Student Actions

Teacher Actions

• Develop accurate and appropriate procedural fluency as they solve for a variable in equations of varying types (one-step, two-step, and multistep) including using the distributive property and solving equations with variables on both sides.

• Develop a deep and flexible conceptual understanding when determining how and when to apply knowledge of solving equations with mathematical situations from areas that may include geometry, science, and statistics.

• Develop strategies for problem-solving and mathematical reasoning by choosing appropriate equations and applying logical strategies to model and assess the reasonableness of solutions in mathematical situations.

• Develop the ability to communicate mathematically by correctly interpreting and explaining their solutions in the original context of the problems. 

• Use and connect mathematical representations by providing opportunities for  students to examine a variety of models for a given problem including graphs, tables, diagrams, text, and equations.

• Build procedural fluency from conceptual understanding by providing students with situational problems involving one-variable linear equations that have a wide range of complexity.

• Pose purposeful questions to encourage student thinking at a deeper level, and look for alternate ways of solving. 

• Elicit and use evidence of student thinking by engaging students in discussion, allowing students to provide explanations, and model their strategies for solving equations in various mathematical contexts.

• Implement tasks that promote reasoning and problem-solving by allowing students to accurately interpret and assess the reasonableness of the solution in the context of the mathematical situation. 

Key Understandings

Misconceptions 

• Properties of equality and inverse operations can be used to find missing measures and/or values in the context of mathematical situations. 

• Solutions to equations representing contexts of mathematical models could include units to describe a rational-valued answer.

• Check the validity of the solution in the context of the problem. 

• Students may misuse properties of equality while isolating a variable to solve an equation.

• Students may replace an incorrect variable with a given value when solving a mathematical situation.

• Students may use the incorrect formula to solve a problem.

• Students may have solved for the incorrect variable when multiple variables are in an equation prior to calculating a solution.

• Students may misinterpret the role of the variable in the context of a mathematical situation.

• Students fail to check the validity of the solution in the original problem. 

  Knowledge Connections

Prior Knowledge

Leads to 

• Use substitution to simplify and evaluate algebraic expressions. (PA.A.3.1)

• Justify steps in generating equivalent expressions by combining like terms and using order of operations (to include grouping symbols). Identify the properties used, including the properties of operations (associative, commutative, and distributive). (PA.A.3.2)

• Represent real-world situations using equations and inequalities involving one variable. (PA.A.4.3)

• Collect, display, and interpret data using scatter plots. Use the shape of the scatter plot to find the informal line of best fit, make statements about the average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels, and units. (PA.D.1.3). 

• Apply the properties of polygons, and use them to represent and apply mathematical models involving perimeter and area (e.g., triangles, special quadrilaterals, regular polygons up to 12 sides, composite figures). (G.2D.1.7)

• Represent, use, and apply mathematical models and other tools (e.g., nets, measuring devices, formulas) to solve problems involving surface area and volume of three-dimensional figures (prisms, cylinders, pyramids, cones, spheres, composites of these figures). (G.3D.1.1) 

• Use ratios derived from similar three-dimensional figures to make conjectures, generalize, and to solve for unknown values such as angles, side lengths, perimeter, and circumference of a face, area of a face, and volume. (G.3D.1.2)