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

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.

Oral questions. Written exercise. Observation of practical work.

Numbers

Cubes and Cube Roots - Cubes of Numbers Greater Than 10
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 greater than 10 using mathematical tables;
Apply cube calculations to real life situations;
Appreciate the use of mathematical tables.

Discuss the concept of cubes of numbers greater than 10.
Use mathematical tables to find cubes of numbers greater than 10.
Solve problems involving cubes of large numbers.

How do we work out the cubes of numbers?

Top Scholar KLB Mathematics Learners Book Grade 9, page 12.
Mathematical tables.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 13.
Top Scholar KLB Mathematics Learners Book Grade 9, page 15.
Cubes of different sizes.
Factor trees.

Oral questions. Written exercise. Group activity.

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

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.

Oral questions. Written exercise. Assignment.

Numbers

Cubes and Cube Roots - Application of Cubes and Cube Roots
Indices and Logarithms - Expressing Numbers in Index Form

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

Apply cubes and cube roots in real life situations;
Solve problems involving cubes and cube roots;
Appreciate the relevance of cubes and cube roots in everyday life.

Discuss applications of cubes and cube roots in real life.
Solve real-life problems involving cubes and cube roots.
Create projects demonstrating applications of cubes and cube roots.

Where do we apply cubes and cube roots in real life situations?

Top Scholar KLB Mathematics Learners Book Grade 9, page 21.
Real-life objects with cubic shapes.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 26.
Charts showing numbers in index form.

Oral questions. Written exercise. Project work.

Numbers

Indices and Logarithms - Laws of Indices: Multiplication
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 multiplication;
Apply the laws of indices in different situations;
Appreciate the simplicity brought by using laws of indices.

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

How do we express numbers in powers?

Top Scholar KLB Mathematics Learners Book Grade 9, page 28.
Charts showing laws of indices.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 29.
Top Scholar KLB Mathematics Learners Book Grade 9, page 30.

Oral questions. Written exercise. Assignment.

Numbers

Indices and Logarithms - Powers of 10 and Common Logarithms
Indices and Logarithms - Using IT for Indices and Logarithms

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.

Oral questions. Written exercise. Group presentation.

Numbers

Compound Proportions and Rates of Work - Introduction to Proportions
Compound Proportions and Rates of Work - Dividing Quantities into Proportional Parts

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

Understand the concept of proportion in real life situations;
Identify proportional relationships;
Appreciate the importance of proportions in everyday contexts.

Discuss the concept of proportions with examples from daily life.
Identify proportional relationships in various contexts.
Solve simple proportion problems.

What are proportions?

Top Scholar KLB Mathematics Learners Book Grade 9, page 35.
Charts showing proportional relationships.
Real-life examples of proportions.
Counters (bottle tops, small stones).
Charts showing proportional division.

Oral questions. Written exercise. Observation.

Numbers

Compound Proportions and Rates of Work - Direct Proportion
Compound Proportions and Rates of Work - Inverse Proportion

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

Identify direct proportional relationships;
Solve problems involving direct proportion;
Show interest in applying direct proportion to real-life situations.

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

What are proportions?

Top Scholar KLB Mathematics Learners Book Grade 9, page 36.
Charts showing direct proportion.
Graphs of direct proportion.
Charts showing inverse proportion.
Graphs of inverse proportion.

Oral questions. Written exercise. Group work.

Numbers

Compound Proportions and Rates of Work - Relating Different Ratios
Compound Proportions and Rates of Work - Working Out Compound Proportions
Compound Proportions and Rates of Work - Solving Problems Using Compound Proportions

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

Relate different ratios in real life situations;
Compare ratios to determine greater or lesser ratios;
Show interest in using ratios for comparison.

Compare and write different ratios.
Convert ratios to equivalent fractions for comparison.
Solve problems involving comparison of ratios.

What are proportions?

Top Scholar KLB Mathematics Learners Book Grade 9, page 37.
Charts showing different ratios.
Real-life examples of ratio comparison.
Top Scholar KLB Mathematics Learners Book Grade 9, page 39.
Charts showing compound proportions.
Calculators.
Worksheets with compound proportion problems.

Oral questions. Written exercise. Group activity.

