Sums and Products of Rational and Irrational Numbers

What students learn

Students learn to decide whether a sum or a product is rational or irrational: they name its case, test a product for a zero factor, and work out any pair of irrationals.

See inside

Watch out

Is 0 × √7 rational or irrational?

The mistakes it targets

• Lets an irrational factor decide a product without checking for a zero factor
• Makes up a rule for two irrationals instead of working them out
• Calls a repeating decimal irrational because it never ends
• Calls a nonzero rational times an irrational rational
• Classifies a rounded decimal instead of the exact number

The interactive Teacher Deck (32 slides, PowerPoint)

• The Learn page taught on screen: 9 fill-in blanks, each filled on its own click as students write it
• The worked example one slide per step (four steps), each with the reason for the step
• Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
• Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
• Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
• A completed deck PDF (19 pages) with every slide fully built, to print or post

The student packet (9 pages)

• Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
• Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
• Apply: two word problems and one error analysis
• Assess: an exit ticket of four items, two per page, with an I-can self-rating
• Homework (page 5): eight new problems, two warm-up, four standard and two stretch
• Answer key (pages 6–7): every problem worked step by step, five common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
• Color and ink-saver editions of the whole packet