Lesson Notes By Weeks and Term v3 - Primary 6
Plane Figures
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Plane Figures
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Subject: General Mathematics
Class: Primary 6
Term: 3rd Term
Week: 2
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 identify the basic properties of plane figures such as: rectangle and a square
Introduction to Plane Figures: A plane figure is a two-dimensional (2D) shape, meaning it has length and width but no depth. These figures can be drawn on a flat surface like a sheet of paper or a blackboard. Examples include circles, triangles, and quadrilaterals. For this lesson, the focus is on two specific quadrilaterals: the rectangle and the square. A. The Rectangle A rectangle is a quadrilateral, which means it is a polygon with four sides. It is characterized by specific properties that make it distinct.
Properties of a Rectangle: Number of Sides and Vertices: A rectangle has four straight sides and four vertices (corners). A vertex is the point where two sides meet.
Opposite Sides are Equal: The sides opposite each other are equal in length. This means if one pair of opposite sides measures 10 cm each, the other pair of opposite sides will have a different (or equal, in the case of a square) length, for example, 5 cm each.
Opposite Sides are Parallel: The opposite sides of a rectangle are parallel. Parallel lines are lines that never meet, no matter how far they are extended.
All Angles are Right Angles: Each of the four interior angles of a rectangle measures exactly 90 degrees (90°). These are called right angles.
Sum of Interior Angles: The sum of all four interior angles is 360° (90° + 90° + 90° + 90° = 360°).
Diagonals: A diagonal is a line segment connecting two non-adjacent vertices. In a rectangle, the two diagonals are equal in length and bisect each other (meaning they cut each other into two equal parts).
Example 1 (Nigerian Context): Consider a typical classroom blackboard or a school gate. The blackboard has four sides. The top side is equal in length to the bottom side. The left side is equal in length to the right side. All four corners are square, indicating 90-degree angles. Thus, the blackboard is a rectangle. B. The Square A square is a special type of rectangle because it possesses all the properties of a rectangle, but with an additional condition regarding its sides.
Properties of a Square: Number of Sides and Vertices: Like a rectangle, a square has four straight sides and four vertices (corners).
All Sides are Equal: All four sides of a square are equal in length. This is the key distinguishing property from a general rectangle.
Opposite Sides are Parallel: Similar to a rectangle, the opposite sides of a square are parallel.
All Angles are Right Angles: All four interior angles of a square are right angles, measuring exactly 90 degrees (90°).
Sum of Interior Angles: The sum of all four interior angles is 360° (90° + 90° + 90° + 90° = 360°).
Diagonals: The two diagonals of a square are equal in length, bisect each other, and intersect at a right angle (90°). They also bisect the vertex angles (meaning they cut the 90° vertex angles into two 45° angles).
Example 2 (Nigerian Context): Consider a floor tile commonly used in Nigerian homes or a small picture frame. The floor tile has four sides. If all four sides can be measured and found to be equal (e.g., all 30 cm long). All four corners are square (90-degree angles). Thus, the floor tile is a square.
Summary Comparison: | Property | Rectangle | Square | | :------------------------- | :---------------------------------------------- | :----------------------------------------------- | | Number of Sides | 4 | 4 | | Number of Vertices | 4 | 4 | | Opposite Sides Length | Equal | Equal (all sides are equal) | | All Sides Length | Not necessarily equal (only opposite are equal) | All sides are equal | | Opposite Sides Parallel| Yes | Yes | | All Angles | Right angles (90°) | Right angles (90°) | | Diagonals | Equal length, bisect each other | Equal length, bisect each other at 90°, bisect vertex angles | Materials: Real-life objects: rectangular exercise book, square floor tile, rectangular phone, square picture frame, rectangular door, window. Charts or flashcards with drawings of squares and rectangles, clearly labeled. Rulers, protractors (optional, for demonstration of 90-degree angles). Worksheets with diagrams. Marker and whiteboard/chalk and blackboard.
Teacher Activities: Introduction (10 minutes): Begin by displaying various everyday objects (e.g., a rectangular textbook, a square floor tile, a rectangular door). Ask students to identify the shapes of these objects. Facilitate a brief discussion to activate prior knowledge about "shapes." Introduce the term "plane figures" and state that the lesson will focus on two important ones: rectangles and squares. Explanation of Rectangle Properties (15 minutes): Draw a large rectangle on the board. Using a ruler, demonstrate how to measure and show that opposite sides are equal. Label sides clearly (e.g., AB = CD, AD = BC). Point to the vertices and explain they are corners where sides meet. Use a protractor (if available) to show that each angle is 90 degrees. Emphasize the term "right angle." Discuss that opposite sides are parallel, explaining what parallel means using an analogy (e.g., train tracks). Engage students by asking them to identify rectangular objects in the classroom (windows, desks, cupboard doors). Explanation of Square Properties (15 minutes): Draw a large square on the board. Demonstrate that all four sides are equal in length. Label sides clearly (e.g., AB = BC = CD = DA). Reinforce that it also has four right angles and four vertices. Explain that a square is a special type of rectangle because it has all the properties of a rectangle, plus the property of having all sides equal. Ask students to identify square objects in the classroom (floor tiles, some wall clocks).
Comparison and Contrast (10 minutes): Create a simple comparison table on the board, highlighting the similarities and differences between squares and rectangles based on the properties discussed (e.g., all sides equal vs. opposite sides equal). Facilitate a short question-and-answer session to check understanding and address misconceptions.
