Plane Figures, 2D Shapes, Triangles, Irregular Polygons and Properties for Primary 6

Class: Primary 6
Term: 3rd Term
Week: 4
Age: 11 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Geometry and Measurement
Previous Lesson: Types, Measuring with Protractor and Straight, Line Angles.
Topic: PLANE FIGURES
Subject Matter: Identifying 2-dimensional shapes in the environment, properties of basic 2D shapes including rectangle circle and quadrilaterals, properties of isosceles equilateral right angle and scalene triangles, drawing irregular polygons and stating properties, quantitative aptitude on polygons.

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

• Identify 2-dimensional (2D) shapes found in their environment.
• State the properties of basic 2D shapes such as rectangles, circles, and quadrilaterals.
• Describe the properties of isosceles, equilateral, right-angled, and scalene triangles.
• Explain the characteristics of irregular polygons.

Affective Domain:

• Appreciate the presence and importance of geometric shapes in everyday life.
• Show interest in learning about different types of plane figures.
• Demonstrate a willingness to solve problems related to 2D shapes and polygons.

Psychomotor Domain:

• Draw examples of 2D shapes.
• Draw and label different types of triangles based on their properties.
• Sketch irregular polygons.
• Solve quantitative aptitude problems involving perimeter and area of simple polygons.

Social Domain:

• Participate actively in class discussions about plane figures.
• Collaborate with peers to identify shapes and solve problems.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum (Primary Mathematics)
• State Unified Scheme of Work (Primary 6 Mathematics)
• New Concept Mathematics for Primary Schools Book 6
• Pupils’ Mathematics Textbook for Primary 6
• https://www.mathsisfun.com/geometry/plane-shapes.html
• https://www.splashlearn.com/math-vocabulary/geometry/plane-shapes

Instructional Materials

The teacher will teach this lesson with the aid of:

• Charts showing various 2D shapes (rectangle, circle, triangle, quadrilaterals)
• Geometric models of 2D shapes
• Ruler, pencil, protractor
• Whiteboard and markers
• Textbook, workbook, formula book

Rationale for the Lesson

This lesson helps pupils understand the basic shapes they see daily, from windows to coins. Understanding plane figures is important for solving practical problems and forms a foundation for more advanced geometry in the future.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic shapes like squares, rectangles, and circles, and can count sides and corners of simple figures.

Lesson Content/Board Summary

PLANE FIGURES

1. Identification of 2-Dimensional (2D) Shapes

2-Dimensional (2D) shapes are flat figures that have only two dimensions: length and width. They do not have thickness.

Examples of 2D shapes found in the environment include:

• The face of a clock (circle)
• A window pane (rectangle or square)
• A school chalkboard (rectangle)
• A slice of pizza (triangle)
• A football field (rectangle)

2. Properties of Basic 2D Shapes

The properties describe the characteristics of each shape, such as the number of sides, angles, and whether sides are equal.

• Rectangle:
  • It has 4 sides and 4 vertices (corners).
  • Opposite sides are equal in length.
  • All 4 interior angles are right angles (90 degrees).
• Circle:
  • It is a perfectly round shape with no straight sides or corners.
  • All points on its boundary are equidistant from its center.
  • It has a radius (distance from center to boundary) and a diameter (distance across the circle through the center).
• Quadrilaterals:
  • A quadrilateral is any polygon with 4 sides, 4 vertices, and 4 interior angles.
  • Examples include squares, rectangles, rhombuses, parallelograms, trapeziums, and kites.
  • The sum of the interior angles of any quadrilateral is 360 degrees.

3. Properties of Triangles

A triangle is a polygon with three sides, three vertices, and three interior angles. The sum of the interior angles of any triangle is 180 degrees.

Triangles can be classified based on their sides or angles:

• Isosceles Triangle:
  • It has two sides of equal length.
  • The angles opposite the equal sides are also equal.
• Equilateral Triangle:
  • It has three sides of equal length.
  • All three interior angles are equal (each 60 degrees).
• Scalene Triangle:
  • It has no sides of equal length.
  • All three interior angles are different.
• Right-angled Triangle:
  • It has one interior angle that measures exactly 90 degrees.
  • The side opposite the right angle is called the hypotenuse.

4. Irregular Polygons

A polygon is a closed 2D shape made up of straight line segments. A regular polygon has all sides and all angles equal (e.g., square, equilateral triangle).

An irregular polygon is a polygon that does not have all sides equal in length and/or all angles equal in measure.

Properties of irregular polygons:

• Sides are of different lengths.
• Interior angles are of different measures.
• They do not have rotational symmetry like regular polygons (unless specific cases).

Example: A shape with 5 sides of varying lengths and 5 angles of varying measures is an irregular pentagon.

5. Quantitative Aptitude on Polygons

Quantitative aptitude questions on polygons often involve calculating perimeter, area, or identifying properties based on given information.

NOTE: Remember that perimeter is the total distance around the outside of a shape, and area is the amount of surface a shape covers.

Example 1: A rectangular garden has a length of 10 meters and a width of 6 meters. Calculate its perimeter.

Solution:

Step 1: Write down the formula for the perimeter of a rectangle.

Perimeter = 2 × (Length + Width)

Step 2: Substitute the given values into the formula.

Perimeter = 2 × (10 m + 6 m)

Step 3: Perform the addition inside the bracket.

Perimeter = 2 × (16 m)

Step 4: Perform the multiplication.

Perimeter = 32 m

Example 2: The perimeter of a square plot of land is 48 meters. Find the length of one side of the plot.

Solution:

Step 1: Recall the property of a square.

A square has 4 equal sides.

Step 2: Write down the formula for the perimeter of a square.

Perimeter = 4 × Side

Step 3: Substitute the given perimeter into the formula.

