Solve: find bearing of R from P, bearing of Q from R, and bearing of Q from P using the given three-point diagram

How do we determine the bearing of one point from another?

- Mentor Mathematics Grade 9 pg. 183–188
- Protractors and rulers
- Graph paper
- Maps and compass diagrams
- Digital devices
- Mentor Mathematics Grade 9 pg. 186–191
- Mentor Mathematics Grade 9 pg. 188–192

- Written assignments - Oral questions - Observation

Geometry

Scale Drawing — Identifying and determining angles of elevation by accurate scale drawing

By the end of the lesson, the learner should be able to:
- define angle of elevation as the angle by which the line of sight is raised from the horizontal to see an object above;
- make accurate scale drawings to determine angles of elevation;
- calculate heights and horizontal distances from scale drawings involving angles of elevation.

In groups, learners are guided to:
- Walk to the assembly ground; observe the top of the flagpost; discuss line of sight and the angle of elevation
- Make scale drawings: observer 80 m from an object 40 m high — choose scale 1 cm : 10 m, draw, and measure angle of elevation = 27°
- Solve: tower shadow 35 m long, height 15 m — find angle of elevation; Kirigo's eye at 172 cm views top of a post 8 m away at 60° — find the height of the post

How do we determine the angle of elevation using scale drawing?

- Mentor Mathematics Grade 9 pg. 191–196
- Graph paper
- Protractors and rulers
- Digital devices

- Written tests - Oral questions - Observation

Geometry

Scale Drawing — Identifying and determining angles of depression by accurate scale drawing

By the end of the lesson, the learner should be able to:
- define angle of depression as the angle by which the line of sight is lowered from the horizontal to see an object below;
- make accurate scale drawings to determine angles of depression;
- determine horizontal distances and heights from scale drawings involving angles of depression.

In groups, learners are guided to:
- Discuss the difference between elevation and depression using sketches; establish that the angle of depression equals the alternate angle of elevation
- Make scale drawing: eagle at height 600 m, horizontal distance 960 m to chick — find angle of depression = 32°
- Solve: boat 310 m from a 60 m lighthouse; plane at altitude 8 km between two airports with angles of depression 25° and 31° — find distance between airports and shortest distance to airport B

How do we determine the angle of depression using scale drawing?

- Mentor Mathematics Grade 9 pg. 196–201
- Graph paper
- Protractors and rulers
- Digital devices

- Written assignments - Oral questions - Observation

Geometry

Scale Drawing — Describing land boundaries using bearing and distance from a reference point
Similarity and Enlargement — Identifying similar figures; properties: proportional corresponding sides and equal corresponding angles

By the end of the lesson, the learner should be able to:
- describe the boundary points of a piece of land using bearing and distance from an external reference point;
- construct a scale drawing of the land from a bearing-and-distance table;
- appreciate the use of scale drawing in real-life land surveying.

In groups, learners are guided to:
- Take triangular piece of land PQR; join each vertex to reference point O; measure the bearing and distance for each vertex and record in a table
- Reconstruct the scale drawing of the farm from the bearing-and-distance data
- Solve: quadrilateral farm boundaries described from an external point with A(334°, 225 m), F(352°, 305 m), G(27°, 335 m), H(64°, 335 m)
- Discuss careers in scale drawing and surveying with parents or guardians

How do we use bearing and distance to describe and draw a piece of land?

- Mentor Mathematics Grade 9 pg. 200–203
- Protractors and rulers
- Graph paper
- Maps
- Digital devices
- Mentor Mathematics Grade 9 pg. 205–209
- Ruler and protractor
- Cut-out shapes

- Written exercises - Oral questions - Observation

Geometry

Similarity and Enlargement — Drawing similar figures by scaling all sides by the same ratio; equal corresponding angles

By the end of the lesson, the learner should be able to:
- draw a figure similar to a given figure by multiplying all sides by the same scale ratio;
- ensure all corresponding angles remain equal in the drawn figure;
- apply similar figures to real-life contexts such as plots and photographs.

In groups, learners are guided to:
- Use the side ratio as a scale: draw rhombus PQRS similar to ABCD (sides 3 cm) but twice as big — sides 6 cm, same angles 70° and 110°
- Draw similar triangles (e.g. right-angled triangle 3-4-5 scaled to QR = 6 cm), rectangles (AB = 8 cm, BC = 6 cm scaled to QR = 9 cm), and parallelograms
- Solve real-life problems: drawing similar rectangular plots of land; two rectangular photographs with given corresponding dimensions

How do we draw a figure similar to a given one?

