Lesson Notes By Weeks and Term v3 - Primary 6
Perimeter
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Perimeter
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Subject: General Mathematics
Class: Primary 6
Term: 2nd Term
Week: 5
Theme: Measurement
This page supports the lesson note with a companion video and a short classroom-ready summary.
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Pupils should be able to discover that difference rectangle with same area have different perimeters
Measurement Perimeter Term: 2nd Term Week: 21 ---
1. Overview and Learning Objectives This lesson introduces Primary 6 students to the concept of perimeter, specifically focusing on rectangular shapes. Building on prior knowledge of area and perimeter, the lesson aims to develop students' understanding that while two rectangles can occupy the same amount of space (have the same area), the distance around them (their perimeter) can be different. This concept is foundational for practical applications in everyday life, where understanding the dimensions of a shape beyond just its area is crucial for planning and cost estimation.
Specific Performance Objective: Students will be able to demonstrate, through calculations and observation, that two different rectangular shapes can have the same area but require different lengths of material to go around their boundaries (different perimeters).
Real-world Applications in Nigeria: Understanding this concept is vital for: Farmers and Landowners: When fencing a plot of land in rural or urban areas, knowing that a long, narrow plot might require more fencing material than a squarer plot of the same area, thus impacting cost.
Builders and Artisans: Calculating the length of skirting boards for a room, framing for pictures, or decorative trim for furniture, where the perimeter is the critical measurement.
Tailors and Seamstresses: Estimating the amount of lace or binding needed for the edge of a tablecloth or a piece of clothing, even if the fabric's area is fixed.
Urban Planners/Architects: Designing public spaces or buildings where the layout can significantly affect the material needed for boundaries or walkways.
2. Key Concepts and Explanations This lesson revolves around the definitions and formulas for area and perimeter of rectangles, and the critical observation of their relationship when the area is constant. a)
Area of a Rectangle: Definition: The area of a rectangle is the amount of surface it covers or the space it occupies. It is measured in square units (e.g., square centimetres, square metres).
Formula: Area (A) = Length (L) × Breadth (B)
Units: cm2, m2, km2 b)
Perimeter of a Rectangle: Definition: The perimeter of a rectangle is the total distance around its boundary or outer edge. It is a linear measurement.
Formula: Perimeter (P) = 2 × (Length (L) + Breadth (B))
Units: cm, m, km c) The Relationship Between Area and Perimeter (Central Concept for the Lesson): A fundamental concept in geometry is that shapes with the same area do not necessarily have the same perimeter, and vice-versa. For a given area, a rectangle that is closer to a square shape will generally have a smaller perimeter, while a rectangle that is very long and narrow will have a larger perimeter. This discovery is the core objective of this lesson. Worked
Examples: Example 1: Comparing Rectangular Plots of Land Consider two rectangular plots of land, Plot A and Plot B, both with an area of 36 square metres (36 m2).
Plot A: Length (L) = 12 m, Breadth (B) = 3 m Plot B: Length (L) = 9 m, Breadth (B) = 4 m Let's calculate the area and perimeter for each plot: For Plot A:
1. Area (A): A = L × B A = 12 m × 3 m A = 36 m2
2. Perimeter (P): P = 2 × (L + B) P = 2 × (12 m + 3 m) P = 2 × (15 m) P = 30 m For Plot B:
1. Area (A): A = L × B A = 9 m × 4 m A = 36 m2
2. Perimeter (P): P = 2 × (L + B) P = 2 × (9 m + 4 m) P = 2 × (13 m) P = 26 m Observation: Both Plot A and Plot B have the same area (36 m2).
However, their perimeters are different: Plot A has a perimeter of 30 m, while Plot B has a perimeter of 26 m. This demonstrates that different rectangles can have the same area but different perimeters. Plot B, which is closer to a square (9m x 4m vs 12m x 3m), requires less fencing material. *Example has an area of 144 square units. a) If its length is 16 units, what is its breadth? Calculate its perimeter. b) If its length is 12 units, what is its breadth? Calculate its perimeter. c) What observation can be made from your calculations in (a) and (b)?
6. Evaluation and Assessment Formative Assessment: Observation: The teacher observes students' engagement and accuracy during the discovery activity (Phase 2), noting their ability to form rectangles with a given area and calculate perimeters.
Questioning: During class discussion (Phase 3), the teacher asks targeted questions to gauge individual student understanding of the core concept.
Quick Check: A short "thumbs up/down" or "agree/disagree" response to statements like, "All rectangles with the same area must have the same perimeter." Summative Assessment (Aligned to Evaluation Guide): Students will be assessed on their ability to calculate perimeters of rectangles with equal areas but with different lengths and breadths.
Assessment Questions:
1. A school is building two new rectangular flower beds, Bed P and Bed Q. Both beds will have an area of 24 square meters. Bed P has a length of 8 meters and a breadth of 3 meters. Bed Q has a length of 6 meters and a breadth of 4 meters. a) Calculate the perimeter of Bed P. (2 marks) b) Calculate the perimeter of Bed Q. (2 marks) c) Based on your calculations, state whether Bed P and Bed Q have the same perimeter or different perimeters, even though their areas are equal. (1 mark)
2. A tailor needs to cut two different rectangular pieces of fabric for a project. Each piece must have an area of 72 cm
2. Piece 1 has a length of 18 cm. Piece 2 has a breadth of 9 cm. a) Determine the breadth of Piece 1 and the length of Piece 2. (2 marks) b) Calculate the perimeter of Piece 1. (2 marks) c) Calculate the perimeter of Piece 2. (2 marks) d) Explain the relationship between the areas and perimeters of the two fabric pieces. (1 mark)
Marking Scheme / Rubric: Correct Calculation of Breadth/Length: 1 mark per correct breadth/length.
