s3. Web viewStandard: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform

Goddard: Sixth Grade Common Core State Standards (CCSS) Mathematics

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 6.EE.1Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions.Standard: Write and evaluate numerical expressions involving whole-number exponents.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐

Level 3: Strategic Thinking ☐ Level 4: Extended Thinking ☐Know (nouns) Definition

List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. numerical expressions: an expression that combines numbers and one or more operation symbol whole-number: a counting number, positive integer exponent: a symbol or a number place above and after a number to denote the power to which the latter is raised

Be Able to Do (Verbs) Level I Level II Level III Level IV Level V

List the verbs that are key learning targets, then determine the cognitive demand level (Bloom’s/SEC) with verbs in context by placing a checkmark in the appropriate square:

Knowledge/ Remembering

Memorize facts, definitions, &

formulas

Comprehension/ Understanding

Perform Procedures

ApplicationDemonstrate

understanding of math

AnalysisConjecture,

Generalize, Prove

Synthesis/Evaluate/ Create; Solve non-routine problems; make connections

write: compose in words or characters ☒ ☐ ☐ ☐ ☐ evaluate: to solve ☐ ☐ ☐ ☐ ☒ involving: to include as necessary ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

FORMTEXT The student will relate the number raised to a power, write numerical expressions involving whole-number exponents evaluate numerical expressions involving whole-number exponents.Essential Questions:

How can you write and evaluate a numerical expression involving whole-number exponents?

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What learning progressions are needed to master this standard? Give specific, measurable skill statements.

Learning Sequence Prior skill(s) needed Check Level of Rigor/Cognitive Demand(Depth of Knowledge

Recognize and use exponents. I ☒ II ☐ III ☐ IV ☐ V ☐ Write expressions using various operations with exponents. I ☒ II ☐ III ☐ IV ☐ V ☐ Use and understand the order of operations. I ☒ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)

Instructional Resources/Tools:

Assessment Item Type: Selected Response ☒ Extended Constructed Response ☒ Technology Enhanced ☒ Performance Task ☒ Oral Response ☐ Eligible as summative item ☒Example: Provide possible instructional learning example/formative assessment item(s) for this standard:

Example 1: 3 + 62

Example 2: Example 3:

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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 6.EE.2Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions.Standard: Write, read, and evaluate expressions in which letters stand for numbers.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. expressions: a phrase that combines numbers and one or more operation symbol letters: a symbol or character used to represent a speech sound numbers: the sum, total, or count of a collection of units





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


write: compose in words or characters ☒ ☐ ☐ ☐ ☐ read: to look carefully so as to understand the

meaning of something written☒ ☐ ☐ ☐ ☐

evaluate: to solve ☐ ☐ ☐ ☐ ☒ stand: the position or place of ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

FORMTEXT The student will formulate a relationship given in words into an algebraic expressions. The student will identify parts of algebraic expression. The student can recognize an expression as being represented by being a product, difference, sum, or quotient. The student can evaluate an algebraic expression. The student can substitute values in formulas to solve real world problems. The student can apply the order of operations.Essential Questions:

How can you write an expression where letters stand for numbers? How can you read expressions in which letters stand for numbers? How can you solve an expression in which letters stand for numbers?

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Knowing how to compute all operations. I ☒ II ☐ III ☐ IV ☐ V ☐ Know how to solve Order of Operations. I ☐ II ☒ III ☐ IV ☐ V ☐ The student will need to know how to work a problem right to left and left to right. I ☐ II ☐ III ☐ IV ☒ V ☐ Students need to know that a letter can stand in the place of a number. I ☐ II ☐ III ☒ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)Daily work/board work, Formatives and pre-made tests as per the district curriculum.


Key words – “Less than” and “More than”. Teach the students to switch the problem around and think backwards.


Example 1: Subtract “y” from 5 = 5-y.Example 2: 14 more than a number = s+14 – See key words of “more than”. Example 3: 6 less than a number = p-6 – See key words of “less than”.

