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

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.

Oral questions. Written exercise. Group activity.

Numbers

Cubes and Cube Roots - Determining Cube Roots by Factor Method
Cubes and Cube Roots - Determining Cube Roots from Mathematical Tables

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

Determine cube roots of numbers by factor method;
Apply cube root calculations to real life situations;
Appreciate the relationship between cubes and cube roots.

Demonstrate finding cube roots using factor method.
Discuss the relationship between cube and cube root.
Solve problems involving cube roots.

How do we work out the cube roots of numbers?

Top Scholar KLB Mathematics Learners Book Grade 9, page 15.
Cubes of different sizes.
Factor trees.
Top Scholar KLB Mathematics Learners Book Grade 9, page 16.
Mathematical tables.
Calculators.

Oral questions. Written exercise. Group work.

Numbers

Cubes and Cube Roots - Cube Roots of Numbers Greater Than 1000
Cubes and Cube Roots - Cube Roots of Numbers Between 0 and 1

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

Determine cube roots of numbers greater than 1000 using mathematical tables;
Apply cube root calculations to real life situations;
Appreciate mathematical tables as tools for calculation.

Discuss the concept of cube roots of numbers greater than 1000.
Use mathematical tables to find cube roots of large numbers.
Solve problems involving cube roots of large numbers.

How do we work out the cube roots of numbers?

Top Scholar KLB Mathematics Learners Book Grade 9, page 17.
Mathematical tables.
Calculators.
Top Scholar KLB Mathematics Learners Book Grade 9, page 18.

Oral questions. Written exercise. Group presentation.

Numbers

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:

Work out cubes and cube roots using calculators;
Apply cube and cube root calculations to real life situations;
Appreciate the use of technology in mathematical calculations.

Demonstrate how to use a calculator to find cubes and cube roots.
Compare results from mathematical tables and calculators.
Solve real-life problems using a calculator.

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

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

Oral questions. Written exercise. Practical assessment.

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

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

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.

Oral questions. Written exercise. Group activity.

Numbers

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:

Apply compound proportions to solve complex real-life problems;
Develop strategies for solving compound proportion problems;
Show interest in the versatility of proportional reasoning.

Work out complex problems involving compound proportions.
Develop step-by-step approach to solving compound proportion problems.
Apply proportional reasoning to real-life scenarios.

Why do we work fast?

Top Scholar KLB Mathematics Learners Book Grade 9, page 39.
Worksheets with compound proportion problems.
Calculators.
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. Group presentation.

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

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:

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.

Oral questions. Written exercise. Digital project.

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

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.

Oral questions. Written exercise. Project work.

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

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

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

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

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

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

Oral questions. Written exercise. Group presentation.

Algebra

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

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

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

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

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

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

Oral questions. Written exercise. Assignment.

Algebra

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

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

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

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

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

Top Scholar KLB Mathematics Learners Book Grade 9, page 65.
Charts showing line equations.
Graph paper.
Top Scholar KLB Mathematics Learners Book Grade 9, page 67.
Charts showing lines with different gradients.

Oral questions. Written exercise. Group presentation.

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
Equations of Straight Lines - Real Life Applications

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

Oral questions. Written exercise. Group work.

Algebra

Linear Inequalities - Introduction to Inequalities
Linear Inequalities - Solving Linear Inequalities (Addition and Subtraction)

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

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

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

How do we represent linear inequalities in graphs?

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

Oral questions. Written exercise. Observation.

Algebra

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 multiplication and division;
Apply linear inequalities to real life situations;
Appreciate the rule for inequality sign when multiplying or dividing by negative numbers.

Discuss inequality operations with multiplication and division.
Demonstrate the effect of multiplication by negative numbers on inequality signs.
Solve inequalities involving multiplication and division.

How do we represent linear inequalities in graphs?

Top Scholar KLB Mathematics Learners Book Grade 9, page 76.
Charts showing inequality rules.
Number lines.
Top Scholar KLB Mathematics Learners Book Grade 9, page 77.
Worksheets with inequality problems.

Oral questions. Written exercise. Class assignment.

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

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

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

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

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

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

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

MEASUREMENTS

Surface Area of Triangular, Rectangular and Square-Based Pyramids

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

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

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

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

-Mathematics learners book grade 9 page 96;
-Manila paper for making nets;
-Scissors;
-Rulers;
-Objects with triangular pyramid shapes;
-Glue.
-Mathematics learners book grade 9 page 97;
-Objects with rectangular pyramid shapes;

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

MEASUREMENTS

Area of a Sector and Segment of a Circle

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

-Define a sector of a circle;
-Calculate the area of a sector using the formula A = (θ/360°) × πr²;
-Relate angle at the center to the area of a sector;
-Show interest in calculating area of sectors.

