Mathematics 6 (Grade 6)
3: Expressions & Equations (6.EE)
In this unit, students 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 understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple onestep equations. Students 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.
What should my child know and be able to do?
Students will:
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.A.2
Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.A.2.A
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.
6.EE.A.2.C
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in realworld problems. Perform arithmetic operations, including those involving wholenumber 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.
Compute fluently with multidigit numbers and find common factors and multiplies.
6.NS.B.4
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.A.2.B
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.
6.EE.A.3
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.
6.EE.A.4
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 onevariable equations and inequalities.
6.EE.B.5
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6.EE.B.6
Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
6.EE.B.7
Solve realworld and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
6.EE.B.8
Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.C.9
Use variables to represent two quantities in a realworld 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.
Students will:
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.A.2
Write, read, and evaluate expressions in which letters stand for numbers.
 Check for Understanding: Evaluating Expressions with Variables Word Problems
 Review/Rewind: Evaluating Expressions with Two Variables
 Enrichment Tasks: Distance to School
6.EE.A.2.A
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.
 Check for Understanding: Writing Expressions with Variables  Writing Expressions 2  Writing Expressions with Variables Word Problems
 Review/Rewind: Writing Basic Expressions with Variables
 Enrichment Tasks: Writing Expressions
6.EE.A.2.C
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in realworld problems. Perform arithmetic operations, including those involving wholenumber 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.
 Check for Understanding: Evaluate Expressions in One Variable  Evaluate Expressions in Two Variables  Evaluating Expression with Variables Word Problems
 Review/Rewind: OneStep Equations: Division  OneStep Equations: Multiplication
 Enrichment Tasks: Rectangular Perimeter 1
Compute fluently with multidigit numbers and find common factors and multiplies.
6.NS.B.4
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
 Check for Understanding: Greatest Common Factor (GCF)  Least Common Multiple (LCM)  GCF and LCM Word Problems  Distributive Property
 Review/Rewind: Greatest Common Factor Explained  Least Common Multiple
 Enrichment Tasks: Adding Multiples  Florist Shop
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.A.2.B
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.
 Check for Understanding: Identifying Parts of Expressions
 Review/Rewind: Parts of an Expression (Vocabulary)
6.EE.A.3
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.
 Check for Understanding: Combining Like Terms  Equivalent Forms of Expressions 1
 Review/Rewind: Introduction to Combining Like Terms
 Enrichment Tasks: Pan Balance
6.EE.A.4
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.
 Check for Understanding: Equivalent Forms of Expressions 1
 Review/Rewind: Equivalent Forms of Expressions
 Enrichment Tasks: Equivalent Expressions  Rectangular Perimeter 2
Reason about and solve onevariable equations and inequalities.
6.EE.B.5
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
 Check for Understanding: Testing Solutions to Equations
 Review/Rewind: Testing Solutions to Equations
 Enrichment Tasks: Log Ride
6.EE.B.6
Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
 Check for Understanding: Constructing and Solving Linear Equations Word Problems
 Review/Rewind: What is a Variable?
 Enrichment Tasks: Firefighter Allocation  Triangular Tables
6.EE.B.7
Solve realworld and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
 Check for Understanding: OneStep Equation Intuition  OneStep Equations  OneStep Equations With Multiplication  Constructing and Solving Linear Equations Word Problems
 Review/Rewind: One Step Word Problem: Super Yoga (Part 1)  Super Yoga (Part 2)
 Enrichment Tasks: Morning Walk  Fruit Salad
6.EE.B.8
Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
 Check for Understanding: Use Inequalities to Describe Real World Contexts  Inequalities on a Number Line
 Review/Rewind: Graphing Inequalities on a Number Line
 Enrichment Tasks: Fishing Adventures 1
Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.C.9
Use variables to represent two quantities in a realworld 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.
 Check for Understanding: Dependent and Independent Variables
 Review/Rewind: Dependent and Independent Variables
 Enrichment Tasks: Chocolate Bar Sales
What are some signs of student mastery?

Tools & Technology
Algebra Tiles (NCTM)  Use these tiles to solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra. Geoboard (NLVM)  Use this tool to create polygons and find the area or perimeter of the figure. (Java) Who Wants to be a Hundredaire? Students are given a written expression and need to choose the appropriate algebraic expression that matches. (Adobe Flash required) Like Terms Invaders Students will identify like terms in a matching game. (Adobe Flash required) Graphing Inequalities on a Number Line Students will choose the appropriate circle and then the direction of the shading on a number line. (Adobe Flash required) 
More 4 U
Interested in learning more about the use of Algebra Tiles in math class? Watch this video on "Solving One and Two Step Equations with Algebra Tiles." This video teaches how tape diagrams can be used to solve and understand the solutions to algebraic equations.

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