MATHS Targeted Standards (N) Concept: Number and Quantity (RN) Domain: The Real Number System Cluster: Use properties of rational and irrational number
MATHS.NRN.03 Explain why the sum or product of two rational numbers is 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.
Student Learning Targets:
Knowledge Targets
I can identify the properties of the real number system, i.e., commutative, associative, distributive, closure, inverse, and identity properties.
Reasoning Targets
I can apply the properties of the real number system to simplify an expression.
Skills (Performance) Targets
I can use the properties of real numbers to simplify an expression and solve an equation.
I can show by example the sum of a rational number and an irrational number is irrational.
I can show by example the product of a nonzero rational number and an irrational number is irrational.
I can use the closure property or show by example the sum or product of two rational numbers is rational.
Product Targets
I can
I can
Proficiency Scale
Score
Description
Sample Activity
4.0
In addition to Score 3.0, the student demonstrates indepth 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 indepth 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.