"Students in the middle grades should learn algebra both as a set of concepts and competencies tied to the representation of quantitative relationships and as a style of mathematical thinking for formalizing patterns, functions, and generalizations. In the middle grades, students should work more frequently with algebraic symbols than in lower grades. It is essential that they become comfortable in relating symbolic expressions containing variables to verbal, tabular, and graphical representations of numerical and quantitative relationships. Students should develop an initial understanding of several different meanings and uses of variables through representing quantities in a variety of problem situations. They should connect their experiences with linear functions to their developing understandings of proportionality, and they should learn to distinguish linear relationships from nonlinear ones. In the middle grades, students should also learn to recognize and generate equivalent expressions, solve linear equations, and use simple formulas. Whenever possible, the teaching and learning of algebra can and should be integrated with other topics in the curriculum."
Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results.
Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results.
Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs.
The standards for grades eight through twelve are organized differently from those for kindergarten through grade seven. In this section strands are not used for organizational purposes as they are in the elementary grades because the mathematics studied in grades eight through twelve falls naturally under discipline headings: algebra, geometry, and so forth. Many schools teach this material in traditional courses; others teach it in an integrated fashion. To allow local educational agencies and teachers flexibility in teaching the material, the standards for grades eight through twelve do not mandate that a particular discipline be initiated and completed in a single grade. The core content of these subjects must be covered; students are expected to achieve the standards however these subjects are sequenced.
"By the end of Grade 8, a student should be able to do the following:
- Describe the historical development of patterns, functions, and algebra.
- Explain how patterns, functions, and algebra relate to a variety of careers.
- Discover, describe, generalize and extend, linear, geometric, exponential, and simple quadratic patterns and relationships and represent them using variables and expressions.
- Analyze functional relationships to explain how a change in one quantity results in a change in another.
- Detect patterns and functions from statistical data and predict future outcomes.
- Use a calculator and computer software to formulate conclusions about number patterns and mathematical relationships.
- Apply and adapt patterns and functions to represent and solve problems.
- Represent and analyze relationships using tables, verbal rules, equations, and graphs.
- Convert among tables, symbols and graphic representations of functions.
- Demonstrate that a variety of problem situations can be modeled by the same type of function.
- Analyze the effect of parameter changes on the graphs of functions.
- Represent student-centered experiences that involve variable quantities using expressions, equations, inequalities, and matrices.
- Use tables, graphs, and rules as tools to interpret expressions, equations, and inequalities.
- Use operations on expressions to solve linear equations and inequalities.
- Use and apply mathematical abstraction and symbolic representation."
For Student Work/Assessments, Grade-Specific Concepts/Skills, and Best Practices, visit the School District of Philadelphia Curriculum Frameworks and click on "The FRAMEWORKS GRID."