Every day you measure things: how tall a plant grew, how much juice is in a pitcher, how long a movie lasts, how much fence a garden needs. In this chapter you will learn to choose the right unit, to convert from one unit to another, to work with time and money, to find the perimeter and area of rectangles, and to read line plots with fractions.
1. Customary units of length, weight and capacity
In the United States we often use customary units. We measure length in inches, feet, yards and miles, weight in ounces and pounds, and capacity (how much a container holds) in cups, pints, quarts and gallons.
| Measure | Customary equivalents |
|---|---|
| Length | 1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 ft 1 mile (mi) = 5,280 ft |
| Weight | 1 pound (lb) = 16 ounces (oz) |
| Capacity | 1 cup (c) = 8 fluid ounces 1 pint (pt) = 2 c 1 quart (qt) = 2 pt 1 gallon (gal) = 4 qt |
Pick a unit that fits the object. A pencil is about 7 inches long, a classroom door is about 7 feet tall, a long soccer field is about 100 yards, and the walk to a far park may be 2 miles. An apple weighs a few ounces, a backpack weighs a few pounds. A bathtub holds many gallons, while a cup of milk is just 1 cup.
2. Metric units of length, mass and volume
The metric system is used in science and in most of the world. Its units are linked by 10, 100 and 1,000, which makes them easy to convert. A paper clip is about 3 centimeters long, a door is about 2 meters tall, and a road trip may be 50 kilometers. A paper clip has a mass of about 1 gram and a bag of flour about 1 kilogram. A spoonful of medicine is a few milliliters, and a large soda bottle holds 2 liters.
| Measure | Metric equivalents |
|---|---|
| Length | 1 centimeter (cm) = 10 millimeters (mm) 1 meter (m) = 100 cm 1 kilometer (km) = 1,000 m |
| Mass | 1 kilogram (kg) = 1,000 grams (g) |
| Volume | 1 liter (L) = 1,000 milliliters (mL) |
3. Converting within a measurement system
Converting means writing the same measure with a different unit. The measure does not change, only its name does.
- Find how many small units make 1 large unit (use the tables).
- Multiply the number of large units by that number.
- Write the answer with the small unit.
To go from a smaller unit to a larger unit, divide instead.
You can also convert several steps in a row. To change gallons to cups, go gallons to quarts, quarts to pints, pints to cups: \( 2 \text{ gal} = 8 \text{ qt} = 16 \text{ pt} = 32 \text{ c} \).
4. Time and elapsed time
Remember that 1 hour = 60 minutes and 1 minute = 60 seconds. Elapsed time is the amount of time that passes between a start time and an end time. A number line helps: jump first to the next full hour, then jump by hours, then add the last minutes.
To find an end time, do the jumps the other way: start at the beginning time and add the hours and the minutes.
5. Perimeter and area of rectangles
The perimeter is the distance around a shape. The area is the amount of flat space inside it, counted in square units (square centimeters, square feet…).
\[ P = 2 \times (\ell + w) \qquad \text{and} \qquad A = \ell \times w . \]
If you know the area and one side, divide to find the other side: a rectangle with area 72 square feet and width 8 ft has length \( 72 \div 8 = 9 \) ft. An L-shaped figure can be split into two rectangles, or built as a big rectangle with a corner taken away. Then add or subtract the areas.
6. Line plots with fractions
A line plot shows data above a number line. Each data value gets one mark (a circle or an X) above its place on the line. When the measures are fractions, the tick marks on the line are fractions too.
This line plot shows the heights of 12 bean plants. Four plants are \( 2\dfrac{1}{2} \) inches tall. Three plants are taller than \( 2\dfrac{1}{2} \) inches (one at \( 2\dfrac{3}{4} \) and two at 3). The tallest plant is 3 inches and the shortest is 2 inches, so the difference is 1 inch.
- Read the title and the scale under the line.
- Count the marks above each tick.
- To add all the data, multiply each fraction by its number of marks, then add the results.
7. Word problems and money
For a measurement word problem, read twice, find the question, choose the operations, and check that your answer has a unit that makes sense. When a problem mixes units, convert them to the same unit first.
With money, write amounts with a decimal point and two decimal places, like $4.50. Remember that 100 cents make 1 dollar, so $0.25 is 25 cents. To find change, subtract the cost from the amount paid.
Key takeaways
- Customary: 1 ft = 12 in, 1 yd = 3 ft, 1 mi = 5,280 ft, 1 lb = 16 oz, 1 gal = 4 qt, 1 qt = 2 pt, 1 pt = 2 c.
- Metric: 1 m = 100 cm, 1 cm = 10 mm, 1 km = 1,000 m, 1 kg = 1,000 g, 1 L = 1,000 mL.
- Large unit to small unit: multiply. Small unit to large unit: divide.
- 1 h = 60 min. Elapsed time: jump to the next hour, then by hours, then add minutes.
- Rectangle: \( P = 2 \times (\ell + w) \) in units, \( A = \ell \times w \) in square units.
- On a line plot, count the marks above each fraction; compare and add fractions to answer questions.
- Money: line up the decimal points, and change = amount paid minus total cost.
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