[list][*]Subject: [i]Mathematics and Geometry[/i][br][/*][*]Class: [i]VII [/i][br][/*][*]Duration: [i]50 min[/i][br][/*][*]ICT tools:[i] teacher's computer and projector, computers for students or tablets.[/i][i] [/i][i][/i][/*][/list]

[i]Problem-solving, using metric relations in right triangle.[/i]

[i]At the end of the lesson, students will be able to:[br][list][*][i]apply metric relationships in a right triangle to determine some of its elements;[/i][br][/*][*][i][i]deduce metric relationships in a right triangle using those known;[/i][br][/i][/*][*][i][i][i]interpret the perpendicularity of two lines in relation to solving the right triangle;[/i][br][/i][/i][/*][*][i][i][i][i]transpose the results into practice, applying right triangles' proprieties given in problem-solving situations.[/i][/i][/i][/i][/*][/list][/i]

During the lesson, students will be able to:[br][list][*]identifying the elements of a right triangle including the catheti, the hypotenuse, the catheti projections on the hypotenuse, the height on the hypotenuse, the right angle and acute angles;[/*][*]identify and write in a short form, hypothesis, and conclusion of a problem;[br][/*][*]draw geometric figures described within a problem and identify the relevant items;[/*][*]apply the Pythagorean relationship to solve problems, including the deduction of other theorems.[/*][/list]

[i]A. Didactic methods: exercise, observation, problem-solving; [br]B. Courses: Radical Publishing Math-book, Problem-book Mate 2000 + 16/17, boards, computers, video, GeoGeobra platform; [br]C. Types of activity: frontal conversation and individual work.[br][br][i][b]Lesson moments:[br][br][/b][/i][u] i) Introductive moment (2 min.)[br][/u]The teacher organizes the class and presents the lesson topic: deepening the knowledge of the metric relations in right triangle, deducting other important relationships, problem-solving. [br][br][u]II) [i][i][u]Introduction and update knowledge[/u][/i][/i] (10 min.)[br][/u]Presents interactive sheet "Pythagorean Theorem - a proof without words". Students will be given plenty of time to study, discuss, and write down the findings. Then summarizes the theorems of the cathetus and height.[br][br][u]III) Learning of new knowledge (20 min.)[br][/u]One by one, in the form of problems, are enounced the reciprocal of the Pythagoras Theorem, and the second theorem of height. Students are advised to, and how to, build a frame for the problem-solving: identifying the hypothesis, conclusion, and construction of the geometrical figure. We will ask for demonstration ideas, students will debate, find the solution, then write down the proofs, on the blackboard and notebooks.[br][br][u]IV) The deepening of new knowledge and evaluation (15 min.)[/u][br]Students will use interactive sheet "Practice Pythagoras Theorem Applications" to generate new problems, solve them and check the results. It is concluded that a right triangle can be solved when are known at least three elements, from the relevant 6 (2 catheti, 1 hypotenuse, two projections of catheti, height on the hypotenuse).[br][br][u]V) Rating the lesson and ensure the knowledge transfer (3 min.)[br][/u]Students are invited to evaluate the lesson. The teacher will inform the students about using GeoGebra Graph Calculator at their homes, being available on mobile phones, too. Then they will get their homework, problems from their math-books.[/i]

[i]Interactive files:[br] [i]"Pythagoras' Theorem - a proof without words" [url=https://ggbm.at/VXsEdufA]https://ggbm.at/VXsEdufA[/url][/i][i] [br]"Practice Pythagoras Theorem Applications" [url=https://ggbm.at/fnR6JazX]https://ggbm.at/fnR6JazX[/url][/i][/i]

[i][i][list][*]Students do not need special GeoGebra knowledge, just the usual ICT skills;[/*][*]To conduct a lesson in good condition with ICT resources, we must have an internet connection, video projector and computers running smoothly;[/*][*]If you experience difficulties operating ICT resources, you could use only the textbooks, blackboard, and notebooks.[/*][/list][/i][/i]