4.0 Geometry

4.1 Coordinates and Graphs - Drawing perpendicular lines on the Cartesian plane

By the end of the lesson, the learner should be able to:
- Explain the meaning of perpendicular lines
- Draw and measure angles between perpendicular lines accurately
- Show interest in recognizing perpendicular lines from their graphs

The learner is guided to:
- Draw straight lines on the same Cartesian plane
- Identify the point where the two lines intersect
- Measure the angle between the two lines at the point of intersection
- Verify that perpendicular lines intersect at 90°

How do we identify perpendicular lines on a graph?

- Master Mathematics Grade 9 pg. 160
- Graph papers
- Protractors
- Rulers
- Set squares

- Observation - Class activities - Written tests

4.0 Geometry

4.1 Coordinates and Graphs - Relating gradients of perpendicular lines and applications
4.2 Scale Drawing - Compass bearing

By the end of the lesson, the learner should be able to:
- State the relationship between gradients of perpendicular lines
- Apply the relationship m₁ × m₂ = -1 to solve problems
- Appreciate solving real-life problems involving graphs of straight lines

The learner is guided to:
- Work out the gradient of each perpendicular line
- Multiply the gradients of two perpendicular lines
- Apply the concept to determine equations of perpendicular lines
- Interpret graphs representing real-life situations

What is the relationship between gradients of perpendicular lines?

- Master Mathematics Grade 9 pg. 162
- Graph papers
- Calculators
- Real-life graph examples
- Master Mathematics Grade 9 pg. 166
- Pair of compasses
- Protractors
- Rulers
- Charts showing compass directions

- Written assignments - Class activities

4.0 Geometry

4.2 Scale Drawing - True bearings
4.2 Scale Drawing - Determining the bearing of one point from another (1)

By the end of the lesson, the learner should be able to:
- Explain what true bearings are
- Convert compass bearings to true bearings and measure them accurately
- Appreciate expressing direction using true bearings

The learner is guided to:
- Discuss that true bearings are measured clockwise from North
- Express bearings in three-digit format
- Draw diagrams showing true bearings
- Convert between compass and true bearings

How do we express direction using true bearings?

- Master Mathematics Grade 9 pg. 169
- Protractors
- Rulers
- Compasses
- Map samples
- Master Mathematics Grade 9 pg. 171
- Pencils
- Graph papers

- Written tests - Class activities

4.0 Geometry

4.2 Scale Drawing - Determining the bearing of one point from another (2)

By the end of the lesson, the learner should be able to:
- State the bearing of places from maps
- Determine bearings from scale drawings and solve related problems
- Appreciate applying bearing concepts to real-life situations

The learner is guided to:
- Use maps of Kenya to determine bearings of different towns
- Work out bearings of points from given diagrams
- Determine reverse bearings
- Apply bearing concepts to real-life situations

Why is it important to know bearings in real life?

- Master Mathematics Grade 9 pg. 171
- Atlas/Maps of Kenya
- Protractors
- Rulers
- Digital devices

- Class activities - Written tests

4.0 Geometry

4.2 Scale Drawing - Locating a point using bearing and distance (1)

By the end of the lesson, the learner should be able to:
- Explain how to choose appropriate scales for scale drawings
- Convert actual distances to scale lengths accurately
- Show interest in representing actual distances on paper

The learner is guided to:
- Draw sketch diagrams showing relative positions
- Choose suitable scales
- Convert actual distances to scale lengths
- Mark North lines and measure angles

How do we represent actual distances on paper?

- Master Mathematics Grade 9 pg. 173
- Rulers
- Protractors
- Compasses
- Plain papers

- Observation - Written assignments

4.0 Geometry

4.2 Scale Drawing - Locating a point using bearing and distance (2)

By the end of the lesson, the learner should be able to:
- Describe the process of locating points using bearing and distance
- Draw accurate scale diagrams and determine unknown measurements
- Appreciate the accuracy of scale drawings in representing real situations

The learner is guided to:
- Use given bearings and distances to locate points
- Draw accurate scale diagrams
- Measure and determine unknown distances and bearings from diagrams
- Verify accuracy of their drawings

How accurate are scale drawings in representing real situations?

