MEASUREMENTS

Area of a Pentagon

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.

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°).

How do we determine the area of different surfaces?

-Mathematics learners book grade 9 page 87;
-Cut-outs of regular pentagons;
-Chart with diagrams of pentagons;
-Calculator;
-Ruler and protractor.

-Observation; -Oral questions; -Written exercises; -Group presentations.

MEASUREMENTS

Area of a Pentagon

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

-Work out the area of a regular pentagon when different measurements are given;
-Solve problems involving the height and side length of a pentagon;
-Interpret and solve word problems involving area of pentagons;
-Appreciate the use of geometry in calculating areas of pentagons.

In groups and individually, learners are guided to:
-Work out problems on area of pentagons with given side lengths;
-Calculate the area of pentagons where vertices are at a given distance from the center;
-Relate the height of triangles formed in a pentagon to the area;
-Solve practical problems involving area of pentagons.

How can we calculate the area of a pentagon in different situations?

-Mathematics learners book grade 9 page 89;
-Pentagonal objects;
-Calculator;
-Worked examples on the board.

-Written exercises; -Homework assignments; -Group work assessment; -Mathematical problem-solving tasks.

MEASUREMENTS

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 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 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 many triangles can be formed by joining the center of a hexagon to each vertex?

-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 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.

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

MEASUREMENTS

Surface Area of Triangular and Rectangular-Based Prisms

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

-Draw a rectangular prism and identify its faces, edges, and vertices;
-Develop a net for a rectangular prism;
-Calculate the surface area of a rectangular prism using its net;
-Show interest in relating surface area to real-life applications.

In groups, learners are guided to:
-Collect objects that are rectangular prisms;
-Draw and sketch nets of rectangular 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 rectangular prism?

-Mathematics learners book grade 9 page 95;
-Manila paper for making nets;
-Scissors;
-Rulers;
-Objects with rectangular prism shapes (boxes);
-Glue.

-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.

-Observation of practical work; -Oral questions; -Written exercises; -Model making 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 rectangular-based pyramid and identify its faces, edges, and vertices;
-Develop a net for a rectangular-based pyramid;
-Calculate the surface area of a rectangular-based pyramid;
-Appreciate the relationship between nets and surface area calculations.

In groups, learners are guided to:
-Draw and sketch nets of rectangular-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;
-Solve problems involving surface area of rectangular-based pyramids.

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

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

-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.
-Mathematics learners book grade 9 page 101;

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

MEASUREMENTS

Surface Area of a Cone in Real Life Situations

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

-Identify and draw a cone;
-Develop a net for a cone;
-Identify the parts of a cone (base, curved surface, apex, slant height);
-Show interest in relating cones to real-life objects.

In groups, learners are guided to:
-Collect objects with conical shapes;
-Draw and discuss features of cones;
-Draw circles and cut out sectors to form cone nets;
-Fold sectors to form cones and observe the relationship between the sector angle and the cone dimensions;
-Discuss and share findings with other groups.

What are some real-life objects that have a conical shape?

-Mathematics learners book grade 9 page 102;
-Circular paper cut-outs;
-Scissors;
-Rulers;
-Protractors;
-Conical objects (funnels, party hats);
-Glue.

-Observation of practical work; -Oral questions; -Model making assessment; -Group presentations.

MEASUREMENTS

Surface Area of a Cone in Real Life Situations

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

-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:
-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 surface area of a cone?

-Mathematics learners book grade 9 page 103;
-Cone models;
-Rulers;
-Scientific calculators;
-Charts showing formulas for surface area of cones.

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

MEASUREMENTS

Surface Area of a Sphere in Real Life Situations

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

-Identify and draw a sphere;
-Identify spherical objects in the environment;
-Calculate the surface area of a sphere using the formula A = 4πr²;
-Develop interest in calculating surface area of spheres.

