Module 18: Mathematics
3D geometry and longitudes/latitudes.
Use this workbook to practice core KCSE communication skills and record evidence of progress.
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SECTION: MATHEMATICS
MODULE: 18
Part A: Units
1. Three dimensional geometry
a. Geometrical properties of common solids
b. Skew lines and projection of a line onto a plane
c. Length of a line in 3 dimensional geometry
d. The angle between: a line and a line, a line and a plane, a plane and a plane
e. Angles between skew lines
2. Longitudes and latitudes
a. Definition of the great and small circles in relation to a sphere
b. The equator and the Greenwich meridian
c. Radii of small and great circles
d. Position of a plane on the surface of the earth
e. Distance between two points along a circle of latitude
f. Time and longitude
g. Speed in knots and kilometers per hour
Part B: Project
Solve practical problems in 3D geometry and time-longitude.
Project Title: 3D Geometry and Longitude Practice
Objective: Apply 3D geometry and latitude-longitude calculations to real scenarios.
Project Instructions:
- 1. Draw a common solid and label skew lines and planes.
- 2. Calculate the length of a line in 3D using given dimensions.
- 3. Find an angle between a line and a plane.
- 4. Compute distance between two points along a circle of latitude.
- 5. Solve a time-longitude problem using knots or km/h.
- 6. Consult your coach where necessary.
Evidence to Submit:
- • 3D diagrams and calculations.
- • Latitude distance and time solutions.
- • Final answers with units.
Submission
Part C: Training Others
Teach a peer about 3D geometry and longitude calculations.
Guidance:
- • Explain skew lines and projections.
- • Demonstrate finding angles between lines and planes.
- • Solve a simple time-longitude example together.
Reflection:
- • What did the learner understand well?
- • Which step needed more explanation?
- • What support do you need from your coach?
Submission
Part D: Assessment
Competency Levels:
1 = Expectations not met
2 = Partially met
3 = Satisfactorily met
4 = Excellently met
Self-assessment:
- • 3D geometry concepts:
- • Angles between lines and planes:
- • Longitude, latitude, and time:
Coach assessment:
- • 3D geometry concepts:
- • Angles between lines and planes:
- • Longitude, latitude, and time:
Submission
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Keep your learning rhythm steady and record your reflections as you progress.