5.6 Measurement Units, Conversions, Elapsed Time & Money
Key Takeaways
- There is no reference sheet for grade 3 FAST Mathematics, so grade 3 students must know their measurement relationships from memory; grades 4 through 8 receive conversions on a pop-up reference sheet.
- Converting from a larger unit to a smaller unit multiplies and produces a bigger number; converting from a smaller unit to a larger unit divides and produces a smaller number.
- Metric conversions move by powers of ten, so they are decimal-point shifts; customary conversions require memorized ratios such as 1 pound = 16 ounces and 1 gallon = 4 quarts.
- Elapsed time is computed by counting up through friendly landmarks rather than by borrowing, because an hour is 60 minutes and not 100.
- Money problems are decimal problems: align the decimal points, work in dollars throughout or cents throughout, and never mix the two.
5.6 Measurement Units, Conversions, Elapsed Time & Money
Quick Answer: Converting from a larger unit to a smaller one multiplies (4 feet is 48 inches), and from a smaller unit to a larger one divides (48 inches is 4 feet). Metric conversions move by powers of ten and are decimal-point shifts. Customary conversions require memorized ratios. Elapsed time is counted up through landmark times, never subtracted like base-ten numbers, because an hour holds 60 minutes. Money is decimal arithmetic - align the decimal points and stay in one unit. Grade 3 gets no reference sheet at all; grades 4-8 get conversions in a pop-up window.
Where This Sits in the Blueprint
Measurement is the M strand, and on FAST it is reported inside a combined category:
| Grade | Reporting category containing measurement | Representative benchmarks |
|---|---|---|
| Grade 3 | Geometric Reasoning, Measurement, and Data Analysis and Probability (23-29%) | MA.3.M.1.1-1.2 (length, mass, liquid volume, real-world problems); MA.3.M.2.1-2.2 (time to the nearest minute, elapsed time) |
| Grade 4 | Geometric Reasoning, Measurement, and Data Analysis and Probability (31-37%) | MA.4.M.1.1-1.2 (units and conversions within a system); MA.4.M.2.1-2.2 (time, money) |
| Grade 5 | Geometric Reasoning, Measurement, and Data Analysis and Probability (23-29%) | MA.5.M.1.1 (conversions, including with decimals); MA.5.M.2.1 (multi-step money problems) |
[!IMPORTANT] The grade 3 reference-sheet gap is real. FDOE's calculator and reference sheet policy states plainly: there is no reference sheet for Grade 3 FAST Mathematics. Grades 4 through 8 receive conversions and some formulas in a pop-up window. A grade 3 student who does not know that a foot is 12 inches has no way to look it up mid-test.
The Two Systems
Customary Units (memorize these)
| Length | Weight | Liquid volume | Time |
|---|---|---|---|
| 1 foot = 12 inches | 1 pound = 16 ounces | 1 cup = 8 fluid ounces | 1 minute = 60 seconds |
| 1 yard = 3 feet | 1 ton = 2,000 pounds | 1 pint = 2 cups | 1 hour = 60 minutes |
| 1 mile = 5,280 feet | 1 quart = 2 pints | 1 day = 24 hours | |
| 1 mile = 1,760 yards | 1 gallon = 4 quarts | 1 week = 7 days |
The liquid-volume chain is worth internalizing as a ladder: gallon → 4 quarts → 8 pints → 16 cups → 128 fluid ounces. Each rung doubles except the first.
Metric Units (powers of ten)
| Length | Mass | Liquid volume |
|---|---|---|
| 1 centimeter = 10 millimeters | 1 gram = 1,000 milligrams | 1 liter = 1,000 milliliters |
| 1 meter = 100 centimeters | 1 kilogram = 1,000 grams | |
| 1 meter = 1,000 millimeters | ||
| 1 kilometer = 1,000 meters |
Because every metric relationship is a power of ten, a metric conversion is just a decimal-point move. Converting 3.4 kilometers to meters shifts the point three places right: 3,400 m. Converting 250 milliliters to liters shifts three places left: 0.25 L.
The Unit-Ratio Method
Multiplying or dividing by guesswork is where students lose these items. The unit ratio removes the guess. Write the conversion as a fraction whose value is 1, arranged so the unwanted unit cancels.
Convert 7 gallons to fluid ounces.
Gallons cancel against gallons, quarts against quarts, and so on down the chain, leaving fluid ounces. Because gallons are larger than fluid ounces, the number got bigger - the direction check passes.
Convert 96 inches to yards.
Inches are smaller than yards, so the number got smaller. Direction check passes again.
