Standard 7: Concepts of Whole Number Operations

In grades K-4, the curriculum should include concepts of addition, subtraction, multiplication, and division of whole numbers so that students can:

Develop meaning for the operations by modeling and discussing a rich variety of problem situations

Benchmarks 11B (Common Themes: Models)
Grades K-2, page 268
A model of something is different from the real thing but can be used to learn something about the real thing.

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades K-2, page 290
Explain to other students how they go about solving numerical problems.

Benchmarks 12D (Habits of Mind: Communication Skills)
Grades 3-5, page 296
Make sketches to aid in explaining procedures or ideas.
 

Relate the mathematical language and symbolism of operations to problem situations and informal language

Benchmarks 2C (The Nature of Mathematics: Mathematical Inquiry)
Grades K-2, page 36
Numbers and shapes can be used to tell about things.

Benchmarks 12D (Habits of Mind: Communication Skills)
Grades 3-5, page 296
Write instructions that others can follow in carrying out a procedure.
 
• Recognize that a wide variety of problem structures can be represented by a single operation

Benchmarks 9E (The Mathematical World: Reasoning)
Grades 6-8, page 233
Sometimes people invent a general rule to explain how something works by summarizing observations. But people tend to overgeneralize, imagining general rules on the basis of only a few observations.

Benchmarks 2C page 37 (The Nature of Mathematics: Mathematical Inquiry)
Grades 6-8
Mathematicians often represent things with abstract ideas, such as numbers or perfectly straight lines, and then work with those ideas alone. The "things" from which they abstract can be ideas themselves(for example, a proposition about "all equal-sided triangles" or all "odd numbers).
 

• Develop operations sense

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades K-2, page 290
Give rough estimates of numerical answers to problems before doing them formally.

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades K-2, page 290
Readily give the sums and differences of single-digit numbers in familiar contexts where the operation makes sense and judge the reasonableness of the answer.