6TH GRADE PACING GUIDEMATH INNOVATIONS UNIT 4: A BALANCING ACT

January-Mid MarchStandards: 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

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. b) Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression 2(8+7) as a

product of two factors; view (8+7) as both a single entity and a sum of two terms. c) 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 = s2 to find the volume and surface areas of a cube with sides of length s = ½.6.EE.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.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.6.EE.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.6 Use variables to represent numbers and write expressions when solving a real-world 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.7 Solve real-world 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.9 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 a 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.

Standard/Target Section/Lesson # Days Formative AssessmentSection 1: Making Sense of Equality ACT: If bananas cost $0.24 and oranges cost $0.38, what is

the total cost of x bananas and y oranges? A. (x + y)($.24+$.38) B. $.24x + $.38y C. $.62(x + y) D. $.24/x + $.38/y

6.EE.2b Knowledge Target: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient). Knowledge Target: Identify parts of an expression as a single entity, even if not a monomial.6.EE.6 Knowledge Target: Recognize that a variable can

1.1 Understanding Equivalence Patterns*Add: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient).*Add: Identify parts of an expression as a

2

Lewis County Middle School

Standard/Target Section/Lesson # Days Formative Assessmentrepresent an unknown number, or, depending on the purpose at hand, any number in a specified set. Reasoning Target: Relate variables to a context. Reasoning Target: Write expressions when solving a real-world or mathematical problem.

single entity, even if not a monomial.

6.EE.2a Knowledge Target: Use numbers and variables to represent desired operations. Reasoning Target: Translating written phrases into algebraic expressions. Reasoning Target: Translating algebraic expressions into written phrases.

1.2 Representing Balance with Scales, Bars and Equations

2 #8 Set 1; PARCC2 #8, 27; KPREP #2, 2A

Vocabulary 1Geometry Quiz

6.EE.2c Knowledge Target: Substitute specific values for variables. Knowledge Target: Evaluate algebraic expressions including those that arise from real-world problems.

1.3 Divide and Conquer 3 PARCC #16; PARCC2 #32

6.EE.3 Knowledge Target: Generate equivalent expressions using the properties of operations (e.g. distributive property, associative property, adding like terms with the addition property of equality, etc.). Reasoning Target: Apply the properties of operations to generate equivalent expressions.

1.4 Combine, Simplify and Solve*Add: More on properties, especially the distributive property.

3 PARCC #5, 6; PARCC2 #4

Study Guide 1Quiz 1Section 2: Using Models and Symbols to Represent SituationsGeometry Quiz

6.EE.7 Knowledge Target: Define inverse operation. Knowledge Target: Know how inverse operations can be used in solving one-variable equations.

2.1 Magical Expressions 2

6.EE.7 Reasoning Target: Apply rules of the form x + p = q and px = q, for cases in which p,q and x are all nonnegative rational numbers, to solve real world and mathematical problems. (There is only one unknown quantity.) Reasoning Target: Develop a rule for solving one-step equations using inverse operations with nonnegative rational coefficients. Reasoning Target: Solve and write equations for real-world mathematical problems containing one unknown.

2.2 Writing Equations Symbolically 2 PARCC2 #22

6.EE.1 Knowledge Target: Write numerical expressions involving whole number exponents (e.g., 34 = 3x3x3x3). Knowledge Target: Evaluate numerical expressions involving whole number exponents (e.g., 34 = 3x3x3x3 = 81). Knowledge Target: Solve order of operations problems that

2.3 Out of Order 4 ACT #1, 8, 15, 69; PARCC #7; KPREP #6

Lewis County Middle School

Standard/Target Section/Lesson # Days Formative Assessmentcontain exponents (e.g., 3 + 22 – (2 + 3) = 2).6.EE.2c Knowledge Target: Apply order of operations when there are no parentheses for expressions that include whole number exponents.

Geometry Quiz6.EE.5 Knowledge Target: Recognize solving an equation or inequality as a process of answering “which values from a specified set, if any make the equation or inequality true?” Knowledge Target: Know that the solutions of an equation or inequality are the values that make the equation or inequality true. Knowledge Target: Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

2.4 Solving Equations 1 ACT #31

6.EE.5 Knowledge Target: Recognize solving an equation or inequality as a process of answering “which values from a specified set, if any make the equation or inequality true?” Knowledge Target: Know that the solutions of an equation or inequality are the values that make the equation or inequality true. Knowledge Target: Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

2.5 Looking at Inequalities 2 PARCC #8; PARCC2 #20

Study Guide 1Quiz 1Section 3: Making Generalizations3.1 Count on Me 13.2 What’s Next: Describing Recursive Patterns

3

Geometry Quiz6.EE.4 Knowledge Target: Recognize when two expressions are equivalent. Reasoning Target: Prove (using various strategies) that two equations are equivalent no matter what number is substituted.

3.3 Using Explicit Rules to Describe Patterns

2 ACT #23; PARCC2 #14

3.4 Guess My Rule 26.EE.9 Knowledge Target: Define independent and dependent variables. Knowledge Target: Use variables to represent two quantities in a real-world problem that change in relationship to one another. Reasoning Target: Write an equation to express one quantity (dependent) in terms of the other quantity (independent). Reasoning Target: Analyze the relationship between the dependent variable and the independent variable using tables and graphs. Reasoning

3.5 Charts and Graphs for Linear Equations*Add: Define independent and dependent variables.

2 PARCC #10

Lewis County Middle School

Standard/Target Section/Lesson # Days Formative AssessmentTarget: Relate the data in a graph and table to the corresponding equation.

Study Guide 1Quiz 1Study Guide 1Unit Exam 1

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School