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

3-18-2013 VARIABLE VARIABLES

TECHING THE CCCS

MATHEMATICS STANDARDS

GRADES 6-8

MATH GRADE 6: DEPENDENT AND INDEPENDENT VARIABLES

STRAND	CPI	SKILLS	Resources
Expressions & Equations	The goal: Students will be able to apply and extend previous understandings of arithmetic to algebraic expressions, reason about and solve one-variable equations and inequalities, and represent and analyze quantitative relationships between dependent and independent variables.	More specifically, students will understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students will understand that expressions in different forms can be equivalent, and they will use the properties of operations to rewrite expressions in equivalent forms. Students will learn that the solutions of an equation are the values of the variables that make the equation true. Students will use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students will construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.	Algebraic Reasoning Algebra Algebra Games Math By Design Maths Masters Algebra Virtual Manipulatives Exploriments Identifying Variables Controls and Variables Math Words Variables and Expressions on Khan Academy Differentiated Lesson Plan
Represent and analyze quantitative relationships between dependent and independent variables.	Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.		Patterns Linear Sequences and  Quadratic Sequences Positive Linear   Function Machine Algebra and Graphing  Graphing Independent and Dependent Variables Review Lesson IXL practice Practice Problems Shmoop Lesson Sample Problems Project Idea Linear Relationships Lesson Graphing Functions on Math Planet SMART notebook Lesson Linear Equation Project

2-19-2013 It's Still Algebra to Me

TECHING THE CCCS

MATHEMATICS STANDARDS

GRADES 6-8

MATH GRADE 6: algebraic expressions

STRAND	CPI	SKILLS	Resources
Expressions & Equations	The goal: Students will be able to apply and extend previous understandings of arithmetic to algebraic expressions, reason about and solve one-variable equations and inequalities, and represent and analyze quantitative relationships between dependent and independent variables.	More specifically, students will understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use   expressions and formulas to solve problems. Students will understand that expressions in different forms can be equivalent, and they will use the properties of operations to rewrite expressions in equivalent forms. Students will learn that the solutions of an equation are the values of the variables that make the equation true. Students will use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students will construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.	Algebraic Reasoning Algebra Algebra Games Math By Design Maths Masters Algebra Virtual Manipulatives Exploriments
Apply and extend previous understandings of arithmetic to algebraic expressions.			Pre-Algebra on Shmoop  Algebra: The Supplement
	Write and evaluate numerical expressions involving whole-number exponents.		Powers and Roots Base and Exponent Evaluate Squares Evaluate Cubes Evaluating Exponents Exponents Scientific Notation practice site
	Write, read, and   evaluate expressions in which letters stand for numbers.	Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.	Function Machine Formulas and More on Formulas Writing Algebraic Expressions Writing Expressions Online Learning Khan Academy: Writing Expressions Algebraic Expressions Millionaire IXL practice
		Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.	Translate Sentences into Equations Writing Equations The Mystery Number Song Escape from Planet X Handout - Parts of an Algebraic Expression Basic Definitions and Examples Algebra 1 Basics Video
		Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.	Evaluating Expressions w/ 1 variable Practice Evaluating Expressions w/ 2 variables Practice Balancing Equations Evaluate Expressions Evaluating Expressions Evaluating Polynomials Practice with Evaluating Expressions Math Planet Video Lesson
	Apply the properties of operations to generate equivalent expressions.	For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression   3y.	Properties of Operations Properties Practice Solving with Inverse Operations Order and Zero Properties of Addition Properties
	Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).	For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Reason about and solve one-variable equations and inequalities.	Algebra Four What are Equivalent Expressions Video Lesson Plan Video Lesson with Algebra Tiles