Literal Equations and Rearranging Formulas
I can solve a formula for any one of its letters, using the same moves as solving for x.
What students learn
Students learn to rearrange a formula to solve for a chosen letter: they treat the other letters as numbers, undo what is added or subtracted, then divide the whole side, and say when a letter cannot be 0.
See inside
The key rule
Treat the other letters as numbers. Undo what is added or subtracted first, then divide the whole side by what multiplies the letter.
A = lw → w = A/l
Dividing by l needs l ≠ 0.
Watch out
Solve 4x + 2y = 10 for y.
The mistake: 2y = 10 − 4x, so y = 5 − 4xOnly the 10 was divided by 2. The 4x was not.
The fix: y = (10 − 4x)/2 = 5 − 2xDivide the whole side by 2: both terms.
The mistakes it targets
- Divides or multiplies only part of a side, leaving a term out
- Divides by 2 to undo a multiplication by 1/2
- Adds a term instead of subtracting it from both sides
- Divides by a letter without saying it cannot be 0
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: 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, four 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.