Student Activities: Observation and Identification: Students observe the real-life objects displayed by the teacher and identify their shapes as either rectangular or square.
Drawing: Students draw a square and a rectangle in their exercise books, labeling sides and indicating right angles.
Property Listing: Students, individually or in pairs, list three key properties for a rectangle and three for a square as they are discussed by the teacher.
Class Discussion: Students actively participate in discussions, answer questions, and point out properties of objects identified in the classroom.
Hands-on Exploration: Students use rulers to verify properties on physical objects (e.g., measuring sides of their textbooks, pencil cases).
Group Activity: In small groups, students are given different cut-out shapes (some rectangles, some squares) and asked to sort them and state why each is a rectangle or a square. The teacher guides students through these practice questions, providing support and clarifying concepts as needed.
Question 1: Look at the following shapes. Identify which one is a rectangle and which one is a square. (Imagine two simple drawings: one clearly a rectangle with unequal adjacent sides, one clearly a square with equal sides, both having right angles.)
Solution: Shape A (Rectangle): This is a rectangle because its opposite sides are equal in length, and all its angles are right angles. Its adjacent sides are not equal.
Shape B (Square): This is a square because all its four sides are equal in length, and all its angles are right angles.
Commentary: This question checks basic visual identification based on side lengths and angles.
Question 2: A gate for a compound in Port Harcourt has four sides. Its top side measures 2.5 meters, its bottom side measures 2.5 meters, its left side measures 1.8 meters, and its right side measures 1.8 meters. All its corners are straight. What plane figure describes the shape of this gate? State two properties of this shape.
Solution: Shape: The gate is a rectangle.
Properties: Opposite sides are equal in length (2.5m and 1.8m). All its angles are right angles (90 degrees).
Commentary: This question applies the properties to a real-world object described with specific measurements, reinforcing the definition of a rectangle.
Question 3: A tailor in Kano is cutting a piece of fabric for a handkerchief. He wants it to be a square. What two specific properties must this handkerchief have to be a perfect square?
Solution: All four sides must be equal in length. All four angles must be right angles (90 degrees).
Commentary: This question requires students to recall the defining properties of a square in a practical context.
Question 4: Explain how a square is similar to a rectangle and how it is different.
Solution: Similarities: Both a square and a rectangle have four sides, four vertices, and all their interior angles are right angles (90 degrees). Also, their opposite sides are parallel.
Differences: The main difference is that in a square, all four sides are equal in length, whereas in a rectangle, only the opposite sides are equal in length.
Commentary: This question assesses the understanding of both individual and comparative properties, crucial for deeper conceptual understanding.
Differentiation (for Diverse Learners): Visual Learners: Provide pre-drawn diagrams of squares and rectangles on charts. Use colourful cut-out shapes. Display real objects for identification.
Auditory Learners: Explain properties verbally, encouraging repetition and discussion. Use mnemonics or rhymes for remembering properties.
Kinesthetic Learners: Allow students to use rulers to measure sides of classroom objects. Have them draw shapes in sand or using geo-boards. Engage them in activities where they physically sort shape cards.
Group Work: Pair struggling learners with more capable peers for collaborative learning and peer tutoring during activities.
Remediation (for Struggling Learners): Simplified Focus: Focus only on 1-2 key properties at a time (e.g., "four sides" and "right angles" first, then "equal sides").
Manipulatives: Use physical cut-out squares and rectangles. Have them trace the shapes and physically count sides and vertices.
Repetitive Practice: Provide worksheets with fill-in-the-blanks or matching exercises for properties.
One-on-One Support: Offer direct, individualized instruction to clarify concepts and address specific difficulties.
Visual Aids: Continuously refer to large, clear drawings on the board or charts.
Extension (for High-Achieving Learners): Advanced Properties: Introduce additional properties such as symmetry (lines of symmetry, rotational symmetry) for squares and rectangles.
Drawing Challenges: Challenge them to draw squares and rectangles given specific side lengths or conditions using rulers and protractors accurately.
Problem-Solving: Present problems involving perimeter and area calculations for squares and rectangles (e.g., "A rectangular farmland is 20m long and 15m wide. What is its perimeter?").
Shape Comparison: Encourage them to research and compare squares and rectangles with other quadrilaterals like rhombuses, parallelograms, or trapeziums, identifying similarities and differences in their properties.
Real-World Design Project: Task them to design a floor plan for a small room using only square and rectangular tiles, explaining why these shapes are chosen for flooring.
Urban Planning and Architecture in Nigeria: Students can observe and discuss how land plots are often divided into rectangular or square shapes for housing, markets, and farming in Nigerian communities. Architects use these shapes for designing rooms, windows, and doors, considering dimensions and stability. Understanding properties helps in estimating material requirements for construction (e.g., how much wood for a door frame).
Textile and Craft Industry: Many traditional Nigerian fabrics (like Ankara or Adire) and modern textile designs incorporate geometric patterns based on squares and rectangles. Tailors and fashion designers use knowledge of these shapes to cut fabric precisely for clothes, tablecloths, or bags. Students can identify square or rectangular motifs in local clothing or woven mats.
Agriculture and Land Management: Farmers in Nigeria often create rectangular or square beds for planting different crops. This makes irrigation, weeding, and harvesting more organized and efficient. Students can relate the concept of equal sides or opposite sides to measuring and laying out farm plots for optimal yield. Knowledge of square and rectangle properties is fundamental for calculating areas of plots for farming.