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?

 Master Grade 9 Textbook page 168
-Plain paper
-Colored pencils
-Charts showing compass directions
-Maps

-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?

Master Grade 9 Textbook page 171
-Protractor
-Ruler
-Plain paper
-Charts showing true bearings

-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?

Master Grade 9 Textbook page 175
-Protractor
-Ruler
-Plain paper
-Worksheets with diagrams
-Charts with bearing examples

-Oral questions -Practical activity -Written exercise -Checklist

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;
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?

Master Grade 9 Textbook page 182
-Protractor
-Ruler
-Plain paper
-Drawing board
-Manila paper for presentations
-Worksheets

-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;
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?

Master Grade 9 Textbook page 186
-Protractor
-String
-Weight (about 25g)
-Cardboard
-Straight piece of wood
-Charts showing angles of elevation

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

Geometry

Scale Drawing - Angle of depression
Scale Drawing - Determining angles 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;
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?

Master Grade 9 Textbook page 190
-String
-Weight
-Protractor
-Charts showing angles of depression

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Scale Drawing - Application in simple surveying

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

Apply scale drawing in simple surveying;
Record measurements 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?

Master  Grade 9 Textbook page 195
-Drawing paper
-Ruler
-Set square
-Pencil
-Field book (notebook)
-Charts 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;
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?

Master  Grade 9 Textbook page 199
-Protractor
-Ruler
-Plain paper
-Drawing board
-Field book
-Charts with examples

-Oral questions -Scale drawing -Written exercise -Presentation

Geometry

Scale Drawing - Project work on scale drawing
Similarity and Enlargement - Similar figures and properties

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?

Master  Grade 9 Textbook page 202
-Measuring tape
-Compass
-Drawing paper
-Colored pencils
-Manila paper
-Drawing insruments

-Project work -Group presentation -Peer assessment -Observation

Geometry

Similarity and Enlargement - Identifying similar objects
Similarity and Enlargement - Drawing similar figures

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

Identify similar objects in the environment;
Determine if given figures are similar;
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?

Master  Grade 9 Textbook page 204
-Ruler
-Protractor
-Various geometric objects
-Charts with examples
-Worksheets with diagrams

-Oral questions -Group work -Written exercise -Observation

Geometry

Similarity and Enlargement - Properties of enlargement

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

Determine properties of enlargement of different figures;
Locate the center of enlargement and find scale factors;
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?

Master  Grade 9 Textbook page 209
-Ruler
-Tracing paper
-Colored pencils
-Grid paper
-Charts showing enlargements
-Diagrams for tracing

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Similarity and Enlargement - Negative scale factors
Similarity and Enlargement - Drawing images of objects

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

Determine properties of enlargement with negative scale factors;
Locate centers of enlargement with negative scale factors;
Appreciate the concept of negative scale factors in enlargements.

Learners trace diagrams showing an object and its image where the center of enlargement is between them.
Learners join corresponding points to locate the center of enlargement.
Learners find the ratio of distances from the center to corresponding points and note that the image is on the opposite side of the object.

What happens when an enlargement has a negative scale factor?

Master  Grade 9 Textbook page 211
-Ruler
-Tracing paper
-Grid paper
-Colored pencils
-Charts showing negative scale factor enlargements
-Diagrams for tracing

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Similarity and Enlargement - Linear scale factor
Similarity and Enlargement - Using coordinates in enlargement

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

Determine the linear scale factor of similar figures;
Calculate unknown dimensions using linear scale factors;
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?

Master Grade 9 Textbook page 216
-Ruler
-Calculator
-Similar objects of different sizes
-Charts with examples
-Worksheets

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

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:

Apply similarity concepts to solve real-life problems;
Calculate heights and distances using similar triangles;
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?

Master  Grade 9 Textbook page 219
-Ruler
-Calculator
-Drawing paper
-Charts with real-life applications
-Manila paper for presentations

-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;
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?

Master Grade 9 Textbook page 222
-Ruler
-Protractor
-Calculator
-Drawing paper
-Charts showing sine ratio
-Manila paper

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

Geometry

Trigonometry - Cosine ratio
Trigonometry - Tangent ratio

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

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

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?

Master Grade 9 Textbook page 223
-Ruler
-Protractor
-Calculator
-Drawing paper
-Charts showing cosine ratio
-Worksheets

-Oral questions -Practical activity -Written exercise -Observation

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;
Find the sine values of different angles using tables;
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?

Master Grade 9 Textbook page 227
-Mathematical tables
-Calculator
-Worksheets
-Chart showing how to read tables
-Sample exercises

-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;
Compare values obtained from tables and calculators;
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?

Master Grade 9 Textbook page 233
-Scientific calculators
-Mathematical tables
-Worksheets
-Chart showing calculator keys
-Sample exercises

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Trigonometry - Calculating lengths using trigonometric ratios
Trigonometry - Calculating angles using trigonometric ratios

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

Apply trigonometric ratios to calculate lengths of right-angled triangles;
Use sine, cosine, and tangent ratios to find unknown sides;
Appreciate the application of trigonometry in solving real-life problems.

Learners consider a right-angled triangle and find the trigonometric ratio appropriate for finding an unknown side.
Learners find the value of the ratio from tables or calculators and relate it to the expression to find the unknown side.
Learners solve problems involving finding sides of right-angled triangles.

How do we use trigonometric ratios to find unknown sides in right-angled triangles?

Master Grade 9 Textbook page 234
-Scientific calculators
-Mathematical tables
-Ruler
-Drawing paper
-Charts with examples
-Worksheets

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

Geometry

Trigonometry - Application in heights and distances
Trigonometry - Application in navigation

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

Apply trigonometric ratios to solve problems involving heights and distances;
Calculate heights of objects using angles of elevation;
Value the use of trigonometry in real-life situations.

Learners solve problems involving finding heights of objects like flag poles, towers, and buildings using angles of elevation.
Learners apply sine, cosine, and tangent ratios as appropriate to calculate unknown heights and distances.
Learners discuss real-life applications of trigonometry in architecture, navigation, and engineering.

How do we use trigonometry to find heights and distances in real-life situations?

Master Grade 9 Textbook page 237
-Scientific calculators
-Mathematical tables
-Ruler
-Drawing paper
-Charts with real-life examples
-Manila paper

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

Geometry
Data Handling and Probability

Trigonometry - Review and mixed applications
Data Interpretation - Appropriate class width

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

Apply trigonometric concepts in mixed application problems;
Solve problems involving both scale drawing and trigonometry;
Value the integration of different geometric concepts in problem-solving.

Learners solve a variety of problems that integrate different geometric concepts learned.
Learners apply scale drawing, bearings, similar figures, and trigonometric ratios to solve complex problems.
Learners discuss how different geometric concepts interconnect in solving real-world problems.

How can we integrate different geometric concepts to solve complex problems?

Master Grade 9 Textbook page 240
-Scientific calculators
-Mathematical tables
-Ruler
-Protractor
-Drawing paper

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

Data Handling and Probability

Data Interpretation - Finding range and creating groups

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?

Master Grade 9 Textbook page 245
-Calculator
-Manila paper
-Data sets
-Chart with examples
-Colored markers

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

Data Handling and Probability

Data Interpretation - Frequency distribution tables
Data Interpretation - Creating frequency tables with different class intervals

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

Draw frequency distribution tables of grouped data;
Use tally marks to organize data into frequency tables;
Value the importance of organizing data in tables.

Learners are presented with data on the number of tree seedlings that survived in 50 different schools.
Learners copy and complete a frequency distribution table using tally marks and frequencies.
Learners discuss and share their completed tables with other groups.

How do we organize data in a frequency distribution table?

Master Grade 9 Textbook page 247
-Chart paper
-Ruler
-Calculator
-Manila paper
-Colored markers
-Graph paper
-Worksheets with data

-Oral questions -Group presentations -Written exercise -Checklist

Data Handling and Probability

Data Interpretation - Modal class
Data Interpretation - Mean of ungrouped data

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

Identify the modal class of grouped data;
Determine the class with the highest frequency;
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?

Master Grade 9 Textbook page 248
-Calculator
-Ruler
-Graph paper
-Chart showing frequency distribution tables

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

Data Handling and Probability

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

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

Calculate the mean of grouped data;
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?

Master Grade 9 Textbook page 250
-Calculator
-Graph paper
-Manila paper
-Chart with examples
-Worksheets

-Oral questions -Written exercise -Group presentations -Checklist

Data Handling and Probability

Data Interpretation - Median of grouped data

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

Determine the median of grouped data;
Find cumulative frequencies to locate the median class;
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?

Master  Grade 9 Textbook page 252
-Calculator
-Chart showing cumulative frequency tables
-Worksheets

-Oral questions -Written exercise -Group presentations -Observation

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?

Master Grade 9 Textbook page 253
-Calculator
-Graph paper
-Chart showing median formula
-Worksheets

-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?

Master Grade 9 Textbook page 256
-Coins
-Chart paper
-Table for recording outcomes
-Manila paper
-Dice
-Chart showing probability scale (0-1)

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

Data Handling and Probability

Probability - Complementary 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?

Master Grade 9 Textbook page 258
-Calculator
-Chart showing complementary events
-Worksheets with problems
-Manila paper

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

Data Handling and Probability

Probability - Mutually exclusive events
Probability - Experiments with 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;
Appreciate the concept of mutually exclusive events.

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?

Master Grade 9 Textbook page 258
-Coins
-Chart with examples of mutually exclusive events
-Dice
-Chart showing probability calculations
-Worksheets with problems

-Oral questions -Group discussions -Written exercise -Observation

Data Handling and Probability

Probability - Independent events
Probability - Calculating probabilities of independent events

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

Perform experiments involving independent events;
Understand that outcome of one event doesn't affect another;
Show interest in applying independent events probability in real-life.

Learners toss a fair coin and a fair die at the same time and record outcomes.
Learners repeat the experiment several times.
Learners discuss that the outcome of the coin toss doesn't affect the outcome of the die roll (independence).

What makes events independent from each other?

Master Grade 9 Textbook page 260
-Coins and dice
-Table for recording outcomes
-Chart showing examples of independent events
-Chart showing multiplication rule
-Worksheets with problems

-Oral questions -Practical activity -Group discussions -Observation

Data Handling and Probability

Probability - Tree diagrams for single outcomes
Probability - Complex tree diagrams

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

Draw a probability tree diagram for a single outcome;
Represent probability situations using tree diagrams;
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?

Master Grade 9 Textbook page 262
-Chart paper
-Ruler
-Worksheets with blank tree diagrams
-Chart showing completed tree diagrams
-Calculator
-Chart showing complex tree diagrams
-Worksheets with problems

-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: