Solving Quadratics by Completing the Square
I can solve a quadratic by completing the square, adding the term to both sides.
The problem this sheet solves
Students who learned completing the square on an EXPRESSION carry the compensation habit across, and students who learn it on an equation first carry the both-sides habit back. An expression has no second side, so the number is added and subtracted; an equation has one, so it goes there. Same number, and the equals sign decides. The sheet leads with the balance rather than a rule, reusing the tilted pan-balance figure from the one-step equations sheet because it is the same illegal move six units later. It also refuses to hide odd b: two items complete with a fraction and still finish in whole numbers, because a method that only works on even b is not a method.
The key rule
Add (b/2)2 to BOTH sides. The left becomes a perfect square, the right becomes a number, and then it is rooted.
The same number, in two places.
Watch out
The mistake: A student writes x2 + 6x + 9 = 7, so (x + 3)2 = 7.
The fix: The 9 was right and went to one place instead of two. Adding to one side changes the answers. Put it on the right too: (x + 3)2 = 16.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.