Why it matters on the HSPT
Measurement questions are not about deep math. They are about knowing the conversion and doing the multiplication or division in the right direction, and they appear in word problems about recipes, trips, and shopping, in comparison items that put 2 feet next to 20 inches, and in geometry items where a side is in feet and the answer wants inches. The conversions have to be memorized, since the test gives none of them.
The rules
The direction rule. Before you touch a number, ask whether you are moving to a smaller unit or a larger one. Smaller units mean more of them, so multiply. Larger units mean fewer, so divide. Four feet is 48 inches, because inches are smaller and there will be more of them. Forty-eight inches is 4 feet for the same reason in reverse.
Length. Twelve inches make a foot, 3 feet make a yard, and 5,280 feet make a mile. In metric, 10 millimeters make a centimeter, 100 centimeters make a meter, and 1,000 meters make a kilometer. Metric conversions are just moving a decimal point.
Weight. Sixteen ounces make a pound and 2,000 pounds make a ton. In metric, 1,000 grams make a kilogram.
Capacity. Eight fluid ounces make a cup, 2 cups make a pint, 2 pints make a quart, and 4 quarts make a gallon. So a gallon is 16 cups or 128 fluid ounces. In metric, 1,000 milliliters make a liter.
Two-step conversions. Yards to inches goes through feet: 2 yards is 6 feet is 72 inches. Gallons to cups goes through quarts and pints, or use the memorized 16 cups per gallon.
Chaining units. When you do not know a direct conversion, chain the ones you know and cancel units as you go. Two hours to seconds is 2 hours times 60 minutes per hour times 60 seconds per minute, which is 7,200 seconds; the hours cancel, then the minutes cancel, and seconds are left. Writing the units and crossing them out is the check that you multiplied instead of divided. If a question hands you an unusual conversion, such as 5 miles equals 8 kilometers, set up a proportion with the same unit on top on both sides, or find the multiplier: 70 miles is 14 times 5 miles, so it is 14 times 8 kilometers, which is 112.
Temperature. The test never asks you to convert between Fahrenheit and Celsius from memory. It asks for a sensible temperature, or hands you the formula and a number to plug in. Anchor four facts: water freezes at 32 Fahrenheit and 0 Celsius, boils at 212 Fahrenheit and 100 Celsius, and a comfortable room is about 68 to 72 Fahrenheit, which is about 20 Celsius. So 50 Celsius is halfway to boiling, far too hot for a bedroom, and 35 Fahrenheit is just above freezing.
Time. Sixty seconds in a minute, 60 minutes in an hour, 24 hours in a day, 7 days in a week, 52 weeks or 12 months or 365 days in a year. Elapsed time is easiest in pieces: count up to the next round hour, then by whole hours, then the leftover minutes. Add the pieces. When minutes pass 60, carry an hour.
Money. A dollar is 100 cents. A quarter is 25, a dime 10, a nickel 5, a penny 1. Money problems are decimal problems with two places; the decimals lesson covers the arithmetic.
Units in geometry. Perimeter is in the unit given; area is in square units; volume is in cubic units. If the sides are in feet, the area is in square feet, and 1 square foot is 144 square inches, not 12.
Convert before you price. When a price is per square yard and the room is measured in feet, change the feet to yards first, then find the area. A 30 by 15 foot gym is 10 by 5 yards, which is 50 square yards, and at 20 dollars per square yard it costs 1,000 dollars. Finding 450 square feet and multiplying by 20 gives 9,000, the trap answer that is always among the choices. Converting the area afterward also works, 9 square feet per square yard, but converting the sides first is one step shorter.
Worked examples
Example 1
How many inches are in 3 yards?
- A.36
- B.72
- C.108
- D.144
Show answer
Answer: C: 108
Three yards is 9 feet, and 9 feet is 9 times 12, which is 108 inches. Choice A, 36, is one yard; choice B, 72, is two.
Example 2
A recipe calls for 3 pints of milk. How many cups is that?
