Class: Primary 6
Term: 2nd Term
Week: 6
Age: 11 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Measurement and Geometry
Previous Lesson: Money and Conversion: Taxes, Shares, Dividends and Currency Exchange.
Topic: LENGTH
Subject Matter: Pythagoras rule for right-angled triangles, identifying hypotenuse, opposite and adjacent sides, using a² + b² = c² to calculate unknown side, quantitative aptitude on Pythagoras rule.

Specific Objectives

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

Cognitive Domain:

Define a right-angled triangle.
Identify the hypotenuse, opposite, and adjacent sides in a right-angled triangle.
State the Pythagoras rule (a² + b² = c²).
Apply the Pythagoras rule to calculate unknown side lengths.
Solve quantitative aptitude problems involving the Pythagoras rule.

Affective Domain:

Appreciate the importance of the Pythagoras rule in solving real-world problems.
Show willingness to apply the Pythagoras rule accurately.
Develop a logical approach to solving geometric problems.

Psychomotor Domain:

Draw a right-angled triangle and label its sides correctly.
Accurately calculate unknown side lengths using the Pythagoras rule.

Collaborate 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 Primary Schools.
Lagos State Unified Scheme of Work for Primary Schools.
New General Mathematics for Primary Schools, Book 6.

Instructional Materials

The teacher will teach this lesson with the aid of:

Textbook, workbook.
Posters and charts showing different right-angled triangles.
Chalk/marker and whiteboard/blackboard.
Ruler and protractor.

Rationale for the Lesson

Understanding the Pythagoras rule helps pupils to solve practical problems involving distances and lengths in everyday life. It enables them to find unknown sides of right-angled shapes, which is important for various construction and measurement tasks.

Prerequisite/Previous Knowledge

Pupils should have prior knowledge of different types of triangles, identifying angles, basic arithmetic operations (addition, subtraction, multiplication), and squares and square roots of numbers.

Lesson Content/Board Summary

Pythagoras Rule for Right-Angled Triangles

What is a Right-Angled Triangle?

A right-angled triangle is a triangle that has one angle exactly equal to 90 degrees (a right angle).

Identifying Sides of a Right-Angled Triangle

The sides of a right-angled triangle have special names:

Hypotenuse: This is the longest side of the right-angled triangle. It is always opposite the right angle.
Opposite Side: This side is opposite to a given acute angle.
Adjacent Side: This side is next to a given acute angle and is not the hypotenuse.

The Pythagoras Rule (a² + b² = c²)

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

The formula is: a² + b² = c²

Where:

‘c’ represents the length of the hypotenuse.
‘a’ and ‘b’ represent the lengths of the other two sides.

Calculating Unknown Sides

To find an unknown side using the Pythagoras rule:

If the hypotenuse (c) is unknown: c = √(a² + b²)
If one of the shorter sides (a) is unknown: a = √(c² – b²)
If the other shorter side (b) is unknown: b = √(c² – a²)

Example 1: Find the length of the hypotenuse of a right-angled triangle with sides 3 cm and 4 cm.

Solution: a = 3 cm, b = 4 cm. c² = 3² + 4² = 9 + 16 = 25. c = √25 = 5 cm.

Example 2: A ladder 13 m long leans against a wall. The foot of the ladder is 5 m away from the base of the wall. How high up the wall does the ladder reach?

Solution: c = 13 m (hypotenuse), a = 5 m (distance from wall). b² = c² – a² = 13² – 5² = 169 – 25 = 144. b = √144 = 12 m.

Quantitative Aptitude Problems on Pythagoras Rule

These are word problems that require applying the Pythagoras rule to solve real-life situations, such as finding distances, heights, or lengths in scenarios like ladders against walls, diagonal paths, or television screen sizes.

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 reviews the previous lesson on types of triangles. The teacher then asks pupils to identify a right angle and gives examples of where right angles are found in the classroom.
Pupils’ Activity: Pupils respond to greetings, recall previous lesson, and identify right angles.
Learning Point: Pupils recall prior knowledge of triangles and angles, preparing them for the lesson.

Step 2: Introduction to Right-Angled Triangles and their Sides

Time: 10 minutes
Teaching Skill: Explanation/Identification
Teacher’s Activity: The teacher draws a right-angled triangle on the board and explains its features, specifically the 90-degree angle. The teacher then introduces and explains the terms: hypotenuse, opposite, and adjacent sides, demonstrating how to identify each.
Pupils’ Activity: Pupils observe the drawing, listen attentively, and identify the sides of the triangle as guided by the teacher.
Learning Point: Pupils understand the characteristics of a right-angled triangle and can identify its sides.

Step 3: Introduction of the Pythagoras Rule

Time: 10 minutes
Teaching Skill: Explanation/Formula Presentation
Teacher’s Activity: The teacher introduces the Pythagoras rule (a² + b² = c²) and explains what each variable represents. The teacher writes the formula on the board and emphasizes that it only applies to right-angled triangles.
Pupils’ Activity: Pupils listen, write down the Pythagoras rule, and ask questions for clarification.
Learning Point: Pupils learn the Pythagoras rule and its application to right-angled triangles.

Step 4: Application of the Pythagoras Rule (Finding Hypotenuse)

Time: 8 minutes
Teaching Skill: Demonstration/Problem Solving
Teacher’s Activity: The teacher works through Example 1 (finding the hypotenuse) from the board summary, explaining each step clearly. The teacher encourages pupils to ask questions.
Pupils’ Activity: Pupils follow the teacher’s example, copy the solution, and attempt similar problems if given.
Learning Point: Pupils can apply the Pythagoras rule to calculate the length of the hypotenuse.

Step 5: Application of the Pythagoras Rule (Finding a Shorter Side)

Time: 7 minutes
Teaching Skill: Demonstration/Problem Solving
Teacher’s Activity: The teacher works through Example 2 (finding a shorter side) from the board summary, emphasizing how the formula is rearranged. The teacher provides another simple practice problem for pupils to try.
Pupils’ Activity: Pupils observe, copy the solution, and attempt the practice problem.
Learning Point: Pupils can apply the Pythagoras rule to calculate the length of an unknown shorter side.

Step 6: 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?
Name the longest side of a right-angled triangle.
State the Pythagoras rule.
In a right-angled triangle, if the two shorter sides are 6 cm and 8 cm, what is the length of the hypotenuse?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: [Included in Step 6]
Teaching Skill: Summarization/Consolidation
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the Pythagoras rule and its importance. The teacher assigns homework, which includes solving more problems from the textbook.
Pupils’ Activity: Pupils listen to the summary, ask any final questions, and note down the homework.
Learning Point: Pupils consolidate their understanding of the Pythagoras rule.

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

Lesson Keywords

Right-angled triangle – A triangle with one angle measuring 90 degrees.
Hypotenuse – The longest side of a right-angled triangle, opposite the right angle.
Opposite side – The side across from a given acute angle in a right-angled triangle.
Adjacent side – The side next to a given acute angle in a right-angled triangle, which is not the hypotenuse.
Pythagoras rule – The mathematical rule (a² + b² = c²) that relates the lengths of the sides of a right-angled triangle.

Differentiation

For pupils who are struggling, the teacher will provide simpler examples with smaller numbers and offer one-on-one guidance. Advanced pupils will be given more complex quantitative aptitude problems or encouraged to explore real-world applications of the rule in different scenarios.

Note for teachers using this lesson plan

Ensure pupils have a solid understanding of squares and square roots before teaching this lesson. Use visual aids extensively to help pupils identify the sides of the right-angled triangle correctly. Encourage pupils to draw diagrams for all problems to aid understanding.