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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 6.EE.2aCluster: Apply and extend previous understandings of arithmetic to algebraic expressions.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. expression: a phrase that combines numbers and one or more operation symbol operations: any procedure such as addition, multiplication, subtraction, or division done to a specific set of numbers or quantities numbers: the sum, total, or count of a collection of units letters: a symbol or character used to represent a speech sound





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


write: compose in words or characters ☒ ☐ ☐ ☐ ☐ record: to set down in writing as for the purpose

of keeping information☒ ☐ ☐ ☐ ☐

standing: the position or place of ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

The students will recognize when an expression is representing a sum and/or difference of terms versus a product and/or quotient of terms.Essential Questions:

How can you write an expression where letters stand for numbers? How can you read expressions in which letters stand for numbers? How can you solve an expression in which letters stand for numbers? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

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Knowing how to compute all operations. I ☒ II ☐ III ☐ IV ☐ V ☐ Know how to solve Order of Operations. I ☐ II ☒ III ☐ IV ☐ V ☐ The student will need to know how to work a problem right to left and left to right. I ☐ II ☐ III ☐ IV ☒ V ☐ Students need to know that a letter can stand in the place of a number. I ☐ II ☐ III ☒ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?) Daily work/board work, Formatives and pre-made tests as per the district curriculum.




Example 1: Subtract “y” from 5 = 5-y.Example 2: 14 more than a number = s+14 – See key words of “more than”. Example 3: 6 less than a number = p-6 – See key words of “less than”.

6

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 6.EE.2bCluster: Apply and extend previous understandings of arithmetic to algebraic expressions.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. parts: a portion or division of a whole expression: a phrase that combines numbers and one or more operation symbol mathematical terms: a word or group of words designating something mathematical entity: something having real or distinct existence; a thing





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


identify: to recognize ☒ ☐ ☐ ☐ ☐ using: to employ for some purpose make use of ☒ ☐ ☐ ☐ ☐ view: to see or to look at ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

FORMTEXT The student will identify parts of an algebraic expression by using correct mathematical terms recognize an expression as both a single value and as two or more terms in which an operation is performedEssential Questions:

Why do we use variables? When are algebraic expressions used in real life? How can a variable transform itself? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

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Knowing how to compute all operations. I ☒ II ☐ III ☐ IV ☐ V ☐ Know how to solve Order of Operations. I ☐ II ☒ III ☐ IV ☐ V ☐ The student will need to know how to work a problem right to left and left to right. I ☐ II ☐ III ☐ IV ☒ V ☐ Students need to know that a letter can stand in the place of a number. I ☐ II ☐ III ☒ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?) Daily work/board work, Formatives and pre-made tests as per the district curriculum.




Example 1: Describe the expression 2(8+7) as a product of two factors; view (8+7) as both and entity and a sum of two terms. Example 2: Key words – 7 more than 8 times two. Example 3:

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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 6.EE.2cCluster: Apply and extend previous understandings of arithmetic to algebraic expressions.Standard: 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.

Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒Level 3: Strategic Thinking ☐ Level 4: Extended Thinking ☐

Know (nouns) DefinitionList the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context.

expression: a phrase that combines numbers and one or more operation symbol values: relative worth variables: a symbol that represents a quantity or function formulas: a rule or principle problems: a statement requiring a solution Operations: any procedure such as addition, multiplication, subtraction, or division done to a specific set of numbers or quantities Whole-number: a counting number, positive integer Exponents: a symbol or a number place above and after a number to denote the power to which the latter is raised Order: a sequence Parentheses: either or both pair of signs () using in writing to mark off a remark or symbol





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


evaluate: to solve ☐ ☐ ☐ ☐ ☒ include: to be part of ☒ ☐ ☐ ☐ ☐ arise: come into being or notice ☒ ☐ ☐ ☐ ☐ used: to employ for a purpose ☒ ☐ ☐ ☐ ☐ perform: to carry out; execute Involving: to be part of; include Specify: to mention or to state in detail

☒ ☐ ☐ ☐ ☐

This standard means a student will know and be able to do…(use your own words)

FORMTEXT The student will evaluate an algebraic expression for a given value, substitute values in formulas to solve real-world problems apply the order of operations when evaluating both arithmetic and algebraic expressions.