Correct Formula for Perimeter: 0.5 mark for writing the formula.
Correct Substitution into Formula: 0.5 mark for substituting values. Correct Final Perimeter Calculation (with units): 1 mark for correct answer with unit.
Correct Observation/Explanation: 1 mark for accurately stating the relationship (same area, different perimeters). * Partial marks for correct steps even if the final answer is incorrect due to minor calculation errors.
7. Real-life Applications / Integration
1. Cost of Fencing/Walling in Agriculture and Housing: In rural Nigeria, farmers need to fence their farm plots. Homeowners also build walls around their compounds. A family buying a plot of land with 500 m2 area might find two options: a 50m x 10m plot or a 25m x 20m plot. Both have the same area.
However, the 50m x 10m plot has a perimeter of 2(50+10) = 120m, while the 25m x 20m plot has a perimeter of 2(25+20) = 90m. This means the first plot would require more fencing material and thus cost more to fence or wall, even though the usable land area is the same. This knowledge helps in making informed financial decisions.
2. Designing Rooms and Furniture in Carpentry/Construction: When designing a rectangular living room with a specific floor area (e.g., 30 m2), the architect or builder must consider the perimeter. A 10m x 3m room will require 2(10+3) = 26m of skirting board, whereas a 6m x 5m room (same area) will require 2(6+5) = 22m of skirting. This impacts the cost of materials like skirting, decorative cornices, or even the length of electrical wiring required around the room's edges. Similarly, a carpenter making a rectangular table top of a certain area might consider the amount of edge banding or trim needed.
3. Tailoring and Fabric Design: A tailor creating rectangular tablecloths often works with a specific fabric area. If a customer wants a tablecloth with an area of 180 cm2, the tailor could make it 30 cm x 6 cm or 20 2 × (L + B) P = 2 × (9 m + 4 m) P = 2 × (13 m) P = 26 m Observation: Both Plot A and Plot B have the same area (36 m2).
However, their perimeters are different: Plot A has a perimeter of 30 m, while Plot B has a perimeter of 26 m. This demonstrates that different rectangles can have the same area but different perimeters. Plot B, which is closer to a square (9m x 4m vs 12m x 3m), requires less fencing material.
Example 2: Classroom Floor Tiles A school needs to cover a rectangular section of a classroom floor with tiles. The section has an area of 20 square units.
Option 1: Length = 10 units, Breadth = 2 units Option 2: Length = 5 units, Breadth = 4 units For Option 1:
1. Area (A): A = L × B = 10 units × 2 units = 20 square units
2. Perimeter (P): P = 2 × (L + B) = 2 × (10 units + 2 units) = 2 × 12 units = 24 units For Option 2:
1. Area (A): A = L × B = 5 units × 4 units = 20 square units
2. Perimeter (P): P = 2 × (L + B) = 2 × (5 units + 4 units) = 2 × 9 units = 18 units Observation: Both options cover the same floor area (20 square units), but Option 1 requires a perimeter of 24 units, while Option 2 requires 18 units. If the school wanted to put a skirting board around this section, Option 2 would require less material.
3. Teaching and Learning Activities Phase 1: Introduction and Review (10 minutes)
Teacher Activity: Begins by reviewing the concepts of area and perimeter of a rectangle, asking students to define each and recall their formulas. Draws a simple rectangle on the board, labels length and breadth, and asks students to calculate its area and perimeter.
Poses a question: "If two rooms have the exact same floor space (area), do you think they will always need the same amount of skirting board (perimeter)?" This sets the stage for discovery.
Student Activity: Students define area and perimeter and state their formulas. Students calculate the area and perimeter of the sample rectangle drawn by the teacher. Students engage in thinking about the posed question, forming initial hypotheses.
Phase 2: Discovery Activity (20 minutes)
Teacher Activity: Divides the class into small groups (3-4 students per group). Distributes square grid papers (or actual square tiles/cut-outs if available) to each group. Instructs each group to create as many different rectangles as possible, each having a fixed area (e.g., 24 square units, 30 square units, or 36 square units, depending on class ability). Provides a table for students to record their findings: | Rectangle Name | Length (units) | Breadth (units) | Area (sq units) | Perimeter (units) | | :------------- | :------------- | :-------------- | :-------------- | :---------------- | | Rectangle 1 | | | | | | Rectangle 2 | | | | | | ... | | | | | Circulates among groups, guiding students, asking probing questions (e.g., "Are these rectangles truly different in shape?", "What do you notice about their areas?", "Now, calculate their perimeters."), and ensuring accurate calculations.
Student Activity: Students work collaboratively in groups to draw or construct different rectangles on grid paper or with tiles, ensuring each rectangle has the specified fixed area. For each unique rectangle formed, students identify its length and breadth. Students calculate the area and perimeter for each rectangle using the correct formulas. Students record their findings systematically in the provided table. Students observe and discuss the relationships between the areas and perimeters within their groups.
Phase 3: Class Discussion and Conclusion (15 minutes)
Teacher Activity: Calls upon groups to share their findings from the discovery activity. Facilitates a class discussion, asking questions like: "What did your group observe about the areas of the