In this lesson, students practice examining a proof by contradiction using sums of even and odd numbers. First, students examine some concrete examples of sums and products of even and odd numbers to evaluate whether some claims are always, sometimes, or never true. Next, students follow a proof by contradiction that shows that the sum of an even and odd number must always be odd.

In the associated Algebra 1 lesson, students examine a similar proof by contradiction about sums and products of rational and irrational numbers. They are supported by following a similar process with more familiar types of numbers. Students reason abstractly and quantitatively (MP2) when they think of specific examples to prove or disprove a statement.