Numbers

Integers - Addition of Integers
Integers - Subtraction of Integers

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

Perform basic operations on integers in different situations;
Work out combined operations on integers in different situations;
Appreciate the use of integers in real life situations.

Discuss and work out basic operations on integers using number cards and charts.
Play games involving numbers and operations.
Pick integers and perform basic operations.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 1.
Number cards.
Charts with basic operations on integers.
Top Scholar KLB Mathematics Learners Book Grade 9, page 2.
Charts with subtraction operations.

Oral questions. Written exercise. Observation.

Numbers

Integers - Multiplication of Integers
Integers - Division of Integers
Integers - Combined Operations on Integers
Cubes and Cube Roots - Working out Cubes of Numbers by Multiplication
Cubes and Cube Roots - Determining Cubes from Mathematical Tables
Cubes and Cube Roots - Cubes of Numbers Greater Than 10

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

Perform multiplication of integers in different situations;
Work out combined operations involving multiplication of integers;
Appreciate the use of multiplication of integers in real life.

Discuss multiplication of integers using patterns.
Work in groups to create tables of multiplication of positive and negative integers.
Solve problems involving multiplication of integers.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 3.
Charts showing patterns of multiplication of integers.
Multiplication tables.
Top Scholar KLB Mathematics Learners Book Grade 9, page 4.
Division tables.
Worksheets with division problems.
Top Scholar KLB Mathematics Learners Book Grade 9, page 5.
Calculators.
Computers with mathematical software.
Top Scholar KLB Mathematics Learners Book Grade 9, page 8.
Small cubes.
Charts showing cubes of numbers.
Top Scholar KLB Mathematics Learners Book Grade 9, page 11.
Mathematical tables.
Top Scholar KLB Mathematics Learners Book Grade 9, page 12.

Oral questions. Written exercise. Group presentation.

Numbers

Cubes and Cube Roots - Cubes of Numbers Less Than 1
Cubes and Cube Roots - Determining Cube Roots by Factor Method
Cubes and Cube Roots - Determining Cube Roots from Mathematical Tables
Cubes and Cube Roots - Cube Roots of Numbers Greater Than 1000
Cubes and Cube Roots - Cube Roots of Numbers Between 0 and 1

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

Determine cubes of numbers less than 1 using mathematical tables;
Apply cube calculations to real life situations;
Show interest in working with decimal numbers.

Discuss the concept of cubes of numbers less than 1.
Use mathematical tables to find cubes of decimal numbers.
Solve problems involving cubes of decimal numbers.

How do we work out the cubes of numbers?

Top Scholar KLB Mathematics Learners Book Grade 9, page 13.
Mathematical tables.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 15.
Cubes of different sizes.
Factor trees.
Top Scholar KLB Mathematics Learners Book Grade 9, page 16.
Top Scholar KLB Mathematics Learners Book Grade 9, page 17.
Top Scholar KLB Mathematics Learners Book Grade 9, page 18.

Oral questions. Written exercise. Assignment.

Numbers

Cubes and Cube Roots - Using a Calculator for Cubes and Cube Roots
Cubes and Cube Roots - Application of Cubes and Cube Roots
Indices and Logarithms - Expressing Numbers in Index Form
Indices and Logarithms - Laws of Indices: Multiplication
Indices and Logarithms - Laws of Indices: Division

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

Work out cubes and cube roots using calculators;
Apply cube and cube root calculations to real life situations;
Appreciate the use of technology in mathematical calculations.

Demonstrate how to use a calculator to find cubes and cube roots.
Compare results from mathematical tables and calculators.
Solve real-life problems using a calculator.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 19.
Calculators.
Computers with mathematical software.
Top Scholar KLB Mathematics Learners Book Grade 9, page 21.
Real-life objects with cubic shapes.
Top Scholar KLB Mathematics Learners Book Grade 9, page 26.
Charts showing numbers in index form.
Top Scholar KLB Mathematics Learners Book Grade 9, page 28.
Charts showing laws of indices.
Top Scholar KLB Mathematics Learners Book Grade 9, page 29.

Oral questions. Written exercise. Practical assessment.

Numbers

Indices and Logarithms - Laws of Indices: Power of a Power
Indices and Logarithms - Powers of 10 and Common Logarithms
Indices and Logarithms - Using IT for Indices and Logarithms
Compound Proportions and Rates of Work - Introduction to Proportions
Compound Proportions and Rates of Work - Dividing Quantities into Proportional Parts
Compound Proportions and Rates of Work - Direct Proportion

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

Generate the laws of indices for power of a power;
Apply the laws of indices in different situations;
Appreciate the use of laws of indices in simplifying calculations.

Show the laws of indices for power of a power.
Use the laws of indices to work out problems.
Simplify expressions using power of a power law.

How do we express numbers in powers?

