Algebra

Matrices - Determining Compatibility for Addition
Matrices - Determining Compatibility for Subtraction

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

Determine compatibility of matrices for addition;
Identify matrices of the same order;
Show interest in mathematical conditions for operations.

Discuss and identify matrices with equal numbers of rows and columns.
Compare orders of different matrices.
Determine which matrices can be added together.

How do we use matrices in real life situations?

Top Scholar KLB Mathematics Learners Book Grade 9, page 47.
Charts showing matrices of various orders.
Worksheets with matrices.
Top Scholar KLB Mathematics Learners Book Grade 9, page 49.

Oral questions. Written exercise. Assignment.

Algebra

Matrices - Addition of Matrices
Matrices - Subtraction of Matrices

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

Carry out addition of matrices in real life situations;
Add corresponding elements in compatible matrices;
Show interest in using matrices to solve problems.

Add matrices by adding corresponding elements.
Solve real-life problems involving addition of matrices.
Discuss what is represented by rows and columns when adding matrices.

How do we use matrices in real life situations?

Top Scholar KLB Mathematics Learners Book Grade 9, page 51.
Charts showing addition of matrices.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 54.
Charts showing subtraction of matrices.

Oral questions. Written exercise. Assignment.

Algebra

Matrices - Application of Matrices

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

Apply matrices in real life situations;
Use matrices to organize and process information;
Reflect on the use of matrices in real life.

Discuss real-life applications of matrices.
Create and solve problems involving matrices.
Present projects showcasing applications of matrices.

How do we use matrices in real life situations?

Top Scholar KLB Mathematics Learners Book Grade 9, page 57.
Real-life data that can be represented in matrices.
Calculators.

Oral questions. Written exercise. Project work.

Algebra

Equations of Straight Lines - Introduction to Gradient
Equations of Straight Lines - Identifying the Gradient

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

Understand the concept of gradient in real life situations;
Relate gradient to steepness;
Appreciate the concept of gradient in everyday contexts.

Discuss steepness in relation to gradient from the immediate environment.
Compare different slopes in the environment.
Identify examples of gradients in daily life.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 58.
Pictures of hills and slopes.
Charts showing different gradients.
Ladders or sticks for demonstrating gradients.

Oral questions. Written exercise. Observation.

Algebra

Equations of Straight Lines - Measuring Gradient
Equations of Straight Lines - Gradient from Two Known Points

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

Measure gradient as a ratio of vertical to horizontal distance;
Calculate gradients from physical objects;
Appreciate the mathematical definition of gradient.

Measure vertical and horizontal distances of inclined objects.
Calculate gradient as ratio of vertical to horizontal distance.
Compare measured gradients with observed steepness.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 59.
Rulers and measuring tapes.
Inclined objects for measurement.
Top Scholar KLB Mathematics Learners Book Grade 9, page 60.
Graph paper.
Rulers and protractors.

Oral questions. Written exercise. Group work.

Algebra

Equations of Straight Lines - Positive and Negative Gradients

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

Distinguish between positive and negative gradients;
Interpret the meaning of gradient sign;
Appreciate the visual representation of gradient sign.

Draw lines with positive and negative gradients.
Compare the direction of lines with different gradient signs.
Interpret the meaning of positive and negative gradients in real-life contexts.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 61.
Graph paper.
Charts showing lines with different gradients.

Oral questions. Written exercise. Group activity.

Algebra

Equations of Straight Lines - Zero and Undefined Gradients
Equations of Straight Lines - Equation from Two Points

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

Identify lines with zero and undefined gradients;
Relate gradient to direction of lines;
Show interest in special cases of gradients.

Draw horizontal and vertical lines on a Cartesian plane.
Calculate gradients of horizontal and vertical lines.
Discuss the special cases of zero and undefined gradients.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 61.
Graph paper.
Charts showing horizontal and vertical lines.
Top Scholar KLB Mathematics Learners Book Grade 9, page 62.
Calculators.

Oral questions. Written exercise. Group presentation.

Algebra

Equations of Straight Lines - Deriving the Equation from Two Points
Equations of Straight Lines - Equation from a Point and Gradient

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

Derive the equation of a line step-by-step from two points;
Apply algebraic manipulation to derive the equation;
Show interest in mathematical derivations.

