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# National Standards for Grade 8 - Mathematics (page 6)

#### Algebra

By grade 4, students are expected to be able to recognize and extend simple numeric patterns as one foundation for a later understanding of function. They can begin to understand the meaning of equality and some of its properties, as well as the idea of an unknown quantity as a precursor to the concept of variable.

As students move into middle school, the ideas of function and variable become more important. Representation of functions as patterns, via tables, verbal descriptions, symbolic descriptions, and graphs, can combine to promote a flexible grasp of the idea of function. Linear functions receive special attention. They connect to the ideas of proportionality and rate, forming a bridge that will eventually link arithmetic to calculus. Symbolic manipulation in the relatively simple context of linear equations is reinforced by other means of finding solutions, including graphing by hand or with calculators.

 GRADE 8 1) Patterns, relations, and functions a) Recognize, describe, or extend numerical and geometric patterns using tables, graphs, words, or symbols. b) Generalize a pattern appearing in a numerical sequence or table or graph using words or symbols. c) Analyze or create patterns, sequences, or linear functions given a rule. d) Identify functions as linear or non-linear or contrast distinguishing properties of functions from tables, graphs, or equations. e) Interpret the meaning of slope or intercepts in linear functions. 2) Algebraic representations a) Translate between different rep­resentations of linear expressions using symbols, graphs, tables, diagrams, or written descriptions. b) Analyze or interpret linear relationships expressed in symbols, graphs, tables, diagrams, or written descriptions. c) Graph or interpret points that are represented by ordered pairs of numbers on a rectangular coordinate system. d) Solve problems involving coor­dinate pairs on the rectangular coordinate system. e) Make, validate, and justify conclusions and generalizations about linear relationships. f) Identify or represent functional relationships in meaningful contexts including proportional, linear, and common non-linear (e.g., compound interest, bacte­rial growth) in tables, graphs, words, or symbols. 3) Variables, expressions, and operations a) Write algebraic expressions, equations, or inequalities to represent a situation. b) Perform basic operations, using appropriate tools, on linear algebraic expressions (including grouping and order of multiple operations involving basic operations, exponents, roots, simplifying, and expanding). 4) Equations and inequalities a) Solve linear equations or inequalities (e.g., ax + b = c or ax + b = cx + d or ax + b > c). b) Interpret "=" as an equivalence be­tween two expressions and use this interpretation to solve problems. c) Analyze situations or solve problems using linear equations and inequalities with rational coefficients symbolically or graphically (e.g., ax + b = c or ax + b = cx + d). d) Interpret relationships between symbolic linear expressions and graphs of lines by identifying and computing slope and intercepts (e.g., know in y = ax + b, that a is the rate of change and b is the vertical intercept of the graph). e) Use and evaluate common formulas [e.g., relationship between a circle’s circumference and diameter (C = ï°d), distance and time under constant speed].

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