Writing a Function Rule from a Table
I can write the rule for a table by finding the step and the start, then checking every row.
What students learn
Students learn to find a table's step (the change in y for each 1 in x) and its start (y at x = 0), write y = (step)x + (start), and test the rule on every row.
See inside
The key rule
y = (step)x + (start). The step multiplies x; the start is y at x = 0. Then check the rule on every row.
y = (step)x + (start)
If x jumps by 2, the step is the change in y ÷ 2.
Watch out
The pairs are (1, 5), (2, 8) and (3, 11). Write the rule.
The mistake: up 3 each time, so y = x + 3At x = 1 that gives 4, not 5.
The fix: y = 3x + 2; check: 3(1) + 2 = 5, 3(2) + 2 = 8, 3(3) + 2 = 11The step multiplies x; every row checks.
The mistakes it targets
- Adds the step instead of multiplying x by it
- Takes the y change as the step when x jumps by more than 1
- Checks only the rows the rule was built from
- Uses the first output as the start instead of y at x = 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: 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.