MEASUREMENTS

Area of a Pentagon

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

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

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

How do we determine the area of different surfaces?

-Mathematics learners book grade 9 page 87;
-Cut-outs of regular pentagons;
-Chart with diagrams of pentagons;
-Calculator;
-Ruler and protractor.

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

MEASUREMENTS

Area of a Pentagon
Area of a Hexagon

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

-Work out the area of a regular pentagon when different measurements are given;
-Solve problems involving the height and side length of a pentagon;
-Interpret and solve word problems involving area of pentagons;
-Appreciate the use of geometry in calculating areas of pentagons.

In groups and individually, learners are guided to:
-Work out problems on area of pentagons with given side lengths;
-Calculate the area of pentagons where vertices are at a given distance from the center;
-Relate the height of triangles formed in a pentagon to the area;
-Solve practical problems involving area of pentagons.

How can we calculate the area of a pentagon in different situations?

-Mathematics learners book grade 9 page 89;
-Pentagonal objects;
-Calculator;
-Worked examples on the board.
-Mathematics learners book grade 9 page 90;
-Cut-outs of regular hexagons;
-Chart with diagrams of hexagons;
-Ruler and protractor;
-Calculator.

-Written exercises; -Homework assignments; -Group work assessment; -Mathematical problem-solving tasks.

MEASUREMENTS

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

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

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

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

Where do we find hexagonal shapes in our daily lives?

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

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

MEASUREMENTS

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

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

-Draw a rectangular prism and identify its faces, edges, and vertices;
-Develop a net for a rectangular prism;
-Calculate the surface area of a rectangular prism using its net;
-Show interest in relating surface area to real-life applications.

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

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

-Mathematics learners book grade 9 page 95;
-Manila paper for making nets;
-Scissors;
-Rulers;
-Objects with rectangular prism shapes (boxes);
-Glue.
-Mathematics learners book grade 9 page 96;
-Objects with triangular pyramid shapes;

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

MEASUREMENTS

Surface Area of Triangular, Rectangular and Square-Based Pyramids
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

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

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

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

How do we determine the volume of a triangular prism?

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

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

MEASUREMENTS

Volume of Triangular, Rectangular and Square-Based Pyramids

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

-Identify triangular-based pyramids;
-Calculate the volume of a triangular-based pyramid using the formula V = ⅓ × area of base × height;
-Solve problems involving volume of triangular-based pyramids;
-Show interest in calculating volumes of pyramids.

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

How do we use the volume of solids in real-life situations?

-Mathematics learners book grade 9 page 108;
-Triangular-based pyramid models;
-Rulers;
-Scientific calculators;
-Charts showing formulas for volume of pyramids.
-Mathematics learners book grade 9 page 109;
-Rectangular and square-based pyramid models;

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

MEASUREMENTS

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

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

-Identify cones and their properties;
-Calculate the volume of a cone using the formula V = ⅓ × πr² × h;
-Solve problems involving volume of cones;
-Show interest in calculating volumes of cones.

In groups, learners are guided to:
-Identify and discuss models of cones;
-Identify the base radius and height of cones;
-Calculate the volume using the formula V = ⅓ × πr² × h;
-Solve practical problems involving volume of cones;
-Discuss and share results with other groups.

How do we determine the volume of a cone?

-Mathematics learners book grade 9 page 110;
-Cone models;
-Rulers;
-Scientific calculators;
-Charts showing formulas for volume of cones.
-Mathematics learners book grade 9 page 112;
-Spherical objects (balls);
-Measuring tape/rulers;
-Charts showing formulas for volume of spheres.

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

MEASUREMENTS

Volume of a Frustum in Real Life Situations

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

-Define a frustum;
-Identify frustums of cones and pyramids;
-Calculate the volume of a frustum;
-Show genuine interest in calculating volumes of frustums.

In groups, learners are guided to:
-Identify and discuss models of frustums;
-Understand how a frustum is formed by cutting a cone or pyramid;
-Learn the formula for volume of a frustum;
-Calculate the volume of different frustums;
-Discuss and share results with other groups.

What is a frustum and how is it formed?

-Mathematics learners book grade 9 page 113;
-Frustum models;
-Rulers;
-Scientific calculators;
-Charts showing formulas for volume of frustums.
-Mathematics learners book grade 9 page 114;

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

MEASUREMENTS

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

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

-Identify different instruments and tools used in weighing;
-Describe the functions of various weighing instruments;
-Use weighing instruments correctly;
-Show interest in using weighing instruments.

