Class: Junior Secondary School 2 (JSS 2 / JS2)
Term: Third Term
Week: 2
Age: 13 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Bearing: Identifying the Cardinal Points.
Topic: THE PYTHAGORAS RULE
Subject Matter: The right-angled triangle, Using Pythagoras rule to solve right-angled triangles: Pythagoras triples

Specific Objectives

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

Cognitive Domain:

Define a right-angled triangle.
State the Pythagoras rule.
Identify Pythagorean triples.

Affective Domain:

Appreciate the importance of the Pythagoras rule in solving real-life problems.
Develop interest in solving geometrical problems involving right-angled triangles.

Psychomotor Domain:

Draw and label a right-angled triangle.
Apply the Pythagoras rule to calculate the length of an unknown side of a right-angled triangle.

Work collaboratively with peers to solve problems related to Pythagoras rule.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Junior Secondary Schools.
State Unified Scheme of Work.
New General Mathematics for Junior Secondary Schools 2.
https://www.google.com/search?q=Pythagoras+rule+for+JSS2
https://nigerianschools.com.ng/mathematics

Instructional Materials

The teacher will teach this lesson with the aid of:

Whiteboard/Blackboard
Markers/Chalk
Ruler
Protractor
Set squares
Charts showing examples of right-angled triangles and the Pythagoras rule.

Rationale for the Lesson

This lesson is important because it introduces pupils to a fundamental concept in geometry, enabling them to understand the relationship between the sides of a right-angled triangle. This knowledge helps pupils solve various problems in geometry and in real-life situations involving distances and heights.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic shapes, types of triangles, squares, and square roots.

Lesson Content/Board Summary

THE PYTHAGORAS RULE

The Right-Angled Triangle

A right-angled triangle is a triangle that has one of its angles exactly 90 degrees (a right angle).

Key features of a right-angled triangle:

It has one angle that measures 90°.
The side opposite the 90° angle is called the hypotenuse. It is always the longest side of the triangle.
The other two sides are called the opposite and adjacent sides, or simply the legs of the triangle.

(Imagine a diagram here: A right-angled triangle with sides labeled ‘a’, ‘b’, and ‘c’ (hypotenuse) and the right angle marked.)

The Pythagoras Rule/Theorem

The Pythagoras rule states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (legs).

If ‘a’ and ‘b’ are the lengths of the two shorter sides (legs) and ‘c’ is the length of the hypotenuse, the rule is:

a² + b² = c²

Where:

a = length of one shorter side
b = length of the other shorter side
c = length of the hypotenuse (the longest side)

Using Pythagoras Rule to Solve Right-Angled Triangles

The Pythagoras rule can be used to find the length of any side of a right-angled triangle if the lengths of the other two sides are known.

Example 1: Finding the Hypotenuse

Find the length of the hypotenuse (c) of a right-angled triangle with sides a = 3 cm and b = 4 cm.

(Imagine a diagram here: A right-angled triangle with legs 3cm and 4cm, and hypotenuse ‘c’.)

Step 1: Write the Pythagoras rule: a² + b² = c²
Step 2: Substitute the given values: 3² + 4² = c²
Step 3: Calculate the squares: 9 + 16 = c²
Step 4: Add the values: 25 = c²
Step 5: Find the square root of both sides: c = √25
Step 6: State the result: c = 5 cm

Example 2: Finding a Shorter Side

A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. Find the length of the other shorter side (a).

(Imagine a diagram here: A right-angled triangle with hypotenuse 13cm, one leg 5cm, and the other leg ‘a’.)

Step 1: Write the Pythagoras rule: a² + b² = c²
Step 2: Substitute the given values (let b = 5 cm, c = 13 cm): a² + 5² = 13²
Step 3: Calculate the squares: a² + 25 = 169
Step 4: Isolate a² by subtracting 25 from both sides: a² = 169 – 25
Step 5: Calculate the difference: a² = 144
Step 6: Find the square root of both sides: a = √144
Step 7: State the result: a = 12 cm

Pythagorean Triples

A Pythagorean triple is a set of three positive integers (whole numbers) a, b, and c, such that a² + b² = c². They represent the side lengths of a right-angled triangle.

