Writing a Function Rule from a Table
I can write the rule for a table by finding the step and the start, then checking another row.
The problem this sheet solves
Given a table instead of a rule, students reach for the first thing that looks like a pattern. One habit reads only the first row and writes a rule that fits that row and nothing else. A second, sneakier habit finds the right number — the constant difference — and puts it in the wrong place, adding it on instead of multiplying by it. Both produce a confident, wrong equation, and neither shows up as a wrong-looking answer until a second row is actually tested. This sheet will not let either habit go unchecked. Every single item — all six practice problems, all three apply items, all four assess items — ends the same way: check the rule on a row you did not use to build it. Two items deliberately step x by 2 instead of 1, so the raw output difference is NOT the multiplier, and the sheet's one worked example honestly shows a table where no linear rule fits at all, rather than pretending every table has one.
The key rule
Find the STEP (how far the output moves when x goes up by 1) and the START (the output at x = 0, one step back from the first row). Write y = (step)x + (start), then CHECK it on a row that is not the first.
A step of 3 means 3x. It never means + 3.
Watch out
The mistake: The outputs go up by 3, so the rule is y = x + 3. That fits no row at all: at x = 2 it gives 5 and the table says 8.
The fix: The step 3 MULTIPLIES, so y = 3x + 2. Test it on the second row: 3(2) + 2 = 8, which is what the table says.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
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.