In groups, learners are guided to:
-Draw circles of different radii on paper;
-Mark points on the circumference to form sectors with different angles;
-Cut along radii and arc to form sectors;
-Measure angles at the center and calculate the area of sectors;
-Discuss and share results with other groups.

How does the angle at the center affect the area of a sector?

-Mathematics learners book grade 9 page 99;
-Circular paper cut-outs;
-Protractors;
-Scissors;
-Rulers;
-Scientific calculators.
-Mathematics learners book grade 9 page 101;

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

MEASUREMENTS

Surface Area of a Cone in Real Life Situations

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

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

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

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

-Mathematics learners book grade 9 page 102;
-Circular paper cut-outs;
-Scissors;
-Rulers;
-Protractors;
-Conical objects (funnels, party hats);
-Glue.
-Mathematics learners book grade 9 page 103;
-Cone models;
-Scientific calculators;
-Charts showing formulas for surface area of cones.

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

MEASUREMENTS

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

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

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

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

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

-Mathematics learners book grade 9 page 104;
-Spherical objects (balls, oranges);
-Measuring tape/rulers;
-Scientific calculators;
-Charts showing formulas for surface area of spheres.
-Mathematics learners book grade 9 page 105;
-Triangular prism models;
-Rulers;
-Charts showing formulas for volume of triangular prisms.

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

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

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

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

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

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

How do we calculate the volume of a frustum?

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

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

MEASUREMENTS

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

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

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

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

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

-Mathematics learners book grade 9 page 118;
-Weighing instruments;
-Various objects to weigh;
-Charts showing relationship between different units of mass.
-Mathematics learners book grade 9 page 119;
-Spring balance;
-Digital devices for research.

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

MEASUREMENTS

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

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

-Define density;
-Understand the relationship between mass, volume, and density;
-Calculate density using the formula D = m/V;
-Show genuine interest in determining density of various substances.

In groups, learners are guided to:
-Measure the mass of different objects;
-Determine the volume of objects using water displacement method;
-Calculate the density of objects using the formula D = m/V;
-Complete a table with mass, volume, and density of different objects;
-Discuss and share findings with other groups.

How do we determine the density of an object?

-Mathematics learners book grade 9 page 121;
-Weighing instruments;
-Measuring cylinders;
-Various objects (coins, stones, metal pieces);
-Water;
-Scientific calculators.
-Mathematics learners book grade 9 page 122;
-Scientific calculators;
-Chart showing densities of common materials;
-Examples of applications of density in real life.

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

MEASUREMENTS

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

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

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

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

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

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

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

MEASUREMENTS

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

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

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

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

How do we observe speed in daily activities?

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

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

MEASUREMENTS

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

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

Money - Identifying Currencies Used in Different Countries
Money - Converting Currency from One to Another in Real Life Situations

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

-Identify currencies used in different countries;
-Match currencies with their respective countries;
-Recognize currency symbols;
-Show interest in learning about different currencies.

In groups, learners are guided to:
-Use digital devices to search and print pictures of currencies from: a) Neighboring countries b) Other African countries c) Common currencies used globally;
-Make a collage of different currencies on a piece of carton;
-Match currencies with their respective countries;
-Identify currency symbols (e.g., $, €, £, ¥);
-Display and present their collages to other groups.

Why do different countries use different currencies?

-Mathematics learners book grade 9 page 138;
-Digital devices for research;
-Pictures/samples of different currencies;
-Manila paper or carton;
-Charts showing currencies and their countries.
-Mathematics learners book grade 9 page 141;
-Exchange rate tables from newspapers or online sources;
-Scientific calculators;
-Digital devices for checking current exchange rates;
-Charts showing examples of currency conversions.

-Observation; -Oral questions; -Group presentations; -Assessment of currency collages.

MEASUREMENTS

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

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

-Convert Kenyan currency to foreign currency;
-Use exchange rate tables to convert currencies;
-Solve problems involving currency conversion;
-Show interest in understanding international currency exchange.

In groups, learners are guided to:
-Review the concept of exchange rates;
-Understand that the selling rate is used when converting Kenyan Shillings to foreign currency;
-Convert Kenyan Shillings to various foreign currencies using the selling rate;
-Solve problems involving currency conversion;
-Discuss real-life situations where currency conversion is necessary;
-Discuss and share results with other groups.

How do exchange rates affect international trade?

-Mathematics learners book grade 9 page 142;
-Exchange rate tables from newspapers or online sources;
-Scientific calculators;
-Digital devices for checking current exchange rates;
-Charts showing examples of currency conversions.
-Mathematics learners book grade 9 page 143;
-Digital devices for research;
-Charts showing export duty rates;
-Examples of export scenarios.

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

MEASUREMENTS

Money - Working Out Import Duties Charged on Goods
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
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 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.
-Mathematics learners book grade 9 page 149;
-Weighing scales/balances;
-Scientific calculators.
-Mathematics learners book grade 9 page 151;

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