Topic: Ratio/proportion/percent 
Mathematics 
 Standard 1. Uses a variety of strategies in the problemsolving process 
  Level III (Grade 68) 
   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 35) 
   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 68) 
   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 68) 
   Benchmark 6.  Uses proportional reasoning to solve mathematical and realworld 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 912) 
   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 35) 
   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 68) 
   Benchmark 5.  Understands the relationships between two and threedimensional representations of a figure (e.g., scale drawings, blueprints, planar cross sections) 
    Knowledge/skill statements 
     1.  Understands that scale drawings are twodimensional representations of threedimensional figures 
     2.  Understands that blueprints are twodimensional representations of threedimensional figures 
     3.  Understands that planar cross sections are twodimensional representations of threedimensional figures 
     4.  Understands the relationship between two and threedimensional representations of figures 
  Level IV (Grade 912) 
   Benchmark 8.  Uses trigonometric ratio methods to solve mathematical and realworld 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 68) 
   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 68) 
   Benchmark 7.  Understands special values (e.g., minimum and maximum values, x and yintercepts, slope, constant ratio or difference) of patterns, relationships, and functions 
    Knowledge/skill statements 
     1.  Understands x and yintercepts 
     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 912) 
   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 912) 
   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 