Standard 9: Algebra

In grades 5-8, the mathematics curriculum should include explorations of algebraic concepts and processes so that students can:

• Understand the concepts of variable, expression, and equation

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.
 

• Represent situations and number patterns with tables, graphs, verbal rules, and equations and explore the interrelationships of these representations

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.

 
• Develop confidence in solving linear equations using concrete, informal, and formal methods

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.
 

• Investigate inequalities and nonlinear equations informally

Benchmarks 11D (Common Themes: Scale)
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.
 
• Apply algebraic methods to solve a variety of real-world and mathematical problems

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.
 

• Analyze tables and graphs to identify properties and relationships

Benchmarks 9C (The Mathematical World: Shapes)
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.