Top Scholar KLB Mathematics Learners Book Grade 9, page 30.
Charts showing laws of indices.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 33.
Mathematical tables.
Top Scholar KLB Mathematics Learners Book Grade 9, page 34.
Computers with mathematical software.
Top Scholar KLB Mathematics Learners Book Grade 9, page 35.
Charts showing proportional relationships.
Real-life examples of proportions.
Counters (bottle tops, small stones).
Charts showing proportional division.
Top Scholar KLB Mathematics Learners Book Grade 9, page 36.
Charts showing direct proportion.
Graphs of direct proportion.

Oral questions. Written exercise. Assignment.

Numbers

Compound Proportions and Rates of Work - Inverse Proportion
Compound Proportions and Rates of Work - Relating Different Ratios
Compound Proportions and Rates of Work - Working Out Compound Proportions
Compound Proportions and Rates of Work - Solving Problems Using Compound Proportions
Compound Proportions and Rates of Work - Introduction to Rates of Work

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

Identify inverse proportional relationships;
Solve problems involving inverse proportion;
Appreciate the difference between direct and inverse proportion.

Discuss inverse proportion with real-life examples.
Identify the characteristics of inverse proportion.
Solve problems involving inverse proportion.

What are proportions?

Top Scholar KLB Mathematics Learners Book Grade 9, page 36.
Charts showing inverse proportion.
Graphs of inverse proportion.
Top Scholar KLB Mathematics Learners Book Grade 9, page 37.
Charts showing different ratios.
Real-life examples of ratio comparison.
Top Scholar KLB Mathematics Learners Book Grade 9, page 39.
Charts showing compound proportions.
Calculators.
Worksheets with compound proportion problems.
Top Scholar KLB Mathematics Learners Book Grade 9, page 40.
Charts showing rates of work.
Real-life examples of work rates.

Oral questions. Written exercise. Assignment.

Numbers

Compound Proportions and Rates of Work - Calculating Rates of Work
Compound Proportions and Rates of Work - Combined Rates of Work
Compound Proportions and Rates of Work - Rates of Work and Time
Compound Proportions and Rates of Work - Rates of Work and Output
Compound Proportions and Rates of Work - Using IT for Rates of Work

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

Calculate rates of work in real life situations;
Solve problems involving rates of work;
Show interest in efficiency and time management in work.

Work out rates of work.
Discuss factors affecting rates of work.
Solve problems involving rates of work in real-life contexts.

Why do we work fast?

Top Scholar KLB Mathematics Learners Book Grade 9, page 40.
Charts showing rates of work.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 41.
Charts showing combined rates of work.
Worksheets with time and rate problems.
Top Scholar KLB Mathematics Learners Book Grade 9, page 42.
Charts showing productivity and rates.
Computers with spreadsheet software.

Oral questions. Written exercise. Group work.

Algebra

Matrices - Identifying a Matrix
Matrices - Determining the Order of a Matrix
Matrices - Determining the Position of Items in a Matrix
Matrices - Determining Compatibility for Addition
Matrices - Determining Compatibility for Subtraction
Matrices - Addition of Matrices

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

Identify a matrix in different situations;
Represent tabular information as a matrix;
Appreciate the use of matrices in organizing information.

Discuss the use of tables such as football league tables, travel schedules, shopping lists.
Count the number of rows and columns in tables.
Represent tables as matrices.

How do we use matrices in real life situations?

Top Scholar KLB Mathematics Learners Book Grade 9, page 43.
Charts showing tables and matrices.
Real-life examples of tables.
Top Scholar KLB Mathematics Learners Book Grade 9, page 45.
Paper cards for creating matrices.
Worksheets with various matrices.
Top Scholar KLB Mathematics Learners Book Grade 9, page 46.
Paper cards labeled with letters or numbers.
Charts showing element positions.
Top Scholar KLB Mathematics Learners Book Grade 9, page 47.
Charts showing matrices of various orders.
Worksheets with matrices.
Top Scholar KLB Mathematics Learners Book Grade 9, page 49.
Top Scholar KLB Mathematics Learners Book Grade 9, page 51.
Charts showing addition of matrices.
Calculators.

Oral questions. Written exercise. Observation.

Algebra

Matrices - Subtraction of Matrices
Matrices - Application of Matrices
Equations of Straight Lines - Introduction to Gradient
Equations of Straight Lines - Identifying the Gradient
Equations of Straight Lines - Measuring Gradient

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

Carry out subtraction of matrices in real life situations;
Subtract corresponding elements in compatible matrices;
Appreciate the use of matrices in data analysis.

Subtract matrices by subtracting corresponding elements.
Solve real-life problems involving subtraction of matrices.
Discuss what is represented by rows and columns when subtracting matrices.

How do we use matrices in real life situations?

