Units, Precision, and Quantitative Reasoning
I can convert units with conversion factors that cancel, and report an answer only as precisely as its measurements allow.
What students learn
Students learn to convert units and rates with a chain of factors that cancel the unit they have, choose a sensible unit, and give a result no more precisely than its measurement.
See inside
The key rule
In each factor, put the unit you need to cancel on the opposite side (top or bottom) from where it is now. The units left at the end are the units you want.
5 m × (100 cm / 1 m) = 500 cm
Report an answer no more precisely than its measurements.
Watch out
Convert 4 ft to inches.
The mistake: 4 ft × (1 ft / 12 in)Nothing cancels: ft is on top twice.
The fix: 4 ft × (12 in / 1 ft) = 48 inft in the denominator cancels the ft you have.
The mistakes it targets
- Uses a conversion factor upside down
- Treats a converted measurement as more precise than the original
- Changes only one unit of a rate
- Stops after one factor in a multi-step conversion chain
- Writes digits the measurement does not have
The interactive Teacher Deck (31 slides, PowerPoint)
- The Learn page taught on screen: 9 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (three 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, five 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.