- Mentor Mathematics Grade 9 pg. 209–213
- Ruler, protractor, and pair of compasses
- Graph paper
- Digital devices

- Written assignments - Oral questions - Observation

Geometry

Similarity and Enlargement — Identifying an enlargement; locating the centre; determining positive and negative scale factors

By the end of the lesson, the learner should be able to:
- identify a transformation as an enlargement by verifying that image-distance/object-distance from a fixed point is constant;
- locate the centre of enlargement by extending lines through corresponding vertices;
- distinguish between positive and negative scale factors based on the relative positions of object and image.

In groups, learners are guided to:
- Study object ABC and image A'B'C'; join AA', BB', CC' and extend to find centre O; verify OA'/OA = OB'/OB = OC'/OC
- Record scale factor; note that when object and image are on opposite sides of O the scale factor is negative (e.g. –2.5)
- Identify real-life examples of enlargement: magnifying lens, projectors, photocopiers, and maps
- State two features common to object and image under enlargement

How do we use enlargement in real-life situations?

- Mentor Mathematics Grade 9 pg. 213–217
- Ruler
- Squared/graph paper
- Digital devices

- Written exercises - Oral questions - Observation

Geometry

Similarity and Enlargement — Constructing enlarged images given centre O and scale factor k; determining and applying the linear scale factor
Trigonometry — Identifying hypotenuse, opposite, and adjacent sides relative to a given acute angle in a right-angled triangle

By the end of the lesson, the learner should be able to:
- construct the image of a figure under enlargement given centre O and scale factor k (positive and negative);
- calculate the linear scale factor (LSF) as image side ÷ corresponding object side;
- use LSF to find unknown sides and solve real-life problems involving similar figures.

In groups, learners are guided to:
- Enlarge triangle ABC with scale factor 2.5, centre O: join O to each vertex, extend the line, and mark OA' = 2.5 × OA; repeat for B and C; join A'B'C'
- Enlarge with negative scale factor –2: extend lines from each vertex through O to the other side and mark OA' = 2 × OA beyond O
- Calculate LSF for similar rectangles (14 cm → 7 cm: LSF = 0.5); use LSF to find unknown dimensions — e.g. QR of a similar rectangle; widths of similar farm plots

How do we determine and apply the linear scale factor of similar figures?

- Mentor Mathematics Grade 9 pg. 217–222
- Ruler and pair of compasses
- Graph paper
- Digital devices
- Mentor Mathematics Grade 9 pg. 223–225
- Ruler and protractor

- Written tests - Oral questions - Observation

Geometry

Trigonometry — Identifying and calculating tan θ = opp/adj; sin θ = opp/hyp; cos θ = adj/hyp

By the end of the lesson, the learner should be able to:
- define the three trigonometric ratios (tangent, sine, cosine) for an acute angle in a right-angled triangle;
- calculate the decimal value of each ratio from given side lengths;
- appreciate that the ratio remains constant for a fixed angle regardless of triangle size.

In groups, learners are guided to:
- Measure opposite, adjacent, and hypotenuse sides in three similar right-angled triangles drawn to coincide at vertex A; compute opp/adj, opp/hyp, and adj/hyp for each — note the constant values
- Define: tan θ = opp/adj; sin θ = opp/hyp; cos θ = adj/hyp and express as decimals
- Express each trig ratio as a fraction and as a decimal for various triangles with given side lengths

How do we express trigonometric ratios from a right-angled triangle?

- Mentor Mathematics Grade 9 pg. 225–232
- Ruler and protractor
- Graph paper
- Digital devices

- Written assignments - Oral questions - Observation

Geometry

Trigonometry — Reading tables of sine, cosine, and tangent for acute angles; using mean difference columns

By the end of the lesson, the learner should be able to:
- read the sine, cosine, and tangent of acute angles from mathematical tables including the mean difference (ADD/SUBTRACT) column;
- find an angle given its sine, cosine, or tangent from tables;
- note that the cosine table uses the SUBTRACT column (cosine decreases as angle increases).