- Master Mathematics Grade 9 pg. 173
- Rulers
- Protractors
- Compasses
- Graph papers

- Class activities - Written tests

4.0 Geometry

4.2 Scale Drawing - Identifying angles of elevation (1)

By the end of the lesson, the learner should be able to:
- Define angle of elevation
- Identify and sketch right-angled triangles showing angles of elevation
- Develop interest in recognizing situations involving angles of elevation

The learner is guided to:
- Observe objects above eye level
- Identify the angle through which eyes are raised
- Sketch right-angled triangles formed
- Label the angle of elevation correctly

What is an angle of elevation?

- Master Mathematics Grade 9 pg. 175
- Protractors
- Rulers
- Pictures showing elevation
- Models

- Observation - Oral questions

4.0 Geometry

4.2 Scale Drawing - Determining angles of elevation (2)

By the end of the lesson, the learner should be able to:
- Explain the process of determining angles of elevation
- Draw scale diagrams and measure angles of elevation using protractors
- Appreciate applying concepts to real-life situations

The learner is guided to:
- Draw scale diagrams representing elevation situations
- Use appropriate scales
- Measure angles of elevation from scale drawings
- Solve problems involving heights and distances

How do we calculate angles of elevation?

- Master Mathematics Grade 9 pg. 175
- Protractors
- Rulers
- Graph papers
- Calculators

- Written tests - Class activities

4.0 Geometry

4.2 Scale Drawing - Identifying angles of depression (1)

By the end of the lesson, the learner should be able to:
- Define angle of depression
- Identify and sketch situations involving angles of depression
- Show interest in distinguishing between angles of elevation and depression

The learner is guided to:
- Stand at elevated positions and observe objects below
- Identify the angle through which eyes are lowered
- Sketch right-angled triangles formed
- Label the angle of depression correctly

How is angle of depression different from angle of elevation?

- Master Mathematics Grade 9 pg. 178
- Protractors
- Rulers
- Pictures showing depression
- Models

- Observation - Oral questions

4.0 Geometry

4.2 Scale Drawing - Determining angles of depression (2)
4.2 Scale Drawing - Application in simple surveying - Triangulation (1)

By the end of the lesson, the learner should be able to:
- Describe the steps for determining angles of depression
- Draw scale diagrams and measure angles of depression accurately
- Appreciate using angles of depression in real life

The learner is guided to:
- Draw scale diagrams representing depression situations
- Use appropriate scales
- Measure angles of depression from scale drawings
- Apply concepts to real-life problems

How do we use angles of depression in real life?

- Master Mathematics Grade 9 pg. 178
- Protractors
- Rulers
- Graph papers
- Calculators
- Master Mathematics Grade 9 pg. 180
- Set squares
- Compasses
- Plain papers

- Written assignments - Written tests

4.0 Geometry

4.2 Scale Drawing - Application in simple surveying - Triangulation (2)

By the end of the lesson, the learner should be able to:
- Describe how to record measurements in field books
- Draw accurate scale maps using triangulation data
- Appreciate applying triangulation to survey school compound areas

The learner is guided to:
- Measure lengths of offsets
- Record measurements in field book format
- Choose appropriate scales
- Draw accurate scale maps from recorded data

How do we record and use surveying measurements?

- Master Mathematics Grade 9 pg. 180
- Meter rules
- Strings
- Pegs
- Field books

- Written tests - Practical activities

4.0 Geometry

4.2 Scale Drawing - Application in simple surveying - Transverse survey (1)

By the end of the lesson, the learner should be able to:
- Explain transverse survey method
- Identify baselines and draw offsets on either side accurately
- Show interest in understanding different surveying methods

The learner is guided to:
- Draw baselines at the middle of areas to be surveyed
- Draw offsets perpendicular to baselines on both sides
- Measure lengths of offsets from baselines
- Record measurements in tables

How is transverse survey different from triangulation?

- Master Mathematics Grade 9 pg. 180
- Rulers
- Set squares
- Plain papers
- Field books

- Observation - Oral questions

4.0 Geometry

4.2 Scale Drawing - Application in simple surveying - Transverse survey (2)

By the end of the lesson, the learner should be able to:
- Describe the process of completing field books for transverse surveys
- Draw scale maps from transverse survey data
- Appreciate using transverse survey method for road reserves

The learner is guided to:
- Complete field book recordings
- Use appropriate scales to draw maps
- Join offset points to show boundaries
- Compare their work with other members

When do we use transverse survey method?

