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Title of the Experience

Various options for solving equations by using intuitive degradation

Name of the teacher

Viera Kolbaská

Country where it took place

Slovakia

School typology

High Secondary School

Thematic Area

Maths

Experience typology

Teaching in class

Type of contact

Direct

Description of the Experience

The aim of this thematic area is to bring to the students various options for solving equations by using intuitive degradation as well as lead them to solving incomplete quadratic equations and complete decomposition without using a discriminate.

Thematic unit Adjusting equation by a partying it into the linear equation is following these teaching thematic units:

1. Polynomials – explaining the term, operations with polynomials (rehearsing of the elementary school curriculum)

2. Polynomials - multiplication of polynomials, the proportion of polynomials, squaring polynomials

3. Polynomials - decomposition of polynomials by grouping before brackets (including squares), and using the powers of the sum and difference, the difference of the squares of monomials

4. Linear equation with an unknown in the denominator of the fraction (the repetition of simple tasks of elementary school)

After these steps follows:

5. Equation which after using the appeals can be solved by using knowledge of the linear equation

Solving linear equations and quadratic equations is a curriculum that is taught in the second semester of the first year of secondary school.

Teaching of this thematic unit follows rehearsing tasks of polynomials and solving linear equations of the elementary school, which takes place in September. It should help with solving problems in professional subjects.

The problem for the successful implementation of the curriculum of the course is:

1. Varied level of knowledge of students from elementary school (school education programs comprise 70% of the curriculum in the national education program and 30% of the curriculum is specific to the school)

2. Minimum scope of the subject matter of polynomials (pupils learn them in thematic unit of Variable expression in grade 8 and that only the parts of addition, subtraction, multiplication and division by a number)

3. The abovementioned topic of the curriculum is just about the natural exponent and such operations are expanding curriculum with squares

4. Equations that students solve in 8th and 9th grade are at very low level of difficulty given the above points

5. Curriculum about the angle of expression is under-represented in the curriculum and that only in connection with equations with unknown in the denominator

6. Pupils under the decomposition of exponents learn just standing out numbers before the closing parenthesis (distributivity) and are not taught the square of a binomial or the difference of the squares of monomials.

For the above points I used in teaching worksheets (Annex), the use of which allowed me in a shorter period of time with the students to solve more tasks. By these they consolidated their acquired knowledge and intuition gained - insights for solving the following thematic unit. The worksheets allowed also an individual approach to teaching students. Students during their domestic preparation could have used their textbooks, collections and recommended webpage www.kolbi.wbl.sk website. In consultation hours outside the classroom time they could consult their problems with the teacher.

I must say that pupils in small scale made use of the recommended actions. Worksheets used during lessons under the guidance of a teacher proved to be the most effective.

In pointing out the importance of the curriculum to address the challenges of vocational subjects, I found it necessary to use in solving the tasks labeling variables according to these articles and do not use only the variables of x, y, z, a, b, c.

Thematic unit Adjusting equation by a partying it into the linear equation is following these teaching thematic units:

1. Polynomials – explaining the term, operations with polynomials (rehearsing of the elementary school curriculum)

2. Polynomials - multiplication of polynomials, the proportion of polynomials, squaring polynomials

3. Polynomials - decomposition of polynomials by grouping before brackets (including squares), and using the powers of the sum and difference, the difference of the squares of monomials

4. Linear equation with an unknown in the denominator of the fraction (the repetition of simple tasks of elementary school)

After these steps follows:

5. Equation which after using the appeals can be solved by using knowledge of the linear equation

Solving linear equations and quadratic equations is a curriculum that is taught in the second semester of the first year of secondary school.

Teaching of this thematic unit follows rehearsing tasks of polynomials and solving linear equations of the elementary school, which takes place in September. It should help with solving problems in professional subjects.

The problem for the successful implementation of the curriculum of the course is:

1. Varied level of knowledge of students from elementary school (school education programs comprise 70% of the curriculum in the national education program and 30% of the curriculum is specific to the school)

2. Minimum scope of the subject matter of polynomials (pupils learn them in thematic unit of Variable expression in grade 8 and that only the parts of addition, subtraction, multiplication and division by a number)

3. The abovementioned topic of the curriculum is just about the natural exponent and such operations are expanding curriculum with squares

4. Equations that students solve in 8th and 9th grade are at very low level of difficulty given the above points

5. Curriculum about the angle of expression is under-represented in the curriculum and that only in connection with equations with unknown in the denominator

6. Pupils under the decomposition of exponents learn just standing out numbers before the closing parenthesis (distributivity) and are not taught the square of a binomial or the difference of the squares of monomials.

For the above points I used in teaching worksheets (Annex), the use of which allowed me in a shorter period of time with the students to solve more tasks. By these they consolidated their acquired knowledge and intuition gained - insights for solving the following thematic unit. The worksheets allowed also an individual approach to teaching students. Students during their domestic preparation could have used their textbooks, collections and recommended webpage www.kolbi.wbl.sk website. In consultation hours outside the classroom time they could consult their problems with the teacher.

I must say that pupils in small scale made use of the recommended actions. Worksheets used during lessons under the guidance of a teacher proved to be the most effective.

In pointing out the importance of the curriculum to address the challenges of vocational subjects, I found it necessary to use in solving the tasks labeling variables according to these articles and do not use only the variables of x, y, z, a, b, c.

Comments on this Teachers Experience

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Date: 2014.11.09

Posted by **Darina Berčakova** (*Slovakia*)

I teach at vocational school where students have a problem remembering the use of basic formula - (A + B)2 etc ...

The method, described by Ms. Kolbaská is more suitable for students of secondary grammar schools, where is higher amount of mathematics lesson per week and students who enjoy Math. At our type of school we only have two hours per week – this amount is only for presentation and fixation of basic terms. Only the best students from class are able to understand complex operation as standing out in front of brackets (factorization) is.

Otherwise, I really appreciate the Ms. Kolbaská´s work with pupils at Mathematics.

Date: 2014.10.28

Posted by **Darina Berčáková** (*Slovakia*)

Učím na strednej odbornej škole, kde majú žiaci problém so zapamätaním si a používaním základných vzorcov - (A+B)2 ... atď

Spôsob ktorý opisuje pani Kolbaská je vhodny najmä pre žiakov gymnázií, kde je vyššia hodinová dotácia matematiky a žiaci, ktorých matematika baví. Na našom type školy máme do týždňa dve hodiny - to postačuje iba na prebratie a utvrdenie základných pojmov. Vynímanie pred zátvorku a rozklad na súčin pochopia iba tí najlepší matematikári z triedy.

Inak prácu so žiakmi na hodine matematiky pani Kolbaskej hodnotím veľmi kladne.

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