Lesson Notes By Weeks and Term v3 - Primary 5
Length
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Length
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Subject: General Mathematics
Class: Primary 5
Term: 3rd Term
Week: 6
Theme: Mensuration And Geometry
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
Pupils should be able to: find the perimeter of regular shape such as square rectangle, trapezium and polygon; find circumference of a circle when the radius is given. Establish the relationship betweenc and Πdand find the circumference
2. 1.
Length: Length refers to the measurement or extent of something from end to end. In the context of shapes, it often refers to the sides of a polygon or the radius/diameter of a circle. 2.
2. Perimeter of Regular Shapes: The perimeter of a two-dimensional shape is the total distance around its boundary. It is calculated by adding the lengths of all its sides.
Square: A four-sided flat shape with all sides equal in length and all interior angles being 90 degrees.
Formula: Perimeter (P) = side + side + side + side = 4 × side (or 4s)
Explanation: Since all four sides of a square are equal, one can simply multiply the length of one side by 4 to find the perimeter.
Example 1: A square compound wall has a side length of 15 metres. Find the perimeter.
Solution: P = 4 × 15 m = 60 metres.
Rectangle: A four-sided flat shape where opposite sides are equal in length and all interior angles are 90 degrees. It has a length (l) and a width (w) or breadth (b).
Formula: Perimeter (P) = length + width + length + width = 2 × (length + width) or 2(l + w)
Explanation: A rectangle has two equal lengths and two equal widths.
Therefore, adding one length and one width, then multiplying the sum by 2, gives the perimeter.
Example 2: A rectangular football pitch is 100 metres long and 60 metres wide. What is its perimeter?
Solution: P = 2 × (100 m + 60 m) = 2 × (160 m) = 320 metres.
Trapezium (or Trapezoid): A four-sided flat shape with at least one pair of parallel sides. The sides are generally of different lengths.
Method: The perimeter of a trapezium is found by summing the lengths of all its four sides.
Formula: Perimeter (P) = a + b + c + d (where a, b, c, d are the lengths of the four sides).
Explanation: Unlike squares and rectangles, trapeziums do not have a simple multiplication formula as their sides are typically not all equal or parallel in pairs (except for one pair). Students must add all four side lengths.
Example 3: A piece of land shaped like a trapezium has sides measuring 12 m, 8 m, 10 m, and 7 m. Calculate its perimeter.
Solution: P = 12 m + 8 m + 10 m + 7 m = 37 metres.
Regular Polygon: A polygon (a closed shape with straight sides) where all sides are of equal length and all interior angles are equal. Examples include equilateral triangles (3 sides), squares (4 sides), regular pentagons (5 sides), regular hexagons (6 sides), etc.
Method: The perimeter of a regular polygon is found by multiplying the number of sides (n) by the length of one side (s).
Formula: Perimeter (P) = n × s Explanation: Since all sides are equal, counting the number of sides and multiplying by the length of one side is an efficient way to find the perimeter.
Example 4: A regular hexagonal table mat has a side length of 20 cm. Find its perimeter.
Solution: A hexagon has 6 sides. P = 6 × 20 cm = 120 cm. 2.
3. Circumference of a Circle: The circumference of a circle is the total distance around its boundary (its perimeter).
Parts of a Circle: Circle: A round shape where all points on the boundary are equidistant from a central point.
Radius (r): The distance from the centre of the circle to any point on its circumference.
Diameter (d): The distance across the circle passing through its centre. It is twice the radius (d = 2r). Pi ($\pi$): A mathematical constant that represents the ratio of a circle's circumference to its diameter. It is an irrational number, approximately equal to 3.14159... For practical calculations in primary school, $\pi$ is usually approximated as $\frac{22}{7}$ or 3.
1
4. Relationship between Circumference (C), Pi ($\pi$), and Diameter (d): * It has been observed that for (r): The distance from the centre of the circle to any point on its circumference.
Diameter (d): The distance across the circle passing through its centre. It is twice the radius (d = 2r). Pi ($\pi$): A mathematical constant that represents the ratio of a circle's circumference to its diameter. It is an irrational number, approximately equal to 3.14159... For practical calculations in primary school, $\pi$ is usually approximated as $\frac{22}{7}$ or 3.
1
4. Relationship between Circumference (C), Pi ($\pi$), and Diameter (d): It has been observed that for any circle, if one divides its circumference by its diameter, the result is always approximately the same value, which is $\pi$.
Therefore, $\frac{C}{d} = \pi$, which can be rearranged to: C = $\pi$d Calculating Circumference when Radius (r) is given: Since d = 2r, we can substitute '2r' for 'd' in the formula C = $\pi$d.
This gives: C = $\pi$(2r) or C = 2$\pi$r Explanation: When the radius is given, first double it to get the diameter, then multiply by $\pi$. Or, multiply 2 by $\pi$ and then by the radius.
Example 5 (using radius): A circular 'akara' frying pan has a radius of 14 cm. Calculate its circumference. (Use $\pi = \frac{22}{7}$)
Solution: Given radius (r) = 14 cm C = 2$\pi$r C = 2 × $\frac{22}{7}$ × 14 cm C = 2 × 22 × (14/7) cm C = 2 × 22 × 2 cm C = 88 cm Calculating Circumference when Diameter (d) is given: Use the direct relationship: C = $\pi$d Explanation: When the diameter is given, simply multiply it by the value of $\pi$.
Example 6 (using diameter): A circular flower bed has a diameter of 7 metres. Find its circumference. (Use $\pi = \frac{22}{7}$)
Solution:** Given diameter (d) = 7 m C = $\pi$d C = $\frac{22}{7}$ × 7 m C = 22 m --- 3.
