Goddard: Sixth GradeCommon Core State Standards (CCSS) Mathematics

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4
Domain: Expressions and Equations / Code: 6.EE.1
Cluster: 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 / Application
Demonstrate understanding of math / Analysis
Conjecture, 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)
  • 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?

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:
Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4
Domain: Expressions and Equations / Code: 6.EE.2
Cluster: 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 ☒
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.
  • 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

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 / Application
Demonstrate understanding of math / Analysis
Conjecture, Generalize, Prove / Synthesis/Evaluate/ Create; Solve non-routine problems; make connections
  • 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)
  • 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?

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
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. / Instructional Resources/Tools:
Key words – “Less than” and “More than”. Teach the students to switch the problem around and think backwards.
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: 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”.
Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4
Domain: Expressions and Equations / Code: 6.EE.2a
Cluster: 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 ☒
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.
  • 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

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 / Application
Demonstrate understanding of math / Analysis
Conjecture, Generalize, Prove / Synthesis/Evaluate/ Create; Solve non-routine problems; make connections
  • 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.
Learning Sequence / Prior skill(s) needed / Check Level of Rigor/Cognitive Demand
(Depth of Knowledge
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. / Instructional Resources/Tools:
Key words – “Less than” and “More than”. Teach the students to switch the problem around and think backwards.
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: 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”.
Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4
Domain: Expressions and Equations / Code: 6.EE.2b
Cluster: 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 ☒
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.
  • 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

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 / Application
Demonstrate understanding of math / Analysis
Conjecture, Generalize, Prove / Synthesis/Evaluate/ Create; Solve non-routine problems; make connections
  • 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)
  • 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 inwhich an operation is performed

Essential 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.
Learning Sequence / Prior skill(s) needed / Check Level of Rigor/Cognitive Demand
(Depth of Knowledge
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. / Instructional Resources/Tools:
Key words – “Less than” and “More than”. Teach the students to switch the problem around and think backwards.
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: 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:
Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4
Domain: Expressions and Equations / Code: 6.EE.2c
Cluster: 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) Definition
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

  • 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

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 / Application
Demonstrate understanding of math / Analysis
Conjecture, Generalize, Prove / Synthesis/Evaluate/ Create; Solve non-routine problems; make connections
  • 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)
  • 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.

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.
Learning Sequence / Prior skill(s) needed / Check Level of Rigor/Cognitive Demand
(Depth of Knowledge
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?) / 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:
Example 2:
Example 3:
Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4
Domain: Expressions and Equations / Code: 6.EE.3
Cluster: 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 ☐
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.
  • 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

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 / Application
Demonstrate understanding of math / Analysis
Conjecture, Generalize, Prove / Synthesis/Evaluate/ Create; Solve non-routine problems; make connections
  • 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)
  • 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?