Types of Mathematical Relationships

This page delves into specific types of mathematical relationships, focusing on proportional and inversely proportional mappings.

Definition: Proportionale zuordnung describes steady growth where the ratio between corresponding values remains constant $k$.

Example: Using the bread price example, the proportionality factor is 2, as demonstrated by:

• 2:1 = 2
• 4:2 = 2
• 6:3 = 2

Highlight: Antiproportionale zuordnung describes inverse growth where the product of corresponding values remains constant.

Example: In a gardening scenario, as the number of gardeners increases, the time needed for work decreases, maintaining a constant product of 6:

• 1 gardener × 6 hours = 6
• 2 gardeners × 3 hours = 6
• 3 gardeners × 2 hours = 6

Vocabulary:

• Proportionalitätsfaktor: Proportionality factor
• Antiproportionalitätsfaktor: Inverse proportionality factor

Understanding Mathematical Mappings

This page introduces the fundamental concepts of mathematical mappings and their various representations. The content focuses on how values are mapped to each other in mathematical relationships.

Definition: A mapping assigns exactly one value to another value (one x-value is assigned exactly one y-value).

Example: In a real-world application, the price of bread is used where 1 bread costs 2€, 2 breads cost 4€, and so on, demonstrating a proportionale zuordnung beispiele.

Highlight: Three main representation methods are introduced:

1. Arrow diagrams (pfeildiagramm mathe)
2. Coordinate systems
3. Value tables (proportionale zuordnung tabelle)

Vocabulary:

• Ausgangswert: Initial value
• Zugeordneter Wert: Assigned value
• Wertetabelle: Value table

The page demonstrates how to create and read these representations, with particular emphasis on the systematic organization of data in both horizontal and vertical formats.