Tennessee Curriculum Center

Standard 3: Algebra > Patterns, Relations and Functions Thread | Algebra I

Associated Tennessee Learning Expectations
Use algebraic thinking to analyze and generalize patterns.

Developing a Clear Learning Target

About This Topic Thread
Algebra is best learned as a set of concepts and techniques tied to the representation of quantitative relations and as a style of mathematical thinking for formalizing patterns, functions, and generalizations. Although many adults think that algebra is an area of mathematics more suited to middle school or high school students, even young children can be encouraged to use algebraic reasoning as they study numbers and operations and as they investigate patterns and relations among sets of numbers. In the Algebra Standard, the connections of algebra to number and everyday situations are extended in the later grade bands to include geometric ideas.
Preceding Grade Level
Compare and contrast linear and nonlinear functions.
This Grade Level
Use algebraic thinking to analyze and generalize patterns.
Next Grade Level
Use algebraic thinking to analyze and generalize patterns.
Understand, analyze, transform and generalize mathematical patterns, relations and functions using properties and various representations.
Explore the effect of transformations on geometric figures and shapes in the coordinate plane.
Scaffolded (Unpacked) Ideas
  1. Students should be able to understand the relationships among tables, graphs, and symbols and to judge the advantages and disadvantages of each way of representing relationships for particular purposes.
  2. Systematic experience with patterns can build up to an understanding of the idea of function.
  3. Students can study sequences that can best be defined and computed using recursion, such as the Fibonacci sequence, 1, 1, 2, 3, 5, 8, ....
  4. Recursive sequences appear naturally in many contexts and can be studied using technology.
  5. Students should be able to understand the relationships among tables, graphs, and symbols and to judge the advantages and disadvantages of each way of representing relationships for particular purposes.
Academic Vocabulary

Tennessee Academic Vocabulary for Patterns, Relations and Functions | Algebra I

* Terms not included on the TDOE Academic Vocabulary list
Questions to Focus Instruction
  1. How do patterns build a foundation for algebraic reasoning?
  2. How do inverse relationships help students to make sense of mathematical procedures?
  3. How can the regularity in patterns be described verbally rather than with mathematical symbols?