Top Scholar KLB Mathematics Learners Book Grade 9, page 54.
Charts showing subtraction of matrices.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 57.
Real-life data that can be represented in matrices.
Top Scholar KLB Mathematics Learners Book Grade 9, page 58.
Pictures of hills and slopes.
Charts showing different gradients.
Ladders or sticks for demonstrating gradients.
Top Scholar KLB Mathematics Learners Book Grade 9, page 59.
Rulers and measuring tapes.
Inclined objects for measurement.

Oral questions. Written exercise. Group presentation.

Algebra

Equations of Straight Lines - Gradient from Two Known Points
Equations of Straight Lines - Positive and Negative Gradients
Equations of Straight Lines - Zero and Undefined Gradients
Equations of Straight Lines - Equation from Two Points
Equations of Straight Lines - Deriving the Equation from Two Points
Equations of Straight Lines - Equation from a Point and Gradient

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

Determine the gradient of a straight line from two known points;
Calculate gradient using the formula;
Show interest in mathematical approaches to measuring steepness.

Discuss how to calculate gradient from two points.
Plot points on a Cartesian plane and draw lines.
Calculate gradients of lines using the formula.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 60.
Graph paper.
Rulers and protractors.
Top Scholar KLB Mathematics Learners Book Grade 9, page 61.
Charts showing lines with different gradients.
Charts showing horizontal and vertical lines.
Top Scholar KLB Mathematics Learners Book Grade 9, page 62.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 63.
Worksheets with coordinate points.
Top Scholar KLB Mathematics Learners Book Grade 9, page 64.

Oral questions. Written exercise. Assignment.

Algebra

Equations of Straight Lines - Express Equation in Form y = mx + c
Equations of Straight Lines - Interpreting y = mx + c
Equations of Straight Lines - Graphing Lines from Equations
Equations of Straight Lines - x and y Intercepts
Equations of Straight Lines - Using Intercepts to Graph Lines

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

Express the equation of a straight line in the form y = mx + c;
Identify the gradient and y-intercept from the equation;
Appreciate the standard form of line equations.

Discuss and rewrite equations in the form y = mx + c.
Identify the gradient (m) and y-intercept (c) from equations.
Solve problems involving standard form of line equations.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 65.
Charts showing line equations.
Graph paper.
Top Scholar KLB Mathematics Learners Book Grade 9, page 67.
Charts showing lines with different gradients.
Top Scholar KLB Mathematics Learners Book Grade 9, page 68.
Rulers.
Top Scholar KLB Mathematics Learners Book Grade 9, page 70.
Top Scholar KLB Mathematics Learners Book Grade 9, page 71.

Oral questions. Written exercise. Group presentation.

Algebra

Equations of Straight Lines - Parallel and Perpendicular Lines
Equations of Straight Lines - Real Life Applications
Linear Inequalities - Introduction to Inequalities
Linear Inequalities - Solving Linear Inequalities (Addition and Subtraction)
Linear Inequalities - Solving Linear Inequalities (Multiplication and Division)

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

Identify parallel and perpendicular lines from their equations;
Determine the relationship between gradients of parallel and perpendicular lines;
Appreciate geometric relationships in algebraic form.

Discuss the gradient relationship in parallel and perpendicular lines.
Draw parallel and perpendicular lines on graph paper.
Solve problems involving parallel and perpendicular lines.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 71.
Graph paper.
Rulers and protractors.
Top Scholar KLB Mathematics Learners Book Grade 9, page 72.
Real-life data that can be modeled using lines.
Computers with graphing software.
Top Scholar KLB Mathematics Learners Book Grade 9, page 75.
Charts showing inequality symbols.
Real-life examples of inequalities.
Number lines.
Top Scholar KLB Mathematics Learners Book Grade 9, page 76.
Charts showing inequality rules.

Oral questions. Written exercise. Group presentation.

Algebra
MEASUREMENTS
MEASUREMENTS
MEASUREMENTS

Linear Inequalities - Solving Linear Inequalities (Combined Operations)
Linear Inequalities - Graphical Representation in One Unknown
Linear Inequalities - Graphical Representation in Two Unknowns
Area of a Pentagon
Area of a Pentagon
Area of a Hexagon

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

Solve linear inequalities in one unknown involving more than one operation;
Apply complex linear inequalities to real life situations;
Show interest in solving multi-step inequalities.

Form and solve inequalities involving multiple operations.
Apply step-by-step approach to solving complex inequalities.
Solve real-life problems using complex inequalities.

How do we represent linear inequalities in graphs?

Top Scholar KLB Mathematics Learners Book Grade 9, page 77.
Worksheets with inequality problems.
Number lines.
Top Scholar KLB Mathematics Learners Book Grade 9, page 78.
Graph paper.
Top Scholar KLB Mathematics Learners Book Grade 9, page 79.
Rulers and protractors.
-Mathematics learners book grade 9 page 87;
-Cut-outs of regular pentagons;
-Chart with diagrams of pentagons;
-Calculator;
-Ruler and protractor.
-Mathematics learners book grade 9 page 89;
-Pentagonal objects;
-Worked examples on the board.
-Mathematics learners book grade 9 page 90;
-Cut-outs of regular hexagons;
-Chart with diagrams of hexagons;
-Ruler and protractor;
-Calculator.

