We lay out tangram figures and find tricks. Laying out outline figures in class

Lesson Plan , 2009 , 15 Pages , Grade: 1.5

Didactics - Mathematics

"We play with shapes". It is an activity-oriented and creative examination of flat, basic geometric shapes through laying, re-laying and laying out in order to acquire spatial imagination, to promote visual perception skills and basic geometric experiences as well as to initiate a geometric language culture.

1 Theme of the series

"We play with forms." - an action-oriented and creative examination of flat, geometric basic forms by laying, recreating and laying out in order to gain spatial imagination, to promote visual perceptivity and basic geometric experiences as well as to initiate a geometric language culture.

2 Theme of unity

"We lay out tangram figures and find tricks." - Extension and application of the previous knowledge by laying out outline figures with all seven parts of the tangram and first discovering / verbalizing individual laying strategies to promote spatial imagination and geometric representation.

3 Structure of the series

1st unit: "We repeat the geometric shapes." - Repetition of the shape properties of circle, triangle, rectangle and square in a learning corner and expand the knowledge of basic geometric shapes by getting to know the term parallelogram, in order to refresh the knowledge of flat figures and prepare the conceptual prerequisites for the tangram game.

2nd unit: "We get to know the game Tangram and thus create a summer landscape." - Getting to know the subfigures of a tangram by counting and describing these and first testing of the rules of the game by freely laying on the topic of 'summer landscape' with subsequent publication of the collage in the class in order to promote visual perceptiveness and geometric language culture.

3rd unit: "We lay out tangram figures and find tricks." - Extension and application of the previous knowledge by laying out outline figures with all seven parts of the tangram and first discovering / verbalizing individual laying strategies to promote spatial imagination and geometric representation.

4th unit: "We recreate tangram figures and use our tricks." - Application of the knowledge gained to other tangram figures by the children adding tangram figures in different degrees of difficulty, so that the spatial imagination is promoted.

5th unit: "We create a tangram file for free work." - Production of a file for free work by creatively laying and holding on to the outlines, so that the rules of the game and the recognized laying strategies are deepened and a transition from the enactive to the iconic mode of representation is generated by the children themselves.

4 Core concerns of the unit

Expansion of the basic geometric experiences, the spatial imagination as well as promotion of the visual perceptual ability by laying out outline figures with the laying game "Tangram", by relating the flat geometric forms triangle, rectangle, square and parallelogram to each other.

4.1 Central work order

Lay out the figures! Observe the tangram rules!

4.2 Reflection mandate or guiding impulse for the reflection phase

Find tricks to help you lay!

5 Justification of the core concern from a didactic and methodological point of view

5.1. Factual analysis

The content of this unit is the Chinese laying game "Tangram". It is one of the most famous mind games in the world.¹ In contrast to the classic puzzle, the tangram consists exclusively of seven plane shapes of the same color. These are created by the simple halving of sides and diagonals of a square (Fig. 1): two large, congruent isosceles triangles; two small, congruent isosceles triangles; a square; a parallelogram and a medium, isosceles triangle.

Abbildung in dieser Leseprobe nicht enthalten

Fig. 1: "Tangram" taken from Krauthausen/Scherer 2003, p. 64.

All resulting figures are thus equal in area and disassembly. The purpose of the game is that you always put new pieces out of sections. Currently, over 1600 laying figures are known.² The rules of the tangram are simple. All seven shapes should always be used to recreates the image templates, which means that no form may be left.³ The shapes are always attached to each other (the touch at one point is enough, that is, it does not always have to be a form side completely applied) and never placed on top of each other. The replica must correspond exactly to the image template, otherwise the task was not solved. The slightest changes in the replica visibly change the figure laid out.⁴

In this unit, the students fall back on a variety of often unconscious laying strategies:

- Trial and error: Replacement of tangram parts until finding the right solution

à Tilting, moving and rotating individual parts

- start with larger tiles , so that these quickly find a fixed place and thus the number of parts still to be placed is reduced⁵

- Search for Clues : start with unique, easily identifiable subforms at the edge and thus reduce the number of parts still to be put

- Orientation to the outline different subfigures

à form

à length

à Angles/ corners of the surfaces not yet laid out (pointed, blunt)

- Exploitation of Form- Relationships and Congruence :

à Place congruent figures by exchanging several pieces/ large tiles for several small ones and vice versa: for example:

- Kl. Triangle + kl. Triangle = square
- Kl. Triangle + kl. Triangle = mittl. triangle
- Kl. Triangle + kl. Triangle = parallelogram
- Parallelogram + kl. Triangle = trapezoid

[...]

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¹ cf. Müller, Wittmann 1997, p. 10.

² cf. Gawlista 2000, p. 16.

³ cf. Ibid. p. 14

⁴ cf. Schmidt Games, Instructions.

⁵ cf. Gawlista 2000, p. 16.

• College: Studienseminar Hamm
• Grade: 1.5
• Author: Stefanie Hiller (Author)
• Publication Year: 2009
• Pages: 15
• Catalog Number: V1193903
• ISBN (PDF): 9783346627902
• Language: English
• Tags: laying