IMAp06 Geometry 2

Faculty of Education
Spring 2025
Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
In-person direct teaching
Teacher(s)
Mgr. Leni Lvovská, Ph.D. (lecturer), Mgr. Jitka Panáčová, Ph.D. (deputy)
RNDr. Jakub Novák (seminar tutor)
Mgr. Zdena Staňová (seminar tutor)
Guaranteed by
Mgr. Leni Lvovská, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable of Seminar Groups
IMAp06/01: Tue 16:00–17:50 učebna 37, J. Novák
IMAp06/02: Thu 16:00–17:50 učebna 37, J. Novák
IMAp06/03: Wed 11:00–12:50 učebna 37, J. Novák
IMAp06/04: Mon 8:00–9:50 učebna 37, J. Novák
IMAp06/05Erasmus: No timetable has been entered into IS. J. Novák
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main goal is to develop an understanding of the conceptual system of geometry, enhance geometric and spatial imagination, and acquire the ability to independently and creatively expand the conceptual framework. This will enable future teachers to teach geometric concepts with the necessary perspective and guide pupils' learning activities in mathematics effectively at the primary school level.
Learning outcomes
By the end of this course, the student will be able to understand and explain fundamental geometric concepts and relations in the plane and in space, particularly geometric transformations.
Syllabus
  • Symmetries, general properties of symmetries, types of symmetries in the plane. Fixed points and figures.
  • Composition of symmetries, group of symmetries. Direct and indirect symmetries.
  • Construction problems.
  • Parallel projection. Representation of basic solids in parallel projection.
  • Incidence relations in space, relative positions of lines, planes, and solids.
  • Cross sections of solids.
  • Intersections of two planes, of a plane and a line. Intersections of a line with a solid.
  • Actual sizes of cross sections and nets of solids.
Literature
    required literature
  • LVOVSKÁ, Leni and Jakub NOVÁK. Sbírka úloh z elementární geometrie pro studium učitelství 1. stupně základní školy (A collection of exercises in elementary geometry for students of primary school teaching). 1st ed. Masarykova univerzita, 2024, 65 pp. ISBN 978-80-280-0549-8. info
    recommended literature
  • FRANCOVÁ, Marta and Milena VAŇUROVÁ. Rovinné řezy mnohostěnů (Flat sections of polyhedrons). Brno: Masarykova univerzita, 2009. Elportál [online]. ISSN 1802-128X. URL info
  • FRANCOVÁ, Marta and Květoslava MATOUŠKOVÁ. Kapitoly ze základů stereometrie pro studium učitelství 1. stupně základní školy. Vyd. 1. Brno: Vydavatelství Masarykovy univerzity, 1994, 60 s. ISBN 8021008407. info
  • FRANCOVÁ, Marta, Květoslava MATOUŠKOVÁ and Milena VAŇUROVÁ. Texty k základům elementární geometrie : pro studium učitelství 1. stupně základní školy. 2. opr. vyd. Brno: Masarykova univerzita, 1994, 107 s. ISBN 8021008806. info
  • FRANCOVÁ, Marta, Květoslava MATOUŠKOVÁ and Milena VAŇUROVÁ. Sbírka úloh z elementární geometrie. Vyd. 1. Brno: Masarykova univerzita v Brně, 1992, 86 s. ISBN 8021004045. info
    not specified
  • KOUŘIM, Jaroslav, Ondrej ŠEDIVÝ and František KUŘINA. Základy elementární geometrie : pro učitelství 1. stupně ZŠ. 1. vyd. Praha: Státní pedagogické nakladatelství, 1985, 156 s. info
Teaching methods
Problem solving and concise explanation of complex theoretical topics.
Assessment methods
The course concludes with a credit-based written exam. Specific requirements for the exam are detailed in the interactive syllabus of the course. Students must demonstrate mastery of the relevant concepts and the ability to solve elementary proof and construction problems that serve as applications of the theory. A necessary condition for being admitted to the credit test is sufficient personal attendance at seminars (no more than two unexcused absences).
Náhradní absolvování (in Czech)
V případě zahraničního výjezdu je možné předmět absolvovat v~náhradní podobě. Po návratu z~výjezdu je nutné odevzdat vypracované úkoly dle interaktivní osnovy a napsat zápočtovou písemnou práci. Úkoly musí být odevzdány nejméně jeden týden před plánovaným termínem zápočtové písemné práce.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.
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