Classifying Polynomials
I can write a polynomial in standard form and name its degree, leading coefficient and number of terms.
What students learn
Students learn to combine like terms, write a polynomial in standard form, and name its degree, its leading coefficient and its number of terms.
See inside
The key rule
Combine like terms first, then read the degree from the highest term, wherever it sits.
monomial · binomial · trinomial
1, 2 or 3 terms; four or more is just a polynomial. Not polynomials: 5x⁻¹ − 2 and 3/x.
Watch out
For 6x² + 2x⁵ − 1, a student gives the degree as 2.
The mistake: 6x² comes first, so degree 2The first term is not always the highest.
The fix: 2x⁵ + 6x² − 1: degree 52x⁵ has the highest exponent, wherever it sits.
The mistakes it targets
- Reads the degree off the first term
- Counts terms before combining like terms
- Uses the larger exponent as the degree of a term with two variables
- Adds the exponents when combining like terms
- Drops the minus from the leading coefficient
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, 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
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.