Yearly Goals for Algebra I

Yearly Goals for Algebra I

Number, Number Sense, and Operations Standard

ÿ  Identify and justify when properties (closure, identity, inverse, commutative and associative) hold for a set of operations

ÿ  Compare, place in order, and determine equal forms for rational and irrational numbers

ÿ  Explain effects of multiplication, division, powers, and roots on the magnitude of quantities

ÿ  Demonstrate smoothness in working with real numbers

ÿ  Estimate solutions for problem situations that involve square and cube roots

Measurement Standard

ÿ  Convert rates that are in the same measuring system; e.g., mph to feet/second, kilometers per hour to meters per second

ÿ  Use unit analysis to check computations involving measurement

ÿ  Use ratios of lengths in similar 2-D figures or 3-D objects to calculate the ratio of their areas or volumes

ÿ  Use scale drawings and right triangle trig to solve problems with unknown distances and angle measures

ÿ  Solve problems converting units for situations involving distance, area, volumes and rates within the same measuring system

Geometry & Spatial Sense Standard

ÿ  Define basic trig ratios in right triangles: sine, cosine, and tangent

ÿ  Apply proportions and right triangle trig ratios to solve problems with missing lengths and angle measures in similar figures

ÿ  Analyze 2-D figures in a coordinate plane; e.g., use slope/distance formulas to show that a quadrilateral is a parallelogram

Patterns, Functions, & Algebra Standard

ÿ  Define function with ordered pairs in which each domain element has exactly one range element

ÿ  Generalize patterns using functions or relationships and translate among tabular, graphical, and symbolic representations

ÿ  Describe problem situations (linear, quadratic, and exponential) using tabular, graphical and symbolic representations

ÿ  Relationships among zeros of a function, roots of equations, and solutions of equations graphically and in words

ÿ  Functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum

ÿ  Write and use equivalent forms of equations and inequalities in problem situations; e.g., change from normal form to y-intercept form

ÿ  Exponential growth and decay

ÿ  Determine linear equations that represent lines passing through ordered pairs and equations for parallel and perpendicular lines through a specific point

ÿ  2 by 2 systems of linear equations graphically, using substitution, using elimination, both with and without technology

ÿ  Add, subtract, multiply, and divide monomials and polynomials

ÿ  Simplify rational expressions by eliminating common factors and applying properties of integer exponents

ÿ  Model and solve problems involving direct and inverse variation using proportional reasoning

ÿ  Describe the relationship between slope and the graph of a direct variation and inverse variation

ÿ  Describe how changes of values of constants in linear or quadratic equations affect related graphs

Data Analysis & Probability Standard

ÿ  Classify data as single variable or bivariate (two variables) and as quantitative (measurement) or qualitative (categorical)

ÿ  Create scatterplots for two variable data (bivariate) sketch line of best fit, and interpret that slope

ÿ  Analyze and interpret frequency distributions based on spread, symmetry, skewness, clusters and outliers

ÿ  Various types of studies (survey, observation, experiment) and identify possible misuses of statistical data

ÿ  Describe limitations of sampling methods, analyze effects of random vs. biased sampling; e.g., does sample represent the population

ÿ  Infer about relationships in bivariant data, recognize the difference between evidence of relationship and cause/effect

ÿ  Use the Fundamental Counting principle to determine the total number of possible outcomes for math situations

ÿ  Describe, create, and analyze a sample space and use it to calculate probability

ÿ  Identify independent vs. dependent events and explain their differences, common misconceptions, & probabilities associated with those events

ÿ  Use theoretical and experimental probability, including simulations or random numbers to estimate probabilities and solve problems with uncertainty; e.g., compound events, independent events, simple dependent events