Numbers

Integers - Addition of Integers

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

Perform basic operations on integers in different situations;
Work out combined operations on integers in different situations;
Appreciate the use of integers in real life situations.

Discuss and work out basic operations on integers using number cards and charts.
Play games involving numbers and operations.
Pick integers and perform basic operations.

How do we carry out operations of integers in real life situations?

Top Scholar KLB Mathematics Learners Book Grade 9, page 1.
Number cards.
Charts with basic operations on integers.

Oral questions. Written exercise. Observation.

Numbers

Integers - Subtraction of Integers
Integers - Multiplication of Integers

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

Perform basic operations on integers in different situations;
Work out combined operations on integers in different situations;
Apply integers to real life situations.

Discuss and work out subtraction of integers using number cards.
Solve real-life problems involving subtraction of integers.
Identify operations involving subtraction of integers in daily activities.

How do we apply integers in daily activities?

Top Scholar KLB Mathematics Learners Book Grade 9, page 2.
Number cards.
Charts with subtraction operations.
Top Scholar KLB Mathematics Learners Book Grade 9, page 3.
Charts showing patterns of multiplication of integers.
Multiplication tables.

Oral questions. Written exercise. Class assignment.

Numbers

Integers - Division of Integers
Integers - Combined Operations on Integers

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

Perform division operations on integers;
Work out combined operations involving division of integers;
Apply division of integers to real life situations.

Discuss the division of integers.
Create tables showing patterns in division of integers.
Solve real-life problems involving division of integers.

How do we apply integers in daily activities?

Top Scholar KLB Mathematics Learners Book Grade 9, page 4.
Division tables.
Worksheets with division problems.
Top Scholar KLB Mathematics Learners Book Grade 9, page 5.
Calculators.
Computers with mathematical software.

Oral questions. Written exercise. Observation.

Numbers

Cubes and Cube Roots - Working out Cubes of Numbers by Multiplication
Cubes and Cube Roots - Determining Cubes from Mathematical Tables
Cubes and Cube Roots - Cubes of Numbers Greater Than 10

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

Work out cubes of numbers by multiplication;
Apply cubes of numbers in real life situations;
Appreciate the use of cubes in real-life contexts.

Use stacks of cubes to demonstrate the concept of cube.
Work out cubes of numbers using multiplication.
Relate cubes to volume of cubic objects.

How do we work out the cubes of numbers?

Top Scholar KLB Mathematics Learners Book Grade 9, page 8.
Small cubes.
Charts showing cubes of numbers.
Top Scholar KLB Mathematics Learners Book Grade 9, page 11.
Mathematical tables.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 12.

Oral questions. Written exercise. Observation of practical work.

Numbers

Cubes and Cube Roots - Cubes of Numbers Less Than 1
Cubes and Cube Roots - Determining Cube Roots by Factor Method

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

Determine cubes of numbers less than 1 using mathematical tables;
Apply cube calculations to real life situations;
Show interest in working with decimal numbers.

Discuss the concept of cubes of numbers less than 1.
Use mathematical tables to find cubes of decimal numbers.
Solve problems involving cubes of decimal numbers.

How do we work out the cubes of numbers?

Top Scholar KLB Mathematics Learners Book Grade 9, page 13.
Mathematical tables.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 15.
Cubes of different sizes.
Factor trees.

Oral questions. Written exercise. Assignment.

Numbers

Cubes and Cube Roots - Determining Cube Roots from Mathematical Tables
Cubes and Cube Roots - Cube Roots of Numbers Greater Than 1000

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

Determine cube roots of numbers from mathematical tables;
Apply cube root calculations to real life situations;
Show interest in using mathematical tables.

Read the cube roots of numbers from mathematical tables.
Compare cube roots found by factorization and from tables.
Solve problems involving cube roots.

How do we work out the cube roots of numbers?

Top Scholar KLB Mathematics Learners Book Grade 9, page 16.
Mathematical tables.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 17.

Oral questions. Written exercise. Assignment.