- Master Mathematics Grade 9 pg. 180
- Rulers
- Pencils
- Graph papers
- Field books

- Written assignments - Practical activities

4.0 Geometry

4.2 Scale Drawing - Surveying using bearings and distances

By the end of the lesson, the learner should be able to:
- Explain how to record positions using bearings and distances
- Draw scale maps using bearing and distance data
- Appreciate different surveying methods

The learner is guided to:
- Record bearings and distances from fixed points
- Use ordered pairs to represent positions
- Draw North lines and locate points using bearings
- Join points to show boundaries

How do we survey using bearings and distances?

- Master Mathematics Grade 9 pg. 180
- Protractors
- Compasses
- Rulers
- Field books

- Class activities - Written tests

4.0 Geometry

4.3 Similarity and Enlargement - Similar figures

By the end of the lesson, the learner should be able to:
- Define similar figures
- Identify and sort similar figures from collections of objects
- Show interest in recognizing similar figures in the environment

The learner is guided to:
- Collect different objects from the environment
- Sort objects according to similarity
- Discuss criteria used for sorting
- Identify pairs of similar figures from given diagrams

What makes two figures similar?

- Master Mathematics Grade 9 pg. 185
- Various objects
- Cut-outs of shapes
- Charts
- Models

- Observation - Oral questions

4.0 Geometry

4.3 Similarity and Enlargement - Properties of similar figures (1)

By the end of the lesson, the learner should be able to:
- State the properties of similar figures
- Measure corresponding sides and determine ratios accurately
- Appreciate that ratios of corresponding sides are constant

The learner is guided to:
- Trace similar triangles
- Measure lengths of corresponding sides
- Determine ratios of corresponding sides
- Observe that the ratios are equal

What is the relationship between sides of similar figures?

- Master Mathematics Grade 9 pg. 186
- Rulers
- Tracing papers
- Calculators
- Pencils

- Class activities - Written assignments

4.0 Geometry

4.3 Similarity and Enlargement - Properties of similar figures (2)

By the end of the lesson, the learner should be able to:
- Identify that corresponding angles of similar figures are equal
- Use properties to determine unknown sides and angles
- Develop interest in applying properties of similar figures

The learner is guided to:
- Measure corresponding angles of similar figures
- Observe that corresponding angles are equal
- Use ratio of sides to find unknown lengths
- Solve problems involving similar figures

How do we use properties of similar figures?

- Master Mathematics Grade 9 pg. 186
- Protractors
- Rulers
- Calculators
- Practice worksheets

- Written tests - Oral questions

4.0 Geometry

4.3 Similarity and Enlargement - Drawing similar figures

By the end of the lesson, the learner should be able to:
- Describe the steps for constructing similar figures
- Construct and draw similar figures accurately using scale factors
- Show interest in verifying similarity by measuring angles

The learner is guided to:
- Construct triangles with given dimensions
- Construct similar triangles with sides in given ratios
- Measure angles to verify similarity
- Discuss their findings with classmates

How do we construct similar figures accurately?

- Master Mathematics Grade 9 pg. 189
- Rulers
- Compasses
- Protractors
- Plain papers

- Observation - Practical activities

4.0 Geometry

4.3 Similarity and Enlargement - Determining properties of enlargement

By the end of the lesson, the learner should be able to:
- Define centre of enlargement and scale factor
- Locate the centre of enlargement and determine scale factor
- Appreciate that enlargements produce similar figures

The learner is guided to:
- Join corresponding points of objects and images
- Locate the centre where lines meet
- Measure distances from centre to object and image
- Calculate the scale factor

What is the relationship between object and image in enlargement?

- Master Mathematics Grade 9 pg. 190
- Rulers
- Compasses
- Tracing papers
- Models

- Class activities - Written assignments

4.0 Geometry

4.3 Similarity and Enlargement - Positive scale factor (1)
4.3 Similarity and Enlargement - Positive scale factor (2)

By the end of the lesson, the learner should be able to:
- Explain what happens when scale factor is greater than 1
- Draw enlargements with scale factors greater than 1 accurately
- Develop interest in observing that images are larger when scale factor > 1

The learner is guided to:
- Draw lines from centre to object vertices
- Multiply distances by scale factor
- Locate image points along extended lines
- Observe that object and image are on same side of centre

What happens when the scale factor is greater than 1?

