MAT-HS: Numbers and Quantity


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MAT-HS.N-CN.01

MAT-HS Targeted Standards
(N) Concept: Number and Quantity
(CN) Domain: The Complex Number System
Cluster: Perform arithmetic operations with complex numbers.

MAT-HS.N-CN.01 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.

Student Learning Targets:

Knowledge Targets

  • I can recognize every number as a complex number of the form a + bi where a and b are real numbers.
  • I can recognize i as complex and i2 = -1.

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Websites

Vocabulary

 


MAT-HS.N-CN.02

MAT-HS Targeted Standards
(N) Concept: Number and Quantity
(CN) Domain: The Complex Number System
Cluster: Perform arithmetic operations with complex numbers.

MAT-HS.N-CN.02 Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can apply the fact that the complex number i2=-1to perform operations on complex numbers.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web
Vocab

MAT-HS.N-CN.03

MAT-HS Targeted Standards
(N) Concept: Number and Quantity
(CN) Domain: The Complex Number System
Cluster: Perform arithmetic operations with complex numbers.

MAT-HS.N-CN.03 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web
Vocab

MAT-HS.N-CN.04

MAT-HS Targeted Standards
(N) Concept: Number and Quantity
(CN) Domain: The Complex Number System
Cluster: Perform arithmetic operations with complex numbers. 

MAT-HS.N-CN.04 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.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web
Vocab

MAT-HS.N-CN.05

MAT-HS Targeted Standards
(N) Concept: Number and Quantity
(CN) Domain: The Complex Number System
Cluster: Perform arithmetic operations with complex numbers.

MAT-HS.N-CN.05 Represent addition, subtraction, mult iplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

For example, (1 – √3i)³ = 8 because (1 – √3i) has modulus 2 and argument 120°

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web
Vocab

MAT-HS.N-CN.06

MAT-HS Targeted Standards
(N) Concept: Number and Quantity
(CN) Domain: The Complex Number System
Cluster: Perform arithmetic operations with complex numbers.

MAT-HS.N-CN.06 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.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web
Vocab

MAT-HS.N-CN.07

MAT-HS Targeted Standards
(N) Concept: Number and Quantity
(CN) Domain: The Complex Number System
Cluster: Perform arithmetic operations with complex numbers

MAT-HS.N-CN.07 Solve quadratic equations with real coefficients that have complex solutions.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can solve quadratic equations with real coefficients that have solutions of the form a+bi and a-bi.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web
Vocab

MAT-HS.N-CN.08

MAT-HS Targeted Standards
(N) Concept: Number and Quantity
(CN) Domain: The Complex Number System
Cluster: CCC

MAT-HS.N-CN.08 Extend polynomial identities to the complex numbers.

For example, rewrite x² + 4 as (x + 2i)(x – 2i).

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can use polynomial identities to write equivalent expressions in the form of complex numbers.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web
Vocab

MAT-HS.N-CN.09

MAT-HS Targeted Standards
(N) Concept: Number and Quantity
(CN) Domain: The Complex Number System
Cluster: CCC

MAT-HS.N-CN.09 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Student Learning Targets:

Knowledge Targets

  • I can recognize that the Fundamental Theorem of Algebra states that the number of complex solutions to a polynomial equation is equal to the degree of the polynomial

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can show that the Fundamental Theorem of Algebra is true for a quadratic polynomial.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web
Vocab

MAT-HS.N-Q.01

MAT-HS Targeted Standards
(N) Concept: Number and Quantity
(Q) Domain: Quantities
Cluster: Reason quantitatively and use units to solve problems

MAT-HS.N-Q.01 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.

Student Learning Targets:

Knowledge Targets

  • I can select appropriate units and scales for problem situations involving measurement.

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can interpret units in the context of the problem.
  • I can use unit analysis to check the reasonability of your solution.
  • I can choose and interpret an appropriate scale given data to be represented on a graph or display.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web

Vocab

  • unit analysis


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