Mastering Line Division: Bisecting, Trisecting, and More in Technical Drawing SS 1 First Term Lesson Notes Week 6

Technical Drawing, SS 1, First Term, Week 6 on Plane Geometry (Division of Line):

Lesson Plan: Plane Geometry (Division of Line)

Subject: Technical Drawing
Class: SS 1
Term: First Term
Week: 6
Age: 14-16 years
Topic: Plane Geometry
Sub-Topic: Division of a Line
Duration: 40 minutes

Behavioral Objectives

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

1. Bisect a given line accurately.
2. Trisect a given line.
3. Divide a line into a specified number of equal parts.
4. Divide a line into specified ratios and proportions.

Keywords

• Bisect
• Trisect
• Divide
• Equal parts
• Ratios
• Proportions

Set Induction

The teacher will engage students by asking them about situations where equal and proportional division is necessary, such as in dividing land plots or design layouts.

Entry Behavior

Students are familiar with basic concepts of measurement and have used rulers and compasses in previous exercises.

Learning Resources and Materials

• Rulers
• Compasses
• Pencils
• Drawing sheets
• Set squares

Building Background/Connection to Prior Knowledge

Students have previously worked on basic line drawing and measurement, which are foundational for dividing lines accurately in technical drawing.

Embedded Core Skills

• Precision in measurement
• Spatial reasoning
• Application of ratios and proportions
• Geometric constructions

Learning Materials

• Lagos State Scheme of Work for Technical Drawing
• Visual aids illustrating the process of bisecting, trisecting, and dividing lines

Reference

• Lagos State Scheme of Work
• “Technical Drawing for GCE and Engineering” by B.O. Osiyemi (for geometric construction techniques)

Instructional Materials

• Demonstration charts for bisecting and trisecting lines
• Sample drawings showing divided lines and ratios
• Compass and ruler demonstration tools

Content Outline

1. Bisecting a Line:
   • Definition and use of bisection in dividing a line into two equal parts.
   • Step-by-step procedure using a compass and straightedge.
2. Trisecting a Line:
   • Trisecting involves dividing a line into three equal parts.
   • Explanation and demonstration of the method using ruler and compass.
3. Dividing a Line into Equal Parts:
   • General technique for dividing any given line into multiple equal segments.
4. Dividing a Line in a Given Ratio:
   • Concept of ratios and proportions.
   • Steps for dividing a line in a specific ratio or proportion using basic geometric tools.

Fill-in-the-Blank Questions

1. To divide a line into two equal parts, you ______ it (a. trisect, b. bisect, c. partition, d. expand).
2. When a line is divided into three equal parts, it is said to be ______ (a. bisected, b. split, c. trisected, d. segmented).
3. A ______ is used to divide a line into specified ratios (a. ruler, b. compass, c. protractor, d. divider).
4. Dividing a line into four equal parts is called ______ division (a. ratio, b. proportionate, c. quarter, d. bisection).
5. Ratios are used in technical drawing to ensure ______ in measurements (a. proportion, b. exactness, c. irregularity, d. none of the above).
6. A compass is useful for ______ a line accurately (a. bending, b. dividing, c. coloring, d. erasing).
7. ______ and trisecting are common ways to divide a line (a. Measuring, b. Marking, c. Bisecting, d. Joining).
8. ______ is needed to divide a line equally (a. Calculator, b. Measurement, c. Marker, d. Compass).
9. Dividing a line into equal segments means each segment is of the ______ length (a. different, b. random, c. identical, d. none of the above).
10. Technical drawing often uses ______ to maintain precision (a. ratios, b. colors, c. symbols, d. patterns).

Plane Geometry (Division of Line)

Learning Objectives:

1. Bisect a Line:
   • Explanation: Bisecting a line means dividing it into two equal parts. This skill is useful in technical drawing and geometry to create symmetrical shapes and accurate divisions.
   • Steps to Bisect a Line:
     • Draw a line segment and label its endpoints (e.g., A and B).
     • Place the compass point on one endpoint (A) and open it wider than half the length of the line.
     • Draw an arc above and below the line.
     • Repeat this step from the other endpoint (B) so the arcs intersect above and below the line.
     • Draw a straight line through the intersection points of the arcs to create a midpoint.
   • Why it’s Important: Bisecting a line helps in achieving symmetry in technical drawings and is a foundational skill for creating geometric constructions accurately.
2. Trisect a Line:
   • Explanation: Trisecting a line means dividing it into three equal parts. This technique is often applied in various fields like engineering and architecture to evenly space out components.
   • Steps to Trisect a Line:
     • Draw a line segment and label its endpoints (e.g., A and B).
     • Using a ruler, measure the length of the line and divide by three to find the distance of each segment.
     • Mark two points on the line according to the calculated distance, creating three equal segments.
   • Why it’s Important: Trisecting is used to divide space evenly and helps in creating precise technical drawings, ensuring that each section is equally spaced.
3. Divide a Line into Equal Parts or Specified Ratios and Proportions:
   • Explanation: Dividing a line into equal parts or specific ratios allows for accurate scaling and measurement. This technique is essential in technical drawings, where parts of a design often need to be proportional.
   • Steps for Equal Parts:
     • Measure the length of the line and decide on the number of parts to divide it into (e.g., 4, 5, etc.).
     • Calculate the length of each part by dividing the total length by the number of parts.
     • Use a ruler to mark each part along the line.
   • Steps for Specified Ratios:
     • If dividing in a specific ratio (e.g., 2:3), add the ratio parts (2 + 3 = 5).
     • Divide the line into 5 equal sections and mark the divisions to create segments in a 2:3 ratio.
   • Why it’s Important: Dividing lines accurately helps in maintaining proportion, symmetry, and balance in designs, which are key in professional technical drawings.

By mastering these skills, students will be able to divide lines precisely, which is fundamental for creating accurate and proportionate technical drawings.