[list][*]Subject: Mathematics[/*][*]Grade: VII[/*][*]Duration: 50 min. [/*][*]ICT settings: teacher laptop and projector, computers/tablets for students.[/*][/list]

[i]Types of Parallelograms : rectangle, rhombus, square[/i]

[i]At the end of the lesson, students will be able to:[br][list][*]identify/recognize a rectangle (rhombus, square);[br][/*][*]gives the definition and the theorem of characterizing the rectangle (rhombus, square);[/*][*]apply properties of the specific parallelograms in problems solving.[/*][/list][/i]

[i]During the lesson, students will be able to:[br][list][*]identify a rectangle, as being a parallelogram having a right angle;[/*][*]characterize a rectangle, as being a parallelogram having congruent diagonals;[/*][*][i]identify a rhombus, as a parallelogram having two consecutive sides (all sides) congruent;[/i][/*][*][i][i]characterize a rhombus, as being a parallelogram having perpendicular diagonals;[/i][/i][/*][*][i][i]identify a square, as the regular 4-sided polygon;[/i][/i][/*][*]characterize the square, as a polygon being the both, a rectangle, and a rhombus;[/*][*][i][i][i]apply the specific parallelogram properties to problem-solving.[/i][/i][/i][/*][/list][/i]

[i]Strategies and methods:[br][br][/i]The objectives of the lesson will be achieved by combining alternatively a number of participative, active methods, such as modeling (physical and digital models), investigation and discovery, problem-solving and demonstration. Dialogue and evaluation will be done through heuristic conversation, but also individual work with online or frontal evaluation.[br][br][i]Moments of the lesson:[br][br][u]I) Organizational moment and getting the students attention (3 min.)[/u][/i][br][br]The class is organized, the theme and the working methods are announced, including the use of ICT, the auxiliary materials (rectangles, diamonds and squares of paper) are divided.[br][br][u][i]II) Update of knowledge (10 min.)[/i][br][br][/u]The students' homework is verified frontally, reviewing the Parallelogram, definition, and characterization. There will be solved, on the proposal, with the students, 2-3 problems in the homework, which update the definition and the characterizations of the parallelogram.[br][br][i]III) Teaching-Learning the new knowledge (15 min.)[br][/i][br]Give each student its own set of paper modeled geometrical shapes, which were prepared, previously, and invite them to study, measure, fold and unfold, the paper rectangles, rhombuses, squares.[list][*]What are the shapes of the presented objects? Are they sides also parallel? Or congruent? How about the angles? [/*][*]Evoking the structure of the previous lesson, students are invited to investigate the existence of CNS, so that a parallelogram to be a rectangle or a rhombus. Students discuss and draw conclusions, it is possible for some students to be able to declare their properties at this stage. [/*][*]Open the interactive GeoGebra worksheet with the dynamic parallelogram. Students will modify the position and the parallelogram so that it becomes a rectangle (rhombus, square) and will note all the properties observed, then discuss them with each other and with the teacher. We should leave enough time for students to observe the properties on their own.[/*][*]Systematization of new knowledge, noting on notebooks, the 3 NSC: [/*][*] 1) A parallelogram [math]\left[ABCD\right][/math] is a rectangle iff has congruent diagonals. [/*][*] 2) A parallelogram [math]\left[ABCD\right][/math] is romb iff has diagonals perpendicular. [/*][*] 3) A parallelogram [math]\left[ABCD\right][/math] is square, iff it has perpendicular and congruent diagonals.[/*][*]We will demonstrate 1) and 2) frontally, and with the help of students. They could see, for example, in the case of the rectangle, the congruent right triangles. [math]\Delta ABC\equiv\Delta BAD[/math]. And in the case of the rhombus, that the line [math]AC[/math] is a perpendicular bisector for the diagonal [math]\left[BD\right][/math], applying the isosceles triangle theorem for the median, for example. We should accept any other valid proof ideas and we should prove at least one reciprocal theorem, in the front of the class, while leaving some demonstrations (which have anyway and manuals), for homework.[br][/*][/list][br][i][u]IV) Consolidation of knowledge (15)[br][br][/u][/i]We'll propose several problems for solving (see problems 3, 4, 5 below), recommending students to draw the geometrical figures more accurately, and meaningfully, so that, easily to infer the solution.[br][br][i][u]V) Rating the lesson, ensuring retention and the transfer of knowledge (7 min.)[/u][/i] [br][br]Check the new knowledge, through heuristic dialog, then set the homework, a few problems from their mathbooks. The quantity and difficulty, will be differentiated according to the level of each student.[br]

[list][*]GeoGebra Graph Calculator and [/*][*]Parallelogram interactive sheet (characterization and customizations) [url=https://ggbm.at/Dtx4jbcg]https://ggbm.at/Dtx4jbcg[/url][/*][*]Problem 3: [url=https://ggbm.at/AAxCAPqh]https://ggbm.at/AAxCAPqh[/url][/*][*]Problem 4: [url=https://ggbm.at/QXnHmvMF]https://ggbm.at/QXnHmvMF[/url][/*][*]Problem 5: [url=https://ggbm.at/PtEhzYad]https://ggbm.at/PtEhzYad[/url][/*][/list]

[i][i][list][*][i]Ensure prior appointment for ICT resources to function properly;[/i][/*][*][i]If the programming is not possible, the teacher will make drawings on the blackboard, and students could use their phones, being GeoGebra Graph Calculator application that is optimized for mobile;[/i][/*][*][i]If that is not possible, we'll extend the lesson moment, when students use the paper models, until the students intuit and understand results without the use of ICT.[br][br][/i][/*][/list][/i][/i]

[i]I've made the lesson plan such that the students to learn individually, each one at its pace, and I've explained this at the beginning of the lesson. That's why all students have learned something in the lesson, although some more, some less. [/i]

[i]Applications were done to function even on the mobile phones, and everything worked just well.[/i]

[i]Armed with these tools, students easily understood the concepts presented and everybody tried (at least) to apply them to solving problems.[/i]

[i]Mostly, they compared this lesson with those in the classical style, obviously favoring the technology aided ones.[/i]

[i]More applications, more problems to solve.[/i]