MEASUREMENTS

Volume of Triangular and Rectangular-Based Prisms
Volume of Triangular, Rectangular and Square-Based Pyramids

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

-Identify rectangular prisms/cuboids;
-Calculate the volume of a rectangular prism using the formula V = length × width × height;
-Solve problems involving volume of rectangular prisms;
-Appreciate the use of volume calculations in real-life situations.

In groups, learners are guided to:
-Collect objects shaped like rectangular prisms;
-Measure the length, width, and height of rectangular prisms;
-Calculate the volume using the formula V = length × width × height;
-Solve practical problems involving volume of rectangular prisms;
-Discuss and share results with other groups.

How do we determine the volume of different solids?

-Mathematics learners book grade 9 page 107;
-Rectangular prism models (boxes);
-Rulers;
-Scientific calculators;
-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.

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

MEASUREMENTS

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

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

-Identify rectangular and square-based pyramids;
-Calculate the volume of rectangular and square-based pyramids;
-Solve problems involving volume of rectangular and square-based pyramids;
-Appreciate the application of volume calculations in real-life.

In groups, learners are guided to:
-Identify and discuss models of rectangular and square-based pyramids;
-Identify the base and height of the pyramids;
-Calculate the area of the base (rectangle or square);
-Calculate the volume using the formula V = ⅓ × area of base × height;
-Discuss and share results with other groups.

How does the shape of the base affect the volume of a pyramid?

-Mathematics learners book grade 9 page 109;
-Rectangular and square-based pyramid models;
-Rulers;
-Scientific calculators;
-Charts showing formulas for volume of pyramids.
-Mathematics learners book grade 9 page 110;
-Cone models;
-Charts showing formulas for volume of cones.

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

MEASUREMENTS

Volume of a Sphere in Real Life Situations
Volume of a Frustum in Real Life Situations

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

-Identify spheres and their properties;
-Calculate the volume of a sphere using the formula V = ⅘ × πr³;
-Solve problems involving volume of spheres;
-Develop interest in calculating volumes of spheres.

In groups, learners are guided to:
-Identify and discuss models of spheres;
-Measure the radius of spherical objects;
-Calculate the volume using the formula V = ⅘ × πr³;
-Solve practical problems involving volume of spheres;
-Discuss and share results with other groups.

How do we determine the volume of a sphere?

-Mathematics learners book grade 9 page 112;
-Spherical objects (balls);
-Measuring tape/rulers;
-Scientific calculators;
-Charts showing formulas for volume of spheres.
-Mathematics learners book grade 9 page 113;
-Frustum models;
-Rulers;
-Charts showing formulas for volume of frustums.

-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

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

-Calculate the volume of a frustum of a cone;
-Calculate the volume of a frustum of a pyramid;
-Solve problems involving volume of frustums;
-Appreciate the application of volume of frustums in real-life situations.

In groups, learners are guided to:
-Review the formula for volume of a frustum;
-Calculate the volume of a frustum of a cone using the formula V = (1/3)πh(R² + Rr + r²);
-Calculate the volume of a frustum of a pyramid;
-Solve practical problems involving volume of frustums;
-Discuss and share results with other groups.

How do we calculate the volume of a frustum?

-Mathematics learners book grade 9 page 114;
-Frustum models;
-Rulers;
-Scientific calculators;
-Charts showing formulas for volume of frustums.
-Mathematics learners book grade 9 page 117;
-Different types of weighing instruments;
-Various objects to weigh;
-Charts showing different weighing instruments.

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

MEASUREMENTS

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:

-Identify different units of mass;
-Convert units of mass from one form to another;
-Solve problems involving conversion of mass units;
-Appreciate the importance of standardized units of mass.

In groups, learners are guided to:
-Collect and weigh different items using a weighing balance;
-Record measurements in different units;
-Convert between different units of mass (kg, g, mg, etc.);
-Solve problems involving mass conversions;
-Discuss and share results with other groups.

Why do we need to convert units of mass from one form to another?