Derive step-by-step the equation of a line from two points.
Apply algebraic manipulation to simplify the equation.
Verify the derived equation using the given points.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 63.
Graph paper.
Worksheets with coordinate points.
Top Scholar KLB Mathematics Learners Book Grade 9, page 64.
Calculators.

Oral questions. Written exercise. Assignment.

Algebra

Equations of Straight Lines - Express Equation in Form y = mx + c

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

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

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

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 65.
Charts showing line equations.
Graph paper.

Oral questions. Written exercise. Group presentation.

Algebra

Equations of Straight Lines - Interpreting y = mx + c
Equations of Straight Lines - Graphing Lines from Equations

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

Interpret the equation y = mx + c in different situations;
Relate m to gradient and c to y-intercept;
Show interest in interpreting mathematical equations.

Discuss the meaning of m and c in the equation y = mx + c.
Draw lines with different values of m and c.
Interpret real-life scenarios using line equations.

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

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

Oral questions. Written exercise. Group activity.

Algebra

Equations of Straight Lines - x and y Intercepts
Equations of Straight Lines - Using Intercepts to Graph Lines

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

Determine the x and y intercepts of a straight line;
Find intercepts by substituting x=0 and y=0;
Appreciate the geometrical significance of intercepts.

Work out the value of x when y is zero and the value of y when x is zero.
Identify intercepts from graphs of straight lines.
Solve problems involving intercepts.

How do we represent linear inequalities in graphs?

Top Scholar KLB Mathematics Learners Book Grade 9, page 70.
Graph paper.
Rulers.
Top Scholar KLB Mathematics Learners Book Grade 9, page 71.

Oral questions. Written exercise. Assignment.

Algebra

Equations of Straight Lines - Parallel and Perpendicular Lines

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

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

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

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 71.
Graph paper.
Rulers and protractors.

Oral questions. Written exercise. Group presentation.

Algebra

Equations of Straight Lines - Real Life Applications
Linear Inequalities - Introduction to Inequalities

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

Apply equations of straight lines to real life situations;
Model real-life scenarios using line equations;
Recognize the use of line equations in real life.

Discuss real-life applications of line equations.
Create and solve problems involving line equations.
Use IT resources to explore applications of line equations.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 72.
Real-life data that can be modeled using lines.
Computers with graphing software.
Top Scholar KLB Mathematics Learners Book Grade 9, page 75.
Charts showing inequality symbols.
Real-life examples of inequalities.

Oral questions. Written exercise. Project work.

Algebra

Linear Inequalities - Solving Linear Inequalities (Addition and Subtraction)
Linear Inequalities - Solving Linear Inequalities (Multiplication and Division)

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

Solve linear inequalities in one unknown involving addition and subtraction;
Apply linear inequalities to real life situations;
Show interest in using inequalities to solve problems.

Form and work out inequalities in one unknown involving addition and subtraction.
Discuss the rules for solving inequalities.
Solve real-life problems using inequalities.

How do we represent linear inequalities in graphs?

Top Scholar KLB Mathematics Learners Book Grade 9, page 75.
Charts showing inequality symbols.
Number lines.
Top Scholar KLB Mathematics Learners Book Grade 9, page 76.
Charts showing inequality rules.

Oral questions. Written exercise. Group activity.

Algebra

Linear Inequalities - Solving Linear Inequalities (Combined Operations)

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

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

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

How do we represent linear inequalities in graphs?

Top Scholar KLB Mathematics Learners Book Grade 9, page 77.
Worksheets with inequality problems.
Number lines.

Oral questions. Written exercise. Group work.

Algebra

Linear Inequalities - Graphical Representation in One Unknown
Linear Inequalities - Graphical Representation in Two Unknowns

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

Represent linear inequalities in one unknown graphically;
Use number lines to represent solutions;
Appreciate graphical representation as a way of visualizing solutions.

Generate a table of values for boundary lines.
Draw linear inequalities in one unknown on number lines.
Indicate regions that satisfy inequalities.

How do we represent linear inequalities in graphs?

Top Scholar KLB Mathematics Learners Book Grade 9, page 78.
Number lines.
Graph paper.
Top Scholar KLB Mathematics Learners Book Grade 9, page 79.
Rulers and protractors.

Oral questions. Written exercise. Practical activity.

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

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

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.

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

MEASUREMENTS

Area of a Hexagon
Surface Area of Triangular and Rectangular-Based Prisms

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

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

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

Where do we find hexagonal shapes in our daily lives?

