4.0 Geometry

4.1 Coordinates and Graphs - Plotting points on a Cartesian plane
4.1 Coordinates and Graphs - Drawing straight line graphs given equations
4.1 Coordinates and Graphs - Drawing parallel lines on the 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
- Master Mathematics Grade 9 pg. 154
- Graph papers
- Mathematical tables
- Master Mathematics Grade 9 pg. 156
- Set squares

- Observation - Oral questions - Written assignments

4.0 Geometry

4.1 Coordinates and Graphs - Relating gradients of parallel lines
4.1 Coordinates and Graphs - Drawing perpendicular lines on the Cartesian plane
4.1 Coordinates and Graphs - Relating gradients of perpendicular lines and applications
4.2 Scale Drawing - Compass bearing
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:
- Define the gradient of a line
- Calculate and compare gradients of parallel lines
- Appreciate the concept that parallel lines have equal gradients

The learner is guided to:
- Identify two points on each line
- Work out the gradient of the lines
- Compare the gradients of lines identified as parallel
- Express equations in the form y=mx+c and compare gradients

How do gradients help us identify parallel lines?

- Master Mathematics Grade 9 pg. 158
- Graph papers
- Rulers
- Calculators
- Digital devices
- Master Mathematics Grade 9 pg. 160
- Protractors
- Set squares
- Master Mathematics Grade 9 pg. 162
- Real-life graph examples
- Master Mathematics Grade 9 pg. 166
- Pair of compasses
- Charts showing compass directions
- Master Mathematics Grade 9 pg. 169
- Compasses
- Map samples
- Master Mathematics Grade 9 pg. 171
- Pencils

- Oral questions - Written assignments

4.0 Geometry

4.2 Scale Drawing - Determining the bearing of one point from another (2)
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:
- 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
- Master Mathematics Grade 9 pg. 173
- Compasses
- Plain papers
- Graph papers

- Class activities - Written tests

4.0 Geometry

4.2 Scale Drawing - Identifying angles of elevation (1)
4.2 Scale Drawing - Determining angles of elevation (2)
4.2 Scale Drawing - Identifying angles of depression (1)
4.2 Scale Drawing - Determining angles of depression (2)

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
- Graph papers
- Calculators
- Master Mathematics Grade 9 pg. 178
- Pictures showing depression

- Observation - Oral questions

4.0 Geometry

4.2 Scale Drawing - Application in simple surveying - Triangulation (1)
4.2 Scale Drawing - Application in simple surveying - Triangulation (2)
4.2 Scale Drawing - Application in simple surveying - Transverse survey (1)
4.2 Scale Drawing - Application in simple surveying - Transverse survey (2)
4.2 Scale Drawing - Surveying using bearings and distances

By the end of the lesson, the learner should be able to:
- Explain the concept of triangulation in surveying
- Identify baselines and offsets and draw diagrams using triangulation method
- Develop interest in using triangulation for surveying

The learner is guided to:
- Trace irregular shapes to be surveyed
- Enclose the shape with a triangle
- Identify and measure baselines
- Draw perpendicular offsets to the baselines

What is triangulation and how is it used in surveying?

- Master Mathematics Grade 9 pg. 180
- Rulers
- Set squares
- Compasses
- Plain papers
- Meter rules
- Strings
- Pegs
- Field books
- Pencils
- Graph papers
- Protractors

- Observation - Class activities