The Discriminant and Number of Solutions

What students learn

Students learn to write ax² + bx + c = 0, work out D = b² − 4ac, and say from its sign whether the equation has two, one or no real solutions, without solving it.

See inside

Watch out

A student finds D = 0 for x² − 6x + 9 = 0 and writes no real solution.

The mistakes it targets

• Reads a discriminant of 0 as no solution
• Flips the sign of −4ac
• Works out 4ac − b² instead of b² − 4ac
• Leaves a out of 4ac
• Reads does not factor as no real solution
• Reads c before the equation equals 0, or squares a negative b as negative

The interactive Teacher Deck (32 slides, PowerPoint)

• The Learn page taught on screen: 8 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: one word problem, a reasoning prompt 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, six 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