Adding and Subtracting Polynomials
I can add and subtract polynomials, giving the minus sign to every term of the second one.
What students learn
Students learn to add polynomials by combining like terms, and subtract them by changing the sign of every term in the second parentheses, then write the answer in standard form.
See inside
The key rule
When subtracting, change the sign of each term in the second ( ), not just the first; then combine like terms and write the answer in standard form.
a − (b − c) = a − b + c
If every term cancels, the answer is 0.
Watch out
For (6x² − 2x + 5) − (x² + 3x − 4), a student changes only the first sign.
The mistake: −x² + 3x − 4, so 5x² + x + 1+3x and −4 kept their signs.
The fix: −x² − 3x + 4, so 5x² − 5x + 9All three signs change; the first term is right either way.
The mistakes it targets
- Applies the minus to the first term only
- Treats subtracting a negative term as subtracting
- Subtracts in the wrong order
- Adds the exponents when adding like terms
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, four 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
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.