Numbers

Cubes and Cube Roots - Cube Roots of Numbers Between 0 and 1
Cubes and Cube Roots - Using a Calculator for Cubes and Cube Roots
Cubes and Cube Roots - Application of Cubes and Cube Roots

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

Determine cube roots of numbers between 0 and 1 using mathematical tables;
Apply cube root calculations to real life situations;
Show interest in working with decimal numbers.

Discuss cube roots of decimal numbers.
Use mathematical tables to find cube roots of decimal numbers.
Solve problems involving cube roots of decimal numbers.

How do we work out the cube roots of numbers?

Top Scholar KLB Mathematics Learners Book Grade 9, page 18.
Mathematical tables.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 19.
Computers with mathematical software.
Top Scholar KLB Mathematics Learners Book Grade 9, page 21.
Real-life objects with cubic shapes.

Oral questions. Written exercise. Assignment.

Numbers

Indices and Logarithms - Expressing Numbers in Index Form
Indices and Logarithms - Laws of Indices: Multiplication

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

Express numbers in index form in different situations;
Use index form to simplify expressions;
Appreciate the use of indices in representing large numbers.

Discuss indices and identify the base.
Express numbers in index form.
Solve problems involving index form.

How do we express numbers in powers?

Top Scholar KLB Mathematics Learners Book Grade 9, page 26.
Charts showing numbers in index form.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 28.
Charts showing laws of indices.

Oral questions. Written exercise. Group activity.

Numbers

Indices and Logarithms - Laws of Indices: Division
Indices and Logarithms - Laws of Indices: Power of a Power

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

Generate the laws of indices for division;
Apply the laws of indices in different situations;
Show interest in using laws of indices for calculation.

Show the laws of indices using division.
Use the laws of indices to work out problems.
Simplify expressions using division law of indices.

How do we express numbers in powers?

Top Scholar KLB Mathematics Learners Book Grade 9, page 29.
Charts showing laws of indices.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 30.

Oral questions. Written exercise. Group work.

Numbers

Indices and Logarithms - Powers of 10 and Common Logarithms
Indices and Logarithms - Using IT for Indices and Logarithms
Compound Proportions and Rates of Work - Introduction to Proportions

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

Relate powers of 10 to common logarithms;
Apply common logarithms in different situations;
Show interest in using logarithms for calculation.

Discuss and relate powers of 10 to common logarithms.
Use mathematical tables to find common logarithms.
Solve problems involving common logarithms.

How do we express numbers in powers?

Top Scholar KLB Mathematics Learners Book Grade 9, page 33.
Mathematical tables.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 34.
Computers with mathematical software.
Top Scholar KLB Mathematics Learners Book Grade 9, page 35.
Charts showing proportional relationships.
Real-life examples of proportions.

Oral questions. Written exercise. Group presentation.

Numbers

Compound Proportions and Rates of Work - Dividing Quantities into Proportional Parts
Compound Proportions and Rates of Work - Direct Proportion

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

Divide quantities into proportional parts in real life situations;
Express proportional parts as fractions;
Appreciate the importance of proportional division in fair sharing.

Discuss and divide quantities into proportional parts.
Express proportional parts as fractions.
Solve problems involving proportional division.

What are proportions?

Top Scholar KLB Mathematics Learners Book Grade 9, page 35.
Counters (bottle tops, small stones).
Charts showing proportional division.
Top Scholar KLB Mathematics Learners Book Grade 9, page 36.
Charts showing direct proportion.
Graphs of direct proportion.

Oral questions. Written exercise. Practical activity.

Numbers

Compound Proportions and Rates of Work - Inverse Proportion
Compound Proportions and Rates of Work - Relating Different Ratios

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

Identify inverse proportional relationships;
Solve problems involving inverse proportion;
Appreciate the difference between direct and inverse proportion.

Discuss inverse proportion with real-life examples.
Identify the characteristics of inverse proportion.
Solve problems involving inverse proportion.

What are proportions?

Top Scholar KLB Mathematics Learners Book Grade 9, page 36.
Charts showing inverse proportion.
Graphs of inverse proportion.
Top Scholar KLB Mathematics Learners Book Grade 9, page 37.
Charts showing different ratios.
Real-life examples of ratio comparison.

Oral questions. Written exercise. Assignment.