Oral questions. Written exercise. Group work.

MEASUREMENTS

Area of a Hexagon
Surface Area of Triangular and Rectangular-Based Prisms
Surface Area of Triangular and Rectangular-Based Prisms
Surface Area of Triangular, Rectangular and Square-Based Pyramids
Surface Area of Triangular, Rectangular and Square-Based Pyramids

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

-Solve problems involving area of hexagons with different measurements;
-Relate the area of a hexagon to real-life situations;
-Demonstrate ability to work out complex hexagon area problems;
-Show genuine interest in calculating areas of hexagons.

In groups and individually, learners are guided to:
-Calculate the area of hexagons with given side lengths;
-Solve problems where vertices are at a given distance from the center;
-Identify real-life objects with hexagonal shapes and calculate their areas;
-Work out more challenging problems involving hexagons.

Where do we find hexagonal shapes in our daily lives?

-Mathematics learners book grade 9 page 91;
-Hexagonal objects;
-Calculator;
-Worked examples on the board.
-Mathematics learners book grade 9 page 94;
-Manila paper for making nets;
-Scissors;
-Rulers;
-Objects with triangular prism shapes;
-Glue.
-Mathematics learners book grade 9 page 95;
-Objects with rectangular prism shapes (boxes);
-Mathematics learners book grade 9 page 96;
-Objects with triangular pyramid shapes;
-Mathematics learners book grade 9 page 97;
-Objects with rectangular pyramid shapes;

-Written exercises; -Problem-solving tasks; -Peer assessment; -Mathematical problem-solving tasks.

MEASUREMENTS

Area of a Sector and Segment of a Circle
Surface Area of a Cone in Real Life Situations
Surface Area of a Cone in Real Life Situations
Surface Area of a Sphere in Real Life Situations

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

-Define a sector of a circle;
-Calculate the area of a sector using the formula A = (θ/360°) × πr²;
-Relate angle at the center to the area of a sector;
-Show interest in calculating area of sectors.

In groups, learners are guided to:
-Draw circles of different radii on paper;
-Mark points on the circumference to form sectors with different angles;
-Cut along radii and arc to form sectors;
-Measure angles at the center and calculate the area of sectors;
-Discuss and share results with other groups.

How does the angle at the center affect the area of a sector?

-Mathematics learners book grade 9 page 99;
-Circular paper cut-outs;
-Protractors;
-Scissors;
-Rulers;
-Scientific calculators.
-Mathematics learners book grade 9 page 101;
-Mathematics learners book grade 9 page 102;
-Conical objects (funnels, party hats);
-Glue.
-Mathematics learners book grade 9 page 103;
-Cone models;
-Scientific calculators;
-Charts showing formulas for surface area of cones.
-Mathematics learners book grade 9 page 104;
-Spherical objects (balls, oranges);
-Measuring tape/rulers;
-Charts showing formulas for surface area of spheres.

-Observation of practical work; -Oral questions; -Written exercises; -Group work assessment.

MEASUREMENTS

Volume of Triangular and Rectangular-Based Prisms
Volume of Triangular, Rectangular and Square-Based Pyramids
Volume of Triangular, Rectangular and Square-Based Pyramids
Volume of a Cone in Real Life Situations
Volume of a Sphere in Real Life Situations

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

-Identify triangular prisms;
-Calculate the volume of a triangular prism using the formula V = area of base × height;
-Solve problems involving volume of triangular prisms;
-Show interest in calculating volume of triangular prisms.

In groups, learners are guided to:
-Collect objects shaped like triangular prisms;
-Identify the base and height of triangular prisms;
-Calculate the area of the triangular base;
-Calculate the volume using the formula V = area of base × height;
-Discuss and share results with other groups.

How do we determine the volume of a triangular prism?

-Mathematics learners book grade 9 page 105;
-Triangular prism models;
-Rulers;
-Scientific calculators;
-Charts showing formulas for volume of triangular prisms.
-Mathematics learners book grade 9 page 107;
-Rectangular prism models (boxes);
-Charts showing formulas for volume of rectangular prisms.
-Mathematics learners book grade 9 page 108;
-Triangular-based pyramid models;
-Charts showing formulas for volume of pyramids.
-Mathematics learners book grade 9 page 109;
-Rectangular and square-based pyramid models;
-Mathematics learners book grade 9 page 110;
-Cone models;
-Charts showing formulas for volume of cones.
-Mathematics learners book grade 9 page 112;
-Spherical objects (balls);
-Measuring tape/rulers;
-Charts showing formulas for volume of spheres.

