Class: Junior Secondary School 1 (JSS 1 / JS1)
Term: 3rd Term
Week: 7
Age: 12 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Properties of Angles, Angles on a Straight Line.
Topic: SUM OF ANGLES IN A TRIANGLE
Subject Matter: Identification of types of triangles: Finding the sum of angles in a triangle

Specific Objectives

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

Cognitive Domain:

Define a triangle and identify its basic properties.
State the different types of triangles based on their sides and angles.
Recall that the sum of angles in any triangle is 180 degrees.

Affective Domain:

Appreciate the importance of understanding triangle properties in geometry.
Show enthusiasm in solving problems involving angles in a triangle.
Demonstrate carefulness when measuring and calculating angles.

Psychomotor Domain:

Draw and label different types of triangles accurately.
Calculate missing angles in various types of triangles using the sum of angles property.
Use a protractor and ruler to measure angles in a triangle.

Collaborate with peers to solve geometrical problems related to triangles.
Participate actively in classroom discussions regarding triangle properties.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Junior Secondary School (JSS 1)
State Unified Scheme of Work
New General Mathematics for Junior Secondary Schools 1

Instructional Materials

The teacher will teach this lesson with the aid of:

Whiteboard and markers
Protractor and ruler
Pre-drawn or cut-out cardboard triangles of different types
Worksheets with practice problems

Rationale for the Lesson

This lesson helps pupils understand the fundamental properties of triangles, which are essential building blocks in geometry. Knowing how to identify different types of triangles and calculate their angles provides a foundation for solving more complex geometric problems and has practical applications in fields like construction and design.

Prerequisite/Previous Knowledge

Pupils are expected to have prior knowledge of basic plane shapes, types of angles (acute, obtuse, right angle), and how to use a protractor to measure angles.

Lesson Content/Board Summary

SUM OF ANGLES IN A TRIANGLE

1. Definition of a Triangle

A triangle is a plane figure with three straight sides and three angles. It is the simplest polygon. The sum of the interior angles of any triangle is always 180 degrees.

2. Types of Triangles

Triangles can be classified based on the length of their sides or the size of their angles.

A. Classification based on Sides:

Equilateral Triangle: All three sides are equal in length, and all three angles are equal (each 60 degrees).
Isosceles Triangle: Two sides are equal in length, and the angles opposite these equal sides are also equal.
Scalene Triangle: All three sides are of different lengths, and all three angles are different.

B. Classification based on Angles:

Right-angled Triangle: One of its angles is exactly 90 degrees (a right angle).
Acute-angled Triangle: All three angles are acute (less than 90 degrees).
Obtuse-angled Triangle: One of its angles is obtuse (greater than 90 degrees but less than 180 degrees).

3. Sum of Angles in a Triangle

The sum of the interior angles of any triangle is always 180 degrees. If the angles of a triangle are A, B, and C, then A + B + C = 180°.

Worked Examples:

Example 1: Find the missing angle x in the triangle below if two angles are 65° and 75°.

Solution:
Step 1: Recall the sum of angles in a triangle.
Sum of angles = 180°

Step 2: Add the given angles.
65° + 75° = 140°

Step 3: Subtract the sum from 180° to find the missing angle.
x = 180° – 140°
x = 40°

Therefore, the missing angle is 40°.

Example 2: In an isosceles triangle PQR, side PQ = side PR. If angle P = 50°, find angles Q and R.

Solution:
Step 1: State the property of an isosceles triangle.
Since PQ = PR, the angles opposite these sides are equal. So, Angle Q = Angle R.

Step 2: Use the sum of angles in a triangle.
Angle P + Angle Q + Angle R = 180°
50° + Q + R = 180°

Step 3: Substitute Q for R (since Q=R) and solve for Q.
50° + Q + Q = 180°
50° + 2Q = 180°

Step 4: Isolate 2Q.
2Q = 180° – 50°
2Q = 130°

Step 5: Solve for Q.
Q = 130° / 2
Q = 65°

Step 6: State the values of Q and R.
Since Q = R, then Angle Q = 65° and Angle R = 65°.

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 name some plane shapes they know. The teacher then specifically asks them to identify a shape with three sides.
Pupils’ Activity: Pupils respond by naming shapes like square, circle, rectangle, and then identify a triangle as a three-sided shape.
Learning Point: Pupils recall prior knowledge of basic shapes, leading to the introduction of triangles.

