Which of the following is an effective teaching-learning material to introduce basic concepts such as shapes, perimeter, area and characteristics of polygons?

The correct option is Geoboard.

Understanding the Geoboard:
A Geoboard is a mathematical manipulative board with a grid of pegs around which rubber bands can be stretched. It allows students to physically create and explore two-dimensional geometric figures such as triangles, squares, rectangles, and other polygons.

Why Geoboard is Effective for These Concepts:
1. Shapes and Characteristics of Polygons: Students can form various polygons by stretching rubber bands across different pegs, helping them directly observe properties like sides, vertices, and angles.
2. Perimeter: By counting the units/segments along the boundary of the created shape, students visually and tactilely grasp the concept of perimeter.
3. Area: Students can count the square units enclosed inside the shape formed by the rubber band, making the abstract concept of area tangible and easy to understand.

Overview of Other Options:
- Hanoi Tower: A mathematical puzzle used mainly to teach problem-solving strategies, recursion, and sequence concepts.
- Cuisenaire Rods: Colored wooden or plastic rods used primarily for basic arithmetic operations, fractions, and ratio concepts.
- Tangrams: Dissection puzzles consisting of seven flat shapes (tans) used to develop spatial reasoning and composite shape formation, but less effective for systematically measuring perimeter and grid-based area compared to a Geoboard.