In groups, learners are guided to:
-Identify and discuss different types of balances used for weighing;
-Identify commonly used balances in their locality;
-Discuss what different weighing instruments are used for;
-Practice using weighing instruments to measure mass of objects;
-Discuss and share findings with other groups.

How do you weigh materials and objects?

-Mathematics learners book grade 9 page 117;
-Different types of weighing instruments;
-Various objects to weigh;
-Charts showing different weighing instruments.
-Mathematics learners book grade 9 page 118;
-Weighing instruments;
-Charts showing relationship between different units of mass.

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

MEASUREMENTS

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

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

-Define mass and weight;
-Differentiate between mass and weight;
-Convert mass to weight using the formula W = mg;
-Show interest in understanding the relationship between mass and weight.

In groups, learners are guided to:
-Use digital devices to search for definitions of mass and weight;
-Discuss the SI units for mass and weight;
-Measure the mass of various objects;
-Calculate the weight of objects using the formula W = mg;
-Complete a table showing mass and weight of objects;
-Discuss and share findings with other groups.

What is the difference between mass and weight?

-Mathematics learners book grade 9 page 119;
-Weighing instruments;
-Spring balance;
-Various objects to weigh;
-Digital devices for research.
-Mathematics learners book grade 9 page 121;
-Measuring cylinders;
-Various objects (coins, stones, metal pieces);
-Water;
-Scientific calculators.

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

MEASUREMENTS

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

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

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

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

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

Why do we need different units for measuring speed?

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

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

MEASUREMENTS

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

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

-Define velocity;
-Differentiate between speed and velocity;
-Calculate velocity in different directions;
-Show genuine interest in understanding velocity.

In groups, learners are guided to:
-Discuss the difference between speed and velocity;
-Record distance covered, time taken, and direction for various movements;
-Calculate velocity using the formula velocity = displacement/time;
-Express velocity with direction (e.g., 5 m/s eastward);
-Solve problems involving velocity in real-life contexts;
-Discuss and share results with other groups.

What is the difference between speed and velocity?

-Mathematics learners book grade 9 page 129;
-Stopwatch/timer;
-Measuring tape/rulers;
-Scientific calculators;
-Compass for directions.
-Mathematics learners book grade 9 page 130;
-Chart showing examples of acceleration calculations;
-Examples of acceleration in real-life situations.

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

MEASUREMENTS

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

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

-Identify longitudes on a globe;
-Understand the concept of the prime meridian;
-Describe how longitudes are measured in degrees east or west;
-Show interest in understanding the globe and longitudes.

In groups, learners are guided to:
-Use a globe to identify circles that pass through North and South poles;
-Search from the Internet or print media for the meaning of these circles;
-Identify special circles on the globe (Prime Meridian, International Date Line);
-Discuss how longitudes are measured in degrees east or west of the Prime Meridian;
-Discuss and share findings with other groups.

Why does time vary in different places of the world?

-Mathematics learners book grade 9 page 131;
-Globe;
-World map showing longitudes;
-Digital devices for research;
-Charts showing the longitude system.
-Mathematics learners book grade 9 page 133;
-World map showing time zones;
-Charts showing the relationship between longitudes and time.

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

MEASUREMENTS

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

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

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

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

How do we calculate the local time at different longitudes?

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

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

MEASUREMENTS

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

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

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

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

How do time zones affect international communication and travel?

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

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

MEASUREMENTS

Money - Converting Currency from One to Another in Real Life Situations

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

-Understand exchange rates;
-Convert foreign currency to Kenyan currency;
-Use exchange rate tables;
-Appreciate the concept of currency exchange.

In groups, learners are guided to:
-Study exchange rates of international currencies in a table;
-Understand the concept of buying and selling rates;
-Convert foreign currencies to Kenyan Shillings using the buying rate;
-Solve problems involving currency conversion;
-Use digital devices to compare exchange rates from different sources;
-Discuss and share results with other groups.

Why do we change currencies from one form to another?

-Mathematics learners book grade 9 page 141;
-Exchange rate tables from newspapers or online sources;
-Scientific calculators;
-Digital devices for checking current exchange rates;
-Charts showing examples of currency conversions.
-Mathematics learners book grade 9 page 142;

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

MEASUREMENTS

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

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

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

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

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

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

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

MEASUREMENTS

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

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

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

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

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

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

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

MEASUREMENTS

Approximations and Errors - Approximating Quantities in Measurements
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

Geometry

Scale Drawing - Compass directions
Scale Drawing - Compass bearings

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

Identify compass and true bearings in real-life situations;
Draw and discuss the compass directions;
Appreciate the use of compass in navigation.