In groups, learners are guided to:
- Study the structure of trig tables: x° column, 0.0–0.9 main columns, ADD/SUBTRACT difference columns
- Read values step by step: tan 5.8° = 0.1016; tan 6.37° = 0.1116 using ADD column; sin 62.6° = 0.8878; sin 33.47° = 0.5515
- Find an angle from its ratio: tan θ = 0.8571 → θ = 40.6°; sin x = 0.9639 → x = 74.56°; cos x = 0.1234 → x = 82.91° using SUBTRACT column for cosine

How do we use trigonometric tables to find ratios and angles?

- Mentor Mathematics Grade 9 pg. 232–240
- Mathematical trig tables (sin, cos, tan)
- Scientific calculators
- Digital devices

- Written tests - Oral questions - Observation

Geometry

Trigonometry — Using a scientific calculator to find trig ratios and inverse trig functions for acute angles
Trigonometry — Using sin, cos, and tan to calculate unknown sides and angles in right-angled triangles

By the end of the lesson, the learner should be able to:
- use the sin, cos, and tan keys on a scientific calculator to find trig ratios of given angles;
- use the shift + sin/cos/tan keys to find an angle from its ratio (inverse trig);
- compare calculator results with table values and appreciate the efficiency of technology.

In groups, learners are guided to:
- Ensure the calculator is set to degree mode (D displayed at top); discuss calculator key sequences
- Calculate: sin 45° = 0.7071; cos 71° = 0.3256; tan 55° = 1.428 using the calculator — give answers to 4 significant figures
- Find angles: tan⁻¹(0.3764) = 20.63°; sin⁻¹(0.500) = 30°; cos⁻¹(0.9998) = 1.28° using shift + ratio key
- Use IT/digital devices or other resources to explore trig ratios

How do we use a calculator to find trigonometric ratios and angles?

- Mentor Mathematics Grade 9 pg. 240–242
- Scientific calculators
- Mathematical trig tables
- Digital devices
- Mentor Mathematics Grade 9 pg. 238–243

- Written assignments - Oral questions - Observation

Data Handling and Probability

Data Interpretation (Grouped Data) — Determining appropriate class width; drawing frequency distribution tables
Data Interpretation (Grouped Data) — Identifying the modal frequency and modal class from a frequency distribution table

By the end of the lesson, the learner should be able to:
- determine the range and calculate an appropriate class width for a given data set;
- group raw data into classes and draw a frequency distribution table using tally marks;
- appreciate the importance of organising data into groups for easier interpretation.

- Have learners each choose a number between 1 and 100; find the range, determine an appropriate class width (5–12 classes) and form the classes
- Apply: masses of 40 Hekima Junior School learners (range = 28 kg; class width 5 gives 6 classes: 30–34, 35–39, …, 55–59)
- Tally the marks of 60 Tiifu Junior School learners (range = 76; class width 10 gives 8 classes) and complete the frequency distribution table
- Use digital devices or other resources to organise and represent grouped data

How do we interpret data?

- Mentor Mathematics Grade 9 pg. 224–229
- Graph paper and exercise books
- Digital devices
- Mentor Mathematics Grade 9 pg. 229–231
- Frequency distribution tables

- Oral questions - Observation - Written exercises

Data Handling and Probability

Data Interpretation (Grouped Data) — Calculating the mean of grouped data using midpoints (x̄ = Σfx ÷ Σf)
Data Interpretation (Grouped Data) — Building cumulative frequency columns; identifying the median class
Data Interpretation (Grouped Data) — Calculating the median using the formula: Median = L + [(N/2 − cfa) ÷ fm] × im

By the end of the lesson, the learner should be able to:
- find the midpoint of each class by averaging the class limits;
- calculate Σfx by multiplying each midpoint by its frequency;
- determine the mean using the formula x̄ = Σfx ÷ Σf and apply it to real-life data.

- Introduce the midpoint: e.g. midpoint of 0–4 = (0+4)/2 = 2; build an extended table with columns: Class / Midpoint (x) / Frequency (f) / fx
- Work through Example 4: trucks crossing a weighing bridge — Σf = 40, Σfx = 520, mean = 13 tonnes
- Solve: mean of marks of 40 learners using class width 10 (classes 20–29 to 80–89); number of daily calls at a customer care office; number of trees planted in 20 villages
- Use IT devices or other materials to verify mean calculations

How do we calculate the mean of grouped data?

