Multiplying Monomials and Binomials
I can multiply a monomial or a binomial by a binomial using an area box.
The problem this sheet solves
Two terms times two terms gives FOUR products. A student who multiplies the firsts and the lasts has done two correct multiplications and stopped, so telling them to check their arithmetic is useless advice: the arithmetic is fine. What is missing is the count. This sheet uses an area box because a grid answers HOW MANY products there should be before it answers what they are, and a student looking at two answers in a four-cell box can see for themselves that they stopped early. A substitution check at x = 1 gives 24 against 16, which settles it without any appeal to FOIL.
The key rule
Two terms times two terms gives FOUR products, not two. Count the cells before you multiply, then combine the two middle ones.
Four cells. Four products.
Watch out
The mistake: A student writes (x + 3)(x + 5) = x2 + 15.
The fix: x2 + 8x + 15. Only the firsts and the lasts were multiplied, so 5x and 3x were never formed. Test at x = 1: the product is 4 · 6 = 24, and x2 + 15 gives 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.