MEASUREMENTS

Area of a Pentagon
Area of a Hexagon

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

-Identify and state the number of sides in a pentagon;
-Calculate the area of a regular pentagon;
-Apply the formula for finding the area of a pentagon in real-life situations;
-Develop genuine interest in calculating the area of regular pentagons.

-Identify and state the number of sides in a hexagon;
-Calculate the area of a regular hexagon;
-Use triangles to work out the area of a hexagon;
-Show interest in learning about hexagons and their properties.

In groups and individually, learners are guided to:
-Discuss the properties of regular polygons;
-Use cut-outs to work out the area of pentagons;
-Identify objects with pentagonal shapes in their environment;
-Calculate the area of a regular pentagon using the formula A = (5/2)s²sin(72°).
In groups and individually, learners are guided to:
-Discuss the properties of regular hexagons;
-Trace hexagons on paper and join vertices to the center to form triangles;
-Measure the height and base of triangles formed in the hexagon;
-Calculate the area of hexagons using the formula A = (3√3/2)s².

How do we determine the area of different surfaces?
How many triangles can be formed by joining the center of a hexagon to each vertex?

-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.
-Mathematics learners book grade 9 page 91;
-Hexagonal objects;
-Calculator;
-Worked examples on the board.

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

MEASUREMENTS

Surface Area of Triangular and Rectangular-Based Prisms

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

-Draw a triangular prism and identify its faces, edges, and vertices;
-Develop a net for a triangular prism;
-Calculate the surface area of a triangular prism using its net;
-Appreciate the practical applications of surface area calculations.

In groups, learners are guided to:
-Collect from the environment objects that are triangular prisms;
-Draw and sketch nets of triangular prisms;
-Measure dimensions of the faces on the nets;
-Calculate the area of each face and add to find the total surface area;
-Discuss and share results with other groups.

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

-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);

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

MEASUREMENTS

Surface Area of Triangular, Rectangular and Square-Based Pyramids

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

-Draw a triangular-based pyramid and identify its faces, edges, and vertices;
-Develop a net for a triangular-based pyramid;
-Calculate the surface area of a triangular-based pyramid;
-Develop interest in calculating surface areas of pyramids.

In groups, learners are guided to:
-Collect objects shaped like triangular-based pyramids;
-Draw and sketch nets of triangular-based pyramids;
-Measure dimensions of the faces on the nets;
-Calculate the area of each face and add to find the total surface area;
-Discuss and share results with other groups.

How do we determine the surface area of a triangular-based pyramid?

-Mathematics learners book grade 9 page 96;
-Manila paper for making nets;
-Scissors;
-Rulers;
-Objects with triangular pyramid shapes;
-Glue.
-Mathematics learners book grade 9 page 97;
-Objects with rectangular pyramid shapes;

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

MEASUREMENTS

Area of a Sector and Segment of a Circle

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.

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

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 segment of a circle;
-Differentiate between a sector and a segment of a circle;
-Calculate the area of a segment of a circle;
-Show genuine interest in calculating areas of segments.

-Calculate the curved surface area of a cone using the formula A = πrl;
-Calculate the total surface area of a cone using the formula A = πr² + πrl;
-Solve problems involving surface area of cones;
-Appreciate the application of surface area in real-life situations.

In groups, learners are guided to:
-Draw circles and form segments by drawing chords;
-Cut out segments from paper circles;
-Derive the formula for the area of a segment (sector area minus triangle area);
-Calculate the area of segments with different angles and chord lengths;
-Discuss and share results with other groups.
In groups, learners are guided to:
-Measure dimensions of cone models (radius and slant height);
-Calculate the curved surface area of cones;
-Calculate the total surface area of cones (closed cones);
-Solve problems involving surface area of cones in real-life contexts;
-Discuss and share results with other groups.

How do we calculate the area of a segment of a circle?
How do we calculate the surface area of a cone?

-Mathematics learners book grade 9 page 101;
-Circular paper cut-outs;
-Protractors;
-Scissors;
-Rulers;
-Scientific calculators.
-Mathematics learners book grade 9 page 102;
-Conical objects (funnels, party hats);
-Glue.
-Mathematics learners book grade 9 page 103;
-Cone models;
-Rulers;
-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.
-Oral questions; -Written exercises; -Problem-solving assessment; -Peer assessment.

MEASUREMENTS

Volume of Triangular and Rectangular-Based Prisms

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.

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

MEASUREMENTS

Volume of Triangular, Rectangular and Square-Based Pyramids

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

-Identify triangular-based pyramids;
-Calculate the volume of a triangular-based pyramid using the formula V = ⅓ × area of base × height;
-Solve problems involving volume of triangular-based pyramids;
-Show interest in calculating volumes of pyramids.