In groups, learners are guided to:
-Collect objects with spherical shapes;
-Measure the diameter/radius of spherical objects;
-Calculate the surface area of spheres using the formula A = 4πr²;
-Discuss and share findings with other groups;
-Relate surface area of spheres to real-life applications.

What are some real-life objects that have a spherical shape?

-Mathematics learners book grade 9 page 104;
-Spherical objects (balls, oranges);
-Measuring tape/rulers;
-Scientific calculators;
-Charts showing formulas for surface area of spheres.

-Observation; -Oral questions; -Written exercises; -Group presentations.

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.

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

MEASUREMENTS

Volume of Triangular and Rectangular-Based Prisms

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.

-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

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.

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

MEASUREMENTS

Volume of a Frustum in Real Life Situations

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.

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

MEASUREMENTS

Volume of a Frustum in Real Life Situations

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.

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

MEASUREMENTS

Mass, Volume, Weight and Density - Instruments and Tools Used in Weighing
Mass, Volume, Weight and Density - Converting Units of Mass

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

-Identify different instruments and tools used in weighing;
-Describe the functions of various weighing instruments;
-Use weighing instruments correctly;
-Show interest in using weighing instruments.

In groups, learners are guided to:
-Identify and discuss different types of balances used for weighing;
-Identify commonly used balances in their locality;
-Discuss what different weighing instruments are used for;
-Practice using weighing instruments to measure mass of objects;
-Discuss and share findings with other groups.

How do you weigh materials and objects?

-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.

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

MEASUREMENTS

Mass, Volume, Weight and Density - Relating Mass and Weight

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

-Define mass and weight;
-Differentiate between mass and weight;
-Convert mass to weight using the formula W = mg;
-Show interest in understanding the relationship between mass and weight.

In groups, learners are guided to:
-Use digital devices to search for definitions of mass and weight;
-Discuss the SI units for mass and weight;
-Measure the mass of various objects;
-Calculate the weight of objects using the formula W = mg;
-Complete a table showing mass and weight of objects;
-Discuss and share findings with other groups.

What is the difference between mass and weight?

-Mathematics learners book grade 9 page 119;
-Weighing instruments;
-Spring balance;
-Various objects to weigh;
-Digital devices for research.

-Observation; -Oral questions; -Written exercises; -Group presentations.

MEASUREMENTS

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

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.

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

MEASUREMENTS

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

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

-Calculate density given mass and volume;
-Apply the formula D = m/V to solve problems;
-Compare densities of different materials;
-Appreciate the concept of density in everyday life.

In groups, learners are guided to:
-Review the formula for density;
-Solve problems involving density with given mass and volume;
-Compare densities of different materials;
-Discuss real-life applications of density;
-Discuss and share results with other groups.

Why do some objects float and others sink in water?

-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; -Problem-solving 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

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.

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.

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

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.

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

MEASUREMENTS

Time, Distance and Speed - Determining Velocity 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.

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

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.

-Observation; -Oral questions; -Written exercises; -Group presentations.

MEASUREMENTS

Time, Distance and Speed - Relating Longitudes to Time on the Globe
Time, Distance and Speed - Determining Local Time of Places on Different Longitudes

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

-Understand the relationship between longitudes and time;
-Calculate the time difference between places on different longitudes;
-Identify places with the same local time;
-Appreciate the importance of longitudes in determining time.

In groups, learners are guided to:
-Discuss how the earth rotates 360° in 24 hours (15° per hour);
-Complete a table showing degrees of rotation for different time periods;
-Identify pairs of points on a globe that share the same local time;
-Understand that places on the same longitude have the same local time;
-Discuss and share findings with other groups.

How are longitudes related to time?

-Mathematics learners book grade 9 page 133;
-Globe;
-World map showing time zones;
-Digital devices for research;
-Charts showing the relationship between longitudes and time.
-Mathematics learners book grade 9 page 134;
-Scientific calculators;
-Charts showing examples of local time calculations.