-Mathematics learners book grade 9 page 118;
-Weighing instruments;
-Various objects to weigh;
-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; -Practical assessment.

MEASUREMENTS

Mass, Volume, Weight and Density - Determining Mass, Volume and Density
Mass, Volume, Weight and Density - Determining Density of Objects

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.

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

MEASUREMENTS

Mass, Volume, Weight and Density - Determining Mass Given Volume and Density
Mass, Volume, Weight and Density - Determining Volume Given Mass and Density

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

-Rearrange the density formula to find mass;
-Calculate mass given volume and density using the formula m = D × V;
-Solve problems involving mass, volume, and density;
-Show interest in applying density concepts to find mass.

In groups, learners are guided to:
-Review the relationship between mass, volume, and density;
-Rearrange the formula D = m/V to find m = D × V;
-Calculate the mass of objects given their volume and density;
-Solve practical problems involving mass, volume, and density;
-Discuss and share results with other groups.

How can we determine the mass of an object if we know its volume and density?

-Mathematics learners book grade 9 page 123;
-Scientific calculators;
-Chart showing densities of common materials;
-Examples of applications of density in real life.

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

MEASUREMENTS

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 speed;
-Calculate speed in meters per second (m/s);
-Solve problems involving speed in m/s;
-Show interest in calculating speed.

In groups, learners are guided to:
-Participate in timed races over measured distances;
-Record distance covered and time taken;
-Calculate speed using the formula speed = distance/time;
-Express speed in meters per second (m/s);
-Complete a table with distance, time, and speed;
-Discuss and share results with other groups.

How do we observe speed in daily activities?

-Mathematics learners book grade 9 page 124;
-Stopwatch/timer;
-Measuring tape/rulers;
-Scientific calculators;
-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

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.

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

MEASUREMENTS

Time, Distance and Speed - Working Out Acceleration in Real Life Situations

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

-Define acceleration;
-Calculate acceleration using the formula a = (v-u)/t;
-Solve problems involving acceleration;
-Develop interest in understanding acceleration in real-life situations.

In groups, learners are guided to:
-Discuss the concept of acceleration;
-Record initial velocity, final velocity, and time taken for various movements;
-Calculate acceleration using the formula a = (v-u)/t;
-Understand deceleration as negative acceleration;
-Solve problems involving acceleration in real-life contexts;
-Discuss and share results with other groups.

How do we calculate acceleration?

-Mathematics learners book grade 9 page 130;
-Stopwatch/timer;
-Scientific calculators;
-Chart showing examples of acceleration calculations;
-Examples of acceleration in real-life situations.

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

MEASUREMENTS

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:

-Identify longitudes on a globe;
-Understand the concept of the prime meridian;
-Describe how longitudes are measured in degrees east or west;
-Show interest in understanding the globe and longitudes.

In groups, learners are guided to:
-Use a globe to identify circles that pass through North and South poles;
-Search from the Internet or print media for the meaning of these circles;
-Identify special circles on the globe (Prime Meridian, International Date Line);
-Discuss how longitudes are measured in degrees east or west of the Prime Meridian;
-Discuss and share findings with other groups.

Why does time vary in different places of the world?

-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; -Group presentations.

MEASUREMENTS

Time, Distance and Speed - Determining Local Time of Places on Different Longitudes

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;

-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

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

-Apply knowledge of local time to solve various problems;
-Convert between 12-hour and 24-hour time formats;
-Solve real-world problems involving time zones;
-Show genuine interest in understanding global time.

In groups, learners are guided to:
-Review calculations of local time at different longitudes;
-Convert between 12-hour (am/pm) and 24-hour time formats;
-Solve problems involving flight times, international calls, and global events;
-Use digital resources to explore current time in different parts of the world;
-Discuss and share results with other groups.

How do time zones affect international communication and travel?

-Mathematics learners book grade 9 page 137;
-Globe;
-World map showing time zones;
-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.

-Observation; -Oral questions; -Written exercises; -Project work on time zones.

MEASUREMENTS

Money - Converting Currency from One to Another in Real Life Situations

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

-Understand exchange rates;
-Convert foreign currency to Kenyan currency;
-Use exchange rate tables;
-Appreciate the concept of currency exchange.

In groups, learners are guided to:
-Study exchange rates of international currencies in a table;
-Understand the concept of buying and selling rates;
-Convert foreign currencies to Kenyan Shillings using the buying rate;
-Solve problems involving currency conversion;
-Use digital devices to compare exchange rates from different sources;
-Discuss and share results with other groups.

Why do we change currencies from one form to another?

-Mathematics learners book grade 9 page 141;
-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 142;

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

MEASUREMENTS

Money - Working Out Export Duties Charged on Goods
Money - Working Out Import Duties Charged on Goods

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

-Define export duty;
-Calculate export duty on goods;
-Understand the purpose of export duties;
-Appreciate the role of export duties in international trade.

In groups, learners are guided to:
-Use digital devices to search for the meaning of export duty;
-Research the percentage of export duty on different goods in Kenya;
-Calculate export duty on goods using the formula: Export Duty = Value of Goods × Duty Rate;
-Solve problems involving export duties;
-Discuss the purpose and impact of export duties;
-Discuss and share findings with other groups.

What are the types of taxes the government levy on its citizens?

-Mathematics learners book grade 9 page 143;
-Digital devices for research;
-Scientific calculators;
-Charts showing export duty rates;
-Examples of export scenarios.
-Charts showing import duty rates;
-Examples of import scenarios.

-Observation; -Oral questions; -Written exercises; -Research presentation.

MEASUREMENTS

Money - Working Out Excise Duty Charged on Goods
Money - Determining Value-Added Tax (VAT) Charged on Goods and Services

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

-Define excise duty;
-Identify goods and services that attract excise duty;
-Calculate excise duty on goods and services;
-Show interest in understanding taxation systems.

In groups, learners are guided to:
-Use digital devices to search for the meaning of excise duty;
-Research goods that attract excise duty;
-Research percentage of excise duty on goods and services;
-Calculate excise duty on various goods and services;
-Solve problems involving excise duty;
-Discuss and share findings with other groups.

What is excise duty and how is it different from other taxes?

-Mathematics learners book grade 9 page 145;
-Digital devices for research;
-Scientific calculators;
-Charts showing excise duty rates;
-Examples of goods subject to excise duty.
-Supermarket receipts showing VAT;
-Charts showing VAT calculations.

-Observation; -Oral questions; -Written exercises; -Research presentation.

MEASUREMENTS

Approximations and Errors - Approximating Quantities in Measurements
Approximations and Errors - Determining Errors Using Estimations and Actual Measurements

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

-Approximate quantities using arbitrary units;
-Use strides, hand spans, and other body measurements to estimate lengths;
-Compare estimated values with actual measurements;
-Show interest in approximation techniques.

In groups, learners are guided to:
-Measure the lengths of their strides in centimeters;
-Measure the length of the classroom using strides;
-Estimate the length of the classroom in centimeters;
-Use hand spans to estimate lengths of various objects;
-Use thumb lengths to estimate smaller lengths;
-Discuss and share findings with other groups.

How do we estimate measurements of different quantities?

-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.
-Mathematics learners book grade 9 page 149;
-Weighing scales/balances;
-Scientific calculators.

-Observation; -Oral questions; -Practical assessment; -Group presentations.

MEASUREMENTS
Geometry

Approximations and Errors - Determining Percentage Errors Using Actual Measurements
Similarity and Enlargement - Similar figures and properties

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

-Define percentage error;
-Calculate percentage error in measurements;
-Interpret the meaning of percentage error;
-Show interest in minimizing errors in measurements.

In groups, learners are guided to:
-Review the concept of error in measurements;
-Express error as a ratio of the actual value;
-Convert the ratio to a percentage to find percentage error;
-Calculate percentage error using the formula: Percentage Error = (Error/Actual Value) × 100%;
-Solve problems involving percentage error;
-Discuss and share findings with other groups.

Why is percentage error more useful than absolute error?

-Mathematics learners book grade 9 page 151;
-Measuring tapes/rulers;
-Various objects to measure;
-Weighing scales/balances;
-Scientific calculators.
-KLB Mathematics Grade 9 Textbook page 203
-Ruler
-Protractor
-Cut-out shapes
-Charts showing similar figures
-Manila paper

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

Geometry

Similarity and Enlargement - Identifying similar objects
Similarity and Enlargement - Drawing similar figures

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

Identify similar objects in the environment;
Determine if given figures are similar;
Value the concept of similarity in everyday life.

Learners collect and classify objects according to similarity.
Learners identify pairs of similar figures from given diagrams.
Learners discuss real-life examples of similar objects and their properties.

How do we recognize similar objects in our environment?

-KLB Mathematics Grade 9 Textbook page 204
-Ruler
-Protractor
-Various geometric objects
-Charts with examples
-Worksheets with diagrams
-KLB Mathematics Grade 9 Textbook page 206
-Pair of compasses
-Drawing paper
-Calculator

-Oral questions -Group work -Written exercise -Observation

Geometry

Similarity and Enlargement - Properties of enlargement

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

Determine properties of enlargement of different figures;
Locate the center of enlargement and find scale factors;
Value the application of enlargement in real-life situations.

Learners trace diagrams showing an object and its enlarged image.
Learners draw lines through corresponding points to find where they intersect (center of enlargement).
Learners find the ratios of corresponding lengths to determine the scale factor.

How do we determine the center and scale factor of an enlargement?

-KLB Mathematics Grade 9 Textbook page 209
-Ruler
-Tracing paper
-Colored pencils
-Grid paper
-Charts showing enlargements
-Diagrams for tracing

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Similarity and Enlargement - Negative scale factors
Similarity and Enlargement - Drawing images of objects

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

Determine properties of enlargement with negative scale factors;
Locate centers of enlargement with negative scale factors;
Appreciate the concept of negative scale factors in enlargements.

Learners trace diagrams showing an object and its image where the center of enlargement is between them.
Learners join corresponding points to locate the center of enlargement.
Learners find the ratio of distances from the center to corresponding points and note that the image is on the opposite side of the object.

What happens when an enlargement has a negative scale factor?

-KLB Mathematics Grade 9 Textbook page 211
-Ruler
-Tracing paper
-Grid paper
-Colored pencils
-Charts showing negative scale factor enlargements
-Diagrams for tracing
-KLB Mathematics Grade 9 Textbook page 214
-Charts showing steps of enlargement
-Manila paper

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Similarity and Enlargement - Linear scale factor
Similarity and Enlargement - Using coordinates in enlargement

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

Determine the linear scale factor of similar figures;
Calculate unknown dimensions using linear scale factors;
Value the application of linear scale factors in real-life problems.

Learners consider similar cones and find the ratios of their corresponding dimensions.
Learners study similar triangles and calculate the linear scale factor.
Learners use the scale factor to find unknown dimensions of similar figures.

How do we use linear scale factors to calculate unknown dimensions of similar figures?

-KLB Mathematics Grade 9 Textbook page 216
-Ruler
-Calculator
-Similar objects of different sizes
-Charts with examples
-Worksheets
-KLB Mathematics Grade 9 Textbook page 218
-Grid paper
-Colored pencils
-Charts with coordinate examples

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

Geometry

Similarity and Enlargement - Applications of similarity
Trigonometry - Angles and sides of right-angled triangles

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

Apply similarity concepts to solve real-life problems;
Calculate heights and distances using similar triangles;
Value the practical applications of similarity in everyday life.

Learners solve problems involving similar triangles to find unknown heights and distances.
Learners discuss how similarity is used in fields such as architecture, photography, and engineering.
Learners work on practical applications of similarity in the environment.

