Lesson Notes By Weeks and Term v3 - Primary 4
Area
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Area
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Subject: General Mathematics
Class: Primary 4
Term: 2nd Term
Week: 4
Theme: Mensuration And Geometry
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of the cassava farm is 10,000 square metres, which is equal to 1 hectare.
Concept 3: Solving Quantitative Aptitude Problems These problems often involve word descriptions and may require an extra step of thinking or unit conversion.
Worked Example 4: Quantitative Aptitude Problem Problem: A rectangular football field has a length of 110 metres and a breadth of 60 metres. If the school wants to fence the entire field, but only half the area needs to be re-grassed, what is the area that needs re-grassing?
Solution:
1. Identify the goal: Find half the area of the rectangular field.
2. Given: Length (L) = 110 m, Breadth (B) = 60 m.
3. First, find the total area of the field: A = L × B.
4. A = 110 m × 60 m = 6,600 m2.
5. Now, find half of this area for re-grassing: Area for re-grassing = Total Area / 2.
6. Area for re-grassing = 6,600 m2 / 2 = 3,300 m2. * Answer: The area that needs re-grassing is 3,300 square metres. (
Note: The information about fencing is a distractor for area calculation, but relevant for perimeter, which is a different topic).
Definition of Area: Area is the measure of the surface covered by a two-dimensional shape. It quantifies how much flat space a shape occupies. Area is always measured in "square units." Units of Area: The unit of area depends on the unit of length used. If length is in centimetres (cm), area is in square centimetres (cm2). If length is in metres (m), area is in square metres (m2). For very large areas, such as farmlands or estates, hectares (ha) are used. 1 hectare = 10,000 square metres (10,000 m2)
Area of a Rectangle: A rectangle is a four-sided shape with four right angles. Opposite sides are equal in length. The area of a rectangle is found by multiplying its length (L) by its breadth (B) (also known as width).
Formula: Area (A) = Length (L) × Breadth (B) Explanation and Worked
Examples: Concept 1: Finding Area using Unit Squares Before introducing the formula, it is beneficial for students to understand area as counting unit squares. Imagine a rectangle made up of small squares, each with a side length of 1 unit (e.g., 1 cm by 1 cm). If a rectangle is 3 cm long and 2 cm broad, it can be covered by 3 rows of 2 squares each. Total squares = 3 × 2 = 6 square units. This visually demonstrates why we multiply length by breadth.
Worked Example 1: Area of a small rectangular object Problem: A textbook cover has a length of 30 cm and a breadth of 20 cm. What is its area?
Solution:
1. Identify the shape: Rectangle.
2. Identify the given measurements: Length (L) = 30 cm, Breadth (B) = 20 cm.
3. Recall the formula for the area of a rectangle: A = L × B.
4. Substitute the values into the formula: A = 30 cm × 20 cm.
5. Perform the multiplication: A = 600 cm
2. Answer: The area of the textbook cover is 600 square centimetres.
Concept 2: Calculating Area of Larger Shapes (e.g., classroom floor, farmland) For larger areas, metres and square metres are more appropriate. For very large areas like farmlands, hectares are used.
Worked Example 2: Area of a classroom floor Problem: The floor of a Primary 4 classroom is rectangular, with a length of 9 metres and a breadth of 7 metres. Calculate the area of the classroom floor.
Solution:
1. Identify the shape: Rectangle (classroom floor).
2. Given measurements: Length (L) = 9 m, Breadth (B) = 7 m.
3. Formula: A = L × B.
4. Substitute values: A = 9 m × 7 m.
5. Calculate: A = 63 m
2. Answer: The area of the classroom floor is 63 square metres.
Worked Example 3: Area of a small farmland (introducing hectares)
Problem: A cassava farm is rectangular with a length of 200 metres and a breadth of 50 metres. a) Calculate the area of the farm in square metres. b) Convert the area to hectares.
Solution (a - Area in m2):
1. Shape: Rectangle (cassava farm).
2. Given: L = 200 m, B = 50 m.
3. Formula: A = L × B.
4. Substitute: A = 200 m × 50 m.
5. Calculate: A = 10,000 m
2. Solution (b - Conversion to hectares):
1. Recall the conversion: 1 hectare = 10,000 m2.
2. From part (a), the area is 10,000 m2.
3. To convert m2 to hectares, divide by 10,000: Area in hectares = 10,000 m2 / 10,000 = 1 hectare.
Answer: The area of the cassava farm is 10,000 square metres, which is equal to 1 hectare.
Concept 3: Solving Quantitative Aptitude Problems These problems often involve word descriptions and may require an extra step of thinking or unit conversion.
Worked Example 4: Quantitative Aptitude Problem Problem: A rectangular football field has a length of 110 metres and a breadth of 60 metres. If the school wants to fence the entire field, but only half the area needs to be re-grassed, what is the area that needs re-grassing? * Solution:
1. Identify the goal: Introduction (10 minutes)
Teacher Activity: Begin by showing students various flat objects in the classroom (e.g., a book cover, a mat, a piece of paper, the tabletop). Ask students what they observe about these surfaces. Introduce the concept of "how much space" these surfaces cover. Introduce the term "Area." Student Activity: Students identify flat surfaces in the classroom. They can compare the sizes of different surfaces by visual estimation, discussing which surface covers more space.
Activity 1: Counting Unit Squares (15 minutes)
Teacher Activity: Provide students with grid paper and instruct them to draw various rectangles (e.g., 4 units by 3 units, 5 units by 2 units). Guide them to count the total number of small squares inside each rectangle. Introduce the idea that each small square is a "unit square." Student Activity: Students draw rectangles on grid paper and count the squares within. They will record the length, breadth, and total squares for each rectangle, noticing the pattern (Length × Breadth = Total Squares).
Activity 2: Discovering the Formula (15 minutes)
Teacher Activity: After Activity 1, lead a discussion. Ask students if they noticed a quicker way to find the total number of squares without counting each one individually. Guide them to connect the "total squares" to multiplying the "length" (number of squares along one side) by the "breadth" (number of squares along the adjacent side).
Introduce the formula: Area = Length × Breadth. Emphasize the units (cm2, m2).
Student Activity: Students articulate their observations and deduce the formula. They will practice applying the formula to their drawn rectangles, confirming their earlier counts.
Activity 3: Measuring and Calculating Classroom Objects (20 minutes)
Teacher Activity: Divide the class into small groups. Provide each group with a measuring tape or ruler. Assign each group a rectangular object in the classroom to measure (e.g., a desk surface, a chalkboard, a section of the wall, the classroom door). Instruct them to measure the length and breadth to the nearest centimetre or metre and then calculate the area.
Student Activity: In groups, students measure their assigned objects. They record the length and breadth, then apply the A = L × B formula to calculate the area. They write down their findings and share with the class. The teacher circulates to offer assistance and check measurements/calculations.
Activity 4: Understanding Large Areas and Hectares (15 minutes)
Teacher Activity: Discuss scenarios where areas are very large, such as a school compound or a farmer's plot of land in Nigeria. Explain that measuring these in cm2 would be impractical. Introduce metres and square metres (m2) as more suitable units. For even larger areas, introduce the hectare (ha) and explain the conversion: 1 hectare = 10,000 m
2. Provide a hypothetical example of a local farmer's field and calculate its area in m2 and then hectares.
Student Activity: Students listen, ask questions, and practice a simple conversion (e.g., "If a field is 20,000 m2, how many hectares is that?"). They discuss the practicality of using different units for different sizes of land. Conclusion/Review (5 minutes)
Teacher Activity: Recap the definition of area, the formula for a rectangle, and the various units (cm2, m2, hectares). Emphasize the importance of writing the correct units with the answer.
Student Activity: Students verbally reiterate key concepts and ask any lingering questions. The teacher should work through these problems step-by-step on the board, encouraging student participation.
Question 1: A rectangular dining table in a Nigerian home has a length of 150 cm and a breadth of 90 cm. What is the area of the tabletop?
Solution: Identify the shape and measurements: The shape is a rectangle. Length (L) = 150 cm, Breadth (B) = 90 cm.
Recall the formula: Area (A) = Length × Breadth.
Substitute values: A = 150 cm × 90 cm.
Calculate: 150 x 90 000 (150 x 0) 13500 (150 x 9, shifted one place) 13500 State the answer with units: The area of the tabletop is 13,500 cm
2. Commentary: This reinforces the basic application of the formula with two-digit multiplication, using a common household item.
Question 2: A rectangular school garden where students plant vegetables is 25 metres long and 12 metres wide. Calculate the area of the garden.
Solution: Identify the shape and measurements: Rectangle. Length (L) = 25 m, Breadth (B) = 12 m.
Formula: A = L ×
B. Substitute: A = 25 m × 12 m.
Calculate: 25 x 12 50 (25 x 2) 250 (25 x 10) 300 Answer: The area of the school garden is 300 m
2. Commentary: This involves slightly larger numbers and introduces square metres, relevant for school grounds.
Question 3: A farmer in Kaduna State has a rectangular plot of land measuring 300 metres in length and 150 metres in breadth. a) What is the area of the plot in square metres? b) How many hectares is this plot?
Solution: a)
Area in square metres: Shape and measurements: Rectangle. L = 300 m, B = 150 m.
Formula: A = L ×
B. Substitute: A = 300 m × 150 m.
Calculate: 300 × 150 = 45,
0
0
0. Answer: The area of the plot is 45,000 m2. b)
Area in hectares: Recall conversion: 1 hectare = 10,000 m
2. Convert: To convert m2 to hectares, divide the area in m2 by 10,
0
0
0. Calculation: 45,000 m2 / 10,000 m2/hectare = 4.5 hectares.
Answer: The plot is 4.5 hectares.
Commentary: This problem directly addresses performance objective 2 and evaluation guide 2, linking area to large-scale land measurement and introducing hectares, common in agricultural contexts.
Home Improvement and Construction: When a family wants to tile the floor of their living room or paint a wall, they need to calculate the area to know how many tiles or how much paint to buy. For instance, knowing the area of a bedroom floor helps determine the cost of carpeting or the number of floor mats needed. This relates directly to the Nigerian context of building and furnishing homes.
Agriculture and Land Management: Farmers frequently need to know the area of their farmlands. This knowledge helps them estimate crop yields, calculate the amount of fertilizer or seeds required, or determine the fair price for renting or selling a plot of land. For example, if a farmer grows maize, knowing the area of his farm in hectares helps him plan his planting schedule and budget for resources.
Urban Planning and Development: Government agencies and land developers in Nigeria use area calculations extensively. They calculate the area of plots for housing estates, markets, schools, or roads. Understanding large areas in square meters and hectares is fundamental for planning the layout of new settlements or commercial centres.