-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 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.

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.

How does the International Date Line affect time calculations?

-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.

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

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:

-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.

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

MEASUREMENTS

Money - Identifying Currencies Used in Different Countries

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

-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:
-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.

Why do different countries use different currencies?

-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; -Group presentations; -Assessment of currency collages.

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.

-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

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

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.

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

MEASUREMENTS

Money - Working Out Excise Duty Charged on Goods

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.

-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

Approximations and Errors - Approximating Quantities in 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.

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

MEASUREMENTS

Approximations and Errors - Determining Errors Using Estimations and Actual Measurements

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.

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

MEASUREMENTS
Geometry

Approximations and Errors - Determining Percentage Errors Using Actual Measurements
Coordinates and Graphs - Plotting points on a Cartesian plane

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 154
-Graph paper
-Ruler
-Pencils
-Charts with Cartesian plane
-Colored markers

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

Geometry

Coordinates and Graphs - Drawing a straight line graph

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

Generate a table of values from the equation of a straight line;
Draw a straight line graph given an equation;
Appreciate the use of straight line graphs in representing linear relationships.

Learners generate a table of values for a given linear equation (e.g., y=-2x+5).
Learners plot the points on a Cartesian plane and join them to form a straight line.
Learners discuss and compare their results with other groups.

How do we generate a table of values from a linear equation?

-KLB Mathematics Grade 9 Textbook page 155
-Graph paper
-Ruler
-Pencils
-Calculator
-Blackboard illustration

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

Geometry

Coordinates and Graphs - Completing tables for linear equations

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

Complete tables of values for different linear equations;
Plot points from completed tables on a Cartesian plane;
Enjoy drawing straight line graphs from tables of values.

Learners complete tables of values for given linear equations such as y=2x+3.
Learners plot the points on a Cartesian plane and join them using a straight edge to form a straight line graph.
Learners work in pairs to generate their own tables of values for different equations.

How do we use tables of values to draw straight line graphs?

-KLB Mathematics Grade 9 Textbook page 156
-Graph paper
-Ruler
-Pencils
-Calculator
-Charts with prepared tables

-Oral questions -Peer assessment -Written exercise -Checklist

Geometry

Coordinates and Graphs - Drawing parallel lines

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

-Oral questions -Group work -Written exercise -Observation

Geometry

Coordinates and Graphs - Relating gradients of parallel lines

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

Determine the gradients of straight lines;
Relate the gradients of parallel lines;
Value the importance of gradient in determining parallel lines.

Learners work in groups to generate tables of values for equations y=3x-4 and y=3x-1.
Learners draw the lines on the Cartesian plane and determine their gradients.
Learners compare the gradients and discuss the relationship between the gradients of parallel lines.

What is the relationship between the gradients of parallel lines?

-KLB Mathematics Grade 9 Textbook page 158
-Graph paper
-Ruler
-Calculator
-Manila paper
-Digital devices (optional)

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

Geometry

Coordinates and Graphs - Drawing perpendicular lines
Coordinates and Graphs - Relating gradients of perpendicular lines

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

Generate tables of values for perpendicular line equations;
Draw perpendicular lines on the Cartesian plane;
Enjoy identifying perpendicular lines from their equations.

Learners generate tables of values for equations such as y=2x+3 and y=-1/2x+4.
Learners draw the lines on the Cartesian plane and measure the angle at the point of intersection.
Learners discuss and share their findings with other groups.

How can you determine if two lines are perpendicular from their equations?

-KLB Mathematics Grade 9 Textbook page 159
-Graph paper
-Ruler
-Protractor
-Set square
-Calculator
-Charts showing perpendicular lines
-KLB Mathematics Grade 9 Textbook page 160
-Charts with examples of perpendicular lines

-Oral questions -Observation -Written exercise -Checklist

Geometry

Coordinates and Graphs - Applications of straight line graphs

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

Apply graphs of straight lines to real-life situations;
Interpret information from straight line graphs;
Value the use of graphs in representing real-life situations.

Learners work in groups to generate tables of values for parking charges in two different towns.
Learners draw graphs to represent the information on the same Cartesian plane.
Learners find the gradient of the two lines drawn and determine whether they are parallel.

How can straight line graphs help us solve real-life problems?

-KLB Mathematics Grade 9 Textbook page 165
-Graph paper
-Ruler
-Calculator
-Charts showing real-life applications
-Manila paper for presentations

-Oral questions -Group discussion -Written exercise -Presentation

Geometry

Scale Drawing - Compass directions

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

Identify compass and true bearings in real-life situations;
Draw and discuss the compass directions;
Appreciate the use of compass in navigation.

Learners carry out an activity outside the classroom where a member stands with hands spread out.
Learners draw a diagram showing the directions of the right hand, left hand, front, and back, labeling them in terms of North, South, East, and West.
Learners discuss situations where knowledge of compass direction is used.

How do we use compass directions to locate positions?

-KLB Mathematics Grade 9 Textbook page 168
-Magnetic compass
-Plain paper
-Colored pencils
-Charts showing compass directions
-Maps

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Scale Drawing - Compass bearings

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

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Scale Drawing - True bearings

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

Identify true bearings in real-life situations;
Draw and measure true bearings;
Appreciate the difference between compass and true bearings.

Learners trace diagrams showing true bearings.
Learners measure angles from North in the clockwise direction.
Learners draw accurately true bearings such as 008°, 036°, 126°, etc.

What is the difference between compass bearings and true bearings?

-KLB Mathematics Grade 9 Textbook page 171
-Protractor
-Ruler
-Plain paper
-Charts showing true bearings
-Diagrams for tracing

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

Geometry

Scale Drawing - Determining compass bearings

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

Determine the bearing of one point from another;
Measure angles to determine compass bearings;
Enjoy determining bearings in different situations.

Learners consider a diagram showing points Q and R.
Learners find the angle between the North line and line QR.
Learners use the angle to write down the compass bearing of R from Q and discuss their results.

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

-KLB Mathematics Grade 9 Textbook page 173
-Protractor
-Ruler
-Plain paper
-Charts with bearing examples
-Manila paper for group work

-Oral questions -Group work -Written exercise -Observation

Geometry

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:

Determine true bearings in different situations;
Measure angles to find true bearings;
Value the use of true bearings in navigation.

Learners consider a diagram showing points C and D.
Learners identify and determine the bearing of D from C by measurement.
Learners measure the bearing of various points in different diagrams.

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

-KLB Mathematics Grade 9 Textbook page 175
-Protractor
-Ruler
-Plain paper
-Worksheets with diagrams
-Charts with bearing examples
-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

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

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Scale Drawing - Angle of elevation

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

Identify angles of elevation in real-life situations;
Make and use a clinometer to measure angles of elevation;
Appreciate the application of angles of elevation in real-life situations.

Learners perform an activity outside the classroom where they stand next to a flag pole and mark points at eye level and above.
Learners observe how the line of sight forms an angle when looking at higher objects.
Learners make a clinometer and use it to measure angles of elevation of objects in the school environment.

What is an angle of elevation and how do we measure it?

-KLB Mathematics Grade 9 Textbook page 186
-Protractor
-String
-Weight (about 25g)
-Cardboard
-Straight piece of wood
-Charts showing angles of elevation

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

Geometry

Scale Drawing - Determining angles of elevation

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

Determine angles of elevation in different situations;
Use scale drawings to find angles of elevation;
Value the use of scale drawings in solving problems involving elevation.

Learners consider a flag pole AB that is 8 m high with point C on level ground 18 m from the foot of the pole.
Learners make a scale drawing showing A, B, and C using a scale of 1 cm represents 2 m.
Learners measure the angle between AC and CB and display their drawings.

