Evaluating Algebraic Expressions
I can substitute given values into an algebraic expression and simplify with order of operations.
What students learn
Students learn to evaluate an expression or formula for given values, negatives included, by putting each value in parentheses and simplifying in order.
See inside
The key rule
Put each value in parentheses where its letter was. Then simplify in order: inside ( ) first, then exponents, then × and ÷, then + and −, each left to right.
3x + 2, x = −4 → 3(−4) + 2 = −10
A negative value squared is positive: (−3)² = 9, but −3² = −9.
Watch out
Evaluate x² when x = −6.
The mistake: x² = −6² = −36Only the 6 was squared; the − stayed outside.
The fix: x² = (−6)² = (−6)(−6) = 36Keep the value's sign inside the ( ).
The mistakes it targets
- Squares a negative value without putting it in parentheses
- Loses the sign when subtracting a negative
- Squares the negative sign in −x²
- Treats an even power of a negative number as negative
- Ignores the parentheses in a formula and works out of order
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.