[list][*]Subject: Mathematics[br][/*][*]Class: 8th degree[br][/*][*]Duration: 50 minutes[br][/*][*]ICT tools:[i][i] teacher's[/i][/i] [i][i]computer, video, computers for students or smartphones.[/i][/i][i] [i][/i][br][/i][/*][/list]

Solving the equation of the second degree.

[justify]At the end of the lesson, students will be able to:[/justify][list][*]solve any second degree equation using the discriminant;[/*][*]discuss the nature and number of the second degree equation solutions;[/*][*]solve the particular cases, without calculating the discriminant;[/*][*]to decompose quadratic form in the factors with real coefficients;[/*][*]to solve some equations reducible to the second degree equation.[/*][/list]

During the lesson, students will become able to:[br][list][*]applying the canonical form of the quadratic function;[/*][*]identify coefficients involved in the solving formulas, in the right order;[/*][*]calculate the discriminant and solutions, using the solving formulas;[/*][*]discuss the nature and number of solutions according to the discriminant;[/*][*]identify and resolve cases (without using discriminant)[/*][*]decompose the quadratic in factors with real coefficients, or recognize the irreducibility;[/*][*]solve some equations reducible to second degree.[/*][/list]

[i]Strategies and teaching methods[br][br][/i][list][*]Solving formulas will be introduced using the canonical form by demonstration, questioning and conversation;[br][/*][*]To learn formulas (resolution and decomposition) we use exercise method and independent work, computer-assisted; students use interactive sheet prepared in advance to check the results of exercises, which they will work individually, each at their own pace;[/*][*]By questioning, are introduced the more complicated equation (sums, products and fractions), the resolution of which is reduced all at solving the equation of the second degree.[/*][/list][i][b]Activities and lesson stages:[br][br][/b][/i][b] i) Organizing classroom and getting the students attention (2 min.)[br][/b] [br]It organizes classes for lesson, it announces the use of ICT for learning new knowledge.[br][br][b]II) Update of knowledge and putting the problem (8 min.)[br][br][/b] It is proposed to students to solve and then discuss solving the following equation:[br][list=1][*][math]2x=0;3x-6=0;2x\left(3x-6\right)=0;6x^2-12x=0;[/math][br][/*][*][math]x^2=25;x^2-25=0;x^2+25=0[/math][br][/*][*][math]\left(x-1\right)\left(2x+4\right)=0;x^2+x-2=0[/math][br][/*][*][math]\left(x-\sqrt{2}\right)\left(x+\frac{1}{2}\right)=0;2x^2-\left(2\sqrt{2}-1\right)\cdot x-\sqrt{2}=0[/math][/*][/list]The discussion will lead to the conclusion that, although there are cases in which the particular grade II equations is easily solved by decomposition in factors (in sets 1, 2 and 3), in other cases, it is not so obvious decomposition. How can we do in such cases?[br][br][b]III) Teaching and learning new knowledge (25 min.)[/b][br][br]By method of demonstration and explanation, it is introduced solving formulas using discriminant and are discussed type of the solutions and how many they are, on the basis of it. For this, we will transform quadratic to the canonical form so that students can see why we have real solutions only when the discriminant is greater or equal to zero, also where it comes form solutions, why and when we can decompose a quadratic form in first degree factors, or when it is irreducible over the real number.[br][br][math]ax^2+bx+c=0\Longleftrightarrow\left(x+\frac{b}{2a}\right)^2-\frac{\Delta}{4a^2}=0[/math][br][br]We solve some equations on the blackboard so that students can learn the correct identification of the coefficients, then it is proposed to individual students to work using interactive statement "The equation of the second degree". Students will work at your own pace equations on notebooks, then they will check their solving by checking boxes control on the left. Thus, they can check not only solutions but also coefficients and discriminant. On the right side of the sheet, they can find all the necessary formulas, all by selecting the control boxes. Pressing the center button, a new equation is displayed.[br][br][b]IV) Evaluation and strengthening of new knowledge (13 min.)[/b][br][br]Students will receive evaluation sheets (see picture below). Students should solve some of the problems until the end of time, and the rest as homework. To verify the results, students will enter equations in CAS in GeoGebra Graph Calculator. They can receive individual guidance from the teacher when they need them. Towards the end, we will do face to face evaluation which represent a summary of the lesson. [br][br][b]V) Reviews about lesson and homework (2 min.)[/b]

[justify][/justify][list][*]Interactive worksheet „Second degree equation”: [url=https://ggbm.at/YThPxgH4]https://ggbm.at/YThPxgH4[/url][/*][*]„Solve equations in CAS” cu Geogebra Graph Calculator: [url=https://ggbm.at/XRb4r7p2]https://ggbm.at/XRb4r7p2[/url][br][/*][*]Individual worksheets (printed)[/*][/list]

There is a schedule of multimedia laboratory and all computers have GeoGebra installed. If it is no Internet access, or computers can not be used we will use printed sheets only.

- How you implement your lesson plan? [br]I used multimedia computer lab for one child and projector. I presented the respective theoretical calculation formulas for determining the root equation of the second degree. After several measurements, the formulas discussed have submitted application created in GeoGebra and were very excited to check it in determining solutions and intermediate calculations. Students are accustomed to utility and managed to solve all tasks. It was a success recognized by children. [br]- Integrating new technologies into lesson went well? [br]There were technical problems. The only trouble was due speed Internet but have provided this on every computer I copied GeoGebra files that were used by children. Please fill in the box online first, then summarize your answer here.- Students have reached the lesson objectives? [br]Yes. Students have posted second-degree equation coefficients and have found that they can check in calculating the roots of the equation. They realized the importance of their determination in writing its decomposition in order to simplify operations of fractions with real numbers represented by letters. [br]- What lesson have expressed their opinions about your students? [br]They're very excited and recognized that it is very useful the use of specialized software math classes. [br]- What improvements could be made to the method used to make it work better? [br]Students were excited to find that if you enter the equation as a function in GeoGebra it finds its roots as a intersection of the graph function to Ox. Results for them were spectacular.Depending on discriminant they analyzed the graph form of the function and its junctions with axes, actively participated in the lesson and even have improved ICT skills.