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Essential Questions:

How do I justify the steps of simplification? How do you write an inverse variation function? How do you isolate a variable – order of operations? What is simplest form? How is the power rule related to the product rule?What learning progressions are needed to master this standard? Give specific, measurable skill statements.


I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)



Example 1: Example 2: Example 3:

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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 6.EE.3Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions.Standard: 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.

Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒Level 3: Strategic Thinking ☐ Level 4: Extended Thinking ☐


properties: a character or attribute that something has operations: any procedure such as addition, multiplication, subtraction, or division done to a specific set of numbers or quantities; works that change a

number expressions: a phrase that combines numbers and one or more operation symbol





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


apply: to put to use; bring into action ☐ ☐ ☒ ☐ ☐ generate: to produce; create ☐ ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

FORMTEXT The student will create a visual model to show two expressions are equivalent apply the properties of operations (distributive) to generate equivalent expressions.Essential Questions:

What is and how do we use the distributive property in real life? What are equivalent expressions? How can procedures lead you to accurate solutions? How do Mathematical properties make calculations easier?

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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 6.EE.4Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. expressions: a phrase that combines numbers and one or more operation symbol equivalent: equal in value





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


identify: to recognize ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

FORMTEXT The student will determine whether two expressions are equivalent by using the same value to evaluate both expressions, and use the properties of operations to justify that two expressions are equivalent.


When is it necessary to have more than one solution? How is a variable useful in writing a number pattern or expression? How do you know when expressions are equivalent? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 6.EE.5Cluster: Reason about and solve one variable equations and inequalities.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. equation: an expression that is balanced or equal inequality: the condition of being unequal process: series of actions directed to some end question: a problem for discussion; matter of uncertainty values: relative worth Set: a number or group or combination of things Substitution: to take the place of; replace Number: the sum, total, or count of a collection of units





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


understand: to grasp the idea; comprehend ☐ ☒ ☐ ☐ ☐ solving: to find the answer ☐ ☐ ☐ ☐ ☒ answering: solution to a problem ☐ ☐ ☒ ☐ ☐ use: to employ for a purpose ☐ ☐ ☒ ☐ ☐ determine: to settle or decide or conclude after

reasoning, observation, etc. Makes: to produce

☐ ☐ ☒ ☐ ☐


FORMTEXT The student will explain that solving an equation or inequality leads to finding the value or values of the variable that will make a true mathematical statement and substitute a given value into an algebraic equation or inequality to determine whether it is part of the solution set.


What is a true mathematical statement? How do I isolate a variable? – get the variable by itself.

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How do you know or determine when expressions are equivalent? How can expressions, equations and inequalities help us to generalize and describe patterns in our world? How do you use substitution to determine whether a given number is a specified set makes an equation or inequality true?What learning progressions are needed to master this standard? Give specific, measurable skill statements.






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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 6.EE.6Cluster: Reason about and solve one variable equations and inequalities..Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. variables: a symbol that represents this; a quantity or function that may assume any given value numbers: the sum, total, or count of a collection of units expressions: a phrase that combines numbers and one or more operation symbol problem: question proposed for a solution purpose: goal Set: a number or group or combination of things





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


use: to employ for a purpose ☒ ☐ ☐ ☐ ☐ represent: to stand or act in the place of ☐ ☒ ☐ ☐ ☐ write: compose in words or characters ☒ ☐ ☐ ☐ ☐ solving: to find the answer ☐ ☐ ☐ ☐ ☒ understand: to grasp the idea; comprehend ☐ ☒ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

FORMTEXT The student will use a variable to write an algebraic expression that represents a real-world situation when a specific number is unknown; explain and give examples of how a variable can represent a single unknown number or can represent any number in a specified set; and use a variable to write an expression that represents a consistent relationship in a particular pattern.


