In the performance task linked below, students fill out two tables and are challenged to analyze what happens when rational numbers are mixed with irrational numbers. They then answer the critical thinking questions:

Based on the above information(tables), conjecture which of the statements is ALWAYS true, which is SOMETIMES true, and which is NEVER true?

i. The sum of a rational number and a rational number is rational.

ii. The sum of a rational number and an irrational number is irrational.

iii. The sum of an irrational number and an irrational number is irrational.

iv. The product of a rational number and a rational number is rational.

v. The product of a rational number and an irrational number is irrational.

vi. The product of an irrational number and an irrational number is irrational.

See link for full task w/tables and solutions: http://auhsdmath.pbworks.com/w/file/fetch/74932850/Rational%20and%20Irrational%20Numbers.pdf