Learners carry out an activity outside the classroom where a member stands with hands spread out.
Learners draw a diagram showing the directions of the right hand, left hand, front, and back, labeling them in terms of North, South, East, and West.
Learners discuss situations where knowledge of compass direction is used.

How do we use compass directions to locate positions?

-KLB Mathematics Grade 9 Textbook page 168
-Magnetic compass
-Plain paper
-Colored pencils
-Charts showing compass directions
-Maps
-KLB Mathematics Grade 9 Textbook page 170
-Protractor
-Ruler
-Charts showing compass bearings
-Manila paper

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Scale Drawing - True bearings
Scale Drawing - Determining compass bearings

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

Identify true bearings in real-life situations;
Draw and measure true bearings;
Appreciate the difference between compass and true bearings.

Learners trace diagrams showing true bearings.
Learners measure angles from North in the clockwise direction.
Learners draw accurately true bearings such as 008°, 036°, 126°, etc.

What is the difference between compass bearings and true bearings?

-KLB Mathematics Grade 9 Textbook page 171
-Protractor
-Ruler
-Plain paper
-Charts showing true bearings
-Diagrams for tracing
-KLB Mathematics Grade 9 Textbook page 173
-Charts with bearing examples
-Manila paper for group work

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

Geometry

Scale Drawing - Determining true bearings
Scale Drawing - Locating points using compass bearing and distance

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

Determine true bearings in different situations;
Measure angles to find true bearings;
Value the use of true bearings in navigation.

Learners consider a diagram showing points C and D.
Learners identify and determine the bearing of D from C by measurement.
Learners measure the bearing of various points in different diagrams.

How do we determine the true bearing of one point from another?

-KLB Mathematics Grade 9 Textbook page 175
-Protractor
-Ruler
-Plain paper
-Worksheets with diagrams
-Charts with bearing examples
-KLB Mathematics Grade 9 Textbook page 178
-Drawing board
-Charts with examples
-Worksheets

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Scale Drawing - Locating points using true bearing and distance
Scale Drawing - Angle of elevation

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

Locate a point using true bearing and distance;
Create scale drawings showing relative positions;
Enjoy making scale drawings using bearings and distances.

Learners consider towns A and B where the bearing of A from B is 140° and the distance between them is 75 km.
Learners mark point B on paper, draw the bearing of A from B, and use a scale of 1 cm represents 10 km to locate A.
Learners make scale drawings showing the relative positions of multiple points.

How do we use true bearings and distances to create scale drawings?

-KLB Mathematics Grade 9 Textbook page 182
-Protractor
-Ruler
-Plain paper
-Drawing board
-Manila paper for presentations
-Worksheets
-KLB Mathematics Grade 9 Textbook page 186
-String
-Weight (about 25g)
-Cardboard
-Straight piece of wood
-Charts showing angles of elevation

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Scale Drawing - Determining angles of elevation
Scale Drawing - Angle of depression

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

Determine angles of elevation in different situations;
Use scale drawings to find angles of elevation;
Value the use of scale drawings in solving problems involving elevation.

Learners consider a flag pole AB that is 8 m high with point C on level ground 18 m from the foot of the pole.
Learners make a scale drawing showing A, B, and C using a scale of 1 cm represents 2 m.
Learners measure the angle between AC and CB and display their drawings.

How can we use scale drawings to determine angles of elevation?

-KLB Mathematics Grade 9 Textbook page 187
-Protractor
-Ruler
-Plain paper
-Drawing board
-Calculator
-Charts showing examples
-KLB Mathematics Grade 9 Textbook page 190
-Clinometer (made in previous lesson)
-String
-Weight
-Charts showing angles of depression
-Diagrams

-Oral questions -Scale drawing -Written exercise -Presentation

Geometry

Scale Drawing - Determining angles of depression
Scale Drawing - Application in simple surveying

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

Determine angles of depression in different situations;
Use scale drawings to find angles of depression;
Enjoy solving problems involving angles of depression.

Learners consider a stationary boat (B) that is 120 m away from the foot (F) of a cliff of height 80 m.
Learners make a scale drawing showing the positions of A, F, and B using a scale of 1 cm represents 20 m.
Learners measure the angle between the horizontal line passing through A and line AB to find the angle of depression.

How can we use scale drawings to determine angles of depression?

-KLB Mathematics Grade 9 Textbook page 192
-Protractor
-Ruler
-Plain paper
-Drawing board
-Calculator
-Charts with examples
-KLB Mathematics Grade 9 Textbook page 195
-Drawing paper
-Set square
-Pencil
-Field book (notebook)
-Charts with survey examples

-Oral questions -Scale drawing -Written exercise -Assessment rubrics

Geometry

Scale Drawing - Survey using bearings and distances
Scale Drawing - Complex surveying problems

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

Survey an area using bearings and distances;
Create scale drawings from bearing and distance data;
Appreciate the application of bearings in surveying.

Learners study a sketch of a piece of land with positions given in terms of bearings and distances from point A.
Learners mark point A and use the bearings and distances to locate other points.
Learners create scale drawings of areas described by bearings and distances from given tables.

How do surveyors use bearings and distances to map areas?

-KLB Mathematics Grade 9 Textbook page 199
-Protractor
-Ruler
-Plain paper
-Drawing board
-Field book
-Charts with examples
-KLB Mathematics Grade 9 Textbook page 202
-Drawing paper
-Calculator
-Maps

-Oral questions -Scale drawing -Written exercise -Presentation

Geometry
Data Handling and Probability

Scale Drawing - Project work on scale drawing
Data Interpretation - Appropriate class width

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

Apply scale drawing techniques to a real-life situation;
Create a scale map of the school compound or local area;
Appreciate the practical applications of scale drawing.

Learners work in groups to create a scale map of a part of the school compound.
Learners measure distances and determine bearings between key features.
Learners create a detailed scale drawing with a key showing the various features mapped.

How can we apply scale drawing techniques to map our environment?

-KLB Mathematics Grade 9 Textbook page 202
-Measuring tape
-Compass
-Drawing paper
-Colored pencils
-Manila paper
-Drawing instruments
-KLB Mathematics Grade 9 Textbook page 244
-Calculator
-Graph paper
-Rulers
-Colored markers

-Project work -Group presentation -Peer assessment -Observation

Data Handling and Probability

Data Interpretation - Finding range and creating groups
Data Interpretation - Frequency distribution tables

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

Calculate the range of a set of data;
Divide data into suitable class intervals;
Show interest in grouping data for better representation.

Learners are presented with marks scored by 40 students in a mathematics test.
Learners find the range of the data.
Learners complete a table using a class width of 10 and determine the number of classes formed.

How does the range of data help us determine appropriate class intervals?

-KLB Mathematics Grade 9 Textbook page 245
-Calculator
-Manila paper
-Data sets
-Chart with examples
-Colored markers
-KLB Mathematics Grade 9 Textbook page 247
-Chart paper
-Ruler

-Oral questions -Written exercise -Observation -Group work assessment

Data Handling and Probability

Data Interpretation - Creating frequency tables with different class intervals
Data Interpretation - Modal class

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

Construct frequency tables starting with different class intervals;
Use tally marks to represent data in frequency tables;
Appreciate the use of different class intervals in data representation.

Learners construct a frequency table for given data starting from the class interval 60-64.
Learners use tally marks to count frequency of data in each class.
Learners compare and discuss different frequency tables.

How do we choose appropriate starting points for class intervals?

-KLB Mathematics Grade 9 Textbook page 247
-Calculator
-Ruler
-Graph paper
-Manila paper
-Worksheets with data
-KLB Mathematics Grade 9 Textbook page 248
-Chart showing frequency distribution tables
-Colored markers

-Oral questions -Written exercise -Group presentations -Observation

Data Handling and Probability

Data Interpretation - Mean of ungrouped data
Data Interpretation - Mean of grouped data

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

Calculate the mean of ungrouped data in a frequency table;
Multiply each value by its frequency and find their sum;
Show interest in calculating mean in real-life situations.

Learners consider the height, in metres, of 10 people recorded in a frequency distribution table.
Learners complete a table showing the product of height and frequency (fx).
Learners find the sum of frequencies, sum of fx, and divide to find the mean.

How do we calculate the mean of data presented in a frequency table?

-KLB Mathematics Grade 9 Textbook page 249
-Calculator
-Chart showing frequency tables
-Worksheets
-Manila paper
-Colored markers
-KLB Mathematics Grade 9 Textbook page 250
-Graph paper
-Chart with examples

-Oral questions -Written exercise -Observation -Assessment rubrics

Data Handling and Probability

Data Interpretation - Mean calculation in real-life situations
Data Interpretation - Median of grouped data

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

Calculate the mean of grouped data from real-life situations;
Apply the formula for finding mean of grouped data;
Appreciate the use of mean in summarizing data in real life.