How do I isolate a variable? – get the variable by itself. How do you know or determine when expressions are equivalent? How can expressions, equations and inequalities help us to generalize and describe patterns in our world? How do you use substitution to determine whether a given number is a specified set makes an equation or inequality true?

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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 6.EE.7Cluster: Reason about and solve one variable equations and inequalities.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. problem: question proposed for a solution equations: an expression that is balanced or equal form: configuration cases: situation; circumstance nonnegative: all elements are greater than or equal to zero Rational: any number that can be made by dividing one integer by another Number: the sum, total, or count of a collection of units





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


solve: to find the answer ☐ ☐ ☐ ☐ ☒ writing: compose in words or characters ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

FORMTEXT The student will write and solve algebraic equations that represent real world problems.Essential Questions:

How can we use equations to model and solve real-world problems? How do I isolate a variable? – get the variable by itself. How can expressions, equations and inequalities help us to generalize and describe patterns in our world? How do you use substitution to determine whether a given number is a specified set makes an equation or inequality true? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 6.EE.8Cluster: Reason about and solve one variable equations and inequalities..Standard: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. inequality: the condition of being unequal form: configuration constraint: limitation or restriction condition: a particular state problem: question proposed for a solution Solutions: act of solving a problem Number line diagrams: infinite line in which points represent the real numbers





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


write: compose in words or characters ☒ ☐ ☐ ☐ ☐ represent: to stand or act in the place of ☐ ☒ ☐ ☐ ☐ recognize: to identify ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

FORMTEXT The student will write a simple inequality to represent the constraints or condition of numerical values in a real-world or mathematical problem, explain what the solution set of an inequality represents, and show the solution set of an inequality by graphing it on a number line.


How can we use equations to model and solve real-world problems? How do I isolate a variable? – get the variable by itself. How can expressions, equations and inequalities help us to generalize and describe patterns in our world? How do you use substitution to determine whether a given number is a specified set makes an equation or inequality true?

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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 6.EE.9Cluster: Represent and analyze quantitative relationships between dependent and independent variables.Standard: 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.

Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒Level 3: Strategic Thinking ☒ Level 4: Extended Thinking ☐


variables: a symbol that represents this; a quantity or function that may assume any given value quantities: an exact or specified amount or measure problem: question proposed for a solution relationship: a connection, association equation: an expression that is balanced or equal Dependent variable: a variable that depends on one or more other variables Independent variable: a variable in an equation that may have its value freely chosen without considering values of any other variables Graphs: a diagram representing a system of connections among two or more things Tables: to enter in form of a list





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


use: to employ for a purpose ☒ ☐ ☐ ☐ ☐ represent: to stand or act in the place of ☐ ☒ ☐ ☐ ☐ change: convert or transform ☐ ☐ ☐ ☒ ☐ write: compose in words or characters ☒ ☐ ☐ ☐ ☐ express: to represent by a symbol, character,

figure, or formula Analyze: to examine critically Relate: make a connection or establish association

☐ ☒ ☐ ☐ ☐


FORMTEXT The student will explain the difference between the independent variable and the dependent variable and give examples of both, determine the independent and dependent variable in a relationship, write an algebraic equation that represents the relationship between the two

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variables, create a graph by plotting the dependent variable on the x-axis and the independent variable on the y-axis of a coordinate plane, and analyze the relationship between the dependent and independent variables by comparing the table, graph, and equation.


How can we use equations to model and solve real-world problems? How do I isolate a variable? – get the variable by itself. How can expressions, equations and inequalities help us to generalize and describe patterns in our world? How do you use substitution to determine whether a given number is a specified set makes an equation or inequality true? What is an independent and dependent variable?What learning progressions are needed to master this standard? Give specific, measurable skill statements.






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Documents

s3. Web viewStandard: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform