Top-Five Most Difficult Algebra Concepts 1) - Multiplying Polynomials by Monomials. 2) - Modeling Using Exponential Functions. 3) - Averaging Data with Different Units. 4) - Converting Units for Derived Quantities. 5) - Complementary and Supplementary Angles.

Algebraic reasoning. The student applies mathematical process standards to identify and apply number patterns within properties of numbers and operations in order to describe relationships.

When thinking algebraically about a relationship between two numbers, we think of the first number as changing to become another number. For example, as well as thinking of 2 + 5 = 7 as joining two parts (2 and 5) to make a whole (7), we can also think of it as adding 5 will change 2 into 7.

“Algebraic reasoning is a process in which students generalize mathematical ideas from a set of particular instances, establish those generalizations through the discourse of argumentation, and express them in increasingly formal and age-appropriate ways.”

Algebraic thinking includes the ability to recognize patterns, represent relationships, make generalizations, and analyze how things change. In the early grades, students notice, describe, and extend patterns; and they generalize about those patterns.

(3) In Algebraic Reasoning, students will build on the knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra I, continue with the development of mathematical reasoning related to algebraic understandings and processes, and deepen a foundation for studies in subsequent mathematics courses.