4.0 Geometry

4.1 Coordinates and Graphs - Plotting points on a Cartesian plane

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

- Define a Cartesian plane and identify its components
- Plot points accurately on a Cartesian plane using coordinates
- Show interest in learning about coordinate geometry

The learner is guided to:
- Discuss with friends what they remember about plotting points on a Cartesian plane
- Draw a Cartesian plane in their graph book
- Mark the points where given coordinates lie
- Discuss and compare their work with other learners

How do we locate points on a Cartesian plane?

- Master Mathematics Grade 9 pg. 152
- Graph papers/squared books
- Rulers
- Pencils
- Digital devices

- Observation - Oral questions - Written assignments

4.0 Geometry

4.1 Coordinates and Graphs - Drawing straight line graphs given equations
4.1 Coordinates and Graphs - Drawing parallel lines on the Cartesian plane
4.1 Coordinates and Graphs - Relating gradients of parallel lines
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 steps for generating a table of values from an equation
- Draw straight line graphs accurately from linear equations
- Appreciate the relationship between equations and graphs

The learner is guided to:
- Generate a table of values for given linear equations
- Plot the points on a Cartesian plane
- Draw straight lines passing through the plotted points
- Share and discuss their working with other members in class

How do we represent linear equations graphically?

- Master Mathematics Grade 9 pg. 154
- Graph papers
- Rulers
- Pencils
- Mathematical tables
- Master Mathematics Grade 9 pg. 156
- Set squares
- Master Mathematics Grade 9 pg. 158
- Calculators
- Digital devices
- Master Mathematics Grade 9 pg. 160
- Protractors

- Observation - Oral questions - Written tests

4.0 Geometry

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

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
- Master Mathematics Grade 9 pg. 169
- Compasses
- Map samples

- Written assignments - Class activities

4.0 Geometry

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

- Describe the steps for determining bearings between two points
- Measure bearings accurately using a protractor
- Show interest in finding bearings of different places

The learner is guided to:
- Join two points using a straight line
- Locate the point from which bearing is determined
- Draw a North line at that point
- Measure the required angle clockwise from North

How do we find the bearing of one place from another?

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

- Observation - Oral questions - Written assignments

4.0 Geometry

4.2 Scale Drawing - Locating a point using bearing and distance (1)
4.2 Scale Drawing - Locating a point using bearing and distance (2)

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
- Graph papers

- Observation - Written assignments

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)
4.2 Scale Drawing - Identifying angles of depression (1)

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

- Written tests - Class activities

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

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
- Rulers
- Set squares
- Plain papers

- Written tests - Practical activities

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
4.3 Similarity and Enlargement - Similar figures

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

- Class activities - Written tests

4.0 Geometry

4.3 Similarity and Enlargement - Properties of similar figures (1)
4.3 Similarity and Enlargement - Properties of similar figures (2)

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
- Protractors
- Practice worksheets

- Class activities - Written assignments

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
4.3 Similarity and Enlargement - Positive scale factor (1)

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
- Master Mathematics Grade 9 pg. 192
- Graph papers
- Pencils

- Class activities - Written assignments

4.0 Geometry

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

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

- Describe what happens when scale factor is between 0 and 1
- Draw enlargements with fractional scale factors accurately
- Appreciate comparing enlargements with different positive scale factors

The learner is guided to:
- Draw enlargements with fractional scale factors
- Observe that images are smaller than objects
- Note that object and image remain upright
- Practice with various positive scale factors

What happens when the scale factor is between 0 and 1?

- Master Mathematics Grade 9 pg. 192
- Rulers
- Compasses
- Plain papers
- Models
- Master Mathematics Grade 9 pg. 196
- Graph papers
- Tracing papers

- Class activities - Written assignments

4.0 Geometry

4.3 Similarity and Enlargement - Negative scale factor (2)
4.3 Similarity and Enlargement - Enlargement on the Cartesian plane (1)

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

- Written tests - Class activities

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

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
- Maps
- Scale models
- Real objects

- Observation - Oral questions

4.0 Geometry

4.4 Trigonometry - Angles and sides of right-angled triangles
4.4 Trigonometry - Tangent ratio and tables of tangents

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

- Observation - Oral questions

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
5.1 Data Interpretation (Grouped Data) - Identifying the modal class 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
- Master Mathematics Grade 9 pg. 228
- Frequency distribution tables
- Reference materials

- Observation - Oral questions - Written assignments

5.0 Data Handling and Probability

5.1 Data Interpretation (Grouped Data) - Calculating the mean of grouped data (1)
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:

- Explain the process of finding mean of grouped data
- Calculate midpoints of classes
- Show interest in organizing data to find the mean

The learner is guided to:
- Group given data into classes
- Add class limits and divide by 2 to get midpoints
- Work out products of midpoints and frequencies (fx)
- Find the sum of fx values

How do we find the mean of grouped data?

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

- Observation - Written tests

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
5.2 Probability - Identifying mutually exclusive events

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

- Class activities - Written tests - Oral questions

5.0 Data Handling and Probability

5.2 Probability - Experiments of single chance involving mutually exclusive events
5.2 Probability - Experiments involving independent 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
- Master Mathematics Grade 9 pg. 246
- Coins
- Colored balls
- Baskets

- Class activities - Written tests - Practical exercises

5.0 Data Handling and Probability

5.2 Probability - Drawing tree diagrams for single outcomes

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

- Explain what a tree diagram represents
- Draw tree diagrams showing probability outcomes on branches
- Show interest in verifying that sum of probabilities on branches equals 1

The learner is guided to:
- Identify possible outcomes from tossing a coin
- Draw branches and fill in outcomes
- Determine probabilities and place on branches
- Verify that sum of probabilities equals 1
- Draw tree diagrams for various probability situations

How do we represent probability using tree diagrams?

- Master Mathematics Grade 9 pg. 248
- Drawing materials
- Coins
- Calculators
- Chart papers
- Rulers

- Class activities - Written tests - Practical activities