- Understand the concepts of variable, expression, and equation
- Represent situations and number patterns with tables, graphs, verbal rules, and equations and explore the interrelationships of these representations
- Develop confidence in solving linear equations using concrete, informal, and formal methods
- Investigate inequalities and nonlinear equations informally

*Benchmarks* 9B (The Mathematical World: Symbolic Relationships)

Grades 3-5, page 218

Mathematical statements using symbols may be true only when the symbols
are replaced by certain numbers.

*Benchmarks* 9B (The Mathematical World: Symbolic Relationships)

Grades 6-8, page 219

An equation containing a variable may be true for just one value of
the variable.

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

Grades 3-5, page 27

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

*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.

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

Grades 3-5, page 273

Things change in steady, repetitive, or irregular ways - or sometimes
in more than one way at the same time. Often the best way to tell which
kinds of change are happening is to make a table or graph of measurements.

- Apply algebraic methods to solve a variety of real-world and mathematical problems
- Analyze tables and graphs to identify properties and relationships

Grades 3-5, page 277

Finding out what the biggest and smallest possible values of something are is often as revealing as knowing what the usual value is.

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

Grades 6-8, page 274

Symbolic equations can be used to summarize how the quantity of something
changes over time or in response to other changes.

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

Grades 6-8, page 297

Organize information in simple tables and graphs and identify the relationships
they reveal.

Grades 6-8, page 219

Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: always keeps the same proportion to the first, increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease indefinitely, increase or decrease in steps, or do something different from any of these.

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

Grades 6-8, page 297

Read simple tables and graphs produced by others and describe in words
what they show.