Learners are presented with data about plants that survived in 50 sampled schools during an environmental week.
Learners find midpoints of class intervals, multiply by frequencies, and sum them up.
Learners calculate the mean number of plants that survived by dividing the sum of fx by the sum of f.

How is the mean used to summarize real-life data?

-KLB Mathematics Grade 9 Textbook page 251
-Calculator
-Manila paper
-Chart with examples
-Worksheets
-Colored markers
-KLB Mathematics Grade 9 Textbook page 252
-Chart showing cumulative frequency tables

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

Data Handling and Probability

Data Interpretation - Calculating median using formula
Data Interpretation - Median calculations in real-life situations

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

Apply the formula for calculating median of grouped data;
Identify class boundaries, frequencies, and cumulative frequencies;
Show interest in finding median from real-life data.

Learners consider marks scored by 40 learners in a test presented in a table.
Learners complete the column for cumulative frequency and identify the median class.
Learners identify the lower class boundary, cumulative frequency above median class, class width, and frequency of median class to substitute in the formula.

How do we use the formula to calculate the median of grouped data?

-KLB Mathematics Grade 9 Textbook page 253
-Calculator
-Graph paper
-Chart showing median formula
-Worksheets
-Manila paper
-KLB Mathematics Grade 9 Textbook page 254
-Chart with example calculations
-Worksheets with real-life data
-Colored markers

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

Data Handling and Probability

Probability - Equally likely outcomes
Probability - Range of probability

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

Perform experiments involving equally likely outcomes;
Record outcomes of chance experiments;
Appreciate that some events have equal chances of occurring.

Learners work in groups to flip a fair coin 20 times.
Learners record the number of times heads and tails come up.
Learners divide the number of times heads or tails comes up by the total number of tosses to find probabilities.

What makes events equally likely to occur?

-KLB Mathematics Grade 9 Textbook page 256
-Coins
-Chart paper
-Table for recording outcomes
-Manila paper
-Colored markers
-KLB Mathematics Grade 9 Textbook page 257
-Dice
-Chart showing probability scale (0-1)

-Oral questions -Practical activity -Group work assessment -Observation

Data Handling and Probability

Probability - Complementary events
Probability - Mutually exclusive events

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

Calculate probability of complementary events;
Understand that sum of probabilities of complementary events is 1;
Show interest in applying complementary probability in real-life situations.

Learners discuss examples of complementary events.
Learners solve problems where the probability of one event is given and they need to find the probability of its complement.
Learners verify that the sum of probabilities of an event and its complement equals 1.

How are complementary events related in terms of their probabilities?

-KLB Mathematics Grade 9 Textbook page 258
-Calculator
-Chart showing complementary events
-Worksheets with problems
-Manila paper
-Colored markers
-Coins
-Chart with examples of mutually exclusive events
-Flashcards with different scenarios

-Oral questions -Written exercise -Group work assessment -Observation

Data Handling and Probability

Probability - Experiments with mutually exclusive events
Probability - Independent events

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

Perform experiments of single chance involving mutually exclusive events;
Calculate probability of mutually exclusive events;
Value the application of mutually exclusive events in real-life.

Learners toss a fair die several times and record the numbers that show up.
Learners solve problems involving mutually exclusive events like picking a pen of a specific color from a box.
Learners find probabilities of individual events and their union.

How do we calculate the probability of mutually exclusive events?

-KLB Mathematics Grade 9 Textbook page 259
-Dice
-Colored objects in boxes
-Calculator
-Chart showing probability calculations
-Worksheets with problems
-KLB Mathematics Grade 9 Textbook page 260
-Coins and dice
-Table for recording outcomes
-Chart showing examples of independent events
-Manila paper
-Colored markers

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

Data Handling and Probability

Probability - Calculating probabilities of independent events
Probability - Tree diagrams for single outcomes
Probability - Complex tree diagrams
Probability - Complex tree diagrams

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

Calculate probabilities of independent events;
Apply the multiplication rule for independent events;
Appreciate the application of independent events in real-life situations.

Learners solve problems involving independent events.
Learners calculate probabilities of individual events and multiply them to find joint probability.
Learners solve problems involving machines breaking down independently and other real-life examples.

How do we calculate the probability of independent events occurring together?

-KLB Mathematics Grade 9 Textbook page 261
-Calculator
-Chart showing multiplication rule
-Worksheets with problems
-Manila paper
-Colored markers
-KLB Mathematics Grade 9 Textbook page 262
-Chart paper
-Ruler
-Worksheets with blank tree diagrams
-Chart showing completed tree diagrams
-KLB Mathematics Grade 9 Textbook page 263
-Chart showing complex tree diagrams

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