ALEX Classroom Resource


Algebra I Module 1, Topic C: Solving Equations and Inequalities

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Algebra I Module 1, Topic C: Solving Equations and Inequalities


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Type: Lesson/Unit Plan


Throughout middle school, students practice the process of solving linear equations (6.EE.5, 6.EE.7, 7.EE.4, 8.EE.7) and systems of linear equations (8.EE.8). Now, in Module 1, Topic C, instead of just solving equations, they formalize descriptions of what they learned before (variable, solution sets, etc.) and are able to explain, justify, and evaluate their reasoning as they strategize methods for solving linear and non-linear equations (A-REI.1, A-REI.3, A-CED.4). Students take their experience solving systems of linear equations further as they prove the validity of the addition method, learn a formal definition for the graph of an equation and use it to explain the reasoning of solving systems graphically, and graphically represent the solution to systems of linear inequalities (A-CED.3, A-REI.5, A-REI.6, A-REI.10, A-REI.12).

Content Standard(s):
MA2015 (2016)
Grade: 9-12
Algebra I
15 ) Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [A-CED4]

Example: Rearrange Ohm's law V = IR to highlight resistance R.

MA2015 (2016)
Grade: 9-12
Algebra I
16 ) Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. [A-REI1]

MA2019 (2019)
Grade: 9-12
Algebra I with Probability
13. Represent constraints by equations and/or inequalities, and solve systems of equations and/or inequalities, interpreting solutions as viable or nonviable options in a modeling context. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions.
Unpacked Content
Evidence Of Student Attainment:
Given a contextual situation involving constraints,
  • Write equations or inequalities or a system of equations or inequalities that model the situation and justify each part of the model in terms of the context.
  • Solve the equation, inequalities or systems and interpret the solution in the original context including discarding solutions to the mathematical model that cannot fit the real-world situation (e.g., distance cannot be negative).
  • Solve a system by graphing the system on the same coordinate grid and determine the point(s) or region that satisfies all members of the system.
  • Determine the point(s) of the region satisfying all members of the system that maximizes or minimizes the variable of interest in the case of a system of inequalities.
Teacher Vocabulary:
  • Constraint
  • System of equations
  • System of inequalities
  • Profit
  • Boundary
  • Closed half plane
  • Open half plane
  • Half plane
  • Consistent
  • Inconsistent
  • Dependent
  • Independent
  • Region
Students know:
  • When a particular system of two variable equations or inequalities accurately models the situation presented in a contextual problem.
  • Which points in the solution of a system of linear inequalities need to be tested to maximize or minimize the variable of interest.
Students are able to:
  • Graph equations and inequalities involving two variables on coordinate axes.
  • Identify the region that satisfies both inequalities in a system.
  • Identify the point(s) that maximizes or minimizes the variable of interest in a system of inequalities.
  • Test a mathematical model using equations, inequalities, or a system against the constraints in the context and interpret the solution in this context.
Students understand that:
  • A symbolic representation of relevant features of a real-world problem can provide for resolution of the problem and interpretation of the situation and solution.
  • Representing a physical situation with a mathematical model requires consideration of the accuracy and limitations of the model.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.13.1: Define systems of equations, constraints, viable solution, and nonviable solution.
ALGI.13.2: Create a system of equations or inequalities to represent the given constraints (linear).
ALGI.13.3: Create an equation or inequality to represent the given constraints (linear).
ALGI.13.4: Determine if a solution to a system of equations or inequalities is viable or nonviable.
ALGI.13.5: Determine if there is one solution, infinite solutions, or no solutions to a system of equations or inequalities.

Prior Knowledge Skills:
  • Recall how to draw a number line.
  • Recognize the symbols for =, >, <, < and >.
  • Substitute for the variable to find the value of a given expression.
  • Choose the correct value to replace each variable in the algebraic expression (Substitution).
  • Convert mathematical terms to mathematical symbols and numbers.
  • Recall how to order positive and negative numbers. (Use number line if needed).
  • Locate the position of integers and/or rational numbers on a horizontal or vertical number line.

Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.11.11 Select an equation or inequality involving one operation (limit to addition or subtraction) with one variable that represents a real-world problem. Solve the equation.

Tags: algebra, argument, constraints, equations, formulas, inequalities, modeling, solution
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There are fifteen lessons on this topic.

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Author: Hannah Bradley