Geometry

Coordinates and Graphs - Plotting points on a Cartesian plane

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

-Oral questions -Observation -Written exercise -Peer assessment

Geometry

Coordinates and Graphs - Drawing a straight line graph
Coordinates and Graphs - Completing tables for linear equations

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

Generate a table of values from the equation of a straight line;
Draw a straight line graph given an equation;
Appreciate the use of straight line graphs in representing linear relationships.

Learners generate a table of values for a given linear equation (e.g., y=-2x+5).
Learners plot the points on a Cartesian plane and join them to form a straight line.
Learners discuss and compare their results with other groups.

How do we generate a table of values from a linear equation?

-KLB Mathematics Grade 9 Textbook page 155
-Graph paper
-Ruler
-Pencils
-Calculator
-Blackboard illustration
-KLB Mathematics Grade 9 Textbook page 156
-Charts with prepared tables

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

Geometry

Coordinates and Graphs - Drawing parallel lines
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:

Generate tables of values for parallel line equations;
Draw parallel lines on the Cartesian plane;
Appreciate the relationship between parallel lines on a graph.

Learners generate tables of values for equations such as y=x-5 and y=x-3.
Learners use the tables of values to draw the lines on the Cartesian plane.
Learners measure the distance between the two lines at different positions using a set square and discuss their findings.

How can we tell if two lines are parallel by looking at their equations?

-KLB Mathematics Grade 9 Textbook page 157
-Graph paper
-Ruler
-Set square
-Calculator
-Charts showing parallel lines
-KLB Mathematics Grade 9 Textbook page 158
-Manila paper
-Digital devices (optional)
-KLB Mathematics Grade 9 Textbook page 159
-Protractor
-Charts showing perpendicular lines

-Oral questions -Group work -Written exercise -Observation

Geometry

Coordinates and Graphs - Relating gradients of perpendicular lines
Coordinates and Graphs - Applications of straight line graphs
Scale Drawing - Compass directions

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
-KLB Mathematics Grade 9 Textbook page 168
-Magnetic compass
-Plain paper
-Colored pencils
-Charts showing compass directions
-Maps

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

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;
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
-Charts showing compass bearings
-Manila paper
-KLB Mathematics Grade 9 Textbook page 171
-Charts showing true bearings
-Diagrams for tracing

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Scale Drawing - Determining compass bearings
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 the bearing of one point from another;
Measure angles to determine compass bearings;
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
-Charts with bearing examples
-Manila paper for group work
-KLB Mathematics Grade 9 Textbook page 175
-Worksheets with diagrams
-KLB Mathematics Grade 9 Textbook page 178
-Drawing board
-Charts with examples
-Worksheets

-Oral questions -Group work -Written exercise -Observation

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
Scale Drawing - Determining angles 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
-KLB Mathematics Grade 9 Textbook page 192
-Charts with examples

-Oral questions -Scale drawing -Written exercise -Presentation

Geometry

Scale Drawing - Application in simple surveying
Scale Drawing - Survey using bearings and distances
Scale Drawing - Complex surveying problems

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?

-KLB Mathematics Grade 9 Textbook page 195
-Drawing paper
-Ruler
-Set square
-Pencil
-Field book (notebook)
-Charts with survey examples
-KLB Mathematics Grade 9 Textbook page 199
-Protractor
-Plain paper
-Drawing board
-Field book
-Charts with examples
-KLB Mathematics Grade 9 Textbook page 202
-Calculator
-Maps

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

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?

-KLB Mathematics Grade 9 Textbook page 202
-Measuring tape
-Compass
-Drawing paper
-Colored pencils
-Manila paper
-Drawing instruments
-KLB Mathematics Grade 9 Textbook page 203
-Ruler
-Protractor
-Cut-out shapes
-Charts showing similar figures

-Project work -Group presentation -Peer assessment -Observation

Geometry

Similarity and Enlargement - Identifying similar objects
Similarity and Enlargement - Drawing similar figures
Similarity and Enlargement - Properties of enlargement

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?

-KLB Mathematics Grade 9 Textbook page 204
-Ruler
-Protractor
-Various geometric objects
-Charts with examples
-Worksheets with diagrams
-KLB Mathematics Grade 9 Textbook page 206
-Pair of compasses
-Drawing paper
-Calculator
-KLB Mathematics Grade 9 Textbook page 209
-Tracing paper
-Colored pencils
-Grid paper
-Charts showing enlargements
-Diagrams for tracing

-Oral questions -Group work -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?

-KLB Mathematics Grade 9 Textbook page 211
-Ruler
-Tracing paper
-Grid paper
-Colored pencils
-Charts showing negative scale factor enlargements
-Diagrams for tracing
-KLB Mathematics Grade 9 Textbook page 214
-Charts showing steps of enlargement
-Manila paper

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Similarity and Enlargement - Linear scale factor
Similarity and Enlargement - Using coordinates in enlargement
Similarity and Enlargement - Applications of similarity

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?

