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)
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)
Explain to other students how they go about solving numerical problems.

Benchmarks 12D (Habits of Mind: Communication Skills)
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)
Numbers and shapes can be used to tell about things.

Benchmarks 12D (Habits of Mind: Communication Skills)
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)
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)