Topicmd2cd952c775ad535_1528449000663_0Topic

Pythagorean theoremPythagorean theoremPythagorean theorem I

Levelmd2cd952c775ad535_1528449084556_0Level

Second

Core curriculummd2cd952c775ad535_1528449076687_0Core curriculum

VIII. Properties of planar geometric figures. The student:

8) knows and uses the Pythagorean theoremPythagorean theoremPythagorean theorem in practical situation (without the converse theorem).

Timingmd2cd952c775ad535_1528449068082_0Timing

45 minutes

General objectivemd2cd952c775ad535_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmd2cd952c775ad535_1528449552113_0Specific objectives

1. Formulating the Pythagorean theoremPythagorean theoremPythagorean theorem.

2. Geometric prove of the Pythagorean theorem.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesmd2cd952c775ad535_1528450430307_0Learning outcomes

The student:

- formulates the Pythagorean theoremPythagorean theoremPythagorean theorem,

- presents the geometric proof of the Pythagorean theorem.

Methodsmd2cd952c775ad535_1528449534267_0Methods

1. Discussion.

2. Brainstorming.

Forms of workmd2cd952c775ad535_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmd2cd952c775ad535_1528450127855_0Introduction

The teacher informs the students that during this class they will discover the correlation between the sum of the areas of the squares built on the cathetuses of the right‑angled triangleright‑angled triangleright‑angled triangle and the area of the square built on the hypotenusehypotenusehypotenuse. Then they will learn the various proofs of the formulated theorem.

Task
Students provide examples of theorems. They identify the assumptionassumptionassumption and the thesisthesisthesis.

Proceduremd2cd952c775ad535_1528446435040_0Procedure

Task
Students work individually using computers. Their task is to notice the correlation between the sum of the areas of the squares built on the cathetuses of the right‑angled triangleright‑angled triangleright‑angled triangle and the area of the square built on the hypotenusehypotenusehypotenuse.

[Geogebra applet 1]

Based on the exercise, the students formulate the hypotheses through brainstorming and verify them.

The result of the discussion should be the Pythagorean theoremPythagorean theoremPythagorean theorem – if a triangle is right‑angled, the sum of the areas of the squares built on the cathetuses equals the area of the square built on the hypotenusehypotenusehypotenuse.

Students write down the simplified version of the Pythagorean theorem.

The Pythagorean theoremPythagorean theoremPythagorean theorem.

- If a and b are the lengths of the cathetuses and c is the length of the hypotenuse of a right‑angled triangle then there the following correlation obtains:md2cd952c775ad535_1527752263647_0- If a and b are the lengths of the cathetuses and c is the length of the hypotenuse of a right‑angled triangle then there the following correlation obtains:

[Illustration 1]

Task
Students cut out paper geometric figures of coloured on the basis of the drawing. Then they try to prove the Pythagorean theoremPythagorean theoremPythagorean theorem by filling the big square with the figures they cut.

[Illustration 2]

Task
Using the internet resources students find the proof of the Pythagorean theoremPythagorean theoremPythagorean theorem given by a Chinese mathematician Liu Hui in the 1st century.

An extra task:
Students work individually using computers. Their task is to check, if the polygons built on the sides of a right‑angled triangle show the correlation between the areas of the polygons resulting from the Pythagorean theorem.md2cd952c775ad535_1527752256679_0if the polygons built on the sides of a right‑angled triangle show the correlation between the areas of the polygons resulting from the Pythagorean theorem.

[Geogebra applet 2]

Lesson summarymd2cd952c775ad535_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

The Pythagorean theoremPythagorean theoremPythagorean theorem.

- If a and b are the lengths of the cathetuses and c is the length of the hypotenuse of a right‑angled triangle, the following correlation obtains:md2cd952c775ad535_1527752263647_0- If a and b are the lengths of the cathetuses and c is the length of the hypotenuse of a right‑angled triangle, the following correlation obtains:

Selected words and expressions used in the lesson plan

assumptionassumptionassumption

cathetusecathetusecathetuse

hypotenusehypotenusehypotenuse

Pythagorean theoremPythagorean theoremPythagorean theorem

right‑angled triangleright‑angled triangleright‑angled triangle

theoremtheoremtheorem

thesisthesisthesis