Give examples of three categories of fraction models. What real models have you used that correspond to each of these?

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Three categories of fraction models are:

1. Area Models: These models represent fractions using rectangular or circular shapes. The area or part of the whole shape represents the fraction being shown. Some examples of real models for area models are:
- Pizza slices: Each slice represents a fraction of the whole pizza.
- Grid paper: Using a grid with squares, the fraction can be represented by shading a specific number of squares.

2. Set Models: These models represent fractions as a part of a set or collection. Objects are used to represent the whole and the parts. Some examples of real models for set models are:
- Marbles in a jar: If there are 10 marbles in a jar, and 3 of them are red, then the fraction of red marbles can be represented as 3/10.
- Counters in a bag: If there are 20 counters in a bag, and 5 of them are blue, then the fraction of blue counters can be represented as 5/20.

3. Length Models: These models represent fractions using a line or segment. The length of the line represents the whole, and the fraction is shown as a part of that length. Some examples of real models for length models are:
- Ruler: Marking a specific fraction (e.g., 1/4) on a ruler represents that fraction of the whole length.
- Tape measure: Similarly, marking a specific fraction on a tape measure can represent that fraction of the whole length.

These real models can help visualize and understand fractions in a tangible way. Using these models, learners can physically see the relationship between the whole, the parts, and the fractions being represented.