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Lecturer(s)
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Honzík Lukáš, PhDr. Ph.D.
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Course content
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Finding geometric loci (the method of analytic geometry, inductive process). Geometric loci in the plane and space. Methods for solving construction planimetry problems. Constructions of triangles and quadrangles. Apollonius's problems. Construction problems with parameters. Mathematization of word problems (formalization of conditions). The process of solving word problems, basic types of word problems solved at elementary schools (word problems on distance, common work, mixture). Simple optimization problems.
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Learning activities and teaching methods
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Lecture supplemented with a discussion, Collaborative instruction, Discussion, One-to-One tutorial, Group discussion, Seminar classes, Individual study, Lecture, Seminar
- Contact hours
- 26 hours per semester
- Preparation for comprehensive test (10-40)
- 26 hours per semester
- Preparation for an examination (30-60)
- 26 hours per semester
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| prerequisite |
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| Knowledge |
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| master mathematical language and procedures at the level of the bachelor's study field Mathematical Studies |
| Skills |
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| master mathematical language and procedures at the level of the bachelor's study field Mathematical Studies |
| Competences |
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| N/A |
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| describe basic sets of points of a given property in a plane and in space |
| know methods of examination of sets of points of a given property in a plane |
| list basic plane geometric shapes, their properties and construction methods |
| classify word problems and describe the procedure of their solution |
| Skills |
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| using a suitable method to examine a set of points of a given property in a plane |
| to solve simple construction problems including Apollonian problems |
| to solve word problems presented at the 2nd st. Elementary school and simple optimization tasks |
| Competences |
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| N/A |
| N/A |
| teaching methods |
|---|
| Knowledge |
|---|
| Lecture supplemented with a discussion |
| Seminar |
| Collaborative instruction |
| Group discussion |
| Individual study |
| One-to-One tutorial |
| Discussion |
| Task-based study method |
| Lecture |
| Seminar classes |
| Skills |
|---|
| Lecture |
| Seminar |
| Lecture supplemented with a discussion |
| Collaborative instruction |
| Individual study |
| Seminar classes |
| Task-based study method |
| Discussion |
| Competences |
|---|
| Lecture with visual aids |
| Practicum |
| Self-study of literature |
| Individual study |
| assessment methods |
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| Knowledge |
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| Test |
| Oral exam |
| Self-evaluation |
| Skills |
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| Oral exam |
| Test |
| Skills demonstration during practicum |
| Self-evaluation |
| Competences |
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| Test |
| Oral exam |
| Self-evaluation |
| Continuous assessment |
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Recommended literature
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BUDÍNOVÁ, I., PAVLÍČKOVÁ, L. Konstrukční úlohy: učební text pro studenty učitelství matematiky 2. stupně základní školy. Brno: Masarykova univerzita, 2020. ISBN 978-80-210-9818-3.
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HERMAN, J., KUČERA, R., ŠIMŠA, J. Metody řešení matematických úloh I. Brno: Masarykova univerzita, 2011. ISBN 978-80-210-5636-7.
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HERMAN, J., KUČERA, R., ŠIMŠA, J. Metody řešení matematických úloh II. Brno: Masarykova univerzita, 2004. ISBN 80-210-3569-2.
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Odvárko, O. a kol. Metody řešení matematických úloh.. Praha : SPN, 1990. ISBN 80-04-20434-1.
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ODVÁRKO, O. Matematika pro střední školy. Praha: Prometheus, 2023. ISBN 978-80-7196-548-0.
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Polák, J. Středoškolská matematika v úlohách I.. Praha : Prometheus, 2006. ISBN 80-7196-337-2.
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SLÁDKOVÁ, M. Slovní úlohy: jak řešit logické úlohy z matematiky. Brno: Edika, 2024. ISBN 978-80-266-1947-5.
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Švrček, Jaroslav. Vybrané kapitoly z geometrie trojúhelníka. 2. přeprac. vyd. Praha : Karolinum, 2004. ISBN 80-246-0814-6.
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