How can we use scale drawings to determine angles of elevation?

-KLB Mathematics Grade 9 Textbook page 187
-Protractor
-Ruler
-Plain paper
-Drawing board
-Calculator
-Charts showing examples

-Oral questions -Scale drawing -Written exercise -Presentation

Geometry

Scale Drawing - Angle of depression

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

Identify angles of depression in real-life situations;
Measure angles of depression using a clinometer;
Appreciate the application of angles of depression in real-life situations.

Learners perform an activity outside the classroom where they stand next to a flag pole and mark points at eye level and below.
Learners observe how the line of sight forms an angle when looking at lower objects.
Learners use a clinometer to measure angles of depression of objects in their environment.

What is an angle of depression and how is it related to the angle of elevation?

-KLB Mathematics Grade 9 Textbook page 190
-Clinometer (made in previous lesson)
-String
-Weight
-Protractor
-Charts showing angles of depression
-Diagrams

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Scale Drawing - Determining angles of depression
Scale Drawing - Application in simple surveying

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

Determine angles of depression in different situations;
Use scale drawings to find angles of depression;
Enjoy solving problems involving angles of depression.

Learners consider a stationary boat (B) that is 120 m away from the foot (F) of a cliff of height 80 m.
Learners make a scale drawing showing the positions of A, F, and B using a scale of 1 cm represents 20 m.
Learners measure the angle between the horizontal line passing through A and line AB to find the angle of depression.

How can we use scale drawings to determine angles of depression?

-KLB Mathematics Grade 9 Textbook page 192
-Protractor
-Ruler
-Plain paper
-Drawing board
-Calculator
-Charts with examples
-KLB Mathematics Grade 9 Textbook page 195
-Drawing paper
-Set square
-Pencil
-Field book (notebook)
-Charts with survey examples

-Oral questions -Scale drawing -Written exercise -Assessment rubrics

Geometry

Scale Drawing - Survey using bearings and distances

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

Survey an area using bearings and distances;
Create scale drawings from bearing and distance data;
Appreciate the application of bearings in surveying.

Learners study a sketch of a piece of land with positions given in terms of bearings and distances from point A.
Learners mark point A and use the bearings and distances to locate other points.
Learners create scale drawings of areas described by bearings and distances from given tables.

How do surveyors use bearings and distances to map areas?

-KLB Mathematics Grade 9 Textbook page 199
-Protractor
-Ruler
-Plain paper
-Drawing board
-Field book
-Charts with examples

-Oral questions -Scale drawing -Written exercise -Presentation

Geometry

Scale Drawing - Complex surveying problems

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

Solve complex surveying problems involving bearings and distances;
Create scale drawings of multiple points and features;
Show interest in scale drawing applications in real-life.

Learners study problems involving multiple points with bearings and distances between them.
Learners create scale drawings to determine unknown distances and bearings.
Learners discuss real-life applications of scale drawing in surveying and navigation.

How do we determine unknown distances and bearings using scale drawing?

-KLB Mathematics Grade 9 Textbook page 202
-Protractor
-Ruler
-Drawing paper
-Calculator
-Maps
-Charts with examples

-Oral questions -Scale drawing -Written exercise -Assessment rubrics

Geometry

Scale Drawing - Project work on scale drawing

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

Apply scale drawing techniques to a real-life situation;
Create a scale map of the school compound or local area;
Appreciate the practical applications of scale drawing.

Learners work in groups to create a scale map of a part of the school compound.
Learners measure distances and determine bearings between key features.
Learners create a detailed scale drawing with a key showing the various features mapped.

How can we apply scale drawing techniques to map our environment?

-KLB Mathematics Grade 9 Textbook page 202
-Measuring tape
-Compass
-Drawing paper
-Colored pencils
-Manila paper
-Drawing instruments

-Project work -Group presentation -Peer assessment -Observation