- Master Mathematics Grade 9 pg. 192
- Rulers
- Compasses
- Graph papers
- Pencils
- Plain papers
- Models

- Observation - Written tests

4.0 Geometry

4.3 Similarity and Enlargement - Negative scale factor (1)

By the end of the lesson, the learner should be able to:
- State the properties of enlargement with negative scale factors
- Draw enlargements with negative scale factors and position images correctly
- Show interest in recognizing that images are inverted with negative scale factors

The learner is guided to:
- Observe objects and images with negative scale factors
- Note that they are on opposite sides of centre
- Draw enlargements with negative scale factors
- Observe that images are inverted

What is special about negative scale factors?

- Master Mathematics Grade 9 pg. 196
- Rulers
- Compasses
- Graph papers
- Tracing papers

- Observation - Oral questions

4.0 Geometry

4.3 Similarity and Enlargement - Negative scale factor (2)

By the end of the lesson, the learner should be able to:
- Explain the process of determining negative scale factors
- Locate centres of enlargement and apply negative scale factors to various figures
- Appreciate solving problems involving negative enlargements

The learner is guided to:
- Join corresponding vertices to locate centres
- Calculate scale factors from measurements
- Draw enlargements of different shapes with negative scale factors
- Solve problems involving negative enlargements

How do we work with negative scale factors?

- Master Mathematics Grade 9 pg. 196
- Rulers
- Compasses
- Plain papers
- Calculators

- Written tests - Class activities

4.0 Geometry

4.3 Similarity and Enlargement - Enlargement on the Cartesian plane (1)

By the end of the lesson, the learner should be able to:
- State the rule (x,y) → (kx, ky) for enlargement with centre at origin
- Plot and enlarge figures accurately with centre at origin
- Develop interest in applying enlargement rules on coordinate axes

The learner is guided to:
- Plot given points on Cartesian plane
- Apply scale factor to coordinates
- Plot image points and join them
- Verify using measurement from origin

How do we enlarge figures on coordinate axes?

- Master Mathematics Grade 9 pg. 198
- Graph papers
- Rulers
- Calculators
- Pencils

- Observation - Written assignments

4.0 Geometry

4.3 Similarity and Enlargement - Enlargement on the Cartesian plane (2)

By the end of the lesson, the learner should be able to:
- Describe the process of enlarging figures with centre not at origin
- Determine coordinates of images after enlargement and solve related problems
- Appreciate applying both positive and negative scale factors on Cartesian plane

The learner is guided to:
- Plot figures with given vertices
- Enlarge with centres at various points
- Determine image coordinates
- Apply both positive and negative scale factors

What happens when the centre is not at the origin?

- Master Mathematics Grade 9 pg. 198
- Graph papers
- Rulers
- Calculators
- Digital devices

- Written tests - Class activities

4.0 Geometry

4.3 Similarity and Enlargement - Linear scale factor of similar figures (1)

By the end of the lesson, the learner should be able to:
- Define linear scale factor
- Calculate linear scale factor from similar figures and use it to find unknown lengths
- Show interest in applying linear scale factor to practical situations

The learner is guided to:
- Measure corresponding sides of similar figures
- Calculate ratios to find linear scale factor
- Use scale factor to determine unknown dimensions
- Apply to practical situations

What is linear scale factor?

- Master Mathematics Grade 9 pg. 200
- Rulers
- Similar objects
- Calculators
- Models

- Observation - Oral questions

4.0 Geometry

4.3 Similarity and Enlargement - Linear scale factor of similar figures (2)

By the end of the lesson, the learner should be able to:
- Explain applications of linear scale factor in real-life situations
- Solve problems involving scale models and drawings
- Appreciate use of similarity in architecture and mapping

The learner is guided to:
- Work with scale drawings and models
- Determine actual dimensions from scale drawings
- Calculate linear scale factors from given information
- Discuss applications in architecture and mapping

How is linear scale factor used in real life?