Numbers

Compound Proportions and Rates of Work - Working Out Compound Proportions
Compound Proportions and Rates of Work - Solving Problems Using Compound Proportions
Compound Proportions and Rates of Work - Introduction to Rates of Work

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

Work out compound proportions using ratio method;
Apply compound proportions to real life situations;
Appreciate the use of compound proportions in problem-solving.

Determine compound proportions using ratios.
Solve problems involving compound proportions.
Discuss real-life applications of compound proportions.

Why do we work fast?

Top Scholar KLB Mathematics Learners Book Grade 9, page 39.
Charts showing compound proportions.
Calculators.
Worksheets with compound proportion problems.
Top Scholar KLB Mathematics Learners Book Grade 9, page 40.
Charts showing rates of work.
Real-life examples of work rates.

Oral questions. Written exercise. Assignment.

Numbers

Compound Proportions and Rates of Work - Calculating Rates of Work
Compound Proportions and Rates of Work - Combined Rates of Work

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

Calculate rates of work in real life situations;
Solve problems involving rates of work;
Show interest in efficiency and time management in work.

Work out rates of work.
Discuss factors affecting rates of work.
Solve problems involving rates of work in real-life contexts.

Why do we work fast?

Top Scholar KLB Mathematics Learners Book Grade 9, page 40.
Charts showing rates of work.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 41.
Charts showing combined rates of work.

Oral questions. Written exercise. Group work.

Numbers

Compound Proportions and Rates of Work - Rates of Work and Time
Compound Proportions and Rates of Work - Rates of Work and Output

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

Calculate time required to complete tasks based on rates of work;
Apply inverse proportion in rates of work problems;
Show interest in time efficiency and planning.

Discuss the relationship between rate of work and time.
Calculate time required to complete tasks based on work rates.
Solve problems involving time planning based on work rates.

Why do we work fast?

Top Scholar KLB Mathematics Learners Book Grade 9, page 41.
Worksheets with time and rate problems.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 42.
Charts showing productivity and rates.

Oral questions. Written exercise. Group activity.

Numbers
Algebra
Algebra

Compound Proportions and Rates of Work - Using IT for Rates of Work
Matrices - Identifying a Matrix
Matrices - Determining the Order of a Matrix

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

Use IT devices to learn more on compound proportions and rates of work;
Apply compound proportions and rates of work to real life situations;
Appreciate use of technology in learning mathematics.

Play games on rates of work using IT devices.
Use spreadsheets to calculate and analyze rates of work.
Create digital presentations on applications of rates of work.

Why do we work fast?

Top Scholar KLB Mathematics Learners Book Grade 9, page 42.
Computers with spreadsheet software.
Calculators.
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. Digital project.

Algebra

Matrices - Determining the Position of Items in a Matrix
Matrices - Determining Compatibility for Addition

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

Oral questions. Written exercise. Group activity.

Algebra

Matrices - Determining Compatibility for Subtraction
Matrices - Addition of Matrices

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

Determine compatibility of matrices for subtraction;
Identify matrices of the same order;
Appreciate the rules of matrix operations.

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

How do we use matrices in real life situations?

Top Scholar KLB Mathematics Learners Book Grade 9, page 49.
Charts showing matrices of various orders.
Worksheets with matrices.
Top Scholar KLB Mathematics Learners Book Grade 9, page 51.
Charts showing addition of matrices.
Calculators.

Oral questions. Written exercise. Group work.

Algebra

Matrices - Subtraction of Matrices
Matrices - Application of Matrices
Equations of Straight Lines - Introduction to Gradient

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

Oral questions. Written exercise. Group presentation.

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
Equations of Straight Lines - Positive and Negative Gradients

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

Oral questions. Written exercise. Assignment.

Algebra

Equations of Straight Lines - Zero and Undefined Gradients
Equations of Straight Lines - Equation from Two Points
Equations of Straight Lines - Deriving the 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.
Top Scholar KLB Mathematics Learners Book Grade 9, page 63.
Worksheets with coordinate points.

Oral questions. Written exercise. Group presentation.

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
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
Equations of Straight Lines - Parallel and Perpendicular 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.
Rulers and protractors.

