- Select and use appropriate measurement tools (rulers, tape measures, scales, containers, clocks, thermometers).
- Relate direct comparisons of objects to comparisons of numerical measurements or estimates.
Example: Tom, who is four feet tall, is shorter than Jose, who is five feet tall, because 4 is smaller than 5.

Note: The concepts of addition and order are intrinsic in quantities such as length, weight, and volume (capacity). So measuring such quantities provides an independent empirical basis for understanding the properties of numbers that is different from simple counting.

- Round off measurements to whole numbers.
- Recognize the essential role of units in measurement and understand the difference between
*standard*and*non-standard*units.Example: An inch or foot marked on a ruler is a standard unit, whereas a paperclip or a classmate's foot used to measure is a non-standard unit.

- Represent addition by laying rods of different lengths end to end, combining items on a balance, and pouring liquids or sand into different containers.
- Estimate lengths with simple approximations.
- Understand and use comparative words such as
*long, longer, longest; short, shorter, shortest; tall, taller, tallest; high, higher, highest*.

- Use the expressions "o’clock" and "half past."

- Know the values of U.S. coins (penny, nickel, dime, quarter, dollar bill).
- Use the symbols $ and ¢ separately (e.g., $4, 35¢ instead of $PS.4.35).
- Use coins to decompose monetary amounts given in cents.
Example: 17¢ = one dime, one nickel, and two pennies = 10 + 5 + 1 + 1; or 17¢ = three nickels and two pennies = 5 + 5 + 5 + 1 + 1.

- Understand and solve money problems expressed in a different ways, including
*how much more*or*how much less*.Note: Avoid problems that require conversion from cents to dollars or vice versa.

- Recognize and use standard abbreviations: m, cm, yd, ft, and in, as well as the symbolic notation 3'6".
- Understand and use units appropriate to particular situations.
Example: Standard U.S .school notepaper is sized in inches, not centimeters.

- Add and subtract mixed metric units (e.g., 8m,10cm + 3m,5cm) but defer calculation with mixed English units (e.g., 3ft,1in + 1ft,8in) until third grade.
Note: Conversion between systems awaits a later grade.

- Measure to the nearest centimeter or half inch using meter sticks, yardsticks, rulers, and tape measures marked in either metric or English units.
Note: Measure within either system without conversion between systems.

- Create and use hand-made rulers by selecting an unconventional unit length (e.g., a hand-width), marking off unit and half-unit lengths.
- Explore a variety of ways to measure perimeter and circumference.
Examples: Encircle with a tape measure; measure and sum various pieces; wrap with a string and then measure the length of the string. Compare answers obtained by different strategies and explain any differences.

Note: Comparing the result of a direct measurement (encircling) with that of adding component pieces underscores the importance of accuracy and serves as a prelude to understanding the significance of significant digits.

- Recognize, use, and estimate common measures of volume (quarts, liters, cups, gallons) and weight (pound, kilogram).
- Understand and use common expressions such as
*half a cup*or*quarter of a pound*that represent fractional parts of standard units of measurement.

- Demonstrate that the combined length of the shorter pieces from two pairs of rods is shorter than the combined lengths of the two longer pieces.
- Recognize that the same applies to combined pairs of weights or volumes.
Note: Even though this relation may seem obvious, it is an important demonstration of the fundamental relation between addition and order, namely, that if a ≤ b and c ≤ d, then a + c ≤ b + d.

- Know and use the names and approximate magnitudes of common units:
For length: kilometer, meter, centimeter; mile, yard, foot, inch.

For capacity: liter, milliliter; gallon, quart, pint, cup.

For time: year, month, week, day, hour, minute, second.

For money: pennies, nickels, dimes, quarters, dollars.

Note: Many of these units have been introduced in prior grades; others will be introduced in later grades. Here some are pulled together for reinforcement and systematic use. Each year in grades 2-6 some new measures should be introduced and previous ones reinforced. Which are done in which grades is of lesser importance.