48 m = 4 × Side

Step 4: To find the Side, divide both sides of the equation by 4.

Side = 48 m / 4

Side = 12 m

How to solve for other values:

• To find a side if the perimeter and other sides are given:

  Subtract the known side lengths from the total perimeter and then divide by the number of remaining equal sides (e.g., for a rectangle, if perimeter and length are known, find width by: (Perimeter/2) – Length).

• To find missing angles:

  For a triangle, subtract the sum of known angles from 180 degrees. For a quadrilateral, subtract the sum of known angles from 360 degrees.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Set Induction

Teacher’s Activity: The teacher greets the pupils and asks them to look around the classroom and identify any flat shapes they can see (e.g., whiteboard, door, window, book cover). The teacher then introduces the topic “Plane Figures” and explains that these are 2-dimensional shapes.

Pupils’ Activity: Pupils respond by identifying various flat shapes in the classroom. They listen attentively to the teacher’s introduction.

Learning Point: Pupils recall and identify common 2D shapes in their immediate environment.

Step 2: Presentation of 2D Shapes

Time: 8 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher uses charts and real-life examples to introduce and display various 2D shapes such as rectangles, circles, and different types of triangles. The teacher explains what a 2D shape is (flat, length, width). Pupils are encouraged to mention other examples of 2D shapes they know.

Pupils’ Activity: Pupils observe the charts and examples, listen to the explanations, and mention other 2D shapes they are familiar with.

Learning Point: Pupils understand the concept of 2D shapes and identify several examples.

Step 3: Discussion of Properties of Basic 2D Shapes

Time: 8 minutes

Teaching Skill: Questioning/Elaboration

Teacher’s Activity: The teacher guides pupils to discuss the properties of basic 2D shapes like rectangles, circles, and quadrilaterals. For each shape, the teacher asks questions such as “How many sides does a rectangle have?”, “Are its sides equal?”, “What is special about a circle?”. The teacher clarifies and summarizes the properties on the board.

Pupils’ Activity: Pupils actively participate by answering questions and contributing to the discussion about the properties of each shape.

Learning Point: Pupils can state the properties of rectangles, circles, and general quadrilaterals.

Step 4: Exploring Properties of Triangles

Time: 8 minutes

Teaching Skill: Explanation/Drawing

Teacher’s Activity: The teacher introduces the different types of triangles: isosceles, equilateral, right-angled, and scalene. For each type, the teacher explains its definition and properties, drawing examples on the board. Pupils are guided to observe the differences in sides and angles for each triangle type.

Pupils’ Activity: Pupils listen to the explanations, observe the drawings, and describe the properties of each type of triangle.

Learning Point: Pupils identify and describe the properties of isosceles, equilateral, right-angled, and scalene triangles.

Step 5: Drawing and Describing Irregular Polygons

Time: 6 minutes

Teaching Skill: Demonstration/Guided Practice

Teacher’s Activity: The teacher explains what an irregular polygon is, contrasting it with regular polygons. The teacher draws an example of an irregular polygon on the board and points out its varying side lengths and angles. Pupils are then asked to attempt drawing their own irregular polygons in their notebooks.

Pupils’ Activity: Pupils listen to the explanation, observe the teacher’s drawing, and then draw their own irregular polygons, stating some properties.

Learning Point: Pupils understand what an irregular polygon is and can draw one and describe its basic properties.

Step 6: Quantitative Aptitude Practice

Time: 5 minutes

Teaching Skill: Problem-Solving

Teacher’s Activity: The teacher presents simple quantitative aptitude problems related to the perimeter of polygons, similar to the examples in the board summary. The teacher guides pupils through solving one problem and then allows them to try another independently or in pairs.

Pupils’ Activity: Pupils work on the quantitative aptitude problems, applying the formulas and properties learned. They ask questions where necessary.

Learning Point: Pupils apply their knowledge of 2D shapes to solve simple quantitative problems.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. What is a 2-dimensional shape?
2. Mention two 2D shapes you can find in your environment.
3. State two properties of a rectangle.
4. Describe an equilateral triangle.
5. Draw an irregular polygon and state one property.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 3 minutes

Teaching Skill: Summarization

Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of understanding 2D shapes and their properties. The teacher assigns homework, which includes drawing different types of triangles and identifying 2D shapes at home.

Pupils’ Activity: Pupils listen to the summary and copy down the homework assignment.

Learning Point: Pupils consolidate their learning and prepare for further practice.

Home Task: Solve three new exercises on PLANE FIGURES. Show each step and check each answer.

Lesson Keywords

• 2D Shapes – Flat figures with length and width, but no thickness.
• Rectangle – A quadrilateral with four right angles and opposite sides equal.
• Circle – A round 2D shape with all points on its boundary equidistant from its center.
• Quadrilateral – A polygon with four sides.
• Triangle – A polygon with three sides.
• Isosceles – A triangle with two equal sides and two equal angles.
• Equilateral – A triangle with three equal sides and three equal angles.
• Scalene – A triangle with no equal sides and no equal angles.
• Right-angled – A triangle containing one 90-degree angle.
• Polygon – A closed 2D shape made of straight line segments.
• Irregular Polygon – A polygon whose sides and angles are not all equal.
• Perimeter – The total distance around the outside of a shape.

Differentiation

For pupils who grasp concepts quickly, the teacher can provide more complex quantitative aptitude problems involving finding the area of simple shapes or combining shapes. For pupils needing more support, the teacher will provide more one-on-one guidance, use physical models for identification, and simplify drawing tasks.

Note for teachers using this lesson plan

Ensure to have a variety of visual aids and real-life examples of 2D shapes to make the lesson engaging and relatable. Encourage pupils to draw and sketch shapes frequently to reinforce their understanding of properties. Emphasize the practical application of understanding shapes in daily life.