8EE-Analyze+and+solve+linear+equations+and+pairs+of+simultaneous+linear+equations

8.EE.7.Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form //x// = //a//, //a// = //a//, or //a// = //b// results (where //a// and //b// are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.EE.8.Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. //For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.// c. Solve real-world and mathematical problems leading to two linear equations in two variables. //For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.// || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)** === EE.7 2. Reason abstractly and quantitatively. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. EE.8 8.TT.1 Use technology and other resources for assigned tasks. 8.SE.1 Analyze responsible behaviors when using information and technology resources. 8.SI.1 Evaluate information resources based on specified criteria. 8.TT.1 Use technology and other resources for assigned tasks. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking**=== Remembering Understanding Applying Analyzing Evaluating Creating || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**=== sign. Students recognize that the solution to the equation is the value(s) of the variable, which make a true equality when substituted back into the equation. Equations shall include rational numbers, distributive property and combining like terms. Students write equations from verbal descriptions and solve. will discover these cases as they graph systems of linear equations and solve them algebraically. Students graph a system of two linear equations, recognizing that the ordered pair for the point of intersection is the x-value that will generate the given y-value for both equations. Students recognize that graphed lines with one point of intersection (different slopes) will have one solution, parallel lines (same slope, different y-intercepts) have no solutions, and lines that are the same (same slope, same y-intercept) will have infinitely many solutions. By making connections between algebraic and graphical solutions and the context of the system of linear equations, students are able to make sense of their solutions. Students need opportunities to work with equations and context that include whole number and/or decimals/fractions. Students define variables and create a system of linear equations in two variables. For many real world contexts, equations may be written in standard form. Students are not expected to change the standard form to slope-intercept form. However, students may generate ordered pairs recognizing that the values of the ordered pairs would be solutions for the equation.
 * ===**Common Core Standards**===
 * 1) Make sense of problems and persevere in solving them.
 * 2) Reason abstractly and quantitatively.
 * 3) Construct viable arguments and critique the reasoning of others.
 * 4) Model with mathematics.
 * 5) Use appropriate tools strategically.
 * 6) Attend to precision.
 * 7) Look for and make use of structure.
 * 8) Look for and express regularity in repeated reasoning. ||
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**===
 * 8.EE.7** Students solve one-variable equations including those with the variables being on both sides of the equals
 * 8.EE.8** Systems of linear equations can also have one solution, infinitely many solutions or no solutions. Students

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**I can...**
I can solve linear equations with one variable. I can simplify equations to solve problems. I can solve different types of linear equations. I can evaluate system of equations. I can solve system of equations by graphing. I can solve system of equations by algebraic expressions. I can solve real life problems with system of equations.
 * 8.EE.7**
 * 8.EE.8**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Essential Vocabulary**
intersecting, parallel lines, coefficient, distributive property, like terms, substitution, system of linear equations

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation**
Work station for simultaneous equations and function rules: Looking at Lines page 200

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Intervention:**
Hands-on Activities book EE.7 page 176 and EE.8 page 179

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Enrichment:**
Navigating Through Algebra page 81

[[file:fun_websites_for_8th_grade_math.doc]]
===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources**=== Carnegie Learning chapters 1,11, and 12 Mathematics Station Activites EE.8 pages 56,67, and 77 US Debt Clock project
 * Quantiles EE.7a**
 * Quantiles EE.7b**
 * Quantiles EE.8a**
 * Quantiles EE.8b**
 * Quantiles EE.8c**

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===
 * Refer to NC DPI unpacked content pages 15-18**
 * Refer to Arizona Academic Content standards pages 10-12**