Rational and Irrational Numbers
Not all numbers are fractions. √2 cannot be written as a ratio of two integers — its decimal expansion goes on forever without repeating. Students encounter the real number line as a continuum that includes both rational and irrational points, and develop vocabulary (integer, rational, irrational, real) that gives precision to future number conversations.
What students explore
Not all numbers are fractions. √2 cannot be written as a ratio of two integers — its decimal expansion goes on forever without repeating. Students encounter the real number line as a continuum that includes both rational and irrational points, and develop vocabulary (integer, rational, irrational, real) that gives precision to future number conversations.
Key ideas
Distinguish between rational and irrational numbers. Locate irrational numbers on a number line. Determine the decimal approximation of a square root. Explain why √2 is irrational.
Putting it together
Apply these ideas through worked examples, guided practice, and real-world problems.