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Goddard: High School Common Core State Standards (CCSS) Mathematics – Number and Quantity

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: The Real Number System Code: N.RN.1Cluster: Extend the properties of exponents to rational exponents.Standard: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing

for a notation for radicals in terms of rational exponents. For example, we define 5 1/3 to be the cube root of 5 because we want (5 1/3)3 = 5(1/3)3 to hold, so (5 1/3)3 must equal 5.

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.

rational exponents – exponents in a fraction form integer exponents – positive & negative whole numbers and zero radicals – square roots, cube roots, nth roots

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

Explain – communicate meaning and understanding ☐ ☐ ☒ ☐ ☐ Follows – progressing through rules/properties of

exponents☒ ☐ ☐ ☐ ☐

Allowing – permit the possibility ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Move from rational to radical and radical to rational representations of roots incorporating the properties of exponents.Essential Questions:

Can you identify and define an exponent? Can you translate from rational exponent form to radical form and vice versa? Can you explain how radical notation, rational exponents, and properties of integer exponents relate to one another?

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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

Properties of exponents 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:

2

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: The Real Number System Code: N.RN.2Cluster: Extend the properties of exponents to rational exponents.Standard: Rewrite expressions involving radicals and rational exponents using the properties of 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. Expressions – monomials, binomials, and polynomials Radicals – square roots, cube roots, nth roots Rational Exponents – exponents written as fractions Properties of exponents – rules that govern the operations of exponents





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Rewrite – simplify and/or expand meaning, show equivalent form

☐ ☒ ☐ ☐ ☐

Using – to employ, utilize or work with ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Express equivalent forms of expressions using radical and rational exponentsEssential Questions:

Can you explain how radical notation, rational exponents, and properties of integer exponents relate to one another? Can you use the properties of exponents to rewrite an expression with a rational exponent as a radical expression? 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

3

(Depth of Knowledge Properties of exponents 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?)


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:


4

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: The Real Number System Code: N.RN.3Cluster: Use properties of rational and irrational numbers.Standard: Explain why the sum or product of two rational numbers are rational; that the sum of a rational number and an irrational number is irrational; and

that the product of a nonzero rational number and an irrational number is irrational.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. Sum – adding quantities Product – multiplying quantities Rational number – numbers that can be written as fractions (quotient of two integers) Irrational number – numbers that cannot be written as fractions (quotient of two integers) Non-zero rational number – rational number that is not zero





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Explain – communicate meaning and understanding ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Know and justify that when adding or multiplying two rational numbers the result is a rational number; know and justify that when adding or multiplying a non-zero rational number and irrational number the result is an irrational number;

Essential Questions:

Can you distinguish between a rational and irrational number? Can you perform operations using rational and irrational numbers? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

5


Basic mathematical operations I ☐ II ☐ III ☐ IV ☐ V ☐ Identify/define rational and irrational numbers 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?)




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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Quantities Code: N.Q.1Cluster: Reason quantitatively and use units to solve problems.Standard: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas;

choose and interpret the scale and the origin in graphs and data displays.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. Units – standard of measurement Problems – real world situations Solution – answer Multi-step problems – situations requiring more than one step and advanced thought Formulas – consist mathematical relationship between two or more quantities Scale – ratio comparing the representation to the actual amount/size Origin in graphs/data displays – a zero or beginning point, where compared value equal zero





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Use – to employ, utilize or work with ☐ ☒ ☐ ☐ ☐ Understand – comprehending or appreciating the

nature and significance of☐ ☒ ☐ ☐ ☐

Guide – to direct ☐ ☐ ☒ ☐ ☐ Choose – select ☐ ☒ ☐ ☐ ☐ Interpret – give meaning ☐ ☐ ☒ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Interpret and use reasonable units when solving a multi-step problem that may or may not include formulasEssential Questions:

Can you define appropriate units of measure in real world situations? Can you create a proportional scale for use with data to be graphed? Can you recognize units given or needed to solve problems? Can you select appropriate formulas?

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Ability to recognize the reasonableness of a possible answer. I ☐ II ☐ III ☐ IV ☐ V ☐ Calculate unit conversions. I ☐ II ☐ III ☐ IV ☐ V ☐ Manipulate formulas to solve for variables. 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?)




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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Quantities Code: N.Q.2Cluster: Reason quantitatively and use units to solve problems.Standard: Define appropriate quantities for the purpose of descriptive modeling.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. Quantities – amounts, measures, magnitudes, capacities Purpose – intended or desired result Modeling – representing, showing, displaying





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Define – state, express meaning ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Express meaning with appropriate amounts to display a desired result.Essential Questions:

Can you represent, show, display real world situations? Can you express appropriate amounts in real world situations? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


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Read/create/interpret a graph/display I ☐ II ☐ III ☐ IV ☐ V ☐ Choose appropriate scale for the unit of measure 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?)




