GRADE BAND: HIGH SCHOOL Domain: Real Number System
Key standards in “The Real Number” that pd should focus on Cluster: Extend the properties of exponents to rational exponents N-RN 1: 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. N-RN 2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. Cluster: Use properties of rational and irrational numbers N-RN3: 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.
Why this domain is a priority for professional development To really teach this domain well, teachers must have a more robust knowledge about the real number system than these three Standards imply on the surface Teachers tend to know rules and may not know the mathematical structures underlying the rules
What teachers really need to know… The real number system is much more complicated than just taking the rational numbers and adding in √2 and π Questions that teachers need to be able to answer: What is the real number system? Why do we need real numbers? How do real numbers build from and connect to the rational number system? How does a deep understanding of the real number system support future learning of mathematics?
Our final thought: Yes and No Although this domain is important for high school students (and thus high school teachers) and foundational to future learning of mathematics, it is a relatively small portion of what high school students need to learn, so… Is this domain really a priority for professional development? Is this where we want to spend our time and energy during PD for high school teachers?
Existing resources that support these domains and standards
Domains and standards that are in need of new resources