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

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

-Mathematics learners book grade 9 page 108;
-Triangular-based pyramid models;
-Rulers;
-Scientific calculators;
-Charts showing formulas for volume of pyramids.
-Mathematics learners book grade 9 page 109;
-Rectangular and square-based pyramid models;

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

MEASUREMENTS

Volume of a Cone in Real Life Situations

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

-Identify cones and their properties;
-Calculate the volume of a cone using the formula V = ⅓ × πr² × h;
-Solve problems involving volume of cones;
-Show interest in calculating volumes of cones.

In groups, learners are guided to:
-Identify and discuss models of cones;
-Identify the base radius and height of cones;
-Calculate the volume using the formula V = ⅓ × πr² × h;
-Solve practical problems involving volume of cones;
-Discuss and share results with other groups.

How do we determine the volume of a cone?

-Mathematics learners book grade 9 page 110;
-Cone models;
-Rulers;
-Scientific calculators;
-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
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:

-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.

-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:
-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.
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 determine the volume of a sphere?
How do we calculate the volume of a frustum?

-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.
-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

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

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

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

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

-Calculate speed in kilometers per hour (km/h);
-Convert speed from m/s to km/h and vice versa;
-Solve problems involving speed in km/h;
-Appreciate the different units used for expressing speed.

In groups, learners are guided to:
-Review the relationship between mass, volume, and density;
-Rearrange the formula D = m/V to find V = m/D;
-Calculate the volume of objects given their mass and density;
-Solve practical problems involving mass, volume, and density;
-Discuss and share results with other groups.
In groups, learners are guided to:
-Record distance covered by vehicles in kilometers and time taken in hours;
-Calculate speed using the formula speed = distance/time;
-Express speed in kilometers per hour (km/h);
-Convert speed from m/s to km/h using the relationship 1 m/s = 3.6 km/h;
-Complete a table with distance, time, and speed;
-Discuss and share results with other groups.

How can we determine the volume of an object if we know its mass and density?
Why do we need different units for measuring speed?

-Mathematics learners book grade 9 page 123;
-Scientific calculators;
-Chart showing densities of common materials;
-Examples of applications of density in real life.
-Mathematics learners book grade 9 page 124;
-Stopwatch/timer;
-Measuring tape/rulers;
-Sports field or open area.
-Mathematics learners book grade 9 page 125;
-Scientific calculators;
-Chart showing conversion between m/s and km/h;
-Examples of speeds of various objects and vehicles.
-Mathematics learners book grade 9 page 126;
-Chart showing examples of average speed calculations;
-Examples of journey scenarios with varying speeds.

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

MEASUREMENTS

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

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

-Define velocity;
-Differentiate between speed and velocity;
-Calculate velocity in different directions;
-Show genuine interest in understanding velocity.

In groups, learners are guided to:
-Discuss the difference between speed and velocity;
-Record distance covered, time taken, and direction for various movements;
-Calculate velocity using the formula velocity = displacement/time;
-Express velocity with direction (e.g., 5 m/s eastward);
-Solve problems involving velocity in real-life contexts;
-Discuss and share results with other groups.

What is the difference between speed and velocity?

-Mathematics learners book grade 9 page 129;
-Stopwatch/timer;
-Measuring tape/rulers;
-Scientific calculators;
-Compass for directions.
-Mathematics learners book grade 9 page 130;
-Chart showing examples of acceleration calculations;
-Examples of acceleration in real-life situations.

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

-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 across the International Date Line;
-Solve complex problems involving local time at different longitudes;
-Apply knowledge of local time to real-life situations;
-Appreciate the practical applications of understanding local time.

-Identify currencies used in different countries;
-Match currencies with their respective countries;
-Recognize currency symbols;
-Show interest in learning about different currencies.

In groups, learners are guided to:
-Review the calculation of local time at different longitudes;
-Understand the International Date Line and its effect on time/date;
-Calculate local time for places on opposite sides of the International Date Line;
-Solve complex problems involving local time at different longitudes;
-Discuss real-life applications such as international travel and communication;
-Discuss and share results with other groups.
In groups, learners are guided to:
-Use digital devices to search and print pictures of currencies from: a) Neighboring countries b) Other African countries c) Common currencies used globally;
-Make a collage of different currencies on a piece of carton;
-Match currencies with their respective countries;
-Identify currency symbols (e.g., $, €, £, ¥);
-Display and present their collages to other groups.

How does the International Date Line affect time calculations?
Why do different countries use different currencies?

-Mathematics learners book grade 9 page 136;
-Globe;
-World map showing time zones and the International Date Line;
-Scientific calculators;
-Charts showing examples of local time calculations.
-Mathematics learners book grade 9 page 137;
-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.
-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.