Step 2: Definition and Properties of a Triangle

Time: 5 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines a triangle and states its basic properties (three sides, three angles, sum of angles is 180 degrees) while writing on the board.
Pupils’ Activity: Pupils listen attentively, copy notes from the board, and ask questions for clarification.
Learning Point: Pupils learn the formal definition and fundamental properties of a triangle.

Step 3: Identification of Types of Triangles

Time: 10 minutes
Teaching Skill: Demonstration/Categorization
Teacher’s Activity: The teacher uses cut-out triangles to demonstrate and explain the different types of triangles based on sides (equilateral, isosceles, scalene) and angles (right-angled, acute-angled, obtuse-angled). The teacher ensures pupils understand the distinguishing features of each type.
Pupils’ Activity: Pupils observe the cut-out triangles, participate in identifying types, and ask questions. They copy the classifications into their notes.
Learning Point: Pupils can identify and differentiate between various types of triangles.

Step 4: Demonstrating the Sum of Angles in a Triangle

Time: 10 minutes
Teaching Skill: Demonstration/Discovery
Teacher’s Activity: The teacher takes a pre-cut paper triangle, tears off its three angles, and arranges them on a straight line to show that they form a straight angle (180 degrees). The teacher repeats this with another type of triangle to reinforce the concept.
Pupils’ Activity: Pupils observe the demonstration and may be asked to try it with their own paper triangles. They confirm that the sum of the angles equals 180 degrees.
Learning Point: Pupils visually confirm that the sum of angles in any triangle is 180 degrees.

Step 5: Worked Example 1

Time: 5 minutes
Teaching Skill: Problem Solving
Teacher’s Activity: The teacher writes Example 1 from the board summary on the board and guides pupils through the step-by-step solution, emphasizing how to apply the 180-degree rule to find a missing angle.
Pupils’ Activity: Pupils follow along with the teacher, ask questions if confused, and copy the example into their notebooks.
Learning Point: Pupils learn how to calculate a missing angle when two angles are given.

Step 6: Worked Example 2

Time: 5 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher presents Example 2 (isosceles triangle problem) and asks pupils to contribute ideas on how to solve it, guiding them towards the correct steps. The teacher then completes the solution on the board.
Pupils’ Activity: Pupils actively participate in suggesting steps, discussing the problem, and then copying the solution into their notes.
Learning Point: Pupils practice applying the sum of angles rule in a slightly more complex scenario involving isosceles triangles.

Step 7: Evaluation/Review

Time: 5 minutes
Teaching Skill: Questioning/Assessment
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

What is the sum of angles in any triangle?
Mention two types of triangles based on their sides.
Mention two types of triangles based on their angles.
If two angles of a triangle are 50° and 60°, what is the third angle?

Pupils’ Activity: Pupils answer orally and in writing.
Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 5 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the definition of a triangle, its types, and the rule for the sum of its interior angles. The teacher then gives homework assignments.
Pupils’ Activity: Pupils listen to the summary and copy down the homework.
Learning Point: Pupils consolidate their learning and prepare for independent practice.

Home Task: Solve three new exercises on SUM OF ANGLES IN A TRIANGLE. Show each step and check each answer.

Lesson Keywords

Triangle – A plane figure with three straight sides and three angles.
Angle – The space between two intersecting lines or surfaces at or near the point where they meet.
Equilateral – A triangle with all three sides equal and all angles equal (60° each).
Isosceles – A triangle with two equal sides and two equal base angles.
Scalene – A triangle with all sides of different lengths and all angles of different measures.
Right-angled – A triangle containing one 90-degree angle.
Acute-angled – A triangle in which all three angles are acute (less than 90°).
Obtuse-angled – A triangle containing one obtuse angle (greater than 90°).

Differentiation

For struggling pupils, the teacher will provide simpler examples and more direct guidance, possibly using physical manipulation of cut-out triangles. Advanced pupils will be given more challenging problems, such as those involving algebraic expressions for angles or real-world applications of triangle properties.

Note for teachers using this lesson plan

Ensure that pupils actively participate in the demonstrations, especially the one proving the sum of angles. Encourage them to draw and label triangles accurately. Emphasize the importance of showing all steps when solving problems involving missing angles.