Properties of Real Numbers
I can name the property that justifies a step and apply the Distributive Property correctly.
The problem this sheet solves
Students can often state the Distributive Property and still distribute to the first term only. The trouble is that the properties are taught as vocabulary to match rather than as reasons a step is legal, so nothing connects the name to the move. Commutative and Associative get confused with each other for the same reason: order versus grouping is never made concrete. This sheet pairs each property with the transformation it justifies, so students are naming a reason rather than matching a word, which is exactly what every later equation sheet asks of them. Distribution is treated as reaching EVERY term, and the error analysis is built on the incomplete case. It is the vocabulary sheet the justification work later in the course depends on.
The key rule
Commutative changes order. Associative changes grouping. Distributive multiplies EVERY term inside the parentheses, not just the first.
If parentheses are multiplied open, every term inside gets the multiplier.
Watch out
The mistake: Distributing 3(x + 4) as 3x + 4 — only multiplying the first term.
The fix: Multiply EVERY term inside: 3(x + 4) = 3x + 12. The 3 touches both x and 4.
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.