Geometry

Scale Drawing - Compass directions

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 in practical  context;
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
-pencil             -A laptop  showing  compass  bearing

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Scale Drawing - Compass bearings
Scale Drawing - True bearings

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

Identify compass bearings in different situations;
Measure and state positions using compass bearings  similar situations;
Value the importance of compass bearings in navigation.

Learners trace diagrams showing compass bearings.
Learners measure angles from the south and north, and state the position of points using these angles.
Learners draw accurately various compass bearings like N70°E, S50°W, etc.

How do we express directions using compass bearings?

-KLB Mathematics Grade 9 Textbook page 170
-Protractor
-Ruler
-Plain paper     - A smartboard showing true bearings
-Diagrams for tracing

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Scale Drawing - Determining compass bearings

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

Determine the bearing of one point from another  in different  situation;
Measure angles to determine compass bearings in  real  context;
Enjoy determining bearings in different situations.

Learners consider a diagram showing points Q and R.
Learners find the angle between the North line and line QR.
Learners use the angle to write down the compass bearing of R from Q and discuss their results.

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

-KLB Mathematics Grade 9 Textbook page 173
-Protractor
-Ruler
-Plain paper
-digital  device  with bearing examples
-Manila paper for group work

-Oral questions -Group work -Written exercise -Observation

Geometry

Scale Drawing - Determining true bearings

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

Determine true bearings in different situations;
Measure angles to find true bearings  in real contexts;
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
-A laptop  with diagrams true bearings
-Charts with bearing examples

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Scale Drawing - Locating points using compass bearing and distance

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

Locate a point using bearing and distance in real-life situations;
Create scale drawings showing relative positions in various situations;
Appreciate the use of scale drawings in real-life situations.

Learners consider two markets U and V such that the distance between them is 6 km and U is on a bearing of N56°E from V.
Learners mark point V on paper, draw the bearing of U from V, and use a scale of 1 cm represents 1 km to locate U.
Learners display and discuss their constructions.

How do we use compass bearings and distances to locate positions?

-KLB Mathematics Grade 9 Textbook page 178
-Protractor
-Ruler
-Plain paper

-Oral questions -Practical activity -Written exercise -Peer assessment

Geometry

Scale Drawing - Locating points using true bearing and distance

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

Locate a point using true bearing and distance  in different  situations;
Create scale drawings showing relative positions  in practical  situations;
Enjoy making scale drawings using bearings and distances in everyday  life.

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 presentation

-Oral questions -Practical activity -Written exercise -Observation

Geometry

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

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

Identify angles of elevation in real-life situations;
Make and use a clinometer to measure angles of elevation  in different  situations;
Appreciate the application of angles of elevation in real-life situations.

Learners perform an activity outside the classroom where they stand next to a flag pole and mark points at eye level and above.
Learners observe how the line of sight forms an angle when looking at higher objects.
Learners make a clinometer and use it to measure angles of elevation of objects in the school environment.

What is an angle of elevation and how do we measure it?

-KLB Mathematics Grade 9 Textbook page 186
-Protractor
-A  laptop  showing angles of elevation
-Ruler
-Calculator

-Oral questions -Practical activity -Written exercise -Project assessment

Geometry

Scale Drawing - Angle of depression

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

Identify angles of depression in real-life situations;
Measure angles of depression using a clinometer  in practical  context;
Appreciate the application of angles of depression in real-life situations.

Learners perform an activity outside the classroom where they stand next to a flag pole and mark points at eye level and below.
Learners observe how the line of sight forms an angle when looking at lower objects.
Learners use a clinometer to measure angles of depression of objects in their environment.

What is an angle of depression and how is it related to the angle of elevation?

-KLB Mathematics Grade 9 Textbook page 190
-Clinometer (made in previous lesson
-Protractor
-A laptop showing angles of depression
-Diagrams

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Scale Drawing - Determining angles of depression

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  in various   situations;
Enjoy solving problems involving angles of depression  in real life context.

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
-Calculator
-Charts with examples

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

Geometry

Scale Drawing - Application in simple surveying

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

 Find  how  to  use scale drawing in simple surveying;
Record measurements  of  surveying  in a field book;
Value the importance of surveying in mapping.

Learners study a survey of a small island made using a triangle ABC around it.
Learners trace the diagram and draw perpendicular lines from points along the triangle sides to the edge of the island.
Learners measure the lengths of perpendicular lines and record the measurements in a tabular form in a field book.

How do surveyors use scale drawings to create maps?

-KLB Mathematics Grade 9 Textbook page 195
-Drawing paper
-Ruler
-Set square
-Pencil
-Field book (notebook)
-A  laptop with survey examples

-Oral questions -Practical activity -Written exercise -Field book assessment

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  in practical  context;
Create scale drawings from bearing and distance data  from  different  situations;
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
-Drawing paper
-Calculator
-Maps

-Oral questions -Scale drawing -Written exercise -Presentation

Geometry

Scale Drawing - Project work on scale drawing

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  in  various context;
Appreciate the practical applications of scale drawing  in real life.

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

-Project work -Group presentation -Peer assessment -Observation

Geometry

Similarity and Enlargement - Similar figures and properties

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

Identify similar figures and their properties  in  different  situations;
Measure corresponding sides and angles of similar figures  in various situations;
Appreciate the concept of similarity in real-life objects.

Learners study diagrams of similar cross-sections.
Learners measure the corresponding sides of the cross-sections and find the ratio between them.
Learners measure all the corresponding angles and discover that they are equal.

What makes two figures similar?

-KLB Mathematics Grade 9 Textbook page 203
-Ruler
-Protractor
-Cut-out shapes
-A laptop showing similar figures
-Manila paper

-Oral questions -Observation -Written exercise -Checklist

Geometry

Similarity and Enlargement - Identifying similar objects

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

Identify similar objects in the environment;
Determine if given figures are similar  in various   situations;
Value the concept of similarity in everyday life.

Learners collect and classify objects according to similarity.
Learners identify pairs of similar figures from given diagrams.
Learners discuss real-life examples of similar objects and their properties.

How do we recognize similar objects in our environment?

-KLB Mathematics Grade 9 Textbook page 204
-Ruler
-Protractor
-laptop showing Various geometric objects

-Oral questions -Group work -Written exercise -Observation

Geometry

Similarity and Enlargement - Drawing similar figures

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

Draw similar figures in different situations;
Calculate dimensions of similar figures using scale factors  in different   situations;
Enjoy creating similar figures   in  everyday  life.

Learners draw triangle ABC with given dimensions (AB=3cm, BC=4cm, and AC=6cm).
Learners are told that triangle PQR is similar to ABC with PQ=4.5cm, and they calculate the other dimensions.
Learners construct triangle PQR and compare results with other groups.

How do we construct a figure similar to a given figure?

-KLB Mathematics Grade 9 Textbook page 206
-Ruler
-Protractor
-Pair of compasses
-Drawing paper
-Calculator
-A laptop  showing  dimensions of similar   objects.

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

Geometry

Similarity and Enlargement - Properties of enlargement
Similarity and Enlargement - Negative scale factors

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

Determine properties of enlargement of different figures  in  various  situations;
Locate the center of enlargement and find scale factors  in  different  situations ;
Value the application of enlargement in real-life situations.

Learners trace diagrams showing an object and its enlarged image.
Learners draw lines through corresponding points to find where they intersect (center of enlargement).
Learners find the ratios of corresponding lengths to determine the scale factor.

How do we determine the center and scale factor of an enlargement?

-KLB Mathematics Grade 9 Textbook page 209
-Ruler
-Tracing paper
-Colored pencils
-Grid paper
-a laptop showing enlargements
-Diagrams for tracing

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Similarity and Enlargement - Drawing images of objects

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

Find properties of enlargement to draw similar objects and their images in  various  situations;
Use scale factors to determine dimensions of images in practical situations;
Enjoy creating enlarged images of objects in real context.

Learners trace a given figure and join the center of enlargement to each vertex.
Learners multiply each distance by the scale factor to locate the image points.
Learners locate the image points and join them to create the enlarged figure.

How do we draw the image of an object under an enlargement with a given center and scale factor?

-KLB Mathematics Grade 9 Textbook page 214
-Ruler
-Colored pencils
-A laptop showing steps of enlargement.

-Oral questions -Practical activity -Written exercise -Peer assessment

Geometry

Similarity and Enlargement - Linear scale factor

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

Determine the linear scale factor of similar figures  in different   situations;
Calculate unknown dimensions using linear scale factors  in authentic situations;
Value the application of linear scale factors in real-life problems.

Learners consider similar cones and find the ratios of their corresponding dimensions.
Learners study similar triangles and calculate the linear scale factor.
Learners use the scale factor to find unknown dimensions of similar figures.

How do we use linear scale factors to calculate unknown dimensions of similar figures?

-KLB Mathematics Grade 9 Textbook page 216
-Ruler
-Calculator     --A  digital device sowing Similar objects of different sizes

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

Geometry

Similarity and Enlargement - Using coordinates in enlargement

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

Find the coordinates of images under enlargement in various  situations;
Determine the center of enlargement and scale factor from given coordinates in real context;
Appreciate the use of coordinates in describing enlargements.

Learners plot figures and their images on a grid.
Learners find the center of enlargement by drawing lines through corresponding points.
Learners calculate the scale factor using the coordinates of corresponding points.

How do we use coordinate geometry to describe and perform enlargements?

-KLB Mathematics Grade 9 Textbook page 218
-Grid paper
-Ruler
-Colored pencils
-Calculator
-A laptop  showing  coordinate examples

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Similarity and Enlargement - Applications of similarity
Trigonometry - Angles and sides of right-angled triangles

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

Find similarity concepts to solve real-life problems;
Calculate heights and distances using similar triangles in different   context;
Value the practical applications of similarity in everyday life.

Learners solve problems involving similar triangles to find unknown heights and distances.
Learners discuss how similarity is used in fields such as architecture, photography, and engineering.
Learners work on practical applications of similarity in the environment.

How can we use similarity to solve real-life problems?

-KLB Mathematics Grade 9 Textbook page 219
-Ruler
-Calculator
-Drawing paper
-Protractor
-Set square      -ICT  tool  showing  angles  and sides of  a right angled  triangles.

-Oral questions -Problem-solving -Written exercise -Group presentation

Geometry

Trigonometry - Sine ratio

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

Identify sine ratio from a right-angled triangle  in  different situations;
Calculate sine of angles in right-angled triangles;
Value the use of sine ratio in solving problems.

Learners draw triangles with specific angles and sides.
Learners draw perpendiculars from points on one side to another and measure their lengths.
Learners calculate ratios of opposite side to hypotenuse for different angles and discover the sine ratio.

What is the sine of an angle and how do we calculate it?

-KLB Mathematics Grade 9 Textbook page 222
-Ruler
-Protractor
-Calculator
-Drawing paper
-A laptop showing sine ratio
-Manila paper

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

Geometry

Trigonometry - Cosine ratio

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

Identify cosine ratio from a right-angled triangle in different situations;
Calculate cosine of angles in right-angled triangles;
Enjoy solving problems involving cosine ratio in practical  situations.

Learners draw triangles with specific angles and sides.
Learners calculate ratios of adjacent side to hypotenuse for different angles and discover the cosine ratio.
Learners find the cosine of marked angles in various right-angled triangles.

What is the cosine of an angle and how do we calculate it?

-KLB Mathematics Grade 9 Textbook page 223
-Ruler
-Protractor
-Calculator
-Drawing paper
-A  laptop showing cosine ratio

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Trigonometry - Tangent ratio

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

Identify tangent ratio from a right-angled triangle in various context;
Calculate tangent of angles in right-angled triangles;
Appreciate the importance of tangent ratio in problem-solving.

Learners draw triangle ABC with specific angles and mark points on BC.
Learners draw perpendiculars from these points to AC and measure their lengths.
Learners calculate ratios of opposite side to adjacent side for different angles and discover the tangent ratio.

What is the tangent of an angle and how do we calculate it?

-KLB Mathematics Grade 9 Textbook page 225
-Ruler
-Protractor
-Calculator
-Drawing paper
-A laptop showing tangent ratio

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Trigonometry - Reading tables of sines
Trigonometry - Reading tables of cosines and tangents

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

Read tables of trigonometric ratios of acute angles in various situations;
Find the sine values of different angles using tables in different  situations;
Value the importance of mathematical tables in finding trigonometric ratios

Learners study a part of the table of sines.
Learners use the table to look for specific angles and find their sine values.
Learners find sine values of angles with decimal parts using the 'ADD' column in the tables.

How do we use mathematical tables to find the sine of an angle?

-KLB Mathematics Grade 9 Textbook page 227
-Mathematical tables
-Calculator
-Worksheets
-A  laptop  showing how to read tables

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

Geometry

Trigonometry - Using calculators for trigonometric ratios

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

Determine trigonometric ratios of acute angles using calculators  in authentic  contexts;
Compare values obtained from tables and calculators  various  situations;
Value the use of calculators in finding trigonometric ratios.

Learners use calculators to find trigonometric ratios of specific angles.
Learners compare values obtained from calculators with those from mathematical tables.
Learners use calculators to find sine, cosine, and tangent of various angles.

How do we use calculators to find trigonometric ratios?

-KLB Mathematics Grade 9 Textbook page 233
-Scientific calculators
-Mathematical tables

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Trigonometry - Calculating angles using trigonometric ratios

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

Use trigonometric ratios to calculate angles in right-angled triangles;
Apply inverse trigonometric functions to find angles  in practical  contexts;
Enjoy solving problems involving trigonometric ratios in everyday  life.

 Learners consider right-angled triangles with known sides.
Learners calculate trigonometric ratios using the known sides and use tables or calculators to find the corresponding angles.
Learners solve problems involving finding angles in right-angled triangles.

How do we find unknown angles in right-angled triangles using trigonometric ratios?

-KLB Mathematics Grade 9 Textbook page 235
-Scientific calculators
-Mathematical tables
-Ruler

-Oral questions -Group work -Written exercise -Observation

Geometry

Trigonometry - Application in navigation

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

Apply trigonometric ratios in navigation problems;
Calculate distances and bearings using trigonometry  in real situations;
Appreciate the importance of trigonometry in navigation.

Learners solve problems involving finding distances between locations given bearings and distances from a reference point.
Learners calculate bearings between points using trigonometric ratios.
Learners discuss how pilots, sailors, and navigators use trigonometry.

How is trigonometry used in navigation and determining positions?

-KLB Mathematics Grade 9 Textbook page 238
-Scientific calculators
-Mathematical tables
-Ruler
-Protractor
-A laptop  showing  with navigation examples

-Oral questions -Problem-solving -Written exercise -Assessment rubrics

Data Handling and Probability

Data Interpretation - Appropriate class width

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

Determine appropriate class width for grouping data  in various  situations;
Work with data to establish suitable class widths  in practical  contexts;
Appreciate the importance of appropriate class widths in data representation.

Learners work in groups to consider masses of 40 people in kilograms.
Learners find the difference between the smallest and highest mass (range).
Learners group the masses in smaller groups with different class widths and identify the number of groups formed in each case.

How do we determine an appropriate class width for a given set of data?

-KLB Mathematics Grade 9 Textbook page 244
-Calculator
-Rulers            -A laptop  showing  interpretation  about  class width

-Oral questions -Group presentations -Written exercise -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 in practical  situation;
Divide data into suitable class intervals  in  different  situation;
Show interest in grouping data for better representation in real  situations.

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 paper
-Ruler  

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

Data Handling and Probability

Data Interpretation - Modal class

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

Identify the modal class of grouped data  in  different   situation;
Determine the class with the highest frequency  in various  context;
Develop interest in finding the modal class in real-life data.

Learners are presented with assessment marks in a mathematics test for 32 learners.
Learners draw a frequency distribution table to represent the information.
Learners identify and write down the class with the highest frequency (modal class).

What is the modal class and how is it determined?

-KLB Mathematics Grade 9 Textbook page 248
-Calculator
-Ruler
-Graph paper
-A laptop  showing frequency distribution tables

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

Data Handling and Probability

Data Interpretation - Mean of ungrouped 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 in different  situation;
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
-A smartboard showing frequency tables

-Oral questions -Written exercise -Observation -Assessment rubrics

Data Handling and Probability

Data Interpretation - Mean of grouped data

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

Calculate the mean of grouped data  in different   situations;
Find the midpoint of class intervals and use in calculations;
Value the importance of mean in summarizing data.

Learners consider a frequency distribution table representing masses in kilograms of learners in a class.
Learners complete a table by finding midpoints of class intervals and calculating fx.
Learners find the sum of frequencies, sum of fx, and divide to find the mean.

How do we calculate the mean of grouped data?

-KLB Mathematics Grade 9 Textbook page 250
-Calculator
-Graph paper
-Chart with examples

-Oral questions -Written exercise -Group presentations -Checklist

Data Handling and Probability

Data Interpretation - Median of grouped data
Data Interpretation - Calculating median using formula

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

Determine the median of grouped data  in different  situations;
Find cumulative frequencies to locate the median class in different  contexts;
Value the importance of median in data interpretation.

Learners consider the mass of 50 learners recorded in a table.
Learners complete the column for cumulative frequency.
Learners find the sum of frequency, divide by 2, and identify the position of the median mass.

How do we determine the median of grouped data?

-KLB Mathematics Grade 9 Textbook page 252
-Calculator
-A  laptop showing cumulative frequency tables
-Graph paper
-Chart showing median formula

-Oral questions -Written exercise -Group presentations -Observation

Data Handling and Probability

Probability - Equally likely outcomes

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

Perform experiments involving equally likely outcomes  in  various situations;
Record outcomes of chance experiments  in  practical situations;
Appreciate that some events have equal chances of occurring  in real situations.

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

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

Data Handling and Probability

Probability - Range of probability

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

Determine the range of probability of an event  in practical   situations;
Understand that probability ranges from 0 to 1  in every  situation;
Value the concept of probability range in real-life situations.

Learners use a fair die in this activity and toss it 20 times.
Learners record the number of times each face shows up and calculate relative frequencies.
Learners find the sum of the fractions and discuss that probabilities range from 0 to 1.

What is the range of probability values and what do these values signify?

-KLB Mathematics Grade 9 Textbook page 257
-Dice
-Table for recording outcomes
-A  laptop   showing probability scale (0-1)

-Oral questions -Practical activity -Written exercise -Group presentations

Data Handling and Probability

Probability - Complementary events

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

Calculate probability of complementary events  in different  situations;
Understand that sum of probabilities of complementary events is 1  in various situations;
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
-A  laptop showing complementary events

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

Data Handling and Probability

Probability - Mutually exclusive events

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

Identify mutually exclusive events in real-life situations ;
Recognize events that cannot occur simultaneously in various situations;
Appreciate the concept of mutually exclusive events in everyday  life.

Learners flip a fair coin several times and record the face that shows up.
Learners discuss that heads and tails cannot show up at the same time (mutually exclusive).
Learners identify mutually exclusive events from various examples.

What makes events mutually exclusive?

-KLB Mathematics Grade 9 Textbook page 258
-Coins
-a  laptop showing examples of mutually exclusive events

-Oral questions -Group discussions -Written exercise -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  in real situations;
Calculate probability of mutually exclusive events in authentic contexts;
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
-Calculator
-Coins and dice
-Table for recording outcomes
-A  smartboard showing examples of independent events
-Manila paper

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

Data Handling and Probability

Probability - Tree diagrams for single outcomes

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

Draw a probability tree diagram for a single outcome in different contexts;
Represent probability situations using tree diagrams in various situations;
Value the use of tree diagrams in organizing probability information.

Learners write down possible outcomes when a fair coin is flipped once.
Learners find the total number of all outcomes and probability of each outcome.
Learners complete a tree diagram with possible outcomes and their probabilities.

How do tree diagrams help us understand probability situations?

-KLB Mathematics Grade 9 Textbook page 262
-Ruler
-ICT  tool showing completed tree diagrams
-Colored markers

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

Data Handling and Probability

Probability - Complex tree diagrams

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

Draw more complex probability tree diagrams  in  different  situations;
Use tree diagrams to solve probability problems in various context;
Appreciate the value of tree diagrams in visualizing probability in practical situation.

Learners draw tree diagrams for various probability scenarios like balls of different colors in a bag.
Learners use tree diagrams to find probabilities of different outcomes.
Learners interpret tree diagrams to solve probability problems.

How do we use tree diagrams to solve more complex probability problems?

-KLB Mathematics Grade 9 Textbook page 263
-Ruler
-Calculator
-A  laptop showing complex tree diagrams

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