Properties of Real Numbers
I can name the property that justifies a step and apply the Distributive Property correctly.
What students learn
Students learn to name the property behind each step and distribute a number to every term inside the parentheses.
See inside
The key rule
Name the property by what changed from one side to the other. To distribute, multiply the number in front by every term inside the ( ).
6 + 0 = 6: identity · 6 + (−6) = 0: inverse
Commutative swaps two numbers. Associative keeps the order and moves the parentheses.
Watch out
Distribute 3(x + 4).
The mistake: 3(x + 4) = 3x + 4The 3 multiplied only the x.
The fix: 3(x + 4) = 3x + 12The 3 multiplies every term: 3 × 4 = 12.
The mistakes it targets
- Multiplies only the first term inside the parentheses
- Calls a regrouping commutative when only the parentheses moved
- Mixes up the identity and inverse properties
- Loses a sign when distributing a negative number
- Calls any equation with parentheses the Distributive Property
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 9 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: two word problems 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.