Numbers

Compound Proportions and Rates of Work - Introduction to Rates of Work
Compound Proportions and Rates of Work - Calculating Rates of Work

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

Understand the concept of rate of work;
Express rate of work in mathematical form;
Appreciate the importance of measuring work efficiency.

Discuss the concept of rates of work.
Express rates of work in mathematical form.
Relate rates of work to time efficiency in daily activities.

Why do we work fast?

Top Scholar KLB Mathematics Learners Book Grade 9, page 40.
Charts showing rates of work.
Real-life examples of work rates.
Calculators.

Oral questions. Written exercise. Observation.

Numbers

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

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

Calculate combined rates of work when multiple workers or machines work together;
Apply rates of work to real life situations;
Appreciate cooperation and teamwork in accomplishing tasks.

Work out combined rates of work.
Solve problems involving tasks completed by multiple workers.
Discuss real-life scenarios involving combined rates of work.

Why do we work fast?

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

Oral questions. Written exercise. Assignment.

Numbers
Algebra

Compound Proportions and Rates of Work - Rates of Work and Output
Compound Proportions and Rates of Work - Using IT for Rates of Work
Matrices - Identifying a Matrix

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

Calculate output based on rates of work;
Apply direct proportion in rates of work problems;
Appreciate the relationship between rate and productivity.

Discuss the relationship between rate of work and output.
Calculate output based on different work rates.
Solve problems involving productivity and work rates.

Why do we work fast?

Top Scholar KLB Mathematics Learners Book Grade 9, page 42.
Charts showing productivity and rates.
Calculators.
Computers with spreadsheet software.
Top Scholar KLB Mathematics Learners Book Grade 9, page 43.
Charts showing tables and matrices.
Real-life examples of tables.

Oral questions. Written exercise. Assignment.

Algebra

Matrices - Determining the Order of a Matrix
Matrices - Determining the Position of Items in a Matrix

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

Determine the order of a matrix in different situations;
Identify rows and columns in a matrix;
Show interest in describing matrices systematically.

Arrange items in rows and columns and discuss how to represent a matrix.
Organize objects in rows and columns to form matrices.
Give the order of matrices in terms of rows and columns.

How do we use matrices in real life situations?

Top Scholar KLB Mathematics Learners Book Grade 9, page 45.
Paper cards for creating matrices.
Worksheets with various matrices.
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. Practical 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
Matrices - Subtraction of Matrices

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

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

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

How do we use matrices in real life situations?

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

Oral questions. Written exercise. Assignment.

Algebra

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

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

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

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

How do we use matrices in real life situations?

Top Scholar KLB Mathematics Learners Book Grade 9, page 57.
Real-life data that can be represented in matrices.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 58.
Pictures of hills and slopes.
Charts showing different gradients.
Ladders or sticks for demonstrating gradients.

Oral questions. Written exercise. Project work.

Algebra

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

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

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

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

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

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

Oral questions. Written exercise. Group work.

Algebra

Equations of Straight Lines - Positive and Negative Gradients
Equations of Straight Lines - Zero and Undefined 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.
Charts showing horizontal and vertical lines.

Oral questions. Written exercise. Group activity.

Algebra

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:

Determine the equation of a straight line given two points;
Apply the point-slope formula;
Appreciate the use of equations to represent lines.

Work out the equation of a straight line given two points.
Derive the equation using the gradient formula.
Verify equations by substituting points.

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 62.
Graph paper.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 63.
Worksheets with coordinate points.

Oral questions. Written exercise. Group work.

Algebra

Equations of Straight Lines - Equation from a Point and Gradient
Equations of Straight Lines - Express Equation in Form y = mx + c
Equations of Straight Lines - Interpreting 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.
Top Scholar KLB Mathematics Learners Book Grade 9, page 67.
Charts showing lines with different gradients.

Oral questions. Written exercise. Assignment.

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

Oral questions. Written exercise. Group work.

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

Oral questions. Written exercise. Group activity.

Algebra

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

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

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

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

How do we represent linear inequalities in graphs?

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

Oral questions. Written exercise. Practical activity.

MEASUREMENTS

Area of a Pentagon

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

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

In groups and individually, learners are guided to:
-Discuss the properties of regular polygons;
-Use cut-outs to work out the area of pentagons;
-Identify objects with pentagonal shapes in their environment;
-Calculate the area of a regular pentagon using the formula A = (5/2)s²sin(72°).

How do we determine the area of different surfaces?