- Mentor Mathematics Grade 9 pg. 231–234
- Exercise books
- Scientific calculators
- Digital devices
- Mentor Mathematics Grade 9 pg. 234–236
- Mentor Mathematics Grade 9 pg. 236–238

- Written assignments - Oral questions - Observation

Data Handling and Probability

Data Interpretation (Grouped Data) — Mixed problems on class width, frequency tables, modal class, mean, and median
Probability — Experiments involving equally likely outcomes; P(event) = favourable outcomes ÷ total outcomes
Probability — Determining the range of probability; P(certain event) = 1; P(impossible event) = 0; 0 ≤ P(A) ≤ 1; P(A') = 1 − P(A)

By the end of the lesson, the learner should be able to:
- solve mixed problems covering all grouped data concepts: class width, frequency tables, modal class, mean, and median;
- collect, organise, and interpret real-life data;
- appreciate data interpretation in real-life situations such as health, agriculture, and school performance.

In groups, learners are guided to:
- Collect real-life data: use distances from school or home to health facilities using different routes; organise into a frequency table, identify the modal class, calculate mean and median
- Work through comprehensive revision exercises involving full data sets from raw data to table to modal class to mean to median
- Discuss applications: Integrated Science data, Social Studies population data, Agricultural harvest records
- Use digital devices or other materials to search for and interpret real-life data sets

How do we use grouped data interpretation in real-life situations?

- Mentor Mathematics Grade 9 pg. 224–238 (revision)
- Revision exercise sheets
- Scientific calculators
- Digital devices
- Mentor Mathematics Grade 9 pg. 239–241
- Coins and dice
- Coloured pens / objects in a bag
- Mentor Mathematics Grade 9 pg. 241–243

- Written assessment - Oral questions - Peer assessment

Data Handling and Probability

Probability — Identifying mutually exclusive events; P(A or B) = P(A) + P(B) (addition law)

By the end of the lesson, the learner should be able to:
- define mutually exclusive events as events where the occurrence of one prevents the occurrence of the other;
- apply the addition law: P(A or B) = P(A) + P(B) for mutually exclusive events;
- identify mutually exclusive events in real-life situations and solve related problems.

In groups, learners are guided to:
- Toss a coin once; discuss: can head and tail both face up at the same time? Establish mutual exclusivity
- Identify real-life mutually exclusive events: at school or at home; lunch at home or at school; football or volleyball choice
- Roll a die: P(1 or 2) = 1/6 + 1/6 = 2/6; P(even number) = P(2) + P(4) + P(6) = 3/6; P(3 or 5 or 4) = 3/6
- Solve: cards numbered 1–9 (P(odd), P(prime), P(prime or even)); spinner numbered 1–8; word MUTUALLY written on separate cards

How do we calculate the probability of mutually exclusive events?

- Mentor Mathematics Grade 9 pg. 243–247
- Coins and dice
- Number cards
- Spinners
- Digital devices

- Written tests - Oral questions - Observation

Data Handling and Probability

Probability — Performing experiments involving independent events; P(A and B) = P(A) × P(B) (multiplication law)
Probability — Drawing tree diagrams to represent possible outcomes of a single-stage event
Probability — Mixed problems on equally likely outcomes, range, mutually exclusive events, independent events, and tree diagrams

By the end of the lesson, the learner should be able to:
- define independent events as events where the outcome of one does not affect the outcome of the other;
- apply the multiplication law: P(A and B) = P(A) × P(B) for independent events;
- solve real-life problems involving two or more independent events including with and without replacement.

- One learner holds a coin, another holds a die; toss simultaneously — discuss: does the coin outcome affect the die outcome? Establish independence
- Establish: the word "and" in probability means multiply: P(A and B) = P(A) × P(B)
- Work through: basket with 4 red and 3 green balls (with replacement) — P(red then green) = 4/7 × 3/7 = 12/49; P(all red) = 16/49
- Solve: pink and orange marbles without replacement; three learners hitting a target with different individual probabilities; coin-and-die combined experiments
- Apply to real life: rain and lateness; pen and ruler usage in class

How do we calculate the probability of independent events occurring together?

- Mentor Mathematics Grade 9 pg. 247–251
- Coins, dice, and coloured balls/marbles
- Digital devices
- Mentor Mathematics Grade 9 pg. 251–255
- Graph paper or blank paper
- Ruler and pencil
- Mentor Mathematics Grade 9 pg. 239–255 (revision)
- Coins, dice, and coloured marbles/balls
- Revision exercise sheets

- Written assignments - Oral questions - Observation