- A.1.5
- B.3
- C.6
- D.12
Show answer
Answer: C: 6
Cups are smaller than pints, so there are more of them: multiply. Two cups in a pint, so 3 pints is 6 cups. Choice A divides instead of multiplying.
Example 3
Which is the longest?
- A.2 feet
- B.20 inches
- C.0.5 yard
- D.30 centimeters
Show answer
Answer: A: 2 feet
Put everything in inches. Two feet is 24 inches. Half a yard is 18 inches. Thirty centimeters is a little less than a foot, about 12 inches. The longest is 2 feet. Comparing across units is impossible until they match.
Example 4
A movie starts at 11:40 a.m. and ends at 1:55 p.m. How long is it?
- A.1 hour 15 minutes
- B.2 hours 15 minutes
- C.2 hours 35 minutes
- D.3 hours 15 minutes
Show answer
Answer: B: 2 hours 15 minutes
Count in pieces: 20 minutes to noon, then 1 hour to 1:00, then 55 minutes to 1:55. That is 1 hour and 75 minutes, which is 2 hours 15 minutes. Choice A forgets the hour across noon.
Example 5
A bag of flour weighs 5 pounds. How many ounces is that?
- A.50
- B.60
- C.80
- D.100
Show answer
Answer: C: 80
Sixteen ounces in a pound, so 5 pounds is 5 times 16, which is 80 ounces. Choice D uses 20 ounces per pound, a common guess.
Example 6
How many meters are in 3.5 kilometers?
- A.35
- B.350
- C.3,500
- D.35,000
Show answer
Answer: C: 3,500
One kilometer is 1,000 meters, so 3.5 kilometers is 3,500 meters. In metric, converting is moving the decimal point three places for each thousand.
Example 7
A rectangular rug is 2 feet by 3 feet. What is its area in square inches?
- A.72
- B.144
- C.432
- D.864
Show answer
Answer: D: 864
Convert the sides first: 24 inches by 36 inches. The area is 24 times 36, which is 864 square inches. Choice A, 72, converts the area of 6 square feet by multiplying by 12, but a square foot is 144 square inches, and 6 times 144 is also 864.
Example 8
Which is a comfortable temperature for a classroom?
- A.35°F
- B.50°C
- C.20°C
- D.0°C
Show answer
Answer: C: 20°C
Zero Celsius is freezing and 50 Celsius is halfway to boiling, so both are out. Thirty-five Fahrenheit is only three degrees above freezing. Twenty Celsius is about 68 Fahrenheit, a normal indoor temperature. No formula is needed; the anchors do the work.
Example 9
Carpet costs $12 per square yard. How much does it cost to carpet a room that is 18 feet by 12 feet?
- A.$216
- B.$288
- C.$360
- D.$2,592
Show answer
Answer: B: $288
Convert the sides to yards first: 18 feet is 6 yards and 12 feet is 4 yards. The area is 6 times 4, which is 24 square yards, and 24 times 12 dollars is 288 dollars. Choice D prices 216 square feet at the square-yard rate, the trap for skipping the conversion. Choice A is the area in square feet with a dollar sign attached.
Common mistakes
- Multiplying when you should divide. Decide the direction first: smaller unit, more of them.
- Using 10 for a customary conversion. Only metric works in tens. Feet, ounces, and cups do not.
- Converting area by the length factor. A square foot is 144 square inches, not 12.
- Adding elapsed minutes past 60 without carrying. Seventy-five minutes is 1 hour 15 minutes.
- Comparing quantities in different units. Convert first, always.
Pricing square feet at a square-yard rate. A square yard is 9 square feet, not 3. Convert the sides to yards before you find the area, and the trap disappears.
Dividing when you should multiply in a chain. Write the units and cancel them. If the unit you want is not the one left standing, you set the chain up backward.
Practice
Conversions show up in arithmetic, in word problems, and in both geometric and non-geometric comparison items that mix units. The geometry lesson covers the square and cubic units that trip students most.