Radatz & Rickmeyer (1991, 7) state that teaching geometry makes an important contribution to the development of the individual child's ability to open up his or her living or experiential environment. Since the abilities that are important for the development of the geometric structure of the environment, such as spatial perception and visual information reception and processing, do not develop on their own, it is necessary to stimulate and promote geometric experiences and exercises in the elementary school age. Especially the application orientation as well as the structure orientation can be realized very well in geometry lessons. The work in the group phase of the present lesson trains basic cognitive skills such as comparing, distinguishing, ordering, sorting, but also social learning is practiced. The concrete action with materials (Radatz & Rickmeyer, 1991, 8) motivates very many students and thus gives them a positive attitude towards the subject mathematics. Radatz & Rickmeyer (1991,10) count among the geometric content areas of elementary school "recognizing, laying out, making, assembling plane figures and shapes such as squares, rectangles, triangles, circles, and distinguishing them according to properties."

## Table of contents

1 Topic of the teaching unit/ lesson

2 Didactic decisions and justifications

2.1 Objectives for the lesson

2.2 Justifications for the selection of content

2.3 Factual analysis

2.4 Requirements for teaching

3 Methodological decisions and justifications

3.1 Entry situation

3.2 Articulation

3.3 Social forms and forms of action

3.4 Media/ Materials

3.5 Teaching principles

4 Linking knowledge and competence development with planned action situations

5 Planned course of lessons

Bibliography

## 1 Topic of the teaching unit/ lesson

Topic of the teaching unit: Level figures and their properties

Topic of the lesson Getting to know simple basic geometric shapes

Position of the teaching content within the teaching unit:

Abbildung in dieser Leseprobe nicht enthalten

## 2 Didactic decisions and justifications

### 2.1 Objectives for the lesson

The aim of the present lesson is that the children know and are able to name the basic geometric shapes of circle, triangle, square and rectangle, as well as the properties of these basic shapes (expertise). It is also of great importance that the children help each other in the groups and present the work of their group together (social competence).

### 2.2 Justifications for the selection of content

Radatz & Rickmeyer (1991, 7) note that teaching geometry makes an important contribution to the development of the individual child's ability to open up his or her living environment or experience environment. Since the skills that are important for the development of the geometric structure of the environment, such as the idea of space and the visual reception of information and information processing, do not develop by themselves, it is necessary to stimulate and promote the geometric experiences and exercises in primary school age. Especially the application orientation as well as the structural orientation can be realized very well in geometry lessons. The work in the group stage of the present lesson trains basic cognitive skills such as comparing, distinguishing, ordering, sorting, but also social learning is practiced. Concrete action with materials (Radatz & Rickmeyer, 1991, 8) motivates many students and thus gives them a positive attitude towards mathematics. Radatz & Rickmeyer (1991,10) are among the geometric content areas of the elementary school "level figures and forms such as squares, rectangles, triangles, circles recognize, lay, manufacture, assemble and distinguish according to properties."

The sub-framework plan mathematics describes in its performance profile that the pupils should recognize geometric patterns at the end of their primary school years. They should be able to operate with geometric shapes. In addition, they should capture structures and relations, as well as develop viable concepts and model ideas. The sorting of the forms, the promise of the properties of the forms and the presentation of the results contribute to the formation of the competence described above. The sub-framework plan requires connectable knowledge. In the area of space and form, basic geometric knowledge of surfaces is to be imparted. The field of application-capable knowledge includes the knowledge and use of technical terms. Especially the naming of the forms in the development phase and during the presentation, in the phase of securing results, contributes to the development of this connectable knowledge.

### 2.3 Factual analysis

Geometric surfaces occur as bounding surfaces of bodies (Richter, 2). However, they have only 2 expansions: in length and in width. These geometric surfaces are bounded by lines. The lines have only one extension, the length. A line, in turn, is bounded by points that have no expansion and create a line when they move. If a line moves, it creates a surface.