- Master Mathematics Grade 9 pg. 200
- Maps
- Scale models
- Calculators
- Real objects

- Written assignments - Written tests

4.0 Geometry

4.4 Trigonometry - Angles and sides of right-angled triangles

By the end of the lesson, the learner should be able to:
- Define hypotenuse, opposite and adjacent sides
- Identify and name sides with reference to given angles
- Show interest in recognizing right-angled triangles in real situations

The learner is guided to:
- Draw right-angled triangles
- Identify the hypotenuse
- Label opposite and adjacent sides for given angles
- Practice with different orientations of triangles

How do we identify sides of a right-angled triangle?

- Master Mathematics Grade 9 pg. 205
- Rulers
- Set squares
- Models of triangles
- Charts

- Observation - Oral questions

4.0 Geometry

4.4 Trigonometry - Tangent ratio and tables of tangents

By the end of the lesson, the learner should be able to:
- Define tangent of an angle as opposite/adjacent
- Calculate tangent ratios from right-angled triangles and read from tables
- Appreciate that tangent ratio is constant for a given angle

The learner is guided to:
- Work out ratios of opposite to adjacent sides
- Recognize that the ratio is constant for a given angle
- Define tangent as opposite/adjacent
- Read tangent values from tables

What is the tangent of an angle?

- Master Mathematics Grade 9 pg. 207
- Mathematical tables
- Rulers
- Calculators
- Right-angled triangles

- Class activities - Written tests

4.0 Geometry

4.4 Trigonometry - Sine and cosine ratios, tables of sines and cosines
4.4 Trigonometry - Using calculators and applications of trigonometric ratios

By the end of the lesson, the learner should be able to:
- Define sine and cosine of an angle
- Calculate sine and cosine ratios and read values from mathematical tables
- Develop interest in observing that cosine values decrease as angles increase

The learner is guided to:
- Work out ratios of opposite to hypotenuse (sine)
- Work out ratios of adjacent to hypotenuse (cosine)
- Read values from tables of sines and cosines
- Observe that values in cosine tables are subtracted

How are sine and cosine different from tangent?

- Master Mathematics Grade 9 pg. 211
- Mathematical tables
- Rulers
- Calculators
- Models
- Master Mathematics Grade 9 pg. 217
- Scientific calculators
- Protractors
- Real-life problem scenarios

- Observation - Written assignments

5.0 Data Handling and Probability

5.1 Data Interpretation (Grouped Data) - Determining appropriate class width for grouping data
5.1 Data Interpretation (Grouped Data) - Drawing frequency distribution tables of grouped data

By the end of the lesson, the learner should be able to:
- Define class and class width
- Determine appropriate class width from given range of data
- Appreciate the importance of grouping data with many values

The learner is guided to:
- Choose numbers between 1 and 100 and find the range
- Divide the range into equal intervals or classes
- Discuss the width of classes selected
- Compare class widths with other groups

How do we group data with many values?

- Master Mathematics Grade 9 pg. 224
- Writing materials
- Calculators
- Chart papers
- Digital devices
- Master Mathematics Grade 9 pg. 226
- Tally sheets
- Rulers
- Data sets
- Pencils

- Observation - Oral questions - Written assignments

5.0 Data Handling and Probability

5.1 Data Interpretation (Grouped Data) - Identifying the modal class of grouped data
5.1 Data Interpretation (Grouped Data) - Calculating the mean of grouped data (1)

By the end of the lesson, the learner should be able to:
- Define mode, modal frequency and modal class
- Identify the modal class from frequency distribution tables
- Appreciate identifying the class with highest frequency

The learner is guided to:
- Prepare frequency distribution tables for given data
- Identify the highest frequency from the table
- Find the class where the highest frequency lies
- Search for the meaning of mode using digital devices

What is the modal class in grouped data?

- Master Mathematics Grade 9 pg. 228
- Frequency distribution tables
- Digital devices
- Reference materials
- Master Mathematics Grade 9 pg. 230
- Calculators
- Frequency tables
- Writing materials

- Oral questions - Written assignments - Class activities

5.0 Data Handling and Probability

5.1 Data Interpretation (Grouped Data) - Calculating the mean of grouped data (2)
5.1 Data Interpretation (Grouped Data) - Determining the median of grouped data (1)

By the end of the lesson, the learner should be able to:
- State the formula for calculating mean of grouped data
- Apply the formula mean = Σfx/Σf to solve problems
- Appreciate using the Greek symbol Σ in mathematics

The learner is guided to:
- Arrange tables to include midpoint and fx columns
- Calculate Σf and Σfx
- Apply the formula to determine mean
- Solve problems involving mean of grouped data

How do we apply the mean formula to grouped data?