Common Pythagorean Triples include:

(3, 4, 5) because 3² + 4² = 9 + 16 = 25 = 5²
(5, 12, 13) because 5² + 12² = 25 + 144 = 169 = 13²
(8, 15, 17) because 8² + 15² = 64 + 225 = 289 = 17²
(7, 24, 25) because 7² + 24² = 49 + 576 = 625 = 25²

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, reviews the previous lesson on types of triangles, and then introduces the topic by asking pupils to identify a right-angled triangle from a set of diagrams.
Pupils’ Activity: Pupils respond to greetings, recall previous knowledge, and identify the right-angled triangle.
Learning Point: Pupils recall prior knowledge and are introduced to the lesson topic.

Step 2: Definition of a Right-Angled Triangle

Time: 7 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher defines a right-angled triangle, explains its properties, and illustrates it on the board, pointing out the hypotenuse and the other two sides.
Pupils’ Activity: Pupils listen, observe the illustrations, and copy notes on the definition and properties of a right-angled triangle.
Learning Point: Pupils understand the characteristics and parts of a right-angled triangle.

Step 3: Introduction of the Pythagoras Rule

Time: 8 minutes
Teaching Skill: Explanation/Formula Derivation
Teacher’s Activity: The teacher states the Pythagoras rule, writes the formula (a² + b² = c²) on the board, and explains each variable. The teacher emphasizes that the rule applies only to right-angled triangles.
Pupils’ Activity: Pupils listen attentively, ask questions for clarification, and copy the rule and formula into their notebooks.
Learning Point: Pupils learn the Pythagoras rule and its conditions.

Step 4: Application – Finding the Hypotenuse

Time: 8 minutes
Teaching Skill: Demonstration/Problem Solving
Teacher’s Activity: The teacher demonstrates Example 1 (finding the hypotenuse) step-by-step on the board, explaining each calculation clearly. The teacher encourages pupils to follow along.
Pupils’ Activity: Pupils observe the demonstration, ask questions, and solve the example in their notebooks.
Learning Point: Pupils learn to apply the Pythagoras rule to find the hypotenuse.

Step 5: Application – Finding a Shorter Side

Time: 7 minutes
Teaching Skill: Demonstration/Problem Solving
Teacher’s Activity: The teacher demonstrates Example 2 (finding a shorter side) step-by-step, showing how to rearrange the formula. The teacher provides a similar problem for pupils to try.
Pupils’ Activity: Pupils pay attention to the demonstration, work through the example, and attempt the practice problem provided by the teacher.
Learning Point: Pupils learn to apply the Pythagoras rule to find a shorter side.

Step 6: Pythagorean Triples

Time: 5 minutes
Teaching Skill: Explanation/Listing
Teacher’s Activity: The teacher defines Pythagorean triples and lists common examples like (3, 4, 5) and (5, 12, 13), demonstrating how they satisfy the rule.
Pupils’ Activity: Pupils listen, understand the concept of Pythagorean triples, and copy the examples.
Learning Point: Pupils identify and recognize Pythagorean triples.

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 a right-angled triangle?
State the Pythagoras rule.
Identify the hypotenuse in a right-angled triangle.
A right-angled triangle has legs of 6 cm and 8 cm. Calculate the length of its hypotenuse.
Mention two examples of Pythagorean triples.

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

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization/Assignment
Teacher’s Activity: The teacher summarizes the key points of the lesson and assigns homework, which includes solving more problems involving the Pythagoras rule.
Pupils’ Activity: Pupils listen to the summary and copy down the homework assignment.
Learning Point: Pupils consolidate their learning and prepare for further practice.

Lesson Keywords

Pythagoras – A mathematical theorem relating the sides of a right-angled triangle.
Right-angled triangle – A triangle with one angle measuring 90 degrees.
Hypotenuse – The longest side of a right-angled triangle, opposite the right angle.
Pythagorean triples – A set of three positive integers a, b, and c, such that a² + b² = c².
Square root – A number that when multiplied by itself equals a given number.

Differentiation

For struggling learners, the teacher will provide simpler examples and more direct guidance, possibly using pre-drawn triangles. Advanced learners will be given more complex problems, including those involving finding square roots of non-perfect squares or word problems requiring the application of the rule.

Note for teachers using this lesson plan

Ensure pupils have a firm grasp of squares and square roots before this lesson. Use physical models of right-angled triangles or cut-outs to help visualize the concept. Emphasize the importance of correctly identifying the hypotenuse as it is crucial for applying the rule correctly. Encourage pupils to draw diagrams for each problem to aid understanding.