-Observation; -Oral questions; -Written exercises; -Problem-solving assessment.

MEASUREMENTS

Volume of a Frustum in Real Life Situations
Mass, Volume, Weight and Density - Instruments and Tools Used in Weighing
Mass, Volume, Weight and Density - Converting Units of Mass
Mass, Volume, Weight and Density - Relating Mass and Weight

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

-Define a frustum;
-Identify frustums of cones and pyramids;
-Calculate the volume of a frustum;
-Show genuine interest in calculating volumes of frustums.

In groups, learners are guided to:
-Identify and discuss models of frustums;
-Understand how a frustum is formed by cutting a cone or pyramid;
-Learn the formula for volume of a frustum;
-Calculate the volume of different frustums;
-Discuss and share results with other groups.

What is a frustum and how is it formed?

-Mathematics learners book grade 9 page 113;
-Frustum models;
-Rulers;
-Scientific calculators;
-Charts showing formulas for volume of frustums.
-Mathematics learners book grade 9 page 114;
-Mathematics learners book grade 9 page 117;
-Different types of weighing instruments;
-Various objects to weigh;
-Charts showing different weighing instruments.
-Mathematics learners book grade 9 page 118;
-Weighing instruments;
-Charts showing relationship between different units of mass.
-Mathematics learners book grade 9 page 119;
-Spring balance;
-Digital devices for research.

-Observation; -Oral questions; -Written exercises; -Problem-solving assessment.

MEASUREMENTS

Mass, Volume, Weight and Density - Determining Mass, Volume and Density
Mass, Volume, Weight and Density - Determining Density of Objects
Mass, Volume, Weight and Density - Determining Mass Given Volume and Density
Mass, Volume, Weight and Density - Determining Volume Given Mass and Density
Time, Distance and Speed - Working Out Speed in Km/h and m/s
Time, Distance and Speed - Working Out Speed in Km/h and m/s

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

-Define density;
-Understand the relationship between mass, volume, and density;
-Calculate density using the formula D = m/V;
-Show genuine interest in determining density of various substances.

In groups, learners are guided to:
-Measure the mass of different objects;
-Determine the volume of objects using water displacement method;
-Calculate the density of objects using the formula D = m/V;
-Complete a table with mass, volume, and density of different objects;
-Discuss and share findings with other groups.

How do we determine the density of an object?

-Mathematics learners book grade 9 page 121;
-Weighing instruments;
-Measuring cylinders;
-Various objects (coins, stones, metal pieces);
-Water;
-Scientific calculators.
-Mathematics learners book grade 9 page 122;
-Scientific calculators;
-Chart showing densities of common materials;
-Examples of applications of density in real life.
-Mathematics learners book grade 9 page 123;
-Mathematics learners book grade 9 page 124;
-Stopwatch/timer;
-Measuring tape/rulers;
-Sports field or open area.
-Mathematics learners book grade 9 page 125;
-Chart showing conversion between m/s and km/h;
-Examples of speeds of various objects and vehicles.

-Observation; -Oral questions; -Written exercises; -Practical assessment.

MEASUREMENTS

Time, Distance and Speed - Working Out Average Speed in Real Life Situations
Time, Distance and Speed - Determining Velocity in Real Life Situations
Time, Distance and Speed - Working Out Acceleration in Real Life Situations
Time, Distance and Speed - Identifying Longitudes on the Globe
Time, Distance and Speed - Relating Longitudes to Time on the Globe

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

-Define average speed;
-Calculate average speed over a journey;
-Solve problems involving average speed;
-Show interest in calculating average speed in real-life situations.

In groups, learners are guided to:
-Discuss the concept of average speed;
-Record distance covered and time taken for a journey with varying speeds;
-Calculate average speed using the formula average speed = total distance/total time;
-Solve problems involving average speed in real-life contexts;
-Discuss and share results with other groups.

How do we calculate the average speed of a journey?

-Mathematics learners book grade 9 page 126;
-Scientific calculators;
-Chart showing examples of average speed calculations;
-Examples of journey scenarios with varying speeds.
-Mathematics learners book grade 9 page 129;
-Stopwatch/timer;
-Measuring tape/rulers;
-Compass for directions.
-Mathematics learners book grade 9 page 130;
-Chart showing examples of acceleration calculations;
-Examples of acceleration in real-life situations.
-Mathematics learners book grade 9 page 131;
-Globe;
-World map showing longitudes;
-Digital devices for research;
-Charts showing the longitude system.
-Mathematics learners book grade 9 page 133;
-World map showing time zones;
-Charts showing the relationship between longitudes and time.

-Observation; -Oral questions; -Written exercises; -Problem-solving assessment.

MEASUREMENTS

Time, Distance and Speed - Determining Local Time of Places on Different Longitudes
Money - Identifying Currencies Used in Different Countries
Money - Converting Currency from One to Another in Real Life Situations

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

-Calculate local time at different longitudes;
-Understand that time increases eastward and decreases westward;
-Solve problems involving local time at different longitudes;
-Show interest in understanding time zones.

In groups, learners are guided to:
-Review the relationship between longitudes and time;
-Calculate local time at different longitudes given the local time at a reference longitude;
-Understand that for every 15° change in longitude, time changes by 1 hour;
-Solve problems involving local time at different longitudes;
-Discuss and share results with other groups.

How do we calculate the local time at different longitudes?

-Mathematics learners book grade 9 page 134;
-Globe;
-World map showing time zones;
-Scientific calculators;
-Charts showing examples of local time calculations.
-Mathematics learners book grade 9 page 136;
-World map showing time zones and the International Date Line;
-Mathematics learners book grade 9 page 137;
-Digital devices showing current time in different cities;
-Scientific calculators.
-Mathematics learners book grade 9 page 138;
-Digital devices for research;
-Pictures/samples of different currencies;
-Manila paper or carton;
-Charts showing currencies and their countries.
-Mathematics learners book grade 9 page 141;
-Exchange rate tables from newspapers or online sources;
-Digital devices for checking current exchange rates;
-Charts showing examples of currency conversions.

-Observation; -Oral questions; -Written exercises; -Problem-solving assessment.

MEASUREMENTS

Money - Converting Currency from One to Another in Real Life Situations
Money - Working Out Export Duties Charged on Goods
Money - Working Out Import Duties Charged on Goods
Money - Working Out Excise Duty Charged on Goods
Money - Determining Value-Added Tax (VAT) Charged on Goods and Services
Approximations and Errors - Approximating Quantities in Measurements

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

-Convert Kenyan currency to foreign currency;
-Use exchange rate tables to convert currencies;
-Solve problems involving currency conversion;
-Show interest in understanding international currency exchange.

In groups, learners are guided to:
-Review the concept of exchange rates;
-Understand that the selling rate is used when converting Kenyan Shillings to foreign currency;
-Convert Kenyan Shillings to various foreign currencies using the selling rate;
-Solve problems involving currency conversion;
-Discuss real-life situations where currency conversion is necessary;
-Discuss and share results with other groups.

How do exchange rates affect international trade?

-Mathematics learners book grade 9 page 142;
-Exchange rate tables from newspapers or online sources;
-Scientific calculators;
-Digital devices for checking current exchange rates;
-Charts showing examples of currency conversions.
-Mathematics learners book grade 9 page 143;
-Digital devices for research;
-Charts showing export duty rates;
-Examples of export scenarios.
-Charts showing import duty rates;
-Examples of import scenarios.
-Mathematics learners book grade 9 page 145;
-Charts showing excise duty rates;
-Examples of goods subject to excise duty.
-Supermarket receipts showing VAT;
-Charts showing VAT calculations.
-Mathematics learners book grade 9 page 148;
-Measuring tapes/rulers;
-Various objects to measure;
-Charts showing conventional and arbitrary units;
-Open space for measuring with strides.

-Observation; -Oral questions; -Written exercises; -Problem-solving assessment.

MEASUREMENTS
Geometry
Geometry
Geometry

Approximations and Errors - Determining Errors Using Estimations and Actual Measurements
Approximations and Errors - Determining Percentage Errors Using Actual Measurements
Coordinates and Graphs - Plotting points on a Cartesian plane
Coordinates and Graphs - Drawing a straight line graph
Coordinates and Graphs - Completing tables for linear equations

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

-Define error in measurements;
-Determine errors by comparing estimated and actual measurements;
-Calculate absolute errors in measurements;
-Develop genuine interest in understanding measurement errors.

In groups, learners are guided to:
-Estimate the measurements of various items in centimeters;
-Use a ruler to find the actual measurements of the items;
-Find the difference between the estimated and measured values;
-Understand that error = measured value - estimated value;
-Complete a table with estimated values, measured values, and errors;
-Discuss and share findings with other groups.

How do we determine errors in measurements?

-Mathematics learners book grade 9 page 149;
-Measuring tapes/rulers;
-Various objects to measure;
-Weighing scales/balances;
-Scientific calculators.
-Mathematics learners book grade 9 page 151;
-KLB Mathematics Grade 9 Textbook page 154
-Graph paper
-Ruler
-Pencils
-Charts with Cartesian plane
-Colored markers
-KLB Mathematics Grade 9 Textbook page 155
-Calculator
-Blackboard illustration
-KLB Mathematics Grade 9 Textbook page 156
-Charts with prepared tables

-Observation; -Oral questions; -Written exercises; -Practical assessment.

Geometry

Coordinates and Graphs - Drawing parallel lines
Coordinates and Graphs - Relating gradients of parallel lines
Coordinates and Graphs - Drawing perpendicular lines
Coordinates and Graphs - Relating gradients of perpendicular lines
Coordinates and Graphs - Applications of straight line graphs
Scale Drawing - Compass directions

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

Generate tables of values for parallel line equations;
Draw parallel lines on the Cartesian plane;
Appreciate the relationship between parallel lines on a graph.

Learners generate tables of values for equations such as y=x-5 and y=x-3.
Learners use the tables of values to draw the lines on the Cartesian plane.
Learners measure the distance between the two lines at different positions using a set square and discuss their findings.

How can we tell if two lines are parallel by looking at their equations?

-KLB Mathematics Grade 9 Textbook page 157
-Graph paper
-Ruler
-Set square
-Calculator
-Charts showing parallel lines
-KLB Mathematics Grade 9 Textbook page 158
-Manila paper
-Digital devices (optional)
-KLB Mathematics Grade 9 Textbook page 159
-Protractor
-Charts showing perpendicular lines
-KLB Mathematics Grade 9 Textbook page 160
-Charts with examples of perpendicular lines
-KLB Mathematics Grade 9 Textbook page 165
-Charts showing real-life applications
-Manila paper for presentations
-KLB Mathematics Grade 9 Textbook page 168
-Magnetic compass
-Plain paper
-Colored pencils
-Charts showing compass directions
-Maps

-Oral questions -Group work -Written exercise -Observation

Geometry

Scale Drawing - Compass bearings
Scale Drawing - True bearings
Scale Drawing - Determining compass bearings
Scale Drawing - Determining true bearings
Scale Drawing - Locating points using compass bearing and distance

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

Identify compass bearings in different situations;
Measure and state positions using compass bearings;
Value the importance of compass bearings in navigation.

Learners trace diagrams showing compass bearings.
Learners measure angles from the south and north, and state the position of points using these angles.
Learners draw accurately various compass bearings like N70°E, S50°W, etc.

How do we express directions using compass bearings?

-KLB Mathematics Grade 9 Textbook page 170
-Protractor
-Ruler
-Plain paper
-Charts showing compass bearings
-Manila paper
-KLB Mathematics Grade 9 Textbook page 171
-Charts showing true bearings
-Diagrams for tracing
-KLB Mathematics Grade 9 Textbook page 173
-Charts with bearing examples
-Manila paper for group work
-KLB Mathematics Grade 9 Textbook page 175
-Worksheets with diagrams
-KLB Mathematics Grade 9 Textbook page 178
-Drawing board
-Charts with examples
-Worksheets

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Scale Drawing - Locating points using true bearing and distance
Scale Drawing - Angle of elevation
Scale Drawing - Determining angles of elevation
Scale Drawing - Angle of depression
Scale Drawing - Determining angles of depression

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

Locate a point using true bearing and distance;
Create scale drawings showing relative positions;
Enjoy making scale drawings using bearings and distances.

Learners consider towns A and B where the bearing of A from B is 140° and the distance between them is 75 km.
Learners mark point B on paper, draw the bearing of A from B, and use a scale of 1 cm represents 10 km to locate A.
Learners make scale drawings showing the relative positions of multiple points.

How do we use true bearings and distances to create scale drawings?

-KLB Mathematics Grade 9 Textbook page 182
-Protractor
-Ruler
-Plain paper
-Drawing board
-Manila paper for presentations
-Worksheets
-KLB Mathematics Grade 9 Textbook page 186
-String
-Weight (about 25g)
-Cardboard
-Straight piece of wood
-Charts showing angles of elevation
-KLB Mathematics Grade 9 Textbook page 187
-Calculator
-Charts showing examples
-KLB Mathematics Grade 9 Textbook page 190
-Clinometer (made in previous lesson)
-Weight
-Charts showing angles of depression
-Diagrams
-KLB Mathematics Grade 9 Textbook page 192
-Charts with examples

-Oral questions -Practical activity -Written exercise -Observation

Geometry
Data Handling and Probability
Data Handling and Probability

Scale Drawing - Application in simple surveying
Scale Drawing - Survey using bearings and distances
Scale Drawing - Complex surveying problems
Scale Drawing - Project work on scale drawing
Data Interpretation - Appropriate class width
Data Interpretation - Finding range and creating groups

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

Apply scale drawing in simple surveying;
Record measurements in a field book;
Value the importance of surveying in mapping.

Learners study a survey of a small island made using a triangle ABC around it.
Learners trace the diagram and draw perpendicular lines from points along the triangle sides to the edge of the island.
Learners measure the lengths of perpendicular lines and record the measurements in a tabular form in a field book.

How do surveyors use scale drawings to create maps?

