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Topic: Ratio/proportion/percent 

Mathematics

 Standard 1.  Uses a variety of strategies in the problem-solving process
  Level III (Grade 6-8)
   Benchmark 9.Uses a variety of reasoning processes (e.g., reasoning from a counter example, using proportionality) to model and to solve problems
    Knowledge/skill statements
     1.Uses counter examples to model problems
     2.Uses proportionality to model problems
     3.Uses counter examples to solve problems
     4.Uses proportionality to solve problems
 Standard 2.  Understands and applies basic and advanced properties of the concepts of numbers
  Level II (Grade 3-5)
   Benchmark 2.Understands equivalent forms of basic percents, fractions, and decimals (e.g., 1/2 is equivalent to 50% is equivalent to .5) and when one form of a number might be more useful than another
    Knowledge/skill statements
     1.Converts fractions to percents
     2.Converts percents to decimals
     3.Converts fractions to decimals
     4.Knows the equivalence of common fractions and percents
     5.Knows the equivalence of common fractions and decimals
     6.Knows the equivalence of common percents and decimals
  Level III (Grade 6-8)
   Benchmark 1.Understands the relationships among equivalent number representations (e.g., whole numbers, positive and negative integers, fractions, ratios, decimals, percents, scientific notation, exponentials) and the advantages and disadvantages of each type of representation
    Knowledge/skill statements
     1.Understands the equivalence of decimals and percents
     2.Understands the equivalence of whole numbers and fractions
     3.Understands the equivalence of fractions and ratios
     4.Understands the equivalence of whole numbers and ratios
     5.Understands the equivalence of whole numbers and decimals
     6.Understands the equivalence of whole numbers and percents
     7.Understands the equivalence of whole numbers and scientific notation
     8.Understands the equivalence of integers and fractions
     9.Understands the equivalence of integers and ratios
     10.Understands the equivalence of integers and decimals
     11.Understands the equivalence of integers and percents
     12.Understands the equivalence of integers and scientific notation
     13.Understands the equivalence of integers and exponents
     14.Understands the equivalence of fractions and decimals
     15.Understands the equivalence of ratios and decimals
     16.Understands the equivalence of ratios and percents
     17.Understands the equivalence of decimals and scientific notation
     18.Understands the equivalence of decimals and exponents
     19.Understands the equivalence of scientific notation and exponents
     20.Understands the advantages and disadvantages of different number representations
   Benchmark 7.Understands the concepts of ratio, proportion, and percent and the relationships among them
    Knowledge/skill statements
     1.Understands the concept of proportion
     2.Understands the concept of percent
     3. Understands the concept of ratio
     4.Understands the relationship between ratio and proportion
     5.Understands the relationship between ratio and percent
     6.Understands the relationship between proportion and percent
 Standard 3.  Uses basic and advanced procedures while performing the processes of computation
  Level III (Grade 6-8)
   Benchmark 6.Uses proportional reasoning to solve mathematical and real-world problems (e.g., involving equivalent fractions, equal ratios, constant rate of change, proportions, percents)
    Knowledge/skill statements
     1. Determines whether a problem can be solved by calculating percents
     2. Understands the concept of a constant rate of change
     3. Determines whether a problem can be solved using the concept of a constant rate of change
     4.Determines whether a problem can be solved using the concept of proportions
     5.Determines whether a problem can be solved using the concept of equivalent fractions
     6.Understands the concept of equivalent fractions
     7. Understands the concept of equal ratios
     8. Understands the concept of mathematical proportion
     9.Determines whether a problem can be solved using the concept of equal ratios
     10. Uses proportional reasoning to solve mathematical problems involving percents
     11.Uses proportional reasoning to solve mathematical problems involving equivalent fractions
     12. Uses proportional reasoning to solve mathematical problems involving equal ratios
     13. Uses proportional reasoning to solve mathematical problems involving a constant rate of change
     14. Uses proportional reasoning to solve mathematical problems involving proportions
 Standard 4.  Understands and applies basic and advanced properties of the concepts of measurement
