- Link conceptual and procedural knowledge
- Relate various representations of concepts or procedures to one another
- Recognize relationships among different topics in mathematics
- Use mathematics in other curriculum areas
- Use mathematics in their daily lives

Grades 3-5, page 290

State the purpose of each step in a calculation.

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

Grades 3-5, page 296

Make sketches to aid in explaining procedures or ideas.

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

Grades 3-5, page 296

Write instructions that others can follow in carrying out a procedure.

*Benchmarks* 9A (The Mathematical World: Numbers)

Grades 6-8, page 213

A number line can be extended on the other side of zero to represent
negative numbers. Negative numbers allow subtraction of a bigger number
from a smaller number to make sense, and are often used when something
can be measured on either side of some reference point (time, ground level,
temperature, budget).

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* 12E (Habits of Mind: Critical-Response Skills)

Grades K-2, page 268

One way to describe something is to say how it is like something else.

*Benchmarks* 2A (The Nature of Mathematics: Patterns and Relationships)

Grades 3-5, page 27

Mathematical ideas can be represented concretely, graphically, and
symbolically.

*Benchmarks* 11C (Common Themes: Constancy and Change)

Grades 3-5, page 273

Some features of things may stay the same even when other features
change. Some patterns look the same when they are shifted over, or turned,
or reflected or seen form different directions.

*Benchmarks* 11B (Common Themes: Models)

Grades 6-8, page 269

Different models can be used to represent the same thing. What kind
of model to use and how complex it should be depends on its purpose. The
usefulness of a model may be limited if it is too simple or if it is needlessly
complicated. Choosing a useful model is one of the instances in which intuition
and creativity come into play in science, mathematics, and engineering.

*Benchmarks* 11D (Common Themes: Scale)

Grades K-2, page 277

Things in nature and things people make have very different sizes,
weights, ages, and speeds.

*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* 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.