-Mathematics learners book grade 9 page 87;
-Cut-outs of regular pentagons;
-Chart with diagrams of pentagons;
-Calculator;
-Ruler and protractor.
-Mathematics learners book grade 9 page 89;
-Pentagonal objects;
-Worked examples on the board.

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

MEASUREMENTS

Area of a Hexagon

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

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

In groups and individually, learners are guided to:
-Discuss the properties of regular hexagons;
-Trace hexagons on paper and join vertices to the center to form triangles;
-Measure the height and base of triangles formed in the hexagon;
-Calculate the area of hexagons using the formula A = (3√3/2)s².

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

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

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
Volume of Triangular, Rectangular and Square-Based Pyramids

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

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

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

How do we determine the volume of a triangular prism?

-Mathematics learners book grade 9 page 105;
-Triangular prism models;
-Rulers;
-Scientific calculators;
-Charts showing formulas for volume of triangular prisms.
-Mathematics learners book grade 9 page 107;
-Rectangular prism models (boxes);
-Charts showing formulas for volume of rectangular prisms.
-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

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

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

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

How do we determine the volume of a sphere?

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

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

MEASUREMENTS

Volume of a Frustum in Real Life Situations
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:

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

-Observation; -Oral questions; -Written exercises; -Problem-solving 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
Mass, Volume, Weight and Density - Determining Mass Given Volume 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

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

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

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

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

-Mathematics learners book grade 9 page 123;
-Scientific calculators;
-Chart showing densities of common materials;
-Examples of applications of density in real life.
-Mathematics learners book grade 9 page 124;
-Stopwatch/timer;
-Measuring tape/rulers;
-Sports field or open area.

-Observation; -Oral questions; -Written exercises; -Problem-solving 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
Time, Distance and Speed - Determining Velocity 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.
-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

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
Time, Distance and Speed - Determining Local Time of Places on Different Longitudes

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

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

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

How are longitudes related to time?

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

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

MEASUREMENTS

Time, Distance and Speed - Determining Local Time of Places on Different Longitudes

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

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

In groups, learners are guided to:
-Review the calculation of local time at different longitudes;
-Understand the International Date Line and its effect on time/date;
-Calculate local time for places on opposite sides of the International Date Line;
-Solve complex problems involving local time at different longitudes;
-Discuss real-life applications such as international travel and communication;
-Discuss and share results with other groups.

How does the International Date Line affect time calculations?

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

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

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.
-Mathematics learners book grade 9 page 151;

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

Geometry

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

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

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

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

How do we locate a point on a Cartesian plane?

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

-Oral questions -Observation -Written exercise -Peer assessment

Geometry

Coordinates and Graphs - Completing tables for linear equations
Coordinates and Graphs - Drawing parallel lines

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

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

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

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

-KLB Mathematics Grade 9 Textbook page 156
-Graph paper
-Ruler
-Pencils
-Calculator
-Charts with prepared tables
-KLB Mathematics Grade 9 Textbook page 157
-Set square
-Charts showing parallel lines

-Oral questions -Peer assessment -Written exercise -Checklist

Geometry

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

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

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

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

What is the relationship between the gradients of parallel lines?

-KLB Mathematics Grade 9 Textbook page 158
-Graph paper
-Ruler
-Calculator
-Manila paper
-Digital devices (optional)
-KLB Mathematics Grade 9 Textbook page 159
-Protractor
-Set square
-Charts showing perpendicular lines

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

Geometry

Coordinates and Graphs - Relating gradients of perpendicular lines
Coordinates and Graphs - Applications of straight line graphs

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

Determine gradients of perpendicular lines;
Find the relationship between gradients of perpendicular lines;
Appreciate the application of gradient in determining perpendicular lines.

Learners work in groups to generate tables of values for equations such as y=3x+2 and y=-1/3x+1.
Learners draw the lines on the Cartesian plane, determine their gradients, and find the product of the gradients.
Learners discuss the relationship between the gradients of perpendicular lines.

What is the product of the gradients of two perpendicular lines?

-KLB Mathematics Grade 9 Textbook page 160
-Graph paper
-Ruler
-Calculator
-Set square
-Charts with examples of perpendicular lines
-KLB Mathematics Grade 9 Textbook page 165
-Charts showing real-life applications
-Manila paper for presentations

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