Algebra

Matrices - Identifying a Matrix
Matrices - Determining the Order of a Matrix

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

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

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

How do we use matrices in real life situations?

Top Scholar KLB Mathematics Learners Book Grade 9, page 43.
Charts showing tables and matrices.
Real-life examples of tables.
Top Scholar KLB Mathematics Learners Book Grade 9, page 45.
Paper cards for creating matrices.
Worksheets with various matrices.

Oral questions. Written exercise. Observation.

Algebra

Matrices - Determining the Position of Items in a Matrix

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

Determine the position of items in a matrix;
Identify elements by their positions;
Appreciate the importance of positional notation in matrices.

Discuss and identify the position of each item in a matrix.
Use paper cards to create matrices and identify positions.
Solve problems involving position of elements in matrices.

How do we use matrices in real life situations?

Top Scholar KLB Mathematics Learners Book Grade 9, page 46.
Paper cards labeled with letters or numbers.
Charts showing element positions.

Oral questions. Written exercise. Group activity.

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

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.

Oral questions. Written exercise. Assignment.

Algebra

Matrices - Subtraction of Matrices
Matrices - Application of Matrices

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

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

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

How do we use matrices in real life situations?

Top Scholar KLB Mathematics Learners Book Grade 9, page 54.
Charts showing subtraction of matrices.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 57.
Real-life data that can be represented in matrices.

Oral questions. Written exercise. Group presentation.

Algebra

Equations of Straight Lines - Introduction to 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.

Oral questions. Written exercise. Observation.

Algebra

Equations of Straight Lines - Identifying the Gradient
Equations of Straight Lines - Measuring Gradient

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

Identify the gradient in real life situations;
Compare different gradients;
Show interest in measuring steepness in real-life objects.

Incline objects at different positions to demonstrate gradient.
Compare different gradients and identify steeper slopes.
Relate gradient to real-life applications.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 58.
Ladders or sticks for demonstrating gradients.
Pictures of hills and slopes.
Top Scholar KLB Mathematics Learners Book Grade 9, page 59.
Rulers and measuring tapes.
Inclined objects for measurement.

Oral questions. Written exercise. Practical activity.

Algebra

Equations of Straight Lines - Gradient from Two Known Points

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

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

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

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 60.
Graph paper.
Rulers and protractors.

Oral questions. Written exercise. Assignment.

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

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.

Oral questions. Written exercise. Assignment.

Algebra

Equations of Straight Lines - Equation from a Point and Gradient
Equations of Straight Lines - Express Equation in Form y = mx + c

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

Determine the equation of a straight line from a known point and gradient;
Apply the point-slope formula;
Show interest in different ways of finding line equations.

Work out the equation of a straight line given a point and gradient.
Apply the point-slope formula.
Solve problems involving lines with given point and gradient.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 64.
Graph paper.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 65.
Charts showing line equations.

Oral questions. Written exercise. Assignment.

Algebra

Equations of Straight Lines - Interpreting y = mx + c

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.

Oral questions. Written exercise. Group activity.

Algebra

Equations of Straight Lines - Graphing Lines from Equations
Equations of Straight Lines - x and y Intercepts

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

Draw graphs of straight lines from their equations;
Use the gradient and y-intercept to plot lines;
Appreciate the visual representation of equations.

Generate tables of values from line equations.
Plot points and draw lines from the equations.
Compare lines with different gradients and y-intercepts.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 68.
Graph paper.
Rulers.
Top Scholar KLB Mathematics Learners Book Grade 9, page 70.

Oral questions. Written exercise. Practical activity.

Algebra

Equations of Straight Lines - Using Intercepts to Graph Lines

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

Draw graphs of straight lines using intercepts;
Calculate intercepts from line equations;
Show interest in different methods of graphing lines.

Calculate x and y intercepts from line equations.
Draw graphs of lines using the intercepts.
Compare graphing using intercepts versus using tables of values.

How do we represent linear inequalities in graphs?

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

Oral questions. Written exercise. Group work.

Algebra

Equations of Straight Lines - Parallel and Perpendicular Lines
Equations of Straight Lines - Real Life Applications

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

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

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

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 71.
Graph paper.
Rulers and protractors.
Top Scholar KLB Mathematics Learners Book Grade 9, page 72.
Real-life data that can be modeled using lines.
Computers with graphing software.

Oral questions. Written exercise. Group presentation.

Algebra

Linear Inequalities - Introduction to Inequalities

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

Understand the concept of inequality;
Represent inequalities using symbols;
Appreciate the use of inequalities in expressing constraints.

Discuss inequality statements from real-life situations.
Represent inequalities using appropriate symbols.
Identify examples of inequalities in everyday life.

