Writing Linear Models from Tables and Contexts
I can write y = mx + b from a table or a story and test it on every row.
What students learn
Students learn to find the rate from two rows, find b from one row, write y = mx + b, then test the model on every row or fact.
See inside
The key rule
Find m as the change in y ÷ the change in x, then b from one point; the model must fit every row.
y = mx + b
A table's first y is b only when its x is 0.
Watch out
A table has (2, 11), (4, 17) and (6, 23). Sam writes its model.
The mistake: m = 3, b = 11, so y = 3x + 1111 is y at x = 2, not at x = 0.
The fix: 11 = 3(2) + b, so b = 5: y = 3x + 5Find b from a row; then every row fits.
The mistakes it targets
- Takes the first y-value in a table as b
- Takes the first reading in a story as the starting value
- Uses the change in y as the rate without dividing by the x change
- Swaps the rate and the one-time amount, or drops the sign of a decrease
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: one word problem, a reasoning prompt 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.