Student Actions

Teacher Actions

• Develop Accurate and Appropriate Procedural Fluency when using efficient and accurate operations with numbers given an expression to evaluate, and justify the steps to be performed according to the order of operations.

• Develop a Deep and Flexible Understanding when grappling with the idea that evaluating an expression with substitution results in a solution that is determined by a specific value and solutions can vary since variables can be replaced with any value. 

• Implement meaningful tasks that promote reasoning and problem-solving by providing students with opportunities to correct mistakes within problems involving substitution and see that completing steps in different orders produces different results. 

• Build procedural fluency by having students show and discuss their process of substituting and simplifying expressions and justifying their steps. 

Key Understandings

Misconceptions 

• Evaluate an algebraic expression by replacing the variable with the defined values and using order of operations to find the value of the expression. 

• Variables in an algebraic expression can be replaced by any specified value and solutions will vary. 

• Order of Operations is often used improperly. Students believe multiplication should occur before division and addition should occur before subtraction when in reality multiplication and division are one step (from left to right) along with addition and subtraction.

• Students may not recognize the correct operation when substituting values for multiple variables and/or terms with coefficients. It helps to encourage students to use parentheses when substituting.  (ex. 4x when x=3;  students might substitute this as 43 instead of 4(3) ).

• Students may incorrectly simplify an expression involving exponents when substituting with a negative value.   For  example:

For 3x², when x =  -5, students may simplify as 3(-5)² = 3(-25) or (-15)²

• Students may not recognize the operation between the coefficient and the variable is multiplication. 

  Knowledge Connections

Prior Knowledge

Leads to 

• Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or it, for a given variable, an equation or inequality involving a variable is true or false (6.A.1.3).

• Evaluate numerical expressions using calculators and other technologies and justify solutions using order of operations and grouping symbols (7.A.4.2).

• Evaluate linear, absolute value, rational, and radical expressions (A1.A.3.4).

• Use function notation; evaluate a function, including nonlinear, at a given point in its domain algebraically (A1.F.3.2) 

  Sample Assessment Items

The Oklahoma State Department of Education is releasing sample assessment items to illustrate how state assessments might be designed to measure specific learning standards/objectives. These examples are intended to provide teachers and students with a clearer understanding of how the state assesses Oklahoma's academic standards and their objectives. It is important to note that these sample items are not intended to be used for diagnostic or predictive purposes. Ways to incorporate the items.

• PA.A.3.1 Money Earned
• PA.A.3.1 Technology Enhanced Item