Lesson Notes By Weeks and Term v3 - Junior Secondary 2
drawing practice
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drawing practice
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Subject: Basic Technology
Class: Junior Secondary 2
Term: 2nd Term
Week: 2
Theme: Drawing Practice
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Define, identify and construct varioustriangles Construct in scribedand circumscribedcircles to giventriangles Students should be ableto define, identify and construct regular and irregular polygons
This section provides a detailed explanation of the core concepts, definitions, and step-by-step construction methods for triangles, inscribed/circumscribed circles, and polygons.
Teacher Activities: Introduction (10 min): Engage students by asking about shapes they see around them (doors, windows, roof, tiles). Introduce the concept of technical drawing as a universal language. Review basic drawing instruments (pencil, ruler, compass, protractor, set squares). State the lesson objectives clearly.
Demonstration and Explanation (30 min): Triangles: Define and classify triangles. Demonstrate step-by-step construction of an equilateral, isosceles, and scalene triangle on a whiteboard or projector, emphasizing accuracy and proper use of instruments.
Inscribed/Circumscribed Circles: Explain what each means. Demonstrate the construction of an inscribed circle within a given triangle, then a circumscribed circle, clearly showing how to find the incenter and circumcenter respectively.
Polygons: Define polygons, differentiate between regular and irregular. Demonstrate the construction of a regular hexagon (given side) and a regular pentagon (given side or radius of circumscribing circle) on the board. Briefly explain how irregular polygons are drawn by joining points or given dimensions.
Guided Practice (20 min): Provide students with specific dimensions and guide them through constructing one example of each (e.g., an equilateral triangle, an inscribed circle, a regular hexagon) on their drawing sheets. Circulate to observe, provide immediate feedback, and correct common errors.
Activity Facilitation (15 min): Divide students into small groups. Assign each group a different construction task (e.g., Group A: isosceles triangle with inscribed circle; Group B: scalene triangle with circumscribed circle; Group C: regular octagon). Encourage peer learning and discussion within groups.
Review and Wrap-up (5 min): Invite groups to briefly present their constructions or hold up their work for quick review. Recap key definitions and construction steps. Assign independent practice/homework.
Student Activities: Actively listen and observe teacher demonstrations, taking notes where necessary. Ask clarifying questions during explanations and demonstrations. Practice using drawing instruments (ruler, compass, protractor, set squares) accurately. Attempt constructions independently and collaboratively during guided and group practice sessions. Participate in group discussions and peer critique. Present their constructed figures to the class. Complete assigned independent practice exercises. The teacher should guide students through these examples, explaining each step and ensuring students follow along on their drawing sheets.
Question 1: Construct an equilateral triangle with sides of 70mm.
Solution: Draw a horizontal line segment AB, 70mm long. Place the compass point at A, open it to radius AB (70mm). Draw an arc above AB. Place the compass point at B, and with the same radius (70mm), draw another arc to intersect the first arc. Label the intersection point C. Join point C to point A and point C to point B with straight lines. Triangle ABC is the required equilateral triangle.
Commentary: This reinforces the fundamental construction of an equilateral triangle, emphasizing equal sides and radii.
Question 2: Construct a triangle ABC with sides AB = 80mm, BC = 60mm, and AC = 50mm. Then, construct an inscribed circle within this triangle.
Solution: Part 1: Constructing the Triangle Draw a line segment AB, 80mm long. With A as the centre and a radius of 50mm (AC), draw an arc above AB. With B as the centre and a radius of 60mm (BC), draw another arc to intersect the first arc. Label the intersection point
C. Join A to C and B to
C. Triangle ABC is the required scalene triangle.
Part 2: Constructing the Inscribed Circle Bisect Angle A: Place the compass point at A, draw an arc to cut AB and AC. From these two intersection points, draw two more arcs of the same radius to intersect inside the triangle. Draw a line from A through this intersection point (this is the angle bisector).
Bisect Angle B: Repeat the process for angle B. Place the compass point at B, draw an arc to cut AB and BC. From these two intersection points, draw two more arcs of the same radius to intersect inside the triangle. Draw a line from B through this intersection point.
Locate Incenter: The point where the two angle bisectors intersect is the incenter. Label it
O. Find Radius: From O, drop a perpendicular line to any side of the triangle (e.g., AB). To do this, place the compass point at O, open to a convenient radius, and draw arcs that intersect line AB at two points. From these two new points, draw arcs (with a radius greater than half the distance between them) that intersect on the opposite side of AB. Draw a line from O to this intersection point. This line segment is perpendicular to AB and its length is the radius (r) of the inscribed circle.