-Observation; -Oral questions; -Written exercises; -Problem-solving assessment.
-Observation; -Oral questions; -Group presentations; -Assessment of currency collages.

MEASUREMENTS

Money - Converting Currency from One to Another in Real Life Situations
Money - Working Out Export Duties Charged on Goods

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.

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

MEASUREMENTS

Money - Working Out Import Duties Charged on Goods
Money - Working Out Excise Duty Charged on Goods

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

-Define import duty;
-Calculate import duty on goods;
-Identify goods exempted from import duty;
-Show interest in understanding import duties.

In groups, learners are guided to:
-Use digital devices to search for the meaning of import duty;
-Research the percentage of import duty on different goods and services;
-Identify examples of goods exempted from import duty in Kenya;
-Calculate import duty on goods using the formula: Import Duty = Customs Value × Duty Rate;
-Solve problems involving import duties;
-Discuss and share findings with other groups.

What are import duties and why are they charged?

-Mathematics learners book grade 9 page 143;
-Digital devices for research;
-Scientific calculators;
-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.

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

MEASUREMENTS

Money - Determining Value-Added Tax (VAT) Charged on Goods and Services

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

-Define Value Added Tax (VAT);
-Identify goods and services that attract VAT;
-Calculate VAT on goods and services;
-Appreciate the role of VAT in government revenue collection.

In groups, learners are guided to:
-Use digital devices or print media to search for information on VAT;
-Research goods that attract VAT;
-Research the percentage of VAT charged on goods and services;
-Study receipts to identify VAT amounts;
-Calculate VAT on various goods and services;
-Discuss and share findings with other groups.

How is VAT calculated and why is it charged?

-Mathematics learners book grade 9 page 145;
-Supermarket receipts showing VAT;
-Digital devices for research;
-Scientific calculators;
-Charts showing VAT calculations.

-Observation; -Oral questions; -Written exercises; -Analysis of receipts.

MEASUREMENTS
MEASUREMENTS
Geometry

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

-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.

-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:
-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.
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.

How do we estimate measurements of different quantities?
Why is percentage error more useful than absolute error?

-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.
-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; -Practical assessment; -Group presentations.
-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
Similarity and Enlargement - Negative scale factors

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
-KLB Mathematics Grade 9 Textbook page 211
-Charts showing negative scale factor enlargements

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Similarity and Enlargement - Drawing images of objects

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

Apply properties of enlargement to draw similar objects and their images;
Use scale factors to determine dimensions of images;
Enjoy creating enlarged images of objects.

Learners trace a given figure and join the center of enlargement to each vertex.
Learners multiply each distance by the scale factor to locate the image points.
Learners locate the image points and join them to create the enlarged figure.

How do we draw the image of an object under an enlargement with a given center and scale factor?

-KLB Mathematics Grade 9 Textbook page 214
-Ruler
-Grid paper
-Colored pencils
-Charts showing steps of enlargement
-Manila paper

-Oral questions -Practical activity -Written exercise -Peer assessment

Geometry

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

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.

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 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.
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 do we use linear scale factors to calculate unknown dimensions of similar figures?
How can we use similarity to solve real-life problems?

-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
-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 -Group work -Written exercise -Assessment rubrics
-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

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

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Trigonometry - Using calculators for trigonometric ratios
Trigonometry - Calculating lengths using trigonometric ratios
Trigonometry - Calculating angles using trigonometric ratios
Trigonometry - Application in heights and distances

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

Determine trigonometric ratios of acute angles using calculators;
Compare values obtained from tables and calculators;
Value the use of calculators in finding trigonometric ratios.

Use trigonometric ratios to calculate angles in right-angled triangles;
Apply inverse trigonometric functions to find angles;
Enjoy solving problems involving trigonometric ratios.

Learners use calculators to find trigonometric ratios of specific angles.
Learners compare values obtained from calculators with those from mathematical tables.
Learners use calculators to find sine, cosine, and tangent of various angles.
Learners consider right-angled triangles with known sides.
Learners calculate trigonometric ratios using the known sides and use tables or calculators to find the corresponding angles.
Learners solve problems involving finding angles in right-angled triangles.

How do we use calculators to find trigonometric ratios?
How do we find unknown angles in right-angled triangles using trigonometric ratios?