How can we use similarity to solve real-life problems?

-KLB Mathematics Grade 9 Textbook page 219
-Ruler
-Calculator
-Drawing paper
-Charts with real-life applications
-Manila paper for presentations
-KLB Mathematics Grade 9 Textbook page 220
-Protractor
-Set square
-Charts with labeled triangles
-Colored markers

-Oral questions -Problem-solving -Written exercise -Group presentation

Geometry

Trigonometry - Sine ratio
Trigonometry - Cosine ratio

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

Identify sine ratio from a right-angled triangle;
Calculate sine of angles in right-angled triangles;
Value the use of sine ratio in solving problems.

Learners draw triangles with specific angles and sides.
Learners draw perpendiculars from points on one side to another and measure their lengths.
Learners calculate ratios of opposite side to hypotenuse for different angles and discover the sine ratio.

What is the sine of an angle and how do we calculate it?

-KLB Mathematics Grade 9 Textbook page 222
-Ruler
-Protractor
-Calculator
-Drawing paper
-Charts showing sine ratio
-Manila paper
-KLB Mathematics Grade 9 Textbook page 223
-Charts showing cosine ratio
-Worksheets

-Oral questions -Practical activity -Written exercise -Assessment rubrics

Geometry

Trigonometry - Tangent ratio
Trigonometry - Reading tables of sines

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

Identify tangent ratio from a right-angled triangle;
Calculate tangent of angles in right-angled triangles;
Appreciate the importance of tangent ratio in problem-solving.

Learners draw triangle ABC with specific angles and mark points on BC.
Learners draw perpendiculars from these points to AC and measure their lengths.
Learners calculate ratios of opposite side to adjacent side for different angles and discover the tangent ratio.

What is the tangent of an angle and how do we calculate it?

-KLB Mathematics Grade 9 Textbook page 225
-Ruler
-Protractor
-Calculator
-Drawing paper
-Charts showing tangent ratio
-Manila paper
-KLB Mathematics Grade 9 Textbook page 227
-Mathematical tables
-Worksheets
-Chart showing how to read tables
-Sample exercises

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Trigonometry - Reading tables of cosines and tangents
Trigonometry - Using calculators for trigonometric ratios

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

Read tables of cosines and tangents for acute angles;
Find cosine and tangent values using mathematical tables;
Enjoy using mathematical tables to find trigonometric ratios.

Learners study parts of the tables of cosines and tangents.
Learners use the tables to find cosine and tangent values of specific angles.
Learners find values of angles with decimal parts using the 'SUBTRACT' column for cosines and 'ADD' column for tangents.

How do we use mathematical tables to find cosine and tangent values?

-KLB Mathematics Grade 9 Textbook page 229-231
-Mathematical tables
-Calculator
-Worksheets
-Chart showing how to read tables
-Sample exercises
-KLB Mathematics Grade 9 Textbook page 233
-Scientific calculators
-Chart showing calculator keys

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Trigonometry - Calculating lengths using trigonometric ratios
Trigonometry - Calculating angles using trigonometric ratios

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

Apply trigonometric ratios to calculate lengths of right-angled triangles;
Use sine, cosine, and tangent ratios to find unknown sides;
Appreciate the application of trigonometry in solving real-life problems.

Learners consider a right-angled triangle and find the trigonometric ratio appropriate for finding an unknown side.
Learners find the value of the ratio from tables or calculators and relate it to the expression to find the unknown side.
Learners solve problems involving finding sides of right-angled triangles.

How do we use trigonometric ratios to find unknown sides in right-angled triangles?

-KLB Mathematics Grade 9 Textbook page 234
-Scientific calculators
-Mathematical tables
-Ruler
-Drawing paper
-Charts with examples
-Worksheets
-KLB Mathematics Grade 9 Textbook page 235

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

Geometry

Trigonometry - Application in heights and distances
Trigonometry - Application in navigation

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

Apply trigonometric ratios to solve problems involving heights and distances;
Calculate heights of objects using angles of elevation;
Value the use of trigonometry in real-life situations.

