Unit

#### Description:

This is an 8-week unit of instruction for an Algebra I course that covers all the generally required material for the topics of graphing linear equations, solving systems of linear equations, simple linear regression, and applying systems of linear equations to real-life situations. The unit is constructed using a Project-Based Learning approach, where the students work collaboratively to run a class business during the 8 weeks. As they move through the various stages of planning and executing the business, they learn various concepts related to linear equations and how they directly apply to predicting demand or cost/revenue information. Finally, the project incoporates technology education by having the students use Microsoft Excel and Powerpoint to report and analyze the sales results of their business.

#### Subjects:

• Mathematics > General
• Mathematics > Algebra
• Mathematics > Equations
• Mathematics > Graphing
• Mathematics > Problem Solving
• Mathematics > Statistics

• Grade 6
• Grade 7
• Grade 8
• Grade 9
• Grade 10

#### Keywords:

Algebra Linear Equations Graphing Linear Regression

English

Members

#### License Deed:

Creative Commons Attribution 3.0

#### Collections:

Hot Topics - Economics
Algebra Collection A
Update Standards?

#### MA.6.AF.1.1: Mathematics

Write and solve one-step linear equations in one variable.

#### MA.6.AF.1.2: Mathematics

Write and evaluate an algebraic expression for a given situation, using up to three variables.

#### MA.6.AF.1.3: Mathematics

Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process.

#### MA.6.AF.1.4: Mathematics

Solve problems manually by using the correct order of operations or by using a scientific calculator.

#### MA.7.AF.1.1: Mathematics

Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).

#### MA.7.AF.1.2: Mathematics

Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)².

#### MA.7.AF.1.3: Mathematics

Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used.

#### MA.7.AF.1.4: Mathematics

Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly.

#### MA.7.AF.1.5: Mathematics

Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.

#### MA.7.AF.3.1: Mathematics

Graph functions of the form y = nx² and y = nx³ and use in solving problems.

#### MA.7.AF.3.3: Mathematics

Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio ("rise over run") is called the slope of a graph.

#### MA.7.AF.3.4: Mathematics

Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities.

#### MA.7.AF.4.1: Mathematics

Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.

#### MA.8-12.AI.4.0: Mathematics

Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x - 5) + 4(x - 2) = 12.

#### MA.8-12.AI.5.0: Mathematics

Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

#### MA.8-12.AI.6.0: Mathematics

Students graph a linear equation and compute the x-and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).

#### MA.8-12.AI.7.0: Mathematics

Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.

#### MA.8-12.AI.9.0: Mathematics

Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.

#### MA.D.2.3.1: Mathematics

represents and solves real-world problems graphically, with algebraic expressions, equations, and inequalities.

#### MA.D.2.3.2: Mathematics

uses algebraic problem-solving strategies to solve real-world problems involving linear equations and inequalities.

#### MA.D.2.4.2: Mathematics

uses systems of equations and inequalities to solve real-world problems graphically, algebraically, and with matrices.

#### MA.6.MA.6.A.3.1: Mathematics

Write and evaluate mathematical expressions that correspond to given situations.

#### MA.6.MA.6.A.3.2: Mathematics

Write, solve, and graph one- and two- step linear equations and inequalities.

#### MA.6.MA.6.A.3.3: Mathematics

Works backward with two-step function rules to undo expressions.

#### MA.6.MA.6.A.3.4: Mathematics

Solve problems given a formula.

#### MA.6.MA.6.A.3.5: Mathematics

Apply the Commutative, Associative, and Distributive Properties to show that two expressions are equivalent.

#### MA.6.MA.6.A.3.6: Mathematics

Construct and analyze tables, graphs and equations to describe linear functions and other simple relations using both common language and algebraic notation.

#### MA.7.MA.7.A.3.3: Mathematics

Formulate and use different strategies to solve one-step and two-step linear equations, including equations with rational coefficients.

#### MA.7.MA.7.A.3.4: Mathematics

Use the properties of equality to represent an equation in a different way and to show that two equations are equivalent in a given context.

#### MA.8.MA.8.A.1.1: Mathematics

Create and interpret tables, graphs, and models to represent, analyze, and solve problems related to linear equations, including analysis of domain, range and the difference between discrete and continuous data.

#### MA.8.MA.8.A.1.2: Mathematics

Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem.

#### MA.8.MA.8.A.1.3: Mathematics

Use tables, graphs, and models to represent, analyze, and solve real-world problems related to systems of linear equations.

#### MA.8.MA.8.A.1.4: Mathematics

Identify the solution to a system of linear equations using graphs.

#### MA.8.MA.8.A.1.5: Mathematics

Translate among verbal, tabular, graphical and algebraic representations of linear functions.

#### MA.8.MA.8.A.1.6: Mathematics

Compare the graphs of linear and non-linear functions for real-world situations.

#### MA.9-12.MA.912.A.3.1: Mathematics

Solve linear equations in one variable that include simplifying algebraic expressions.

#### MA.9-12.MA.912.A.3.2: Mathematics

Identify and apply the distributive, associative, and commutative properties of real numbers and the properties of equality.

#### MA.9-12.MA.912.A.3.3: Mathematics

Solve literal equations for a specified variable.

#### MA.9-12.MA.912.A.3.4: Mathematics

Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution.

#### MA.9-12.MA.912.A.3.5: Mathematics

Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities.

#### MA.9-12.MA.912.A.3.6: Mathematics

Solve and graph the solutions of absolute value equations and inequalities with one variable.

#### MA.9-12.MA.912.A.3.7: Mathematics

Rewrite equations of a line into slope-intercept form and standard form.

#### MA.9-12.MA.912.A.3.8: Mathematics

Graph a line given any of the following information: a table of values, the x- and y-intercepts, two points, the slope and a point, the equation of the line in slope-intercept form, standard form, or point-slope form.

#### MA.9-12.MA.912.A.3.9: Mathematics

Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line.

#### MA.9-12.MA.912.A.3.10: Mathematics

Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line.

#### MA.9-12.MA.912.A.3.11: Mathematics

Write an equation of a line that models a data set and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.

#### MA.9-12.MA.912.A.3.12: Mathematics

Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph.

#### MA.9-12.MA.912.A.3.13: Mathematics

Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology.

#### MA.9-12.MA.912.A.3.14: Mathematics

Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods.

#### MA.9-12.MA.912.A.3.15: Mathematics

Solve real-world problems involving systems of linear equations and inequalities in two and three variables.
Curriki Rating
On a scale of 0 to 3
3
On a scale of 0 to 3

This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of 2009-07-05.

#### Component Ratings:

Technical Completeness: 3
Content Accuracy: 3
Appropriate Pedagogy: 3

#### Reviewer Comments:

This unit is a subunit of the course "Teaching Linear Equations through Running a Small Business. This unit has several lessons included within it. The entire course is excellent.
Anna Batchelder
May 19, 2010

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