Oral questions. Written exercise. Assignment.

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)
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:

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

Oral questions. Written exercise. Group work.

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

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

MEASUREMENTS

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

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);
-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
Area of a Sector and Segment of a Circle

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.
-Mathematics learners book grade 9 page 99;
-Circular paper cut-outs;
-Protractors;
-Scientific calculators.

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

MEASUREMENTS

Area of a Sector and Segment of a Circle
Surface Area of a Cone in Real Life Situations

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

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

In groups, learners are guided to:
-Draw circles and form segments by drawing chords;
-Cut out segments from paper circles;
-Derive the formula for the area of a segment (sector area minus triangle area);
-Calculate the area of segments with different angles and chord lengths;
-Discuss and share results with other groups.

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

-Mathematics learners book grade 9 page 101;
-Circular paper cut-outs;
-Protractors;
-Scissors;
-Rulers;
-Scientific calculators.
-Mathematics learners book grade 9 page 102;
-Conical objects (funnels, party hats);
-Glue.

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

MEASUREMENTS

Surface Area of a Cone in Real Life Situations
Surface Area of a Sphere in Real Life Situations
Volume of Triangular and Rectangular-Based Prisms

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

-Oral questions; -Written exercises; -Problem-solving assessment; -Peer 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
Volume of a Cone in Real Life Situations

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

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

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

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

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

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

MEASUREMENTS

Volume of a Sphere in Real Life Situations
Volume of a Frustum in Real Life Situations
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.
-Mathematics learners book grade 9 page 114;

-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
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:

-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.
-Mathematics learners book grade 9 page 123;

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

MEASUREMENTS

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

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

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

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

How do we observe speed in daily activities?

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

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

MEASUREMENTS

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

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

-Define average speed;
-Calculate average speed over a journey;
-Solve problems involving average speed;
-Show interest in calculating average speed in real-life situations.

In groups, learners are guided to:
-Discuss the concept of average speed;
-Record distance covered and time taken for a journey with varying speeds;
-Calculate average speed using the formula average speed = total distance/total time;
-Solve problems involving average speed in real-life contexts;
-Discuss and share results with other groups.

How do we calculate the average speed of a journey?

-Mathematics learners book grade 9 page 126;
-Scientific calculators;
-Chart showing examples of average speed calculations;
-Examples of journey scenarios with varying speeds.
-Mathematics learners book grade 9 page 129;
-Stopwatch/timer;
-Measuring tape/rulers;
-Compass for directions.

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

MEASUREMENTS

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

-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.
-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; -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 at different longitudes;
-Understand that time increases eastward and decreases westward;
-Solve problems involving local time at different longitudes;
-Show interest in understanding time zones.

In groups, learners are guided to:
-Review the relationship between longitudes and time;
-Calculate local time at different longitudes given the local time at a reference longitude;
-Understand that for every 15° change in longitude, time changes by 1 hour;
-Solve problems involving local time at different longitudes;
-Discuss and share results with other groups.

How do we calculate the local time at different longitudes?

-Mathematics learners book grade 9 page 134;
-Globe;
-World map showing time zones;
-Scientific calculators;
-Charts showing examples of local time calculations.
-Mathematics learners book grade 9 page 136;
-World map showing time zones and the International Date Line;

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

MEASUREMENTS

Time, Distance and Speed - Determining Local Time of Places on Different Longitudes
Money - Identifying Currencies Used in Different Countries

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

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

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

How do time zones affect international communication and travel?

-Mathematics learners book grade 9 page 137;
-Globe;
-World map showing time zones;
-Digital devices showing current time in different cities;
-Scientific calculators.
-Mathematics learners book grade 9 page 138;
-Digital devices for research;
-Pictures/samples of different currencies;
-Manila paper or carton;
-Charts showing currencies and their countries.

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

MEASUREMENTS

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

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

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

MEASUREMENTS

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

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

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

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

What are import duties and why are they charged?

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

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

MEASUREMENTS

Money - Determining Value-Added Tax (VAT) Charged on Goods and Services
Approximations and Errors - Approximating Quantities in Measurements

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.
-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; -Written exercises; -Analysis of receipts.

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.