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6-A-3-1

Page history last edited by Brenda Butz 6 years, 2 months ago

6.A.3.1 Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.

In a Nutshell

Understanding the relationship between verbal phrases and mathematical symbols allows for translation of words into expressions, equations, or inequalities. Variables are used as placeholders for unknown quantities, and may have more than one value. The equal sign indicates balance between the left and right side of an equation, while the greater than or less than sign shows that both sides are different or unbalanced.

Student Actions	Teacher Actions
Develop a deep and flexible conceptual understanding by exploring how real-world and mathematical situations can be translated into expressions, equations, or inequalities using standard algebraic conventions. Develop the ability to generalize and model by exploring different real-world and mathematical situations that can be modeled using mathematical symbols in the form of expressions, equations, and inequalities. Number lines can also be used to model equations and inequalities. Develop the ability to communicate mathematically to explain how to determine which model is appropriate for a given real-world or mathematical situation.	Build procedural fluency by facilitating student exploration with standard algebraic conventions for writing expressions, equations, and inequalities. Implement tasks that promote reasoning and problem solving by choosing real-world and mathematical situations relevant to a student’s daily life that can be represented as expressions, equations, and inequalities. Facilitate meaningful mathematical discourse among students to build understanding about representing real-world and mathematical situations as expressions, equations, and inequalities by analyzing and comparing student approaches.
Key Understandings	Misconceptions
That expressions, equations, and inequalities can be used to represent patterns and relationships found in the real world. Variables are used to represent unknown quantities. A variable in an inequality can represent more than one value. That the equal sign in an equation means “is the same as”. Be able to use number lines to model equations and inequalities. How to translate real-world and mathematical situations into mathematical statements using rational numbers, operational symbols, variables, and inequality symbols (=, <, , >, ) when necessary to form equations or inequalities.	Think variables can only represent one number. Have trouble distinguishing between letters used to represent variables and letters used to represent units of measure (e.g., 5m and 5 m as in meters, or 3h and 3 h, as in hours) Have trouble using the standard algebraic notation for multiplying a variable by a coefficient. That is, students may write x * 5 = 10 instead of 5x = 10. Have trouble choosing between an operational sign or inequality symbol for phrases like “more than” or “less than”. Not choose the correct inequality symbol for verbal phrases such as “at most” or “no more than”.