AAAS Educational Benchmark On Scale

Read here about an educational agenda, activity or curriculum that relates to the concept of scale.


The improvement of concepts of scale is one of the four unifying science education themes recommended by the American Association for the Advancement of Science in their benchmarks for science literacy, New York: Oxford University Press Inc., 1993.

The four themes are Systems (11A), Models (11B), Constancy (11C), Patterns of Change (11C) and Scale (11D).

These themes are then assigned to maps of scientific knowledge to guide curriculum construction. Two examples of scale in the maps:
  • To reduce the chance of system failure, performance testing is often conducted using small scale models, computer simulations, analogous systems, or just the parts of the system thought to be least reliable. 3B/6
  • Estimate distances and travel times from maps and the actual size of objects from scale drawings. 12B/5

It is a major factor in the map, "Proportional Reasoning: Ratios And Proportionality", which includes related objectives such as
  • An important kind of relationship between things is when one thing is a part of a whole.
  • Fractions are numbers we use to stand for a part of something.
  • Some interesting relationships between two variables include the variables always having the same difference or the same ratio.
  • The expression a/b can mean different things: a parts of size 1/b each, a divided by b, or a compared to b.
  • Use whole numbers and simple everyday fractions in ordering, counting, identifying, measuring, and describing things and experiences.
  • Add, subtract, multiply, and divide whole numbers mentally, on paper, and with a calculator.
  • Use fractions and decimals, translating when necessary between decimals and commonly encountered fractions.
  • Use ratios and proportions, including constant rates, in appropriate problems.
  • Use calculators to compare amounts proportionally.
  • Describe and compare things in terms of their number, shape, texture, size, weight, color, and motion.
  • Use numerical data in describing and comparing objects and events.
  • Use, interpret, and compare numbers in several equivalent forms such as integers, fractions, decimals, and percents.
  • When the linear size of a shape changes by some factor, its area and volume change disproportionately: area in proportion to the square of the factor, and volume in proportion to its cube. Properties of an object that depend on its area or volume also change disproportionately.
  • Sometimes in sharing or measuring there is a need to use numbers between whole numbers.
  • Shapes can match exactly or have the same shape in different sizes.
  • Estimate distances and travel times from maps and the actual size of objects from scale drawings.
  • Readily give the sums and differences of single-digit numbers in familiar contexts where the operation makes sense to them and they can judge the reasonableness of the answer.

The "Proportional Reasoning: Ratios And Proportionality" map connects with other main areas as follows
  • To And From Mathematical Processes
  • To And From Symbolic Representation
  • To Averages And Comparisons
  • To Correlation To Averages And Comparisons
  • To Evidence And Reasoning In Inquiry
  • To Graphic Representation
  • To Mathematical Models
  • To Mathematical Processes
  • To Scientific Investigations
  • To Statistical Reasoning
  • To Symbolic Representation