3-31-2014 GRADE 8 LINEAR EQUATIONS AND PROPORTIONS

TECHING THE CCCS

MATHEMATICS STANDARDS

GRADES 6-8

MATH GRADE 8: linear equations and proportions

Mathematics     Grade 8
Formulate and reason about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations
Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions (y/x = m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin. They understand that the slope (m) of a line is a constant rate of change, so that if the input or x-coordinate changes by an amount A, the output ory-coordinate changes by the amount m·A. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and y-intercept) in terms of the situation.  Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.
Understand the connections between proportional relationships, lines, and linear equations.			Resources
	8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.	For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.	Utah Core Standards Resources IXL Practice Scatter Plot Excel Calculating Slope Save Our Dumb Planet Slope and Intercept Slope and y-Intercept Cab Fares
	8.EE.6. Use similar triangles to explain why the slope m is the same between any two            distinct points on a non-                vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.		T-chart  Graphing Slope Linear Equation Test Linear Function Graphing Equations and Inequalities Linear Function and Graph Line Plotter Slope of a Line Determining Slope Slope Tutorial

3-28-14 8th Grade Solving Linear Expressions and Proportions

TECHING THE CCCS

MATHEMATICS STANDARDS

GRADES 6-8

MATH GRADE 8: SOLVE Linear expressions and proportions

Mathematics     Grade 8     Expressions & Proportions
Formulate and reason about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations
Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions (y/x = m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin. They understand that the slope (m) of a line is a constant rate of change, so that if the input or x-coordinate changes by an amount A, the output ory-coordinate changes by the amount m·A. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and y-intercept) in terms of the situation.  Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.
Understand the connections between proportional relationships, lines, and linear equations.			Resources
	8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.	For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.	Utah Core Standards Resources IXL Practice Scatter Plot Excel Calculating Slope Save Our Dumb Planet Slope and Intercept Slope and y-Intercept Cab Fares
	8.EE.6. Use similar triangles to explain why the slope m is the same between any two            distinct points on a non-                vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.		T-chart  Graphing Slope Linear Equation Test Linear Function Graphing Equations and Inequalities Linear Function and Graph Line Plotter Slope of a Line Determining Slope Slope Tutorial

3-27-2014 8TH GRADERS SOLVE LINEAR EQUATIONS

TECHING THE CCCS

MATHEMATICS STANDARDS

GRADES 6-8

MATH GRADE 8: SOLVE LINEAR EQUATIONS

Mathematics     Grade 8
Formulate and reason about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations
Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions (y/x = m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin. They understand that the slope (m) of a line is a constant rate of change, so that if the input or x-coordinate changes by an amount A, the output or y-coordinate changes by the amount m·A. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and y-intercept) in terms of the situation.  Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.
Analyze and solve linear equations and pairs of simultaneous linear equations.			Resources
	8.EE.7. Solve linear equations in one variable.	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, ora = b results (where a and b are different numbers).	Algebra Help Save the Zogs Balance Beam Balance Beam II Linear Equation Solver Easy Algebra Equations and Inequalities Linear Equation Study Guide Word Problem Equations One Unknown One Step Equations
		Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.	Regents Linear Equations Transparent Algebra Expanding Expressions Expanding and Simplifying Expansion and Factorization
	8.EE.8. Analyze and solve pairs of simultaneous linear equations.	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.	Virtual Math Lab Linear Relationships Intersection of 2 lines Math Matters Simultaneous Equations
		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.	2 Equation Drills Linear Equations Solver Linear Equation Solver II Web Calculator 2 Equations, 2 Unknowns Substitution Method Systems Tutorial
		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.	Word Problems that lead to Simultaneous Equations Graphing Systems Algebra Class Word Problems Pump Up! Worksheets