Learning goals: Teacher Facing Explain (orally and in writing) why the product of a non-zero rational and irrational number is irrational. Explain (orally and in writing) why the sum of a rational and irrational number is irrational. Explain (orally and in writing) why the sum or product of two rational numbers is rational. Full lesson plan (warm-up, activities, synthesis, cool-down prompt) from Alg1.7 Quadratic Equations, Algebra 1.