-KLB Mathematics Grade 9 Textbook page 216
-Ruler
-Calculator
-Similar objects of different sizes
-Charts with examples
-Worksheets
-KLB Mathematics Grade 9 Textbook page 218
-Grid paper
-Colored pencils
-Charts with coordinate examples
-KLB Mathematics Grade 9 Textbook page 219
-Drawing paper
-Charts with real-life applications
-Manila paper for presentations

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

Geometry

Trigonometry - Angles and sides of right-angled triangles
Trigonometry - Sine ratio
Trigonometry - Cosine ratio

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

Identify angles and sides of right-angled triangles in different situations;
Distinguish between the hypotenuse, adjacent side, and opposite side;
Appreciate the relationship between angles and sides in right-angled triangles.

Learners draw right-angled triangles with acute angles and identify the longest side (hypotenuse).
Learners identify the side which together with the hypotenuse forms the angle θ (adjacent side).
Learners identify the side facing the angle θ (opposite side).

How do we identify different sides in a right-angled triangle?

-KLB Mathematics Grade 9 Textbook page 220
-Ruler
-Protractor
-Set square
-Drawing paper
-Charts with labeled triangles
-Colored markers
-KLB Mathematics Grade 9 Textbook page 222
-Calculator
-Charts showing sine ratio
-Manila paper
-KLB Mathematics Grade 9 Textbook page 223
-Charts showing cosine ratio
-Worksheets

-Oral questions -Observation -Written exercise -Checklist

Geometry

Trigonometry - Tangent ratio
Trigonometry - Reading tables of sines

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

Identify tangent ratio from a right-angled triangle;
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
-Charts showing tangent ratio
-Manila paper
-KLB Mathematics Grade 9 Textbook page 227
-Mathematical tables
-Worksheets
-Chart showing how to read tables
-Sample exercises

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Trigonometry - Reading tables of cosines and tangents
Trigonometry - Using calculators for trigonometric ratios
Trigonometry - Calculating lengths using trigonometric ratios

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

Read tables of cosines and tangents for acute angles;
Find cosine and tangent values using mathematical tables;
Enjoy using mathematical tables to find trigonometric ratios.

Learners study parts of the tables of cosines and tangents.
Learners use the tables to find cosine and tangent values of specific angles.
Learners find values of angles with decimal parts using the 'SUBTRACT' column for cosines and 'ADD' column for tangents.

How do we use mathematical tables to find cosine and tangent values?

-KLB Mathematics Grade 9 Textbook page 229-231
-Mathematical tables
-Calculator
-Worksheets
-Chart showing how to read tables
-Sample exercises
-KLB Mathematics Grade 9 Textbook page 233
-Scientific calculators
-Chart showing calculator keys
-KLB Mathematics Grade 9 Textbook page 234
-Ruler
-Drawing paper
-Charts with examples

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Trigonometry - Calculating angles using trigonometric ratios
Trigonometry - Application in heights and distances

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;
Enjoy solving problems involving trigonometric ratios.

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
-Drawing paper
-Charts with examples
-Worksheets
-KLB Mathematics Grade 9 Textbook page 237
-Charts with real-life examples
-Manila paper

-Oral questions -Group work -Written exercise -Observation

Geometry
Data Handling and Probability

Trigonometry - Application in navigation
Trigonometry - Review and mixed applications
Data Interpretation - Appropriate class width

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

Apply trigonometric ratios in navigation problems;
Calculate distances and bearings using trigonometry;
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
-Maps
-Charts with navigation examples
-KLB Mathematics Grade 9 Textbook page 240
-Drawing paper
-Past examination questions
-KLB Mathematics Grade 9 Textbook page 244
-Calculator
-Graph paper
-Manila paper
-Rulers
-Colored markers

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

Data Handling and Probability

Data Interpretation - Finding range and creating groups
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:

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
-Graph paper
-Worksheets with data

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

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?

-KLB Mathematics Grade 9 Textbook page 248
-Calculator
-Ruler
-Graph paper
-Chart showing frequency distribution tables
-Colored markers
-KLB Mathematics Grade 9 Textbook page 249
-Chart showing frequency tables
-Worksheets
-Manila paper

-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
Data Interpretation - Median of grouped data

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?

-KLB Mathematics Grade 9 Textbook page 250
-Calculator
-Graph paper
-Manila paper
-Chart with examples
-Worksheets
-KLB Mathematics Grade 9 Textbook page 251
-Colored markers
-KLB Mathematics Grade 9 Textbook page 252
-Chart showing cumulative frequency tables

-Oral questions -Written exercise -Group presentations -Checklist

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
Probability - Complementary events

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)
-KLB Mathematics Grade 9 Textbook page 258
-Calculator
-Chart showing complementary events
-Worksheets with problems

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

Data Handling and Probability

Probability - Mutually exclusive events
Probability - Experiments with mutually exclusive events
Probability - Independent 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?

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

-Oral questions -Group discussions -Written exercise -Observation

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