3.1 Money, Work, and Measurement Math

Functional Numeracy Starts With the Document

The CASAS Math GOALS 2 series tests functional numeracy: math drawn from a real-life document such as a sale sign, receipt, utility bill, pay stub, work schedule, food label, recipe, mileage note, or measurement instruction. The test is not asking for arithmetic in isolation. It is asking whether you can pick the right numbers, choose the right operation, and produce an answer that fits the situation. GOALS 2 has five test levels aligned to the College and Career Readiness (CCR) Standards, so items range from beginning money handling up to multi-step workplace problems.

Use the same four-step routine on most items:

1. Read the question first. Decide what the answer must represent: total cost, sale price, net pay, change due, average, rate, length, weight, time, or amount left over.
2. Circle only the needed numbers. Ignore extra dates, account numbers, names, store hours, or labels that do not answer the question.
3. Match the units. Dollars, hours, pounds, ounces, miles, minutes, inches, feet, cups, and servings cannot be mixed without conversion.
4. Estimate before selecting. A quick estimate should make the final answer feel possible; an answer that is wildly larger or smaller signals a skipped step.

Core CASAS Math Moves

Percent, Discount, Tax, and Tip

Percent means per hundred. Convert the percent to a decimal before multiplying: 10% = 0.10, 8% = 0.08, 25% = 0.25, and 50% = 0.50. For a discount, find the discount amount first, then subtract it from the original price. For tax, a service fee, or a tip, find the added amount, then add it on.

The most common wrong answer is the discount amount itself. If a $48 item is 25% off, the discount is $12, but the sale price is $36. A faster check for any discount is the complement: 25% off means you still pay 75%, so 48 x 0.75 = $36 in one step. For tip estimates, 10% of a $42 bill is $4.20, so a 20% tip is about $8.40.

Unit Price, Rates, and Averages

Unit price and rate both use division. Unit price gives cost per item, per ounce, per pound, or per gallon, and it lets you compare two package sizes: a 12-ounce can at $3.00 ($0.25/oz) beats a 20-ounce can at $5.40 ($0.27/oz). A rate gives an amount per unit of time, distance, or work, such as miles per hour or 18 boxes per hour.

An average is the total divided by the number of values. Add every value first, then divide by the count. If a worker packed 54, 61, and 59 items on three days, the average is 174 / 3 = 58. Do not divide by a number that simply appears in the document; divide only by how many values you added.

Gross Pay, Net Pay, and Overtime

On a pay stub, gross pay is what was earned before deductions. Net pay is what actually lands in the account after federal and state taxes, Social Security and Medicare, health insurance, retirement, and items like uniforms are subtracted. If the item asks for take-home pay, read the net pay line or compute gross minus total deductions.

Overtime is two calculations. Regular pay covers the regular hours; under United States federal rules overtime begins after 40 hours in a workweek and is paid at 1.5 times the base rate. Compute the regular portion and the overtime portion separately, then add. A worker at $16/hour who logs 43 hours earns 40 x 16 = $640 plus 3 x ($16 x 1.5) = 3 x $24 = $72, for $712.

Measurement and Unit Checks

Measurement tasks cover length, weight, volume, temperature, time, and distance. The safest habit is to write the unit beside every number. If a recipe needs 3/4 cup per batch and a worker makes 4 batches, 3/4 x 4 = 3 cups. If a label says a cleaner needs 2 ounces per gallon and the bucket holds 3 gallons, 2 x 3 = 6 ounces. Keep handy conversions ready: 1 foot = 12 inches, 1 pound = 16 ounces, 1 gallon = 4 quarts, and 1 hour = 60 minutes.

When answer choices carry different units, the unit can settle the item before the arithmetic does. An answer in inches cannot be correct when the question asks for feet unless the conversion is already done.

Final Check Before Choosing

Ask three questions before selecting:

• Did I answer the exact thing asked, such as sale price instead of discount amount?
• Did I use the right unit, such as per pound, per hour, or take-home pay?
• Is the number reasonable next to the document?

This last step matters because CASAS distractors usually come from one skipped step: adding when a discount should subtract, using total shift time instead of paid time, dividing by the wrong count, or forgetting that overtime applies only to the extra hours.