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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Quantities Code: N.Q.3Cluster: Reason quantitatively and use units to solve problems.Standard: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.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. Level of accuracy – precision Limitation on measurement – restrictions of appropriate units Quantities – amount, measures, magnitudes, capacities





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Choose – select ☐ ☒ ☐ ☐ ☐ Reporting – recording, documenting, presenting ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Selecting reasonable precision based on the restriction of units when documenting real-world amounts.Essential Questions:

Can you identify important quantities in a problem or real world situation? Can you choose and justify appropriate restrictions when reporting measurements? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


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Knowing limitations of certain measuring tools I ☐ II ☐ III ☐ IV ☐ V ☐ Calculate unit conversions 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?)




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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: The Complex Number System Code: N.CN.1Cluster: Perform arithmetic operations with complex numbers.Standard: Know there is a complex number i such that i2 = −1, and every complex number has the form a + bi with a and b real.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. Complex number (i) – the result the even nth root of a negative radicand Form – consistent representation Real (number) – numbers that can be expressed on a number line





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Know – assign meaning and definition ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

To assign meaning and value to the results of negative radicands and to represent them appropriately.Essential Questions:

Can you recognize the standard form of complex numbers? Can you identify complex numbers in the form a + bi? What is the definition of the value of i? Can you define the powers of i?What learning progressions are needed to master this standard? Give specific, measurable skill statements.


Evaluate square roots I ☐ II ☐ III ☐ IV ☐ V ☐

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Evaluate rational exponents 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?)




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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: The Complex Number System Code: N.CN.2Cluster: Perform arithmetic operations with complex numbers.Standard: Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex 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. Relation – established rule Commutative – changing the order of values being added or multiplied doesn’t change the result Associative – changing the groupings in a sum or product doesn’t change the result Distributive – multiplying a value into a sum or difference Complex number (i) – the result the even nth root of a negative radicand





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Add – sum or combine ☒ ☐ ☐ ☐ ☐ Subtract – difference ☒ ☐ ☐ ☐ ☐ Multiply – determine the product ☒ ☐ ☐ ☐ ☐ Use – employ, utilize or work with ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Employ the rule for the value i with the various mathematical properties Essential Questions:

Can you use add, subtract, and multiply complex numbers? Can you apply the rules of said properties to complex numbers? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


15

Know commutative, associative, and distributive properties I ☐ II ☐ III ☐ IV ☐ V ☐ Add, subtract, and multiply imaginary numbers 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?)




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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: The Complex Number System Code: N.CN.3Cluster: Perform arithmetic operations with complex numbers.Standard: (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex 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.





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


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

FORMTEXT Essential Questions:



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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?)


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:


18

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: The Complex Number System Code: N.CN.4Cluster: Represent complex numbers and their operations on the complex plane.Standard: (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the

rectangular and polar forms of a given complex number represent the same number.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






19

(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?)




20

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: The Complex Number System Code: N.CN.5Cluster: Represent complex numbers and their operations on the complex plane.Standard: (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this

representation for computation. For example, (-1 + √3 i)3 = 8 because (-1 + √3 i) has modulus 2 and argument 120°.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






21





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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: The Complex Number System Code: N.CN.6Cluster: Represent complex numbers and their operations on the complex plane.Standard: (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of

the numbers at its endpoints.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






23





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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: The Complex Number System Code: N.CN.7Cluster: Use complex numbers in polynomial identities and equations.Standard: Solve quadratic equations with real coefficients that have complex solutions.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. Quadratic equations – polynomial equation with 2 as the highest exponent Real coefficients – number that can be expressed on a number line that immediately precedes a variable Complex solutions – complex numbers that are answers to the given equation





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Solve – answer, decipher, or work out ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Work out answers that include an imaginary component to equations with 2 as the highest exponent and real numbers preceding variables. Essential Questions:

Can you solve quadratic equations? Can you convert negative radicands to complex number form? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


Solving quadratic equations I ☐ II ☐ III ☐ IV ☐ V ☐

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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?)




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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: The Complex Number System Code: N.CN.8Cluster: Use complex numbers in polynomial identities and equations.Standard: (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






27





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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: The Complex Number System Code: N.CN.9Cluster: Use complex numbers in polynomial identities and equations.Standard: (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Vector and Matrix Quantities Code: N.VM.1Cluster: Represent and model with vector quantities.Standard: (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate

symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Vector and Matrix Quantities Code: N.VM.2Cluster: Represent and model with vector quantities.Standard: (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






33





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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Vector and Matrix Quantities Code: N.VM.3Cluster: Represent and model with vector quantities.Standard: (+) Solve problems involving velocity and other quantities that can be represented by vectors.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Vector and Matrix Quantities Code: N.VM.4Cluster: Perform operations on vectors.Standard: (+) Add and subtract vectors.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Vector and Matrix Quantities Code: N.VM.4aCluster: Perform operations on vectors.Standard: Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the

sum of the magnitudes.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. vector-a quantity that shows magnitude(quantity) and direction adding vectors component-wise -Two or more vectors whose sum is the given vector. compenent-wise-notation indicating magnitude and direction parallelogram rule- provides the means to perform vector addition of two vectors in two-dimensional space by creating a parallelogram magnitude –size/quantity





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


add- sum or combine x ☐ ☐ ☐ ☐ understand – comprehending or appreciating the

nature and significance of☐ x ☐ ☐ ☐

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

FORMTEXT Combine two vectors and determine the magnitude and direction of the sum of the two vectorsEssential Questions:

Do you know what a vector is? Can you add/combine magnitudes of vectors? Do you know what a parallelogram is? Do you know what component notation of a vector is? 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: Vector and Matrix Quantities Code: N.VM.4bCluster: Perform operations on vectors.Standard: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.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. vector-a quantity that shows magnitude(quantity) and direction magnitude and direction form– notation indicating the size/quantity of a vector and its direction relative to the coordinate plane magnitude –size/quantity direction-relative north, east, west, south sum- adding/combining quantities





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


determine- to decide or find out ☐ x ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

FORMTEXT add two vectors in magnitude and direction formEssential Questions:

Can you add two vectors? Do you know magnitude and direction form? Can you determine a sum of two vectors in magnitude and direction form? 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: Vector and Matrix Quantities Code: N.VM.4cCluster: Perform operations on vectors.Standard: Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite

direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.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. vector subtraction- to determine the difference between two vectors additive inverse- the sum of two quantities either numerical or variable whose result is zero magnitude- size/ quantity graphically – visual representation on the coordinate plane tips (of a vector) – the terminating point of a vector quantity vector subtraction component-wise – finding the difference in two vectors using component notation





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


understand- comprehending or appreciating the nature and significance of

☐ x ☐ ☐ ☐

represent- to present clearly, to symbolize x ☐ ☐ ☐ ☐ perform- to carry out an action or accomplish a

task☐ x ☐ ☐ ☐

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

FORMTEXT perform the subtraction of two vectors using the additive inverseEssential Questions:

Do you understand subtraction as the additive inverse? Can you graph a vector? Do you understand component form of a vector?

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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Vector and Matrix Quantities Code: N.VM.5Cluster: Perform operations on vectors.Standard: (+) Multiply a vector by a scalar.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Vector and Matrix Quantities Code: N.VM.5aCluster: Perform operations on vectors.Standard: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise,

e.g., as c(vx, vy) = (cvx, cvy).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. scalar multiplication – multiplying a vector quantity by a positive constant factor graphically- – visual representation on the coordinate plane scalar multiplication component-wise – performing scalar multiplication to a vector in component form





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


represent- to present clearly, to symbolize ☐ ☐ ☐ ☐ ☐ reversing- change in the opposite direction ☐ ☐ ☐ ☐ ☐ perform- to carry out an action or accomplish a

task☐ ☐ ☐ ☐ ☐

scaling (vectors) - Multiplying a vector by a number

☐ ☐ ☐ ☐ ☐

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

FORMTEXT multiply a vector in component form by a number and/or represent it graphically Essential Questions:

Can you multiply a vector by a constant? Can you reverse the direction of a vector? Can you represent scalar multiplication graphically? 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: Vector and Matrix Quantities Code: N.VM.5bCluster: Perform operations on vectors.Standard: Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is

either along v (for c > 0) or against v (for c < 0).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. magnitude – size/quantity scalar multiple –the result of multiplying a vector quantity by a positive constant factor direction - relative north, east, west, south





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


compute- to determine the result using mathematical methods; to calculate

x ☐ ☐ ☐ ☐

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

FORMTEXT determine the quantity of a vector and its direction after multiplying by a positive constant factorEssential Questions:

Can you multiply by a constant factor? Can you determine the direction of a vector? 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: Vector and Matrix Quantities Code: N.VM.6Cluster: Perform operations on matrices and use matrices in applications.Standard: (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Vector and Matrix Quantities Code: N.VM.7Cluster: Perform operations on matrices and use matrices in applications.Standard: (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Vector and Matrix Quantities Code: N.VM.8Cluster: Perform operations on matrices and use matrices in applications.Standard: (+) Add, subtract, and multiply matrices of appropriate dimensions.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Vector and Matrix Quantities Code: N.VM.9Cluster: Perform operations on matrices and use matrices in applications.Standard: (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the

associative and distributive properties.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Vector and Matrix Quantities Code: N.VM.10Cluster: Perform operations on matrices and use matrices in applications.Standard: (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers.

The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Vector and Matrix Quantities Code: N.VM.11Cluster: Perform operations on matrices and use matrices in applications.Standard: (+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as

transformations of vectors.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Vector and Matrix Quantities Code: N.VM.12Cluster: Perform operations on matrices and use matrices in applications.Standard: (+) Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






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