- MAFS.912.N-RN.2.3: 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.
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Standard 2: Use properties of rational and irrational numbers. (Algebra 1 - Additional Cluster) Archived
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Cluster Standards
This cluster includes the following benchmarks.
Visit the specific benchmark webpage to find related instructional resources.
Cluster Information
Number: MAFS.912.N-RN.2
Title: Use properties of rational and irrational numbers. (Algebra 1 - Additional Cluster)
Type: Cluster
Subject: Mathematics - Archived
Grade: 912
Cluster: Number & Quantity: The Real Number System
Cluster Access Points
This cluster includes the following Access Points.
- MAFS.912.N-RN.2.AP.3a: Know and justify that when adding or multiplying two rational numbers the result is a rational number.
- MAFS.912.N-RN.2.AP.3b: Know and justify that when adding a rational number and an irrational number the result is irrational.
- MAFS.912.N-RN.2.AP.3c: Know and justify that when multiplying of a nonzero rational number and an irrational number the result is irrational.
Cluster Resources
Vetted resources educators can use to teach the concepts and skills in this topic.
Formative Assessments
- Sum of Rational Numbers: Students are asked to define a rational number and then explain why the sum of two rational numbers is rational.
- Sum of Rational and Irrational Numbers: Students are asked to describe the difference between rational and irrational numbers and then explain why the sum of a rational and an irrational number is irrational.
- Product of Rational Numbers: Students are asked to define a rational number and then explain why the product of two rational numbers is rational.
- Product of Non-Zero Rational and Irrational Numbers: Students are asked to describe the difference between rational and irrational numbers, and then explain why the product of a non-zero rational and an irrational number is irrational.
Lesson Plans
- Rational and Irrational Numbers 2: This advanced lesson assesses how well students reason about the properties of rational and irrational numbers. In particular, this unit aims to help teachers identify and assist students who have difficulties finding irrational and rational numbers to exemplify general statements and reasoning with properties of rational and irrational numbers.
- Rational and Irrational Numbers 1: This lesson assesses students' ability to distinguish between rational and irrational numbers and move between different representations of rational and irrational numbers.
Problem-Solving Tasks
- Calculating the Square Root of 2: This task is intended for instructional purposes so that students can become familiar and confident with using a calculator and understanding what it can and cannot do. This task gives an opportunity to work on the notion of place value (in parts [b] and [c]) and also to understand part of an argument for why the square root of 2 is not a rational number.
- Operations with Rational and Irrational Numbers: This task has students experiment with the operations of addition and multiplication, as they relate to the notions of rationality and irrationality.