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

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

MEASUREMENTS

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

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.
-Mathematics learners book grade 9 page 96;
-Objects with triangular pyramid shapes;

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

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

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.
-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

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

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

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

How do we determine the volume of a sphere?

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

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

MEASUREMENTS

Volume of a Frustum in Real Life Situations

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

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.
-Mathematics learners book grade 9 page 121;
-Measuring cylinders;
-Various objects (coins, stones, metal pieces);
-Water;
-Scientific calculators.

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

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

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

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

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

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

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

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

MEASUREMENTS

Time, Distance and Speed - Working Out Speed in Km/h and m/s

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

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

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

How do we observe speed in daily activities?

-Mathematics learners book grade 9 page 124;
-Stopwatch/timer;
-Measuring tape/rulers;
-Scientific calculators;
-Sports field or open area.
-Mathematics learners book grade 9 page 125;
-Chart showing conversion between m/s and km/h;
-Examples of speeds of various objects and vehicles.

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

MEASUREMENTS

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

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
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

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.
-Mathematics learners book grade 9 page 137;
-World map showing time zones;
-Digital devices showing current time in different cities;
-Scientific calculators.

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

MEASUREMENTS

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:

-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.
-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; -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:

-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.

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

MEASUREMENTS

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

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

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

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

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

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

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

MEASUREMENTS

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

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

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

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

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

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

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

MEASUREMENTS

Approximations and Errors - Approximating Quantities in Measurements

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
Approximations and Errors - Determining Percentage Errors Using 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.
-Mathematics learners book grade 9 page 151;

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

Geometry

Coordinates and Graphs - Plotting points on a Cartesian plane
Coordinates and Graphs - Drawing a straight line graph

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

Plot out points on a Cartesian plane;
Work in groups to locate points on a plane;
Appreciate the use of Cartesian plane in locating positions.

Learners are guided to work in groups and locate the point of intersection of the x-coordinate and the y-coordinates on a Cartesian plane.
Learners plot given points such as P(3,4), Q(4,-2), R(-3,-5) and S(-1,5) on a Cartesian plane.

How do we locate a point on a Cartesian plane?

-KLB Mathematics Grade 9 Textbook page 154
-Graph paper
-Ruler
-Pencils
-Charts with Cartesian plane
-Colored markers
-KLB Mathematics Grade 9 Textbook page 155
-Calculator
-Blackboard illustration

-Oral questions -Observation -Written exercise -Peer assessment

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
Coordinates and Graphs - Relating gradients of 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
-KLB Mathematics Grade 9 Textbook page 158
-Manila paper
-Digital devices (optional)

-Oral questions -Group work -Written exercise -Observation

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
Scale Drawing - Compass bearings

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
-KLB Mathematics Grade 9 Textbook page 170
-Protractor
-Ruler
-Charts showing compass bearings
-Manila paper

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Scale Drawing - True bearings
Scale Drawing - Determining compass 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
-KLB Mathematics Grade 9 Textbook page 173
-Charts with bearing examples
-Manila paper for group work

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

Geometry

Scale Drawing - Determining true bearings

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

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Scale Drawing - Locating points using compass bearing and distance
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 bearing and distance in real-life situations;
Create scale drawings showing relative positions;
Appreciate the use of scale drawings in real-life situations.

Learners consider two markets U and V such that the distance between them is 6 km and U is on a bearing of N56°E from V.
Learners mark point V on paper, draw the bearing of U from V, and use a scale of 1 cm represents 1 km to locate U.
Learners display and discuss their constructions.

How do we use compass bearings and distances to locate positions?

-KLB Mathematics Grade 9 Textbook page 178
-Protractor
-Ruler
-Plain paper
-Drawing board
-Charts with examples
-Worksheets
-KLB Mathematics Grade 9 Textbook page 182
-Manila paper for presentations

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

Geometry

Scale Drawing - Angle of elevation
Scale Drawing - Determining angles 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
-KLB Mathematics Grade 9 Textbook page 187
-Ruler
-Plain paper
-Drawing board
-Calculator
-Charts showing examples

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

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
Scale Drawing - Complex surveying problems

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
-KLB Mathematics Grade 9 Textbook page 202
-Drawing paper
-Calculator
-Maps

-Oral questions -Scale drawing -Written exercise -Presentation

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