The basic geometric shapes to be treated in primary school are the circle, triangle and the special quadrilaterals, rectangle and square (Franke, 199). These forms are called basic geometric shapes, since many surfaces can be traced back to them. The forms circle, triangle and quadrilateral are often known to the children from everyday life, they can also name them.

The Circle

The circle is a flat figure (Franke, 205). Each point of the circle line has the same distance to the center. This distance is called radius. A distance of two circular points passing through the center is called a diameter. The circle is often referred to the most elementary plane basic form, since it can be distinguished from other forms by a toddler as the first. As a rule, children also have no problems identifying circles, because all circles are similar, i.e. they can be transferred into each other by centric stretching. Circles appear very frequently in the environment.

The Triangle

The triangle is a flat figure (Franke, 208). It has three corners and three sides. All sides can be of equal length, one speaks then of equilateral triangles. If two sides are of equal length, it is an isosceles triangle and if all sides are of different lengths, it is an uneven triangle. Triangles can also be distinguished according to their internal angles. If all angles are smaller than 90 degrees, this is called a pointed triangle. It is a right-angled triangle if an angle has exactly 90 degrees. A blunt-angled triangle occurs when an angle is greater than 90 degrees. The sum of the three angles in the plane triangle is 180 degrees. Of all geometric structures, the triangle is the rectilinear flat surface with the lowest number of sides (Richter, 2). In the environment, triangles are relatively rare, there are hardly any surfaces with 3 pointed corners to be found.

The quadrangle

A quadrilateral is any plane geometric figure enclosed by 4 straight lines. A distinction is made between regular and irregular quadrilaterals (Richter, 2). In the case of the regular ones, the lengths and layers of the sides are fixed. There are quadrilaterals with 2 parallel sides, with a parallel side and without parallel sides. The quadrilaterals with 2 parallel sides include the rectangle, the square, the rhombus and the parallelogram.

The square

The square is a quadrilateral (Franke, 214). It has 4 pages. All sides are of the same length. The opposite sides are parallel to each other. The adjacent sides are perpendicular to each other. Often the square is regarded by the children as the prototype of a quadrilateral. Without teaching influence, a square remains the "right square" for the children, although they can also identify other squares as such.

The rectangle

The rectangle is a quadrilateral (Franke, 214). It has 4 pages. The opposite sides are the same length and parallel to each other. The adjacent sides are perpendicular to each other. Rectangles are most easily identified as such by the children when the aspect ratio is 1:2.

### 2.4 Requirements for teaching

#### 2.4.1 Learning requirements of the students

Class 1a of the Pestalozzi primary school in Zweibrücken is attended by 24 pupils, including 17 girls and 7 boys. The performance level of the class can be described as average, even compared to the parallel class. Alisa, Saskia, Cedric and Denise are supported once a week by Mr. Leiner, who comes from the Canadaschule in Zweibrücken (school with the focus on learning), in German. Among the more powerful students in mathematics are Benedict, Jenny, Kim, Ilyas and Nathalie. Relatively weak students are Alisa, Samira, Angelina, Annika, Marie-Luise and Janina. Samira, who is attending the first class for the second time, is suspected of HAVING ADHD, which, however, has not yet been conclusively diagnosed. This repeatedly leads to constant distraction and lack of concentration in the classroom. This often carries over to classmates sitting at their group table. Angelina is often overtired in class and often seems absent. With regard to these two students, the group work in the work phase seems to be very useful, as it motivates them to work. However, care must be taken to ensure that the two do not let the stronger students do the work. Cagla, a Turkish child, occasionally has problems with the German language, which is probably due to the fact that a lot of Turkish is still spoken at home.

The social climate in the class is very pleasant and appreciative. There is rarely a dispute. Only Alisa often has problems, as many children do not accept her, possibly also due to her intrusive nature, and do not accept the constant contact she seeks. However, this problem mainly occurs only during breaks. In class, she is accepted at her group table and the children who sit at her group table usually know how to deal with her. The children work together independently in their table groups. However, some children still have problems with reading comprehension, which means that they often do not all understand the work orders. In order to prevent this, the written work orders are visually supported with small pictograms. The distribution at the group tables is chosen in such a way that there are always some weak students with stronger students, so that questions that arise in the group can be discussed and solved.

