Learning Standards by Strand
Patterns, Relations, and Algebra
for Grades 7-8
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Understand patterns, relations, and functions |
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Represent and analyze mathematical situations and structures using algebraic symbols |
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Use mathematical models to represent and understand quantitative relationships |
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Analyze change in various contexts |
Learning Standards
Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
| 8.P.1 |
Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions, e.g., compounding. |
| 8.P.2 |
Evaluate simple algebraic expressions for given variable values, e.g., 3a2 - b for a = 3 and b = 7. |
| 8.P.3 |
Demonstrate an understanding of the identity (-x)(-y) = xy. Use this identity to simplify algebraic expressions, e.g., (-2)(-x+2) = 2x - 4. |
| 8.P.4 |
Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations. |
| 8.P.5 |
Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems. |
| 8.P.6 |
Identify the roles of variables within an equation, e.g., y = mx + b, expressing y as a function of x with parameters m and b. |
| 8.P.7 |
Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs. |
| 8.P.8 |
Explain and analyze-both quantitatively and qualitatively, using pictures, graphs, charts, or equations-how a change in one variable results in a change in another variable in functional relationships, e.g., C = πd, A = πr2 (A as a function of r), Arectangle = lw (Arectangle as a function of l and w). |
| 8.P.9 |
Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate. |
| 8.P.10 |
Use tables and graphs to represent and compare linear growth patterns. In particular, compare rates of change and x- and y-intercepts of different linear patterns.
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Exploratory Concepts and Skills
for Grades 7-8 and Single-Subject Courses
- Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative and recursive (e.g., Pascal's triangle), and linear functional relationships.
- Use tables, graphs, and appropriate technology to explore quadratic and exponential growth patterns.
- Investigate the use of systems of equations, tables, and graphs to represent mathematical relationships.
- Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.
Selected Problems or Classroom Activities
[ MCAS || NCTM || Other Sources || Interactive || View/Print All]
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