Geometric Constructions: Introduction and Applications Mathematics Jss 2 Second Term Lesson Notes Week 3

Subject: Mathematics

Class: Junior Secondary School 2

Term: First Term

Week: Week 3

Lesson Plan Presentation: Introduction to Geometric Constructions

Learning Objectives:

1. Students will be able to understand and apply basic geometric construction techniques.
2. Students will learn to use tools such as compasses, rulers, and protractors effectively.
3. Students will gain practical experience in constructing various geometric shapes and figures accurately.

Embedded Core Skills:

• Mathematical reasoning
• Spatial visualization
• Fine motor skills
• Problem-solving
• Critical thinking

Instructional Materials:

1. Compasses
2. Rulers
3. Protractors
4. Pencils
5. Erasers
6. Construction paper
7. Worksheets with geometric figures
8. Whiteboard and markers

Reference Materials:

1. Mathematics textbooks
2. Online resources for geometric constructions

Presentation:

1. Introduction to geometric constructions and their importance in mathematics and real-life applications.
2. Demonstration of basic tools and their uses: compasses for drawing circles, rulers for straight lines, and protractors for measuring angles.
3. Explanation of key terminology such as perpendicular, parallel, bisect, and construct.
4. Step-by-step guidance on constructing geometric figures, starting with simple shapes like lines, angles, and triangles, and progressing to more complex figures like polygons and circles.

1. How do I draw a circle of a specific radius and divide it into equal parts?
   • To draw a circle, use a compass with a radius of the desired length. Then, divide the circumference into equal parts by drawing radial lines from the center.
2. What is the formula for calculating the sum of interior angles in a polygon?
   • The formula is (n – 2) * 180 degrees, where n is the number of sides in the polygon.
3. How can I construct a rhombus with a given side length and angle?
   • Start by drawing a segment of the given length. Then, use a protractor to draw an angle at one endpoint, and extend the line to create the other sides.
4. What tools do I need to construct a rectangle with specific dimensions?
   • You will need a ruler, protractor, and compass to ensure accurate measurements and angles.
5. What are some examples of metalwork materials?
   • Common metalwork materials include steel, aluminum, copper, and iron.
6. What are the functions of metalwork tools such as hammers and saws?
   • Hammers are used for shaping and driving nails, while saws are used for cutting metal and other materials.
7. What are the different techniques used in metalwork?
   • Metalwork techniques include forging, casting, machining, and welding, each with its own applications and processes.
8. How is metalwork used in industries like construction and automotive?
   • Metalwork is essential in constructing buildings, bridges, and vehicles, as well as manufacturing machinery and components.
9. What are some safety precautions to consider when working with metal?
   • Safety precautions include wearing protective gear, such as gloves and goggles, and using tools properly to avoid accidents and injuries.
10. Where can I learn more about metalwork and its applications?
    • You can explore online resources, attend workshops, or consult professionals in the field for further guidance and information.

1. Draw a circle of radius 60mm and divide it into 12 equal p

2. Three regular polygons have 5, 7, 9 sides, calculate the su interior angles respectively

3. Construct a rhombus of side 60mm with an angle 50°

4. Construct a rectangle ABCD given length 60mm and brea

5. Study for a class presentation on metalwork and their func resumption.

Here’s the explanation in list format with typical examples for each topic:

1. Drawing a Circle and Dividing it into 12 Equal Parts:
   • Start by drawing a circle with a radius of 60mm using a compass.
   • Next, draw two perpendicular diameters within the circle, intersecting at the center.
   • Divide each quadrant of the circle into three equal parts by drawing radii from the center to the circumference.
   • Label the points where the radii intersect the circumference as A, B, C, D, E, F, G, H, I, J, K, and L.
   • You now have 12 equal parts or sectors on the circumference of the circle.

   Example: This method can be used to create a clock face for a school project, with each sector representing one hour.

2. Calculating the Sum of Interior Angles of Regular Polygons:
   • Use the formula: Sum of interior angles = (n – 2) * 180 degrees, where n is the number of sides.
   • For a polygon with 5 sides (pentagon): Sum = (5 – 2) * 180 = 540 degrees.
   • For a polygon with 7 sides (heptagon): Sum = (7 – 2) * 180 = 900 degrees.
   • For a polygon with 9 sides (nonagon): Sum = (9 – 2) * 180 = 1260 degrees.

   Example: This concept can be applied when designing tiled floors with regular polygonal patterns, ensuring that the angles fit together seamlessly.

3. Constructing a Rhombus with Given Side and Angle:
   • Start by drawing a segment of length 60mm to represent one side of the rhombus.
   • Use a protractor to draw an angle of 50 degrees at one endpoint of the segment.
   • Extend the line from the other endpoint of the segment at the angle of 50 degrees.
   • Using the same length of 60mm, measure and mark the other three sides of the rhombus.
   • Connect the points to form the rhombus.