Learners solve problems involving finding heights of objects like flag poles, towers, and buildings using angles of elevation.
Learners apply sine, cosine, and tangent ratios as appropriate to calculate unknown heights and distances.
Learners discuss real-life applications of trigonometry in architecture, navigation, and engineering.

How do we use trigonometry to find heights and distances in real-life situations?

-KLB Mathematics Grade 9 Textbook page 237
-Scientific calculators
-Mathematical tables
-Ruler
-Drawing paper
-Charts with real-life examples
-Manila paper
-KLB Mathematics Grade 9 Textbook page 238
-Protractor
-Maps
-Charts with navigation examples

-Oral questions -Problem-solving -Written exercise -Group presentation

Geometry
Data Handling and Probability

Trigonometry - Review and mixed applications
Data Interpretation - Appropriate class width

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

Apply trigonometric concepts in mixed application problems;
Solve problems involving both scale drawing and trigonometry;
Value the integration of different geometric concepts in problem-solving.

Learners solve a variety of problems that integrate different geometric concepts learned.
Learners apply scale drawing, bearings, similar figures, and trigonometric ratios to solve complex problems.
Learners discuss how different geometric concepts interconnect in solving real-world problems.

How can we integrate different geometric concepts to solve complex problems?

-KLB Mathematics Grade 9 Textbook page 240
-Scientific calculators
-Mathematical tables
-Ruler
-Protractor
-Drawing paper
-Past examination questions
-KLB Mathematics Grade 9 Textbook page 244
-Calculator
-Graph paper
-Manila paper
-Rulers
-Colored markers

-Oral questions -Problem-solving -Written exercise -Assessment test

Data Handling and Probability

Data Interpretation - Finding range and creating groups

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

Calculate the range of a set of data;
Divide data into suitable class intervals;
Show interest in grouping data for better representation.

Learners are presented with marks scored by 40 students in a mathematics test.
Learners find the range of the data.
Learners complete a table using a class width of 10 and determine the number of classes formed.

How does the range of data help us determine appropriate class intervals?

-KLB Mathematics Grade 9 Textbook page 245
-Calculator
-Manila paper
-Data sets
-Chart with examples
-Colored markers

-Oral questions -Written exercise -Observation -Group work assessment

Data Handling and Probability

Data Interpretation - Frequency distribution tables
Data Interpretation - Creating frequency tables with different class intervals

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

-Oral questions -Group presentations -Written exercise -Checklist

Data Handling and Probability

Data Interpretation - Modal class
Data Interpretation - Mean of ungrouped data

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

Identify the modal class of grouped data;
Determine the class with the highest frequency;
Develop interest in finding the modal class in real-life data.

Learners are presented with assessment marks in a mathematics test for 32 learners.
Learners draw a frequency distribution table to represent the information.
Learners identify and write down the class with the highest frequency (modal class).

What is the modal class and how is it determined?

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

-Oral questions -Group work -Written exercise -Peer assessment

Data Handling and Probability

Data Interpretation - Mean of grouped data
Data Interpretation - Mean calculation in real-life situations

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

Calculate the mean of grouped data;
Find the midpoint of class intervals and use in calculations;
Value the importance of mean in summarizing data.

Learners consider a frequency distribution table representing masses in kilograms of learners in a class.
Learners complete a table by finding midpoints of class intervals and calculating fx.
Learners find the sum of frequencies, sum of fx, and divide to find the mean.

How do we calculate the mean of grouped data?

-KLB Mathematics Grade 9 Textbook page 250
-Calculator
-Graph paper
-Manila paper
-Chart with examples
-Worksheets
-KLB Mathematics Grade 9 Textbook page 251
-Colored markers

-Oral questions -Written exercise -Group presentations -Checklist

Data Handling and Probability

Data Interpretation - Median of grouped data
Data Interpretation - Calculating median using formula

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

Determine the median of grouped data;
Find cumulative frequencies to locate the median class;
Value the importance of median in data interpretation.

