Student Actions

Teacher Actions

• Develop a deep and flexible conceptual understanding by exploring how mathematical situations can be translated into expressions, equations, or inequalities using standard algebraic conventions.

• Develop the ability to generalize and model by exploring different 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 mathematical situation.

• Develop a productive mathematical disposition by justifying the reasonable of their solutions. 

• 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 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 modeling mathematical situations as expressions, equations, and inequalities by analyzing and comparing student approaches. 

Key Understandings

Misconceptions 

• Expressions, equations, and inequalities can be used to represent patterns and relationships found in mathematical situations.

• Variables are used to represent unknown quantities.

• A variable in an inequality can represent more than one value.

• The equal sign in an equation means “is the same as”.

• Translating mathematical situations into mathematical statements use rational numbers, operational symbols, variables, and inequality symbols (=, <,  , >, ) to form equations or inequalities. 

• Students may think variables can only represent one number or value.

• Students may 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) are the same.

• Students may think a multiplication symbol must be used when multiplying a variable by a coefficient.  That is, students may write x * 5 = 10 instead of 5x = 10.

• Students may think  words or phrases like “more than” or “less than” have no baring in choosing between an operational sign or inequality symbol. 

  Knowledge Connections

Prior Knowledge

Leads to 

• Generate equivalent numerical expressions and solve problems using number sense involving whole numbers by applying the commutative property, associative property, distributive property, and order of operations (excluding exponents). (5.A.2.1)

• Determine whether an equation or inequality involving a variable is true or false for a given value of the variable (5.A.2.2).

• Use properties of operations (associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols, and whole number exponents. (7.A.4.1)