  Level IV (Grade 9-12)
   Benchmark 3.Selects and uses an appropriate direct or indirect method of measurement in a given situation (e.g., uses properties of similar triangles to measure indirectly the height of an inaccessible object)
    Knowledge/skill statements
     1.Uses the properties of triangles to measure the height of distant object
     2.Understands the concept of indirect measurement using computations
     3.Understands the concept of direct measurement
 Standard 5.  Understands and applies basic and advanced properties of the concepts of geometry
  Level II (Grade 3-5)
   Benchmark 7.Understands how scale in maps and drawings shows relative size and distance
    Knowledge/skill statements
     1.Understands how scale in maps and drawings depicts relative distance
     2.Understands how scale in maps and drawings depicts relative size
  Level III (Grade 6-8)
   Benchmark 5.Understands the relationships between two- and three-dimensional representations of a figure (e.g., scale drawings, blueprints, planar cross sections)
    Knowledge/skill statements
     1.Understands that scale drawings are two-dimensional representations of three-dimensional figures
     2.Understands that blueprints are two-dimensional representations of three-dimensional figures
     3.Understands that planar cross sections are two-dimensional representations of three-dimensional figures
     4.Understands the relationship between two- and three-dimensional representations of figures
  Level IV (Grade 9-12)
   Benchmark 8.Uses trigonometric ratio methods to solve mathematical and real-world problems (e.g., determination of the angle of depression between two markers on a contour map with different elevations)
    Knowledge/skill statements
     1.Understands the concept of tangent ratio
     2.Understands the concept of cosine ratio
     3.Understands the concept of sine ratio
     4.Determines whether a problem can be solved by using tangent ratios
     5.Determines whether a problem can be solved by using cosine ratios
     6.Determines whether a problem can be solved by using sine ratios
     7.Uses trigonometric ratios to solve problems of angle of depression on a contour map
     8.Understands the concept of angle of depression
  Level V (Grade (College Readiness))
   Benchmark 1.Understands the effect that scale factors have on magnitude (e.g., area, volume)
    Knowledge/skill statements
     1.Understands the effect that scale factors have on area
     2.Understands the effect that scale factors have on volume
 Standard 7.  Understands and applies basic and advanced concepts of probability
  Level III (Grade 6-8)
   Benchmark 5.Understands the relationship between the numerical expression of a probability (e.g., fraction, percentage, odds) and the events that produce these numbers
    Knowledge/skill statements
     1.Understands the concept of percents representing probability
     2.Understands the concept of fractions representing probability
     3.Understands the concept of odds
     4.Understands the relationship between odds and probability
     5.Understands the concept of decimals representing probability
 Standard 8.  Understands and applies basic and advanced properties of functions and algebra
  Level III (Grade 6-8)
   Benchmark 7.Understands special values (e.g., minimum and maximum values, x- and y-intercepts, slope, constant ratio or difference) of patterns, relationships, and functions
    Knowledge/skill statements
     1.Understands x- and y-intercepts
     2.Understands the concept of slope
     3.Understands constant ratio or difference
     4.Understands the concept of maximum

Engineering Education

 Standard 12.  Understands the techniques, tools, and technologies related to the production of technical drawings
  Level IV (Grade 9-12)
   Benchmark 6.Understands the use of scales in technical drawings (e.g., architect, metric, civil, and mechanical engineer’s scales)
    Knowledge/skill statements
     1.Understands the use of scales in technical drawings
     2.Understands the use of an architect scale in technical drawings
     3.Understands the use of a metric scale in technical drawings
     4.Understands the use of a civil engineer’s scale in technical drawings
     5.Understands the use of a mechanical engineer’s scale in technical drawings
 Standard 14.  Uses the design process to solve problems
  Level IV (Grade 9-12)
   Benchmark 7.Understands the process of creating a scale model of an object or structure (e.g., a model automobile, building, bridge)
    Knowledge/skill statements
     1.Understands the process of creating a scale model of an object such as a model automobile
     2.Understands the process of creating a scale model of a structure such as a building
     3.Understands the process of creating a scale model of a structure such as a bridge