1. D: Mathematics is a formal science of structure, order and relationships and is considered the basic language and foundation of all the other sciences. It evolved from counting, measuring and describing shapes.
2. C: Number concepts are the building blocks of all mathematical calculations and representations. Students must understand what a number means, in what ways it can and cannot be used, and its relationship to other numbers. They need to be able to depict numbers concretely, pictorially and symbolically.
3. B: There are basic concepts in algebra that allow generalizations about “unknowns.” Patterns and functions represent change and relationships. Equivalence and balance are critical concepts in understanding algebraic equations.
4. A: Teaching math with a procedural approach or by direct instruction means the problem is solved “by the book.” Most students acquire some level of proficiency but are usually unable to apply anything learned in math class in other academic areas or to situations outside of school.
5. D: Teachers must design lesson plans, compose problems and devise activities that require students explain their thought process, compare methods and approaches, and justify results. Using this approach, students learn the definitions, formulas and methods as a natural outcome of understanding and integrating the new concepts.