Lesson Notes By Weeks and Term v3 - Junior Secondary 2
plain figures
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plain figures
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Subject: Basic Technology
Class: Junior Secondary 2
Term: 2nd Term
Week: 3
Theme: Drawing Practice
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Identify regularplane figures Construct regularplane figures of equal are as Find the area of regular planefigures Enlarge and reduce planefigures
Drawing Practice Plain Figures Term: 2nd Term Week: 6 ---
1. Overview and Learning Objectives This topic introduces students to the fundamental concepts of plain figures, which are two-dimensional geometric shapes. Understanding plain figures is crucial in various fields of Basic Technology, including technical drawing, construction, design, and manufacturing. These basic shapes form the building blocks for more complex designs and structures encountered in daily life and professional practice. Mastery of their identification, construction, area calculation, and scaling is essential for practical application in many Nigerian trades and industries. Upon completion of this lesson, students will be able to: Identify and name common regular plain figures based on their properties. Construct regular plain figures, including those that share an equivalent area with another given figure, using appropriate drawing instruments. Calculate the area of various regular plain figures using relevant formulas. Enlarge and reduce the dimensions of plain figures proportionally using a given scale factor.
Real-world connection (Nigeria): The knowledge of plain figures is fundamental for various Nigerian professionals and artisans. Architects and civil engineers use these principles in designing building layouts, calculating floor areas, and determining material quantities. Carpenters and furniture makers apply these concepts when cutting and assembling wood panels. Fashion designers and tailors use plain figures to draft patterns for garments, ensuring correct fit and fabric utilization. Graphic designers employ these shapes in creating logos, advertisements, and digital art. Even in agriculture, farmers may use area calculations to estimate crop yields or land sizes for planting.
2. Key Concepts and Explanations 2.1 Definition of Plain Figures Plain figures are two-dimensional (2D) shapes that possess only length and breadth, without thickness or depth. They exist on a flat surface and are bounded by lines or curves. Examples include triangles, squares, rectangles, circles, etc. 2.2 Regular vs. Irregular Plain Figures Regular Plain Figures: These are polygons where all sides are equal in length, and all interior angles are equal in measure.
Examples: Equilateral triangle (3 equal sides, 3 equal 60° angles), Square (4 equal sides, 4 equal 90° angles), Regular Pentagon (5 equal sides, 5 equal 108° angles), Regular Hexagon (6 equal sides, 6 equal 120° angles).
Irregular Plain Figures: These are polygons where not all sides are equal in length, or not all interior angles are equal in measure.
Examples: Scalene triangle, Rectangle (unless it's a square), Rhombus (unless it's a square), Trapezium, Irregular pentagon. For JSS2, the focus will primarily be on squares and equilateral triangles as primary examples of regular plain figures for detailed construction and area calculations, alongside rectangles for general area understanding. 2.3 Construction of Regular Plain Figures Students should be proficient in using drawing instruments (ruler, compass, protractor, set squares) for construction. Construction of an Equilateral Triangle (given side length 's'):
1. Draw a line segment AB of length 's'.
2. With A as the center and radius 's', draw an arc.
3. With B as the center and radius 's', draw another arc to intersect the first arc at point C.
4. Join A to C and B to
C. Triangle ABC is an equilateral triangle. Construction of a Square (given side length 's'):
1. Draw a line segment AB of length 's'.
2. At point A, construct a perpendicular line (e.g., using a compass or set square).
3. Measure 's' units along the perpendicular line from A to get point D.
4. With D as the center and radius 's', draw an arc.
5. With B as the center and radius 's', draw another arc to intersect the first arc at point C.
6. Join B to C and D to C. ABCD is a square. 2.4 Construction of Regular Plain Figures of Equal Areas This objective typically involves two steps:
1. Calculating the area of a given regular plain figure.
2. Using that area to determine the dimensions of another regular plain figure that will have the same area, and then constructing it.
Example: Construct an equilateral triangle with the same area as a given square.
1. Given: A square of side length 's1' (e.g., 6 cm). 2. *Step 1: Calculate the area Join B to C and D to C. ABCD is a square. 2.4 Construction of Regular Plain Figures of Equal Areas This objective typically involves two steps:
1. Calculating the area of a given regular plain figure.
2. Using that area to determine the dimensions of another regular plain figure that will have the same area, and then constructing it.
Example: Construct an equilateral triangle with the same area as a given square.
1. Given: A square of side length 's1' (e.g., 6 cm).
2. Step 1: Calculate the area of the square. Area of square = s12 If s1 = 6 cm, Area = 62 = 36 cm2.
3. Step 2: Determine the side length 's2' of the equilateral triangle with this area. Formula for Area of an equilateral triangle = (√3 / 4) s22 Set the areas equal: 36 = (√3 / 4) s22 s22 = (36 4) / √3 = 144 / √3 s2 = √(144 / √3) = 12 / (3^(1/4)) ≈ 9.12 cm (using √3 ≈ 1.732, then 3^(1/4) ≈ 1.316)
4. Step 3: Construct the equilateral triangle with side length s2 ≈ 9.12 cm using the steps outlined in 2.3. 2.5 Finding the Area of Regular Plain Figures Area is the amount of surface enclosed by a two-dimensional shape, measured in square units (e.g., cm2, m2, km2).
Square: Formula: Area (A) = side × side = s2
Example: A square tile used for flooring in a Nigerian home has a side of 30 cm. Area = 30 cm × 30 cm = 900 cm
2. Rectangle: Formula: Area (A) = length × breadth = l × b
Example: A rectangular football pitch marking is 100 m long and 60 m wide. Area = 100 m × 60 m = 6000 m
2. Equilateral Triangle: Formula: Area (A) = (√3 / 4) × s2 (where 's' is the side length) Alternative Formula (using base and height): A = (1/2) × base × height. For an equilateral triangle, height (h) = (√3 / 2) × s.
Example: An equilateral triangular signpost has a side length of 40 cm. Area = (√3 / 4) × 402 = (1.732 / 4) × 1600 = 0.433 × 1600 = 692.8 cm
2. Regular Hexagon: A regular hexagon can be divided into six equilateral triangles.
Formula: Area (A) = 6 × [(√3 / 4) × s2] (where 's' is the side length).
Alternatively (if apothem 'a' is given): Area (A) = (1/2) × perimeter × apothem. Perimeter = 6s. So A = (1/2) × (6s) × a = 3sa.
Example: A regular hexagonal tile has a side length of 10 cm. Area = 6 × [(√3 / 4) × 102] = 6 × (1.732 / 4) × 100 = 6 × 0.433 × 100 = 259.8 cm2. 2.6 Enlargement and Reduction of Plain Figures Enlargement (magnification) or reduction (diminution) means changing the size of a figure proportionally while maintaining its shape. This is done using a scale factor (k).
Scale Factor (k): A ratio that describes how much an object is scaled. If k > 1, it's an enlargement. If 0 < k < 1, it's a reduction. If k = 1, the size remains the same.
Method: To enlarge or reduce a figure, multiply all its linear dimensions (sides, lengths, widths) by the scale factor. New Dimension = Original Dimension × Scale Factor (k)
Effect on Area: If the linear dimensions are scaled by 'k', the area is scaled by k
2. New Area = Original Area × k2 Example of Enlargement: A square with a side of 5 cm needs to be enlarged by a scale factor of
3. New side = 5 cm × 3 = 15 cm. Original Area = 52 = 25 cm
2. New Area = 152 = 225 cm
2. Also, New Area = Original Area × k2 = 25 × 32 = 25 × 9 = 225 cm2. * Example of Reduction: A rectangular building plan (drawing) the area is scaled by k
2. New Area = Original Area × k2 Example of Enlargement: A square with a side of 5 cm needs to be enlarged by a scale factor of
3. New side = 5 cm × 3 = 15 cm. Original Area = 52 = 25 cm
2. New Area = 152 = 225 cm
2. Also, New Area = Original Area × k2 = 25 × 32 = 25 × 9 = 225 cm
2. Example of Reduction: A rectangular building plan (drawing) has dimensions 12 cm by 8 cm. It needs to be reduced by a scale factor of 1/4 (or 0.25). New length = 12 cm × (1/4) = 3 cm. New width = 8 cm × (1/4) = 2 cm. Original Area = 12 × 8 = 96 cm
2. New Area = 3 × 2 = 6 cm
2. Also, New Area = Original Area × k2 = 96 × (1/4)2 = 96 × (1/16) = 6 cm2.
3. Teaching and Learning Activities 3.1 Introduction (10 minutes)
Teacher Activity: Display various real-life objects or images featuring plain figures (e.g., a square floor tile, a triangular road sign, a rectangular phone, a hexagonal bolt head, a circular plate).
Student Activity: Students identify the shapes observed and describe their basic characteristics (e.g., "This is a square, it has four equal sides"). Teacher guides a brief discussion on where these shapes are commonly found in their environment in Nigeria. 3.2 Identifying Regular Plain Figures (15 minutes)
Teacher Activity: Present flashcards or draw various plain figures (regular and irregular) on the board. Introduce definitions of regular and irregular plain figures.
Student Activity: Students identify and categorize the figures as "regular" or "irregular." They name the regular figures and state one key property for each (e.g., "This is a regular hexagon; all its sides are equal"). 3.3 Constructing Regular Plain Figures (20 minutes)
Teacher Activity: Demonstrate step-by-step construction of an equilateral triangle (e.g., side 7 cm) and a square (e.g., side 6 cm) on the board or using a projector, emphasizing accurate use of ruler and compass.
Student Activity: Students follow the teacher's demonstration and construct an equilateral triangle and a square of given dimensions in their exercise books. The teacher circulates to provide assistance. 3.4 Finding the Area of Regular Plain Figures (25 minutes)
Teacher Activity: Introduce the formulas for calculating the area of squares, rectangles, and equilateral triangles. Work through examples, explaining each step clearly.
Example 1: Find the area of a square of side 5 cm.
Example 2: Find the area of a rectangular table top 80 cm long and 50 cm wide.
Example 3: Find the area of an equilateral triangle of side 12 cm (use √3 ≈ 1.732).
Student Activity: Students copy the formulas and worked examples. They then solve additional practice questions provided by the teacher, applying the formulas to different dimensions. 3.5 Constructing Regular Plain Figures of Equal Areas (30 minutes)
Teacher Activity: Guide students through the process of constructing a square of a given side (e.g., 6 cm), calculating its area, then determining the side length of an equilateral triangle that has the same area. Finally, demonstrate the construction of this equilateral triangle. Emphasize the connection between calculation and geometric construction.
Student Activity: Students follow the teacher's steps, first constructing the square, calculating its area, then performing the necessary calculations to find the side length of the equivalent equilateral triangle, and finally constructing the triangle. 3.6 Enlargement and Reduction of Plain Figures (25 minutes)
Teacher Activity: Explain the concept of scale factor. Demonstrate how to enlarge a simple square (e.g., side 3 cm) by a scale factor of 2, showing how all linear dimensions are multiplied. Then demonstrate reduction (e.g., a rectangle 10 cm by 6 cm by a scale factor of 1/2). Discuss the effect on area. * Student Activity: Students draw an original figure (e.g., a square, a rectangle) and then draw its enlarged or reduced version based on a given scale factor. They also calculate the