MAT-HS Targeted Standards (N) Concept: Number and Quantity (RN) Domain: The Real Number System Cluster: Extend the properties of exponents to rational numbers

MAT-HS.N-RN.01 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.

Student Learning Targets:

Knowledge Targets

I can

I can

Reasoning Targets

I can

I can

Skills (Performance) Targets

I can use exponential properties to explain how rational exponents follow from integer exponents.

Product Targets

I can

I can

Alg II Convert Radicals to Rational Exponents Proficiency Scale

Score

Description

Sample Activity

4.0

(advanced)

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

(proficient)

The student can:

rewrite exponents in radical notation and radicals in exponential notation.

The student exhibits no major errors or omissions.

Write x^{2/3 }in radical notation.

Write in exponential notation.

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

(progressing)

There are no major errors or omissions regarding the simpler details and processes as the student can:

Recognize and recall specific terminology, such as:

radical and radical notation

index

rational exponent

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Write x^{1/3}in radical notation.

Rewrite in exponential notation.

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

(beginning)

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.