Learners consider the mass of 50 learners recorded in a table.
Learners complete the column for cumulative frequency.
Learners find the sum of frequency, divide by 2, and identify the position of the median mass.

How do we determine the median of grouped data?

-KLB Mathematics Grade 9 Textbook page 252
-Calculator
-Chart showing cumulative frequency tables
-Worksheets
-Manila paper
-Colored markers
-KLB Mathematics Grade 9 Textbook page 253
-Graph paper
-Chart showing median formula

-Oral questions -Written exercise -Group presentations -Observation

Data Handling and Probability

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 median in real-life data situations;
Apply the median formula to various data sets;
Appreciate the role of median in data interpretation.

Learners are presented with data on number of nights spent by people in a table.
Learners complete the cumulative frequency column and determine the median class.
Learners apply the median formula to calculate the median value.

How is the median used to interpret real-life data?

-KLB Mathematics Grade 9 Textbook page 254
-Calculator
-Chart with example calculations
-Worksheets with real-life data
-Manila paper
-Colored markers
-KLB Mathematics Grade 9 Textbook page 256
-Coins
-Chart paper
-Table for recording outcomes

-Oral questions -Written exercise -Group presentations -Peer assessment

Data Handling and Probability

Probability - Range of probability
Probability - Complementary events

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

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

Data Handling and Probability

Probability - Mutually exclusive events
Probability - Experiments with mutually exclusive events

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

Identify mutually exclusive events in real-life situations;
Recognize events that cannot occur simultaneously;
Appreciate the concept of mutually exclusive events.

Learners flip a fair coin several times and record the face that shows up.
Learners discuss that heads and tails cannot show up at the same time (mutually exclusive).
Learners identify mutually exclusive events from various examples.

What makes events mutually exclusive?

-KLB Mathematics Grade 9 Textbook page 258
-Coins
-Chart with examples of mutually exclusive events
-Flashcards with different scenarios
-Manila paper
-Colored markers
-KLB Mathematics Grade 9 Textbook page 259
-Dice
-Colored objects in boxes
-Calculator
-Chart showing probability calculations
-Worksheets with problems

-Oral questions -Group discussions -Written exercise -Observation

Data Handling and Probability

Probability - Independent events
Probability - Calculating probabilities of independent events

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

Perform experiments involving independent events;
Understand that outcome of one event doesn't affect another;
Show interest in applying independent events probability in real-life.

Learners toss a fair coin and a fair die at the same time and record outcomes.
Learners repeat the experiment several times.
Learners discuss that the outcome of the coin toss doesn't affect the outcome of the die roll (independence).

What makes events independent from each other?

-KLB Mathematics Grade 9 Textbook page 260
-Coins and dice
-Table for recording outcomes
-Chart showing examples of independent events
-Manila paper
-Colored markers
-KLB Mathematics Grade 9 Textbook page 261
-Calculator
-Chart showing multiplication rule
-Worksheets with problems

-Oral questions -Practical activity -Group discussions -Observation

Data Handling and Probability

Probability - Tree diagrams for single outcomes
Probability - Complex tree diagrams

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

Draw a probability tree diagram for a single outcome;
Represent probability situations using tree diagrams;
Value the use of tree diagrams in organizing probability information.

Learners write down possible outcomes when a fair coin is flipped once.
Learners find the total number of all outcomes and probability of each outcome.
Learners complete a tree diagram with possible outcomes and their probabilities.

How do tree diagrams help us understand probability situations?

-KLB Mathematics Grade 9 Textbook page 262
-Chart paper
-Ruler
-Worksheets with blank tree diagrams
-Chart showing completed tree diagrams
-Colored markers
-KLB Mathematics Grade 9 Textbook page 263
-Calculator
-Chart showing complex tree diagrams
-Worksheets with problems

-Oral questions -Practical activity -Group work assessment -Checklist

Data Handling and Probability

Probability - Complex tree diagrams

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