How do we represent linear inequalities in graphs?

Top Scholar KLB Mathematics Learners Book Grade 9, page 75.
Charts showing inequality symbols.
Real-life examples of inequalities.

Oral questions. Written exercise. Observation.

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.

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

MEASUREMENTS

Area of a Pentagon
Area of a Hexagon

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.
-Mathematics learners book grade 9 page 90;
-Cut-outs of regular hexagons;
-Chart with diagrams of hexagons;
-Ruler and protractor;
-Calculator.

-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:

-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.

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

MEASUREMENTS

Surface Area of Triangular and Rectangular-Based Prisms

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

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

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

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

-Mathematics learners book grade 9 page 94;
-Manila paper for making nets;
-Scissors;
-Rulers;
-Objects with triangular prism shapes;
-Glue.
-Mathematics learners book grade 9 page 95;
-Objects with rectangular prism shapes (boxes);

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

MEASUREMENTS

Surface Area of Triangular, Rectangular and Square-Based Pyramids

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

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

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

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

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

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

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

MEASUREMENTS

Volume of Triangular and Rectangular-Based Prisms

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

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

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

How do we determine the volume of a triangular prism?

-Mathematics learners book grade 9 page 105;
-Triangular prism models;
-Rulers;
-Scientific calculators;
-Charts showing formulas for volume of triangular prisms.

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

MEASUREMENTS

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

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

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

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

How do we determine the volume of different solids?

-Mathematics learners book grade 9 page 107;
-Rectangular prism models (boxes);
-Rulers;
-Scientific calculators;
-Charts showing formulas for volume of rectangular prisms.
-Mathematics learners book grade 9 page 108;
-Triangular-based pyramid models;
-Charts showing formulas for volume of pyramids.

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

MEASUREMENTS

Volume of Triangular, Rectangular and Square-Based Pyramids

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

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

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

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

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

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

MEASUREMENTS

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

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

-Identify 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.
-Mathematics learners book grade 9 page 112;
-Spherical objects (balls);
-Measuring tape/rulers;
-Charts showing formulas for volume of spheres.

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

MEASUREMENTS

Volume of a Frustum in Real Life Situations

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

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

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

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

How do we calculate the volume of a frustum?

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

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

MEASUREMENTS

Mass, Volume, Weight and Density - Converting Units of Mass

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

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

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

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

-Mathematics learners book grade 9 page 118;
-Weighing instruments;
-Various objects to weigh;
-Charts showing relationship between different units of mass.

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

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.

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

MEASUREMENTS

Time, Distance and Speed - Working Out Speed in Km/h and m/s
Time, Distance and Speed - Working Out Average Speed in Real Life Situations

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

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

In groups, learners are guided to:
-Record distance covered by vehicles in kilometers and time taken in hours;
-Calculate speed using the formula speed = distance/time;
-Express speed in kilometers per hour (km/h);
-Convert speed from m/s to km/h using the relationship 1 m/s = 3.6 km/h;
-Complete a table with distance, time, and speed;
-Discuss and share results with other groups.

Why do we need different units for measuring speed?

-Mathematics learners book grade 9 page 125;
-Scientific calculators;
-Chart showing conversion between m/s and km/h;
-Examples of speeds of various objects and vehicles.
-Mathematics learners book grade 9 page 126;
-Chart showing examples of average speed calculations;
-Examples of journey scenarios with varying speeds.

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

MEASUREMENTS

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

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
Time, Distance and Speed - Identifying Longitudes on the Globe

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.
-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; -Problem-solving assessment.

MEASUREMENTS

Time, Distance and Speed - Relating Longitudes to Time on the Globe

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.

-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

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.
-Mathematics learners book grade 9 page 142;

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

MEASUREMENTS

Money - Working Out Export 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.

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

MEASUREMENTS

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

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

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

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

What are import duties and why are they charged?

-Mathematics learners book grade 9 page 143;
-Digital devices for research;
-Scientific calculators;
-Charts showing import duty rates;
-Examples of import scenarios.
-Mathematics learners book grade 9 page 145;
-Charts showing excise duty rates;
-Examples of goods subject to excise duty.

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

MEASUREMENTS

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

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

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

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

How is VAT calculated and why is it charged?

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

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

MEASUREMENTS

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

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

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

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

How do we estimate measurements of different quantities?

-Mathematics learners book grade 9 page 148;
-Measuring tapes/rulers;
-Various objects to measure;
-Charts showing conventional and arbitrary units;
-Open space for measuring with strides.
-Mathematics learners book grade 9 page 149;
-Weighing scales/balances;
-Scientific calculators.

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

MEASUREMENTS

Approximations and Errors - Determining Percentage Errors Using Actual Measurements

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.

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