Standard 12: Fractions and Decimals

In grades K-4, the curriculum should include fractions and decimals so that students can:

• Develop concepts of fractions, mixed numbers, and decimals

• Develop number sense for fractions and decimals

Benchmarks 9A (The Mathematical World: Numbers)
Grades 6-8, page 213
Numbers can be written in different forms, depending on how they are being used. How fractions or decimals based on measured quantities should be written depends on how precise the measurements are and how precise an answer is needed.

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades 6-8, page 291
Decide what degree of precision is adequate and round off the result of calculator operations to enough significant figures to reasonably reflect those of the inputs.

• Use models to relate fractions to decimals and to find equivalent fractions

Benchmarks 11B (Common Themes: Models)
Grades 6-8, page 269
Mathematical models can be displayed on a computer then modified to see what happens.

Benchmarks 2A (The Nature of Mathematics: Patterns and Relationships)
Grades 3-5, page 27
Mathematical ideas can be represented concretely, graphically, and symbolically.
 

• Use models to explore operations on fractions and decimals

Benchmarks 11B (Common Themes: Models)
Grades 3-5, page 268
Geometric figures, number sequences, graphs, diagrams, sketches, number lines, maps, and stories can be used to represent objects, events, and processes in the real world, although such representations can never be exact in every detail.
 

• Apply fractions and decimals to problem situations

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades K-2, page 290
Use whole numbers and simple, everyday fractions in ordering, counting, identifying, measuring, and describing things and experiences.

Benchmarks 9A (The Mathematical World: Numbers)
Grades K-2, page 211
Sometimes in sharing or measuring there is a need to use numbers between whole numbers.

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades 3-5, page 290
Use fractions and decimals, translating when necessary between decimals and commonly encountered fractions halves, thirds, fourths, fifths, tenths, and hundredths (but not sixths, sevenths, etc.).