1. Introduction (10 minutes)
Teacher Activity: Begin by asking students to recall what "length" means and how they measure it (e.g., using a ruler, tape measure). Display various 2D shapes (e.g., a square exercise book, a rectangular classroom desk, a circular plate). Ask students how they would find the "distance around" each of these shapes. Introduce the term "perimeter" for shapes with straight sides and "circumference" for circles. Review basic shapes like squares and rectangles and their properties (equal sides, parallel sides).
Student Activity: Students identify measuring tools and discuss how to measure lengths. Students attempt to explain how to find the "distance around" the displayed objects. Students participate in a brief recall of properties of squares and rectangles. 3.
2. Lesson Development (40 minutes)
Phase 1: Perimeter of Regular Shapes (20 minutes)
Teacher Activity: Square and Rectangle: Draw a square on the board, label its sides. Ask students to deduce the perimeter formula. Repeat for a rectangle. Provide examples relevant to Nigerian contexts (e.g., a square farm plot, a rectangular classroom floor). Guide students through step-by-step calculations. Use actual classroom objects (e.g., a textbook, the classroom board) for students to measure and calculate their perimeters.
Trapezium: Draw a trapezium on the board. Explain that its sides are usually of different lengths, but it has one pair of parallel sides. Emphasize that the perimeter is simply the sum of all its four sides. Provide an example, e.g., an irregular plot of land.
Regular Polygon: Draw a regular pentagon or hexagon. Explain that "regular" means all sides are equal. Guide students to derive the formula P = n × s. Give an example (e.g., a regular hexagonal stool top).
Student Activity: Students copy definitions and formulas. Students work in pairs to measure real objects in the classroom (e.g., a window frame, a book cover) and calculate their perimeters using the correct formulas. Students solve given examples on the board, explaining their reasoning. Students draw simple regular polygons and calculate their perimeters.
Phase 2: Circumference of a Circle (20 minutes)
Teacher Activity: Introduction to Circle Parts: Draw a large circle on the board. Use a circular object (e.g., a plate, a wheel) to demonstrate. Clearly define and label the centre, radius (r), and diameter (d). Explain the relationship d = 2r. Explain that the distance around a circle is called the circumference. Introducing Pi ($\pi$): Explain $\pi$ as a special number, approximately 3.14 or $\frac{22}{7}$. Explain that it's a constant ratio for all circles.
Conduct a simple experiment: Use a string to measure the circumference of a circular object (e.g., a plate, a bucket lid) and its diameter. Ask students to divide the circumference by the diameter. Students will observe the result is always close to 3.14 or $\frac{22}{7}$.
Formulas for Circumference: Derive C = $\pi$d from the ratio concept. Derive C = 2$\pi$r by substituting d = 2r. Emphasize when to use $\frac{22}{7}$ (when radius/diameter is a multiple of 7) and when to use 3.14 (for other numbers or when specified). Work through Example 5 and 6, showing detailed steps.
Student Activity: Students identify and label parts of a circle from a diagram. Students actively participate in the string experiment, measuring and calculating the ratio C/d for different circular objects. Students copy the formulas for circumference and work through the examples with the teacher, asking questions for clarification. Students practice substituting values into the formulas to solve simple problems. 3.
3. Conclusion (10 minutes)
Teacher Activity: Recap all the formulas learned for perimeter of squares, rectangles, trapeziums, regular polygons, and circumference of circles. Ask probing questions to check understanding (e.g., "When would you use the formula P = 4s?", "What is the relationship between radius and diameter?", "What does $\pi$ represent?"). Assign homework.
Student Activity: Students summarize the key formulas. Students answer oral questions, demonstrating their understanding. * Students copy down the homework Students practice substituting values into the formulas to solve simple problems. 3.
3. Conclusion (10 minutes)
Teacher Activity: Recap all the formulas learned for perimeter of squares, rectangles, trapeziums, regular polygons, and circumference of circles. Ask probing questions to check understanding (e.g., "When would you use the formula P = 4s?", "What is the relationship between radius and diameter?", "What does $\pi$ represent?"). Assign homework.
Student Activity: Students summarize the key formulas. Students answer oral questions, demonstrating their understanding. * Students copy down the homework assignment. ---
Land Surveying and Fencing in Rural Areas: Farmers in Nigeria often need to fence their farm plots to protect crops from animals. Knowledge of perimeter helps them calculate the exact length of barbed wire or mesh needed, preventing waste and ensuring sufficient material. For irregularly shaped plots, they would measure each side and sum them up.
Example: A community leader wants to fence a new village playground which is a rectangle measuring 50m by 30m. Calculating the perimeter (2 (50+30) = 160m) helps in budgeting for the fence materials.
Building and Construction Industry: Builders use perimeter calculations to determine the amount of foundation work needed for a house, the length of skirting boards for rooms, or the boundary walls for a building site.
Example: A carpenter needs to put a wooden trim around a regular octagonal window frame, where each side is 0.5m. The perimeter (8 0.5m = 4m) tells him how much trim to cut. Tailoring, Fashion and Design: Tailors and fashion designers frequently use perimeter and circumference to measure fabric edges for sewing, adding lace, or creating patterns. For example, determining the length of a ribbon needed to go around the brim of a circular hat, or the hem of a rectangular skirt.
Example: A seamstress is making a circular 'gele' (head tie) and needs to add a fancy trim around its edge. If the gele has a diameter of 0.8 meters, calculating its circumference (using C = $\pi$d) helps her know the exact length of trim required. ---