### Standard 3: Mathematics as Reasoning

In grades K-4, the study of mathematics should emphasize reasoning so that students can:
• Draw logical conclusions about mathematics
• Benchmarks 1B (The Nature of Science: Scientific Inquiry)
Scientists do not pay much attention to claims about how something they know about works unless the claims are backed up with evidence that can be confirmed and with a logical argument.

Benchmarks 12E (Habits of Mind: Critical-Response Skills)
Recognize when comparisons might not be fair because some conditions are not kept the same.

• Use models, known facts, properties, and relationships to explain their thinking
• 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 1B (The Nature of Science: Scientific Inquiry)
When people give different descriptions of the same thing, it is usually a good idea to make some fresh observations instead of just arguing about who is right.

Benchmarks 9E (The Mathematical World: Reasoning)
One way to make sense of something is to think how it is like something more familiar.

Benchmarks 11B (Common Themes: Models)
Seeing how a model works after changes are made to it may suggest how the real thing would work if the same thing were done to it.

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Judge whether measurements and computations of quantities such as length, area, volume, weight, or time are reasonable in a familiar context by comparing them to typical values.

Benchmarks 12E (Habits of Mind: Critical-Response Skills)
Buttress their statements with facts found in books, articles, and databases, and identify the sources used and expect others to do the same.

Benchmarks 11B (Common Themes: Models)
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.

• Justify their answers and solution processes
• Benchmarks 9E (The Mathematical World: Reasoning)
People are more likely to believe your ideas if you can give good reasons for them.

Benchmarks 9E (The Mathematical World: Reasoning)
Reasoning can be distorted by strong feelings.

Benchmarks 12A (Habits of Mind: Values and Attitudes)
Offer reasons for their findings and consider reasons suggested by others.

• Use patterns and relationships to analyze mathematical situations
• Benchmarks 11C (Common Themes: Constancy and Change)
Things can change in different ways, such as size, weight, color, and movement. Some small changes can be detected by taking measurements.

Benchmarks 11C (Common Themes: Constancy and Change)