Unit 3

Expressions, Equations, and Inequalities

Unit Description:

Unit 3 consolidates and expands students’ previous work with generating equivalent expressions and solving equations and inequalities. By the end of this unit students should fluently solve multistep problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. This work is the culmination of many progressions of learning in arithmetic, problem solving and mathematical practices.  In solving word problems leading to one-variable equations of the form px + q = r and p(x + q) = r, as well as px + q < r and px + q > r, students should solve these equations fluently. This will require fluency with rational number arithmetic, as well as fluency to some extent with applying properties of operations to rewrite linear expressions with rational coefficients.  Students use the properties of operations and the relationships between addition and subtraction, and multiplication and division, as they formulate expressions, equations, and inequalities in one variable and use these to solve problems. They solve reallife and mathematical problems using numerical and algebraic expressions, equations, and inequalities. At the end of the unit students’ work with expressions and equations is applied to finding unknown angles in a figure.  By using facts about supplementary, complementary, vertical, and adjacent angles, students are able to write and solve simple equations to solve for the unknown angle.  The work and required fluency expectations in this unit are a major capstone leading to the mathematical development necessary to perform operations with linear equations in Grade 8.

Standards for Mathematical Practice

MP.1 Make sense of problems and persevere in solving them.

MP.2 Reason abstractly and quantitatively.

MP.3 Construct viable arguments and critique the reasoning of others.

MP.4 Model with mathematics.

MP.5 Use appropriate tools strategically.

MP.6 Attend to precision.

MP.7 Look for and make use of structure.

MP.8 Look for and express regularity in repeated reasoning.

Louisiana Student Standards for Mathematics (LSSM)

Enduring Understandings:

*Variables can be used to represent numbers in any type of mathematical problem.

*Understand the difference between an expression and an equation.

*Expressions can be manipulated to suit a particular purpose to solve problems efficiently.

*Mathematical expressions, equations, inequalities, and graphs are used to represent and solve real-world and mathematical problems.

*Constructing simple equations and inequalities to solve real life word problems is a necessary concept.

*Writing and solving real-life and mathematical problems involving simple equations for an unknown angle in a figure helps students as they engage in higher geometry concepts.

*Reason about relationships among two-dimensional figures, which leads to gaining familiarity with the relationships between angles formed by intersecting lines.

*Geometry and spatial sense offer ways to interpret and reflect on our physical environment.

*Analyzing geometric relationships develops reasoning and justification skills.

Essential Questions:

*How can I apply the order of operations and the fundamentals of algebra to solve problems involving equations and inequalities?

*How can I justify that multiple representations in the context of a problem are equivalent expressions?

*How do I assess the reasonableness of my answer?

*How can I use and relate facts about special pairs of angles to write and solve simple equations involving unknown angles?

*What is the total number of degrees in supplementary and complementary angles?

*What is the relationship between vertical and adjacent angles?

*When and how are expressions, equations, and inequalities applied to real world situations?

*What are some possible real-life situations to which there may be more than one solution?

*How does the ongoing use of decimals apply to real-life situations?

*How can geometry be used to solve problems about real-world situations, spatial relationships, and logical reasoning?