- Master Mathematics Grade 9 pg. 230
- Mathematical tables
- Calculators
- Data sets
- Charts
- Master Mathematics Grade 9 pg. 232
- Frequency tables
- Reference materials
- Digital devices

- Class activities - Written assignments - Oral questions

5.0 Data Handling and Probability

5.1 Data Interpretation (Grouped Data) - Determining the median of grouped data (2)
5.1 Data Interpretation (Grouped Data) - Determining the median of grouped data (3)
5.2 Probability - Experiments involving equally and likely outcomes

By the end of the lesson, the learner should be able to:
- Explain the formula for calculating median of grouped data
- Identify L, N, cf₁, fm and C from given data
- Appreciate the components of the median formula

The learner is guided to:
- Discuss the median formula and its components
- Identify the lower class boundary (L) of median class
- Determine cumulative frequency of class above median class
- Identify frequency of median class and class width

How do we use the median formula?

- Master Mathematics Grade 9 pg. 234
- Calculators
- Formula charts
- Frequency tables
- Master Mathematics Grade 9 pg. 236
- Data sets
- Writing materials
- Practice worksheets
- Master Mathematics Grade 9 pg. 239
- Coins
- Dice
- Triangular pyramids
- Baskets and pens

- Class activities - Oral questions - Written assignments

5.0 Data Handling and Probability

5.2 Probability - Range of probability of an event

By the end of the lesson, the learner should be able to:
- State that the sum of all probabilities equals 1
- Determine the range of probability as 0 ≤ P(A) ≤ 1
- Show interest in understanding that P(A) + P(A') = 1

The learner is guided to:
- Toss a coin and work out probability of head and tail
- Add probabilities of all outcomes
- Use dice to determine probabilities of all faces
- Discuss that probability ranges from 0 to 1

What is the range of probability?

- Master Mathematics Grade 9 pg. 241
- Coins
- Dice
- Calculators
- Charts showing probability range

- Class activities - Written tests - Oral questions

5.0 Data Handling and Probability

5.2 Probability - Identifying mutually exclusive events

By the end of the lesson, the learner should be able to:
- Define mutually exclusive events
- Identify mutually exclusive events from given situations
- Appreciate that mutually exclusive events cannot occur simultaneously

The learner is guided to:
- Observe a coin toss and note that both sides cannot face up
- Discuss what the referee does before a football match
- Identify events that exclude each other
- Give examples of mutually exclusive events from daily life

What are mutually exclusive events?

- Master Mathematics Grade 9 pg. 243
- Coins
- Pictures of referees
- Real-life scenarios
- Charts

- Observation - Oral questions - Written assignments

5.0 Data Handling and Probability

5.2 Probability - Experiments of single chance involving mutually exclusive events

By the end of the lesson, the learner should be able to:
- Explain the addition law of probability P(A or B) = P(A) + P(B)
- Calculate probabilities of mutually exclusive events
- Show interest in applying the addition law to solve problems

The learner is guided to:
- Pick pens from a closed bag and note colors
- Work out probabilities using the word "OR"
- Apply the formula P(A or B) = P(A) + P(B)
- Solve problems involving mutually exclusive events

How do we calculate probabilities of mutually exclusive events?

- Master Mathematics Grade 9 pg. 244
- Colored pens
- Bags
- Dice
- Number cards
- Calculators

- Class activities - Written tests - Practical exercises

5.0 Data Handling and Probability

5.2 Probability - Experiments involving independent events
5.2 Probability - Drawing tree diagrams for single outcomes

By the end of the lesson, the learner should be able to:
- Define independent events
- Apply the multiplication law P(A and B) = P(A) × P(B)
- Appreciate that independent events do not affect each other

The learner is guided to:
- Toss a coin and die together and note outcomes
- Discuss whether coin outcome affects die outcome
- Understand that "and" in probability means multiplication
- Solve problems involving independent events

What are independent events?

- Master Mathematics Grade 9 pg. 246
- Coins
- Dice
- Colored balls
- Baskets
- Calculators
- Master Mathematics Grade 9 pg. 248
- Drawing materials
- Chart papers
- Rulers

- Observation - Written assignments - Written tests