- 1 meter = 100 centimeters, 1 yard = 3 feet, 1 foot = 12 inches.
- 1 liter = 1,000 milliliters, 1 gallon = 4 quarts, 1 quart= two pints.
- 1 year = 12 months, 1 week = 7 days, 1 hour = 60 minutes, 1 minute = 60 seconds.
- 1 dollar = 4 quarters = 10 dimes = 100 pennies, 1 quarter= 5 nickels = 25 pennies, 1 dime = 2 nickels = 10 pennies, 1 nickel = 5 pennies.

- Make and record measurements that use mixed units within the same system of measurement (e.g., feet and inches, hours and minutes).
Note: Many situations admit various approaches to measurement. Using different means and comparing results is a valuable activity.

- Understand that errors are an intrinsic part of measurement.
- Understand and use time both as an absolute (12:30 p.m.) and as a duration of a time interval (20 minutes).
- Understand and use idiomatic expressions of time (e.g., "10 minutes past 5," "quarter to 12," "one hour and ten minutes").

Note: Dealing with money enables students to become accustomed to decimal notation, i.e., $1.49 + $0.25 = $1.74.

- Include use of common abbreviations: m, cm, kg, g, l, ml, hr, min, sec, in, ft, lb, oz, $, ¢.
Note: Add and subtract only within a single system, using quantities within students' experience. Use real data where possible, but limit the size and complexity of numbers so that problem solving, not computation, is the central challenge of each task.

- Always use units when recording measurements.
- Know both metric and English units: centimeter, square centimeter, cubic centimeter; meter, square meter, cubic meter; inch, square inch, cubic inch; foot, square foot, cubic foot.
- Use abbreviations: m, cm, in, ft, yd; m
^{2}, cm^{2}, in^{2}, ft^{2}, yd^{2}; sq m, sq cm, sq in, sq ft, sq yd; m^{3}, cm^{3}, in^{3}, ft^{3}and yd^{3}.

Note: Emphasize conversions that are common in daily life. Common conversions typically involve adjacent units—for example, hours and minutes or minutes and seconds, but not hours and seconds. Know common within-system equivalences.

- Use unit cubes to build solids of given dimensions and find their volumes.
- 1 square foot = 12
^{2}square inches; 1 square meter as 100^{2}square centimeters; 1 cubic foot = 12^{3}cubic inches; 1 cubic meter as 100^{3}cubic centimeters.

- Estimate areas of rectangles in square inches and square
centimeters.
Note: Avoid between-system conversions.

Examples: Centimeter vs. inch, foot and yard vs. meter; square centimeter vs. square inch; square yard vs. square meter; cubic foot vs. cubic meter.

- Both recorded data and answers to calculations should be rounded to a degree of precision that is reasonable in the context of a given problem and the accuracy of the measuring instrument.
Note: All measurements of continuous phenomena such as length, capacity, or temperature are approximations. Measurements of discrete items such as people or bytes can be either exact (e.g., size of an athletic team) or approximate (e.g., size of a city).

- Select appropriate units to make measurements of everyday objects, record measurements to a reasonable degree of accuracy, and use a calculator when appropriate to compute answers.
- Know that answers to measurement problems require appropriate units in order to have any meaning.
Note: Include figures whose dimensions are given as fractions or mixed numbers.

- For information: bytes, kilobytes (K or Kb), megabytes (M), gigabytes (G). 1G = 1,000M, 1M = 1,000K, 1K = 1,000 bytes.
Note: Literally, the multiplier is 1,024 = 2

^{10}, but for simplicity in calculation, 1,000 is generally used instead. - For weight: kilogram (kg), gram (g), pound (lb), ounce (oz). 1 kg= 1,000 g, 1 lb = 16 oz.
- For temperature: Centigrade and Fahrenheit degrees. 32°F = 0°C; 212°F = 100°C.

- Understand the role of significant digits in signaling the accuracy of measurements and associated calculations.
Example: Report a city's population as 210,000, not as 211,513.

Note: Measurement is not a focus in grade 6 of these expectations.