-KLB Mathematics Grade 9 Textbook page 233
-Scientific calculators
-Mathematical tables
-Worksheets
-Chart showing calculator keys
-Sample exercises
-KLB Mathematics Grade 9 Textbook page 234
-Ruler
-Drawing paper
-Charts with examples
-KLB Mathematics Grade 9 Textbook page 235
-Scientific calculators
-Mathematical tables
-Ruler
-Drawing paper
-Charts with examples
-Worksheets
-KLB Mathematics Grade 9 Textbook page 237
-Charts with real-life examples
-Manila paper

-Oral questions -Practical activity -Written exercise -Checklist
-Oral questions -Group work -Written exercise -Observation

Geometry

Trigonometry - Application in navigation
Trigonometry - Review and mixed applications

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

Apply trigonometric ratios in navigation problems;
Calculate distances and bearings using trigonometry;
Appreciate the importance of trigonometry in navigation.

Learners solve problems involving finding distances between locations given bearings and distances from a reference point.
Learners calculate bearings between points using trigonometric ratios.
Learners discuss how pilots, sailors, and navigators use trigonometry.

How is trigonometry used in navigation and determining positions?

-KLB Mathematics Grade 9 Textbook page 238
-Scientific calculators
-Mathematical tables
-Ruler
-Protractor
-Maps
-Charts with navigation examples
-KLB Mathematics Grade 9 Textbook page 240
-Drawing paper
-Past examination questions

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

Data Handling and Probability

Data Interpretation - Appropriate class width
Data Interpretation - Finding range and creating groups

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

Determine appropriate class width for grouping data;
Work with data to establish suitable class widths;
Appreciate the importance of appropriate class widths in data representation.

Learners work in groups to consider masses of 40 people in kilograms.
Learners find the difference between the smallest and highest mass (range).
Learners group the masses in smaller groups with different class widths and identify the number of groups formed in each case.

How do we determine an appropriate class width for a given set of data?

-KLB Mathematics Grade 9 Textbook page 244
-Calculator
-Graph paper
-Manila paper
-Rulers
-Colored markers
-KLB Mathematics Grade 9 Textbook page 245
-Data sets
-Chart with examples

-Oral questions -Group presentations -Written exercise -Observation

Data Handling and Probability

Data Interpretation - Frequency distribution tables

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

-Oral questions -Group presentations -Written exercise -Checklist

Data Handling and Probability

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:

Construct frequency tables starting with different class intervals;
Use tally marks to represent data in frequency tables;
Appreciate the use of different class intervals in data representation.

Calculate the mean of ungrouped data in a frequency table;
Multiply each value by its frequency and find their sum;
Show interest in calculating mean in real-life situations.

Learners construct a frequency table for given data starting from the class interval 60-64.
Learners use tally marks to count frequency of data in each class.
Learners compare and discuss different frequency tables.
Learners consider the height, in metres, of 10 people recorded in a frequency distribution table.
Learners complete a table showing the product of height and frequency (fx).
Learners find the sum of frequencies, sum of fx, and divide to find the mean.

How do we choose appropriate starting points for class intervals?
How do we calculate the mean of data presented in a frequency table?

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

-Oral questions -Written exercise -Group presentations -Observation
-Oral questions -Written exercise -Observation -Assessment rubrics

Data Handling and Probability

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

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

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

Data Handling and Probability

Data Interpretation - Calculating median using formula
Data Interpretation - Median calculations in real-life situations

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

Apply the formula for calculating median of grouped data;
Identify class boundaries, frequencies, and cumulative frequencies;
Show interest in finding median from real-life data.

Learners consider marks scored by 40 learners in a test presented in a table.
Learners complete the column for cumulative frequency and identify the median class.
Learners identify the lower class boundary, cumulative frequency above median class, class width, and frequency of median class to substitute in the formula.

How do we use the formula to calculate the median of grouped data?

-KLB Mathematics Grade 9 Textbook page 253
-Calculator
-Graph paper
-Chart showing median formula
-Worksheets
-Manila paper
-KLB Mathematics Grade 9 Textbook page 254
-Chart with example calculations
-Worksheets with real-life data
-Colored markers

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

Data Handling and Probability

Probability - Equally likely outcomes

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

Perform experiments involving equally likely outcomes;
Record outcomes of chance experiments;
Appreciate that some events have equal chances of occurring.

Learners work in groups to flip a fair coin 20 times.
Learners record the number of times heads and tails come up.
Learners divide the number of times heads or tails comes up by the total number of tosses to find probabilities.

What makes events equally likely to occur?

-KLB Mathematics Grade 9 Textbook page 256
-Coins
-Chart paper
-Table for recording outcomes
-Manila paper
-Colored markers

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

Data Handling and Probability

Probability - Range of probability
Probability - Complementary events
Probability - Mutually exclusive events
Probability - Experiments with mutually exclusive 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.

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

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.
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 is the range of probability values and what do these values signify?
What makes events mutually exclusive?

-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
-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 -Practical activity -Written exercise -Group presentations
-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: