Lesson Notes By Weeks and Term v3 - Junior Secondary 2
Plane figures/ Shapes
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Plane figures/ Shapes
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Subject: General Mathematics
Class: Junior Secondary 2
Term: 3rd Term
Week: 2
Theme: Mensuration And Geometry
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State the properties of parallelogram, rhombus and kite Identify the se shapes in the ir environment; Draw plane objects to scale; Convert actual length to scales and vice versa Apply scale drawing to solve measurement problem; solve problems on quantitative aptitude related to plane shapes/figure and scale drawing
Mensuration And Geometry length (8m / 2m/cm = 4cm): 2 marks Calculation of drawing width (6m / 2m/cm = 3cm): 2 marks Accurate drawing of a 4cm by 3cm rectangle: 2 marks Correctly labelled (e.g., "Fish Pond") and scale stated ("1 cm to 2 m"): 2 marks
3. Solve problems on quantitative aptitude related to plane shapes/figures and scale drawing: (13 marks) a) A piece of land on a property survey map measures 5 cm by 3.5 cm.
The scale of the map is 1:2,
0
0
0. Calculate the actual perimeter of the land in meters. (7 marks)
Marking Scheme: Understanding 1:2000 means 1 cm = 2000 cm = 20 m: 2 marks Actual Length = 5 cm 20 m/cm = 100 m: 2 marks Actual Width = 3.5 cm 20 m/cm = 70 m: 2 marks Perimeter = 2(100 + 70) = 2(170) = 340 m: 1 mark b) In a parallelogram ABCD, angle A = (3x + 10)° and angle B = (2x + 50)°. Find the value of x and the measure of angle C. (6 marks)
Marking Scheme: Recognising consecutive angles are supplementary: (3x + 10) + (2x + 50) = 180: 2 marks Solving for x: 5x + 60 = 180 => 5x = 120 => x = 24: 2 marks Angle A = 3(24) + 10 = 72 + 10 = 82°. Angle C = Angle A (opposite angles are equal): 2 marks (Optional check: Angle B = 2(24) + 50 = 48 + 50 = 98°. Angle A + Angle B = 82 + 98 = 180°)
Total Marks: 30
7. Real-life Applications / Integration
1. Architecture and Building Construction: Architects and builders in Nigeria use scale drawings (blueprints) to design houses, schools, and infrastructure like bridges. Students can appreciate how the properties of shapes (e.g., parallelogram for roof trusses, rhombus for decorative window grills) and scale drawing are fundamental to planning, costing, and constructing safe and functional buildings.
2. Mapping and Urban Planning: Local government planners and surveyors in Nigerian cities (e.g., Lagos, Abuja, Kano) rely heavily on scaled maps to design road networks, allocate land for markets or residential areas, and manage urban development. Understanding scale drawing helps students interpret these maps, measure distances between local landmarks, and even contribute to community development discussions.
3. Fashion Design and Tailoring: Nigerian fashion designers and tailors use scale drawings to create patterns for various garments, including traditional outfits like Agbada or Buba and Iro. They scale down the human body measurements to fit a pattern paper, then scale them back up to cut the actual fabric. This ensures correct proportions and fit, directly applying knowledge of scale.
8. Differentiation, Remediation and Extension Differentiation (for Diverse Learners): Group Work: Allow students to work in mixed-ability groups, encouraging peer teaching and collaborative problem-solving, particularly for scale drawing calculations and verifying shape properties.
Visual Aids: Provide physical models of parallelograms, rhombuses, and kites, or cut-out paper shapes, for students to manipulate and discover properties hands-on. Use large, clear diagrams on the board and handouts.
Tiered Worksheets: Provide different levels of complexity in practice problems. Start with basic identification and conversions, moving to multi-step problems for those ready.
Remediation (for Struggling Learners): Focused Review: Conduct a brief review of basic geometry terms (parallel, perpendicular, congruent) before delving into complex quadrilaterals.
Simplified Exercises: Provide worksheets with only one or two properties to identify per shape, or simple, direct scale conversions (e.g., 1 cm to 1 m, rather than 1:50000).
Concrete Manipulatives: Use geoboards and elastic bands or paper cut-outs to allow students to physically construct and manipulate shapes, helping them internalize the properties.
One-on-One Support: Dedicate extra time to work with individual students, breaking down complex steps (especially in scale conversion) into smaller, manageable chunks.
Extension (for High-Achieving Learners): Challenging Problems: Present complex problems involving area calculations of scaled shapes, or problems requiring the determination of an unknown scale from given actual and drawing measurements.
Design Project: Challenge students to design a simple floor plan for a classroom or a small a)
Calculate Drawing Dimensions: Drawing Length = Actual Length / Scale Factor = 12 m / (2 m/cm) = 6 cm. Drawing Width = Actual Width / Scale Factor = 8 m / (2 m/cm) = 4 cm. The dimensions on the drawing will be 6 cm by 4 cm. b)
Drawing: (Teacher should visually inspect student drawings) [Students would draw a rectangle 6 cm long and 4 cm wide on paper, labeled "Yam Barn" with scale "1 cm to 2 m"]
5. Independent Practice (Questions Only)
1. State two properties that a parallelogram has but a kite does not necessarily have.
2. In parallelogram WXYZ, if angle W is 65°, find the measure of angles X, Y, and Z.
3. A kite has diagonals measuring 10 cm and 16 cm. What is the angle at which they intersect?
4. The side of a rhombus is 7.5 cm. If one of its interior angles is 80°, find the measure of the adjacent angle.
5. A new school building in Enugu is 30 m long. If it is to be drawn on a plan using a scale of 1 cm to 5 m, what will be its length on the drawing?
6. On a tourist map of Abuja, a distance of 6.2 cm represents 15.5 km. What is the scale of the map in the form 1:n?
7. A scale drawing of a rectangular football pitch has dimensions 11 cm by 7.5 cm. If the scale used is 1 cm to 10 m, what are the actual dimensions of the football pitch in meters?
8. A contractor is planning a foundation for a house. The actual dimensions are 15 m by 9 m. Draw this foundation to scale using a scale of 1:300. (Hint: convert 1:300 to a verbal scale like 1 cm to X m first).
9. The distance between two villages, Ogbomosho and Ilorin, is 58 km. On a particular map, this distance is represented by 2.9 cm. If a river on the same map measures 1.5 cm, what is the actual length of the river in km?
1
0. Identify which of the following statements is TRUE for ALL rhombuses: A) All angles are 90°. B) Diagonals are equal in length. C) Diagonals bisect each other at right angles. D) Only one pair of opposite angles is equal.
6. Evaluation and Assessment Formative Assessment: Observation: Monitor student engagement during discussions, ability to identify shapes, and participation in drawing activities.
Question and Answer: Pose questions throughout the lesson to check for understanding of properties and scale concepts.
Classwork Review: Collect and review guided practice exercises to identify common misconceptions. Summative Assessment (End-of-Lesson Quiz/Assignment): Instructions: Answer all questions.
1. State the properties of the following: (3 marks each, total 9 marks)
Rhombus: Expected Answer: All four sides are equal. Opposite angles are equal. Diagonals bisect each other at right angles. Diagonals bisect the angles. (Any 3)
Parallelogram: Expected Answer: Opposite sides are parallel and equal. Opposite angles are equal. Consecutive angles are supplementary. Diagonals bisect each other. (Any 3)
Kite: Expected Answer: Two pairs of adjacent sides are equal. One pair of opposite angles is equal. Diagonals intersect at right angles. One diagonal bisects the other. (Any 3)
2. Draw actual length to scale: (8 marks) A rectangular fish pond in Anambra State is 8 meters long and 6 meters wide. Draw this pond to scale using a scale of 1 cm to 2 meters. Clearly label your drawing and state the scale.
Marking Scheme: Calculation of drawing length (8m / 2m/cm = 4cm): 2 marks Calculation of drawing width (6m / 2m/cm = 3cm): 2 marks Accurate drawing of a 4cm by 3cm rectangle: 2 marks Correctly labelled (e.g., "Fish Pond") and scale stated ("1 cm to 2 m"): 2 marks
3. Solve problems on quantitative aptitude related to plane shapes/figures and scale drawing: (13 marks) a) A piece of land on a property survey map measures 5 cm by 3.5 cm.
The scale of the map is 1:2,
0
0
0. Calculate the actual perimeter of the land geoboards and elastic bands or paper cut-outs to allow students to physically construct and manipulate shapes, helping them internalize the properties.
One-on-One Support: Dedicate extra time to work with individual students, breaking down complex steps (especially in scale conversion) into smaller, manageable chunks.
Extension (for High-Achieving Learners): Challenging Problems: Present complex problems involving area calculations of scaled shapes, or problems requiring the determination of an unknown scale from given actual and drawing measurements.
Design Project: Challenge students to design a simple floor plan for a classroom or a small market stall, specifying a scale and including different shapes in their design. They could also create a scale model of a local landmark (e.g., a mini Eyo masquerade statue or a traditional hut).
Research Task: Assign a research task on the history of cartography (map-making) in Nigeria, or how surveyors use scale in their profession, requiring them to present their findings to the class. * Explore Other Quadrilaterals: Introduce other specialized quadrilaterals like isosceles trapezoids or delve into the properties of 3D shapes.