What does the representation with tiles help students develop an understanding of?

• A. Critique the reasoning of others.
• B. Support reasoning with evidence.
• C. Create a basis for the concept of grouping.
• D. Develop understanding of the base-ten system.

Answer: (D)

The representation with tiles is a concrete way to illustrate mathematical concepts, especially in building an understanding of the base-ten system. When students use tiles, they can physically manipulate objects to represent units (ones), tens, hundreds, and so on. This hands-on approach helps students visualize how numbers are constructed and decomposed within the base-ten system.

For example, a group of ten unit tiles can be bundled to represent one ten tile. This not only reinforces the concept of counting in tens but also helps students grasp place value—the foundation of our number system. By working with tiles, students can see how numbers work together within the structure of the base-ten system, facilitating a deeper comprehension of addition, subtraction, and even multiplication as they learn to regroup and reorganize quantities.

This foundational understanding is crucial for their future work in mathematics, as it sets the stage for more advanced concepts and operations.