Draw Inscribed Circle: With O as the centre and radius 'r', draw the circle. It should touch all three sides of the triangle.
Commentary: This question combines triangle construction with a key geometric construction, requiring multiple steps and careful use of instruments. It addresses the second performance objective.
Question 3: Construct a regular hexagon with each side measuring 45mm.
Solution: Draw a horizontal line segment of 45mm, label it AB. (This is a simplified approach, often used in JSS for direct construction.) Alternatively, the more common method: Draw a point O (centre of the hexagon). With O as centre, and a radius equal to the side length (45mm), draw a circle. Mark a point A on the circumference. With A as the centre and the same radius (45mm), draw an arc to cut the circle at point
B. Continue this process: With B as centre and radius 45mm, cut the circle at C. Repeat for D, E, and
F. Join points A, B, C, D, E, F in sequence to form the regular hexagon.
Commentary: This demonstrates the efficient construction of a regular hexagon, leveraging the fact that its side length equals the radius of its circumscribing circle. This directly addresses the third performance objective. Differentiation Strategies (for diverse learners): Visual Aids: Utilize large, clear diagrams on the board or projector. Provide pre-printed construction steps for students to follow.
Peer Tutoring: Pair struggling learners with more capable students during practical sessions.
Simplified Tasks: For students struggling with complex constructions, initially focus on basic triangle construction before moving to inscribed/circumscribed circles. Provide simpler polygons (e.g., square) before pentagons or hexagons.
Chunking Instructions: Break down multi-step constructions into smaller, manageable steps. Remediation Activities (for struggling learners): One-on-One Support: Provide direct, individualized instruction and demonstration for students who are significantly behind.
Review Basic Instruments: Revisit the correct handling and reading of rulers, compasses, and protractors. Ensure they understand how to draw straight lines, arcs, and measure angles accurately.
Repetitive Practice: Provide extra worksheets with simpler, repetitive construction exercises for specific skills (e.g., only bisecting angles, only perpendicular bisectors of lines).
Reduced Complexity: Offer a choice of easier constructions during assessment or independent practice, gradually increasing complexity. Extension / Enrichment Activities (for high-achieving learners): Advanced Polygon Construction: Challenge them to construct more complex regular polygons (e.g., heptagon, nonagon) using the general angle method or approximate methods.
Tessellations: Introduce the concept of tessellations (tiling patterns) and challenge students to create patterns using various regular polygons they have constructed. This links to floor tiling, wall decoration, and fabric design.
Design Project: Task them with a small design project, such as designing a logo for a fictional Nigerian company using only triangles and polygons, or sketching a simple floor plan of a small kiosk or a furniture item, incorporating the geometric shapes learned.
Research: Encourage them to research the historical and cultural significance of geometric patterns in Nigerian art and architecture (e.g., Nsibidi symbols, traditional weaving patterns, Yoruba adire patterns).
Building and Construction (Architecture and Engineering): Application: Architects and civil engineers use technical drawing to create accurate plans for houses, bridges, and other structures. Triangles are fundamental in structural design for stability (e.g., roof trusses, bridge frameworks). Regular polygons are used in tiling patterns, window designs, and specific structural components.
Nigerian Context: Students can relate this to their own homes, local markets, bridges like the Third Mainland Bridge in Lagos, or new school buildings. They can be asked to identify triangular or polygonal shapes in local architecture or infrastructure projects. The skill of drawing to scale is crucial for translating large construction projects onto paper. Craftsmanship and Industrial Design (Carpentry, Fashion, Manufacturing): Application: Carpenters use geometric principles to construct furniture (tables, chairs, cabinets), ensuring they are balanced and sturdy. Fashion designers use polygons to draft clothing patterns. Manufacturers use these drawings to design and produce various items, from car parts to electronic casings.
Nigerian Context: Consider local artisans making wooden furniture in places like Ojuelegba market, tailors (modelling styles from Ankara fabrics), or local welders fabricating metal gates. They all apply principles of geometry and measurement. For example, a carpenter designing a hexagonal table or a tailor cutting fabric for a dress often intuitively uses the concepts taught in this lesson.
Surveying and Land Management: Application: Surveyors use geometric drawing to map land, define property boundaries, and plan infrastructure development. They divide large areas into triangles for accurate measurement (triangulation).
Nigerian Context: This is highly relevant in Nigeria, particularly in property sales, town planning, and agricultural land allocation. Students can understand how drawing skills contribute to solving disputes over land or planning new settlements and roads in their communities.