Learning algebra means learning a language to describe relationships and functions. This language can be a problem, a table, a graph, an expression, an equation, or a function. The concept of function is one of the most important mathematical concepts, and reasoning about patterns helps students understand the concept of function. Reasoning about patterns involves the mathematical process of generalizing or expressing generality. Generalizing patterns means exploring a situation for regularities and relationships, systematically organizing the data, and expressing the pattern or relationship symbolically.
In this unit, students learn to distinguish between arithmetic and geometry sequences in addition to extending them. They investigate patterns graphically and symbolically, represent patterns in tables or graphs, and generalize patterns into a rule or function. Students analyze graphs globally by looking at the shape of the graph and how it changes. Analyzing graphs globally leads to a deeper understanding of function.
An important part of understanding the language of algebra is learning notations, conventions, and mathematical properties. Students work with problems that provide them with opportunities to understand the need for a unique answer and the need for rules that are required to achieve a unique answer. Students investigate computational procedures using order of operations and the distributive property. The distributive property is one of the most useful properties for simplifying and solving algebraic equations. Students use symbols to represent a situation, recognize equivalence, and use inverses or “opposite operations” to solve equations.
Different representations such as tables and graphs are used to describe relationships and regularities. Students construct and use mathematical representations in problems, tables, graphs, and equations. They also learn to make connections among different representations and to translate one representation to another (i.e., table to graph). They explore the interrelationships between number patterns, tables, graphs, expressions, and equations.
Students develop an understanding of expression and equation. They recognize equivalent expressions and equivalent equations. Students learn that algebraic expressions can be manipulated to simplify expressions and to solve equations. They create situations for expressions and equations as a complementary activity to solving equations.
Unit 4 is typically a seven-week unit taught from March through May.
Unit 4 Standards for Math 6 (Math A)(PDF)
Explanation of what your child should understand by the end of each unit (enduring understandings), how he/she will get to that understanding (essential questions), and how he/she will be evaluated (indicators).
Unit 4 Content map for Math 6 (Math A) (PDF)
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