LARGER unit ------ x (how many small ones fit) ------> SMALLER unit
(gallons) (fluid ounces)
SMALLER unit ------ / (how many small ones fit) ------> LARGER unit
(inches) (yards)
Number gets BIGGER going right. Number gets SMALLER going left.
Elapsed Time: Count Up, Do Not Borrow
Time is the one measurement students cannot treat like base ten. Subtracting 2:45 from 5:20 in a column, borrowing 10 instead of 60, produces a wrong answer every time.
How long from 10:47 a.m. to 2:15 p.m.? Count up through landmarks:
10:47 a.m. --+13 min--> 11:00 a.m. --+3 hr--> 2:00 p.m. --+15 min--> 2:15 p.m.
13 min 3 hr 15 min
Total: 3 hours + 13 min + 15 min = 3 hours 28 minutes
The landmarks are always the same: jump to the next whole hour, then take whole hours, then take the remaining minutes. No borrowing, no base-sixty arithmetic.
Working backward. A recital ends at 4:10 p.m. and ran 95 minutes. When did it start? Ninety-five minutes is 1 hour 35 minutes. Back one hour gives 3:10 p.m.; back 35 more minutes gives 2:35 p.m.
[!IMPORTANT] When a duration is given in minutes only, convert it to hours-and-minutes before moving on the clock: 95 minutes is 1 hour 35 minutes, not "0.95 hours" and not "1.35 hours." An hour is 60 minutes, so 95 divided by 60 is 1 remainder 35.
Money as Decimal Arithmetic
Money problems on FAST are decimal problems dressed in dollar signs, and the two failure modes are both mechanical.
Failure 1: misaligned decimal points. Adding $$12.50 + $3.75 + $0.60$ horizontally invites error. Stack them:
12.50
3.75
+ 0.60
------
16.85
Failure 2: mixing dollars and cents. A problem giving "$4.20 and 85 cents" must be converted to one unit before anything else: either $$4.20 + $0.85 = $5.05$, or $420 + 85 = 505$ cents. Never one of each.
Worked multi-step problem. A student has $$20.00$. They buy 3 notebooks at $$2.45$ each and 2 pens at $$1.30$ each. How much change do they receive?
- Notebooks: $3 \times $2.45 = $7.35$
- Pens: $2 \times $1.30 = $2.60$
- Total spent: $$7.35 + $2.60 = $9.95$
- Change: $$20.00 - $9.95 = $10.05$
Estimate as a check: three notebooks near $$2.50$ is about $$7.50$, two pens near $$1.30$ is about $$2.60$, so roughly $$10$ spent and about $$10$ back. The exact answer of $$10.05$ is consistent.
Choosing a Reasonable Unit
Some items do not compute anything - they ask which unit fits. The reasoning is about scale:
| Object | Sensible unit | Why not the alternative |
|---|---|---|
| Thickness of a coin | millimeters | Centimeters would give a fraction under 1 |
| Height of a door | meters or feet | Millimeters gives about 2,000 - true, but unusable |
| Mass of an apple | grams | Kilograms gives 0.15, which is awkward |
| Mass of a car | kilograms or tons | Grams gives over 1,000,000 |
| Water in a bathtub | liters or gallons | Milliliters gives tens of thousands |
The working rule: pick the unit that leaves a number a person would actually say out loud - generally between 1 and 1,000.
Common Exam Traps & Misconceptions
[!WARNING]
Trap 1: Multiplying when you should divide
Converting 5,280 feet to miles is division, not multiplication. Before computing, ask whether the answer should be bigger or smaller than the starting number. Going to a larger unit always gives a smaller number.
[!WARNING]
Trap 2: Treating an hour as 100 minutes
Writing 2 hours 30 minutes as "2.30 hours" and adding it to another time produces nonsense. Thirty minutes is half an hour, which is 0.5 hours. Ninety minutes is 1.5 hours, not 1.30.
[!WARNING]
Trap 3: Crossing between systems
B.E.S.T. requires conversions within a single system in grades 4 and 5. An item will not ask a fourth grader to convert liters to gallons. If a problem seems to demand it, re-read - the two measurements are almost certainly meant to be compared, not converted.
[!WARNING]
Trap 4: Answering the intermediate step
Multi-step money problems frequently list the total spent as a distractor when the question asked for change. Circle what is being asked before computing, and check your final number against that phrase.
A container holds 3 gallons of juice. A serving is 6 fluid ounces. How many complete servings can be poured from the container?
A field trip bus leaves school at 9:35 a.m. and arrives at the museum at 1:20 p.m. How long was the trip?
A student pays for lunch with a $10 bill, buying a sandwich for $4.75, a milk for $1.15, and two apples at $0.65 each. How much change does the student receive?