Units, Precision, and Quantitative Reasoning
I can convert units with a conversion-factor chain and reason about precision.
The problem this sheet solves
Unit conversion fails at the SET-UP, not the calculation. A conversion factor written the wrong way up leaves the unwanted unit uncancelled, and because the multiplication itself is correct there is nothing in the numbers to warn a student. Precision is the companion problem: a measured value reported to eight decimal places claims accuracy the measurement never had. This sheet makes cancellation the thing you check BEFORE multiplying, so the units decide whether the factor is the right way up. The conversion chain is drawn so students can see the unit disappear, and the sheet also covers choosing a sensible unit and reporting a defensible number of digits, which the standard bundles together and most worksheets separate.
The key rule
Set up each conversion factor so the unit you want to CANCEL matches what you already have, in the denominator. The unit you want to KEEP ends up alone.
If a unit doesn't cancel, the factor is upside down — flip it.
Watch out
The mistake: 5 mi × (1 mi / 5280 ft) — the mi doesn't cancel, leaving mi²/ft.
The fix: Flip the factor: 5 mi × (5280 ft / 1 mi) = 26,400 ft — the mi cancels cleanly.
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.