-KLB Mathematics Grade 9 Textbook page 195
-Drawing paper
-Ruler
-Set square
-Pencil
-Field book (notebook)
-Charts with survey examples
-KLB Mathematics Grade 9 Textbook page 199
-Protractor
-Plain paper
-Drawing board
-Field book
-Charts with examples
-KLB Mathematics Grade 9 Textbook page 202
-Calculator
-Maps
-Measuring tape
-Compass
-Colored pencils
-Manila paper
-Drawing instruments
-KLB Mathematics Grade 9 Textbook page 244
-Graph paper
-Rulers
-Colored markers
-KLB Mathematics Grade 9 Textbook page 245
-Data sets
-Chart with examples

-Oral questions -Practical activity -Written exercise -Field book assessment

Data Handling and Probability

Data Interpretation - Frequency distribution tables
Data Interpretation - Creating frequency tables with different class intervals
Data Interpretation - Modal class
Data Interpretation - Mean of ungrouped data
Data Interpretation - Mean of grouped data

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

Draw frequency distribution tables of grouped data;
Use tally marks to organize data into frequency tables;
Value the importance of organizing data in tables.

Learners are presented with data on the number of tree seedlings that survived in 50 different schools.
Learners copy and complete a frequency distribution table using tally marks and frequencies.
Learners discuss and share their completed tables with other groups.

How do we organize data in a frequency distribution table?

-KLB Mathematics Grade 9 Textbook page 247
-Chart paper
-Ruler
-Calculator
-Manila paper
-Colored markers
-Graph paper
-Worksheets with data
-KLB Mathematics Grade 9 Textbook page 248
-Chart showing frequency distribution tables
-KLB Mathematics Grade 9 Textbook page 249
-Chart showing frequency tables
-Worksheets
-KLB Mathematics Grade 9 Textbook page 250
-Chart with examples

-Oral questions -Group presentations -Written exercise -Checklist

Data Handling and Probability

Data Interpretation - Mean calculation in real-life situations
Data Interpretation - Median of grouped data
Data Interpretation - Calculating median using formula
Data Interpretation - Median calculations in real-life situations
Probability - Equally likely outcomes

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

Calculate the mean of grouped data from real-life situations;
Apply the formula for finding mean of grouped data;
Appreciate the use of mean in summarizing data in real life.

Learners are presented with data about plants that survived in 50 sampled schools during an environmental week.
Learners find midpoints of class intervals, multiply by frequencies, and sum them up.
Learners calculate the mean number of plants that survived by dividing the sum of fx by the sum of f.

How is the mean used to summarize real-life data?

-KLB Mathematics Grade 9 Textbook page 251
-Calculator
-Manila paper
-Chart with examples
-Worksheets
-Colored markers
-KLB Mathematics Grade 9 Textbook page 252
-Chart showing cumulative frequency tables
-KLB Mathematics Grade 9 Textbook page 253
-Graph paper
-Chart showing median formula
-KLB Mathematics Grade 9 Textbook page 254
-Chart with example calculations
-Worksheets with real-life data
-KLB Mathematics Grade 9 Textbook page 256
-Coins
-Chart paper
-Table for recording outcomes

-Oral questions -Group work -Written exercise -Assessment rubrics

Data Handling and Probability

Probability - Range of probability
Probability - Complementary events
Probability - Mutually exclusive events
Probability - Experiments with mutually exclusive events
Probability - Independent events
Probability - Calculating probabilities of independent events
Probability - Tree diagrams for single outcomes
Probability - Complex tree diagrams
Probability - Complex tree diagrams

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

Determine the range of probability of an event;
Understand that probability ranges from 0 to 1;
Value the concept of probability range in real-life situations.

Learners use a fair die in this activity and toss it 20 times.
Learners record the number of times each face shows up and calculate relative frequencies.
Learners find the sum of the fractions and discuss that probabilities range from 0 to 1.

What is the range of probability values and what do these values signify?

-KLB Mathematics Grade 9 Textbook page 257
-Dice
-Table for recording outcomes
-Chart showing probability scale (0-1)
-Manila paper
-Colored markers
-KLB Mathematics Grade 9 Textbook page 258
-Calculator
-Chart showing complementary events
-Worksheets with problems
-Coins
-Chart with examples of mutually exclusive events
-Flashcards with different scenarios
-KLB Mathematics Grade 9 Textbook page 259
-Colored objects in boxes
-Chart showing probability calculations
-KLB Mathematics Grade 9 Textbook page 260
-Coins and dice
-Chart showing examples of independent events
-KLB Mathematics Grade 9 Textbook page 261
-Chart showing multiplication rule
-KLB Mathematics Grade 9 Textbook page 262
-Chart paper
-Ruler
-Worksheets with blank tree diagrams
-Chart showing completed tree diagrams
-KLB Mathematics Grade 9 Textbook page 263
-Chart showing complex tree diagrams

-Oral questions -Practical activity -Written exercise -Group presentations