   Example: This construction can be applied in architectural designs for windows or decorative elements on buildings.
4. Constructing a Rectangle with Given Length and Breadth:
   • Start by drawing a line segment of length 60mm using a ruler.
   • Perpendicular to this line, draw another line segment of the desired breadth.
   • Use a protractor to ensure that the angle between the two segments is 90 degrees.
   • Measure and mark the length and breadth on each line segment.
   • Connect the corresponding points to form the rectangle.

   Example: This construction can be used in engineering projects such as designing tables or desks for school classrooms.

5. Studying Metalwork and their Functions for a Class Presentation:
   • Research various types of metals used in metalwork, such as steel, aluminum, copper, and iron.
   • Identify common metalwork tools and their functions, including hammers, saws, drills, and welding equipment.
   • Explore different metalwork techniques, such as forging, casting, machining, and welding.
   • Discuss the applications of metalwork in industries like construction, automotive, aerospace, and jewelry making.
   • Prepare visual aids, such as posters or slides, to illustrate key concepts and examples during the presentation.

   Example: Students can present on the importance of metalwork in the local economy, highlighting industries like shipbuilding and construction that rely heavily on metal fabrication.

1. To draw a circle, you need a __________. a) ruler b) compass c) protractor d) pencil
2. The formula for calculating the sum of interior angles in a polygon is __________. a) n * 180 degrees b) (n – 1) * 180 degrees c) (n – 2) * 180 degrees d) (n + 2) * 180 degrees
3. A rhombus can be constructed with a given side length and angle using a __________. a) compass b) protractor c) ruler d) calculator
4. In constructing a rectangle, the angle between the length and breadth should be __________ degrees. a) 45 b) 90 c) 180 d) 360
5. Common metalwork materials include steel, aluminum, copper, and __________. a) plastic b) glass c) iron d) wood
6. Hammers are used in metalwork for shaping and __________ nails. a) driving b) cutting c) welding d) polishing
7. The technique of heating and shaping metal by hammering is called __________. a) casting b) forging c) machining d) welding
8. Metalwork is essential in constructing buildings, bridges, vehicles, and manufacturing __________. a) clothing b) furniture c) electronics d) food
9. Safety precautions in metalwork include wearing protective gear such as gloves and __________. a) boots b) aprons c) helmets d) goggles
10. Where can you learn more about metalwork and its applications? a) School b) Library c) Workshop d) All of the above
11. A compass is used to draw __________. a) straight lines b) circles c) angles d) rectangles
12. The sum of interior angles in a polygon with 6 sides is __________ degrees. a) 180 b) 360 c) 540 d) 720
13. Which metalwork technique involves joining pieces of metal together using heat? a) Forging b) Casting c) Welding d) Machining
14. What material is commonly used as a protective gear in metalwork? a) Cotton b) Leather c) Plastic d) Rubber
15. Metalwork is important in various industries such as __________. a) Agriculture b) Tourism c) Healthcare d) Construction

Teacher’s Activities:

1. Introduce the topic and learning objectives.
2. Demonstrate how to use geometric construction tools.
3. Guide students through each construction step, providing explanations and answering questions.
4. Provide examples of real-world applications of geometric constructions.

Learners’ Activities:

1. Observe and participate in the teacher’s demonstrations.
2. Practice using geometric construction tools independently.
3. Follow step-by-step instructions to construct geometric figures.
4. Collaborate with peers to solve construction problems and compare results.

Assessment:

• Formative assessment: Observe students’ participation and engagement during the lesson, providing feedback and guidance as needed.
• Summative assessment: Evaluate students’ understanding by assessing the accuracy and completeness of their constructed geometric figures.

Evaluation Questions:

1. What tools are commonly used in geometric constructions?
2. Describe the steps involved in constructing a perpendicular bisector.
3. How do you use a compass to draw a circle with a given radius?
4. What is the purpose of constructing parallel lines?
5. Explain the difference between constructing an equilateral triangle and an isosceles triangle.
6. How can you verify if a triangle is equilateral, isosceles, or scalene using geometric constructions?
7. What construction method would you use to divide a line segment into three equal parts?
8. How can you construct a square with a given side length?
9. What is the significance of constructing congruent angles?
10. How do geometric constructions apply to real-life situations?

Conclusion: In conclusion, geometric constructions are fundamental skills in mathematics and have practical applications in various fields. Through this lesson, students have learned essential techniques for constructing geometric figures accurately and efficiently. By mastering these skills, students can enhance their problem-solving abilities and gain a deeper understanding of geometric concepts.