So far, the students have not gained any experience in the field of geometry, which suggests that they will be happy and motivated. The use of the story to get started and the cardboard theater, as well as the recording from the CD should also contribute to this. The methodical approach in this hour with the group work and the subsequent presentation of the results is already known to the children, so that it no longer has to be explicitly addressed. The students know the principle of feedback - giving from numerous other hours, so that no problems should arise during the presentation at the end of the lesson.

In order to keep the volume of the class calm in the group stage, the students know the silence sign and the gong with the energy chime. They accept these signals very well and follow them. In order to focus attention on the teacher, they know the expression of the "school pretzel", they then cross their arms and look at the teacher.

#### 2.4.2 External requirements

The classroom of the 1a is large and spacious. Thus, it is possible to carry out different forms of social despite the relatively high number of students. The students always sit at 4 group tables, so that you do not have to change them especially for this lesson. The group tables are arranged in such a way that there is enough space in the back of the classroom to form a circle of chairs, as well as the theater seat. For the circle of chairs, each child takes the chair from its place into the circle.

## 3 Methodological decisions and justifications

### 3.1 Entry situation

In order to get into the topic of the lesson, the following possibilities are conceivable:

- The entrance takes place in the theater seat. The teacher reads the story "Of Albert and tidying up". The story is supported by playing with forms in the cardboard theatre and by a recorded CD "Wer spricht denn da?".

- The entry takes place in the circle of chairs. As a silent impulse serves a box standing in the middle of the circle of chairs with many different shapes, which may also be spread out on a base. The children notice that they are different shapes, sort them and then name their properties.

I opted for the first mentioned entry. The story, the play in the cardboard theater, as well as the piece from the CD represent a very high motivation for the students and make them curious about the teaching content and the forms. At the same time, the cardboard theater offers a very good opportunity to present the forms while talking about them, as well as later at the presentation of the group work.

### 3.2 Articulation

The following classification is intended for the division of the teaching processes of this lesson into different phases: Entry (motivation), development, work phase, completion/presentation.

- Entrance

The children are in the theater seat with a view of the blackboard in the back of the hall. On a table in front of them stands the cardboard theater, which is still covered with a cloth to raise the tension a bit. After reading the first part of Albert's story, the cardboard theater is uncovered and the teacher plays with the forms while the recorded CD is played.

- Development

After completing the CD, the teacher asks the question: "Who am I?". At the same time, a form is presented in the cardboard theatre. Next to the cardboard theater are small cards on which the names of the forms are. The children recognize their task and assign the correct names to the forms by placing the name cards in front of the form. The students now express how they have recognized the forms. Here, the technical terms, as soon as they have been mentioned, are secured by visibly hanging them on the table. To connect the language with the action, it is recommended to give the children some forms so that they can feel the characteristics of the forms.

- Working phase

The students receive small baskets from the teacher, in which the material as well as the work orders for the table groups are and go to their group tables. Each table group sorts out a different shape. They then search for the appropriate terms and numbers from the basket and supplement the gap text that is written on a sheet. Then they learn to speak their text. As a result, they hang their shapes with wire on the pole. If a group should be finished earlier, material is ready for them. You can choose their shape from many shapes and then paint them in a certain color.

- Conclusion/Presentation

Here the group work is to be presented. The result is again taken place in the theater seat. The children bring their boxes and poles. A connection is now to be made to the beginning of the hour, in which the story of Albert is continued and so the children are once again motivated to introduce themselves and their group. Now the individual groups present themselves one after the other. Care is taken to ensure that as many children as possible in a group speak the text. After a group has presented itself and its results, the teacher encourages the other children to give them feedback. Once all groups have introduced themselves, there is the possibility to talk to the children again in general about the lesson.

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