6.6 Measurement: Elapsed Time, Money, Units & Conversions

6.6 Measurement: Elapsed Time, Money, Units & Conversions

ETS places measurement inside Geometry and Measurement, Data, Statistics, and Probability on Praxis 5003. Expect story problems about elapsed time, money, length, liquid volume, and mass, plus conversions within the U.S. customary system or within the metric system. Items also test whether a proposed measurement is reasonable for a real object.

Why Measurement Appears on an Elementary Math Subtest

Elementary teachers constantly convert units for science labs, schedule specials across the school day, total cafeteria money, and check whether a student's answer "makes sense." Praxis therefore assesses whether you can move fluently among everyday units without mixing systems or losing track of place value in time and money calculations.

Elapsed Time

To find how much time passes from a start clock time to an end clock time:

1. Count whole hours, then remaining minutes—or convert both times to minutes past a reference (such as noon or midnight) and subtract.
2. When subtracting minutes, if you must “borrow,” borrow 1 hour = 60 minutes, not 100.

Example 1: From 9:45 a.m. to 11:20 a.m.

• From 9:45 to 10:45 is 1 hour; from 10:45 to 11:20 is 35 minutes → 1 hour 35 minutes.

Example 2: A bus leaves at 7:40 and arrives at 9:15.

• Subtract: 9:15 − 7:40. Borrow 1 hour from 9 → 8 hours and 75 minutes; 75 − 40 = 35 minutes; 8 − 7 = 1 hour → 1 hour 35 minutes.

Watch a.m./p.m. labels and overnight spans. Multiple-choice distractors often forget the 60-minute borrow or add minutes incorrectly (for example, writing “1 hour 65 minutes” instead of renaming as 2 hours 5 minutes).

Money

• Keep units consistent: work entirely in cents (integers) or entirely in dollars (decimals), but do not mix mid-problem.
• Unit price = total cost ÷ number of items (or ÷ ounces/pounds for a unit rate).
• Change = amount tendered − cost.
• Multi-item receipts: multiply, then add tax only if the item states a tax rate.

Example: 3 notebooks at $1.75 each cost $5.25. Paying with $10.00 yields $4.75 in change. Unit-rate example: A 20-ounce box of cereal costs $6.99. The unit price is $6.99 ÷ 20 ≈ $0.35 per ounce (useful when comparing brands).

Length, Liquid Volume, and Mass — Relative Sizes

U.S. customary (memorize relationships)

Metric (powers of 10)

Reasonableness check: a reasonable height for a two-story building is about 20 feet, not 20 inches, 20 yards, or 20 miles. A reasonable mass for an apple is a couple hundred grams, not kilograms or milligrams. A classroom water bottle is on the order of 500 mL to 1 L, not 500 L.

Within-System Conversions

Convert by multiplying when going to a smaller unit and dividing when going to a larger unit. Set up a one-line factor so units cancel.

Examples:

• $4\ \text{ft} = 4 \times 12 = 48\ \text{in}$
• $3\ \text{kg} = 3 \times 1{,}000 = 3{,}000\ \text{g}$
• $2.5\ \text{L} = 2.5 \times 1{,}000 = 2{,}500\ \text{mL}$
• $36\ \text{in} = 36 \div 12 = 3\ \text{ft}$
• $5\ \text{gallons} = 5 \times 4 = 20\ \text{quarts} = 20 \times 4 = 80\ \text{cups}$

5003 focuses on conversions inside customary or inside metric. If an item mixes systems, it will supply the needed bridge factor—do not invent one.

Worked Multi-Step Measurement Items

Recipe / volume: A recipe needs 3 cups of broth. You have a 1-quart carton. Since 1 quart = 4 cups, you have enough, with 1 cup left over. If the carton shows 946 mL and you are told 1 cup ≈ 240 mL, then 3 cups ≈ 720 mL, still less than 946 mL—same conclusion when a metric bridge is given.

Mass packing: A teacher packs 24 bags of sand that each have mass 250 g. Total mass is $24 \times 250 = 6{,}000\ \text{g} = 6\ \text{kg}$. If the cart limit is 5 kg, the load is over the limit.

Length project: A bulletin board is 4 ft wide. Border strips come in 18-inch pieces. Convert 4 ft → 48 in; $48 \div 18 = 2$ strips with 12 in left over, so 3 strips are needed if you cannot splice leftover scraps usefully—context decides whether to round up.

Choosing Tools and Units

ETS also expects familiarity with measuring length using standard tools (rulers marked in inches or centimeters) and comparing lengths. When an item shows a diagram with a scale, read the unit on the scale before computing. Prefer metric units for science-style mass/volume and customary units when the story is clearly U.S. classroom/home context—unless the problem states otherwise.

Exam Tips

• Rewrite every measurement in one unit before adding or subtracting.
• For elapsed time, sketch a timeline and rename 60 minutes as 1 hour when needed.
• For reasonableness items, eliminate answers with absurd units first.
• Use the on-screen scientific calculator for multi-digit conversions, but decide multiply versus divide yourself from unit size.
• Double-check money decimals: $3.5$ dollars is $3.50$, not 3.5 cents.