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Poyen School |
| Language of Algebra |
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Evaluate algebraic expressions
The learner will be able to evaluate algebraic expressions, including radicals, by applying the order of operations.
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Translate words to algebraic
The learner will be able to translate word phrases and sentences into expressions, equations, and inequalities and vice versa.
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Laws of integral exponents
The learner will be able to apply the laws of (integral) exponents.
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Scientific notation
The learner will be able to solve problems involving scientific notation, including multiplication and division.
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Polynomial operations
The learner will be able to perform polynomial operations (addition, subtraction, multiplication) with and without manipulatives.
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Simplify algebraic fractions: factor
The learner will be able to simplify algebraic fractions by factoring.
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Undefined expressions
The learner will be able to recognize when an expression is undefined.
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Radical expressions
The learner will be able to simplify radical expressions such as 3 divided by square root of 7. (rationalization of denominator) See 2004 Arkansas Mathematics Frameworks for symbolic representation.
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Operations with radicals
The learner will be able to add, subtract, multiply simple radical expressions. See 2004 Arkansas Mathematics Frameworks for specific examples.
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| Solving Equations & Inequalities |
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Solve multi-step equations/inequalities
The learner will be able to solve multi-step equations and inequalities with rational coefficients 1. Numerically (from a table or guess and check) 2. Algebraically (including the use of manipulatives) 3. Graphically 4. Technologically.
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Systems of 2 linear equations
The learner will be able to solve systems of two linear equations 1. Numerically (from a table or guess and check) 2. Algebraically (including the use of manipulatives) 3. Graphically 4. Technologically.
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Literal equations
The learner will be able to solve linear formulas and literal equations for a specified variable. (Example: Solve for p in I = prt).
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Absolute value equations/inequalities
The learner will be able to solve and graph simple absolute value equations and inequalities See 2004 Arkansas Mathematics Frameworks for specific examples.
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Rates/proportions/percents
The learner will be able to solve real world problems that involve a combination of rates, proportions, and percents.
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Direct and inverse variation
The learner will be able to solve problems involving direct variation and indirect (inverse) variation to model rates of change.
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Coordinate geometry
The learner will be able to use coordinate geometry to represent and/or solve problems (midpoint, length of a line segment, and Pythagorean Theorem).
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Real world problems
The learner will be able to communicate real world problems graphically, algebraically, numerically, and verbally.
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| Linear Functions |
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Distinguish between functions/relations
The learner will be able to distinguish between functions and non-functions/relations by inspecting graphs, ordered pairs, mapping diagrams and/or tables of data.
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Domain and range
The learner will be able to determine domain and range of a relation from an algebraic expression, graphs, sets of ordered pairs, or a table of data.
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Function notation
The learner will be able to know and/or use function notation, including evaluating functions for given values in their domain.
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Independent and dependent variables
The learner will be able to identify independent variables and dependent variables in various representational modes: words, symbols, and/or graphs.
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Interpret slope and intercepts
The learner will be able to interpret the rate of change/slope and intercepts within the context of everyday life. (Example: Telephone charges based on base rate (y intercept) plus rate per minute (slope)).
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Calculate slope
The learner will be able to calculate the slope given: 1. Two points 2. The graph of a line 3. The equation of a line.
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Parallel, perpendicular or neither
The learner will be able to determine by using slope whether a pair of lines are parallel, perpendicular, or neither.
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Slope-intercept form of an equation
The learner will be able to write an equation in slope-intercept, point-slope, and standard forms given: 1. Two points 2. A point and y-intercept 3. X-intercept and y-intercept 4. A point and slope 5. A table of data 6. The graph of a line.
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Effects of change on linear graphs
The learner will be able to describe the effects of parameter changes, slope and/or y-intercept, on graphs of linear functions and vice versa.
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| Non-Linear Functions |
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Factor polynomials
The learner will be able to factoring polynomials: 1. Greatest common factor 2. Binomials (difference of squares) 3. Trinomials.
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Min/max/vertex/zero
The learner will be able to determine the minimum, maximum, vertex, and zeroes, given the graph.
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Solve quadratic equations
The learner will be able to solve quadratic equations using the appropriate methods with and without technology: 1. Factoring 2. Quadratic formula with real number solutions.
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Function families: connections
The learner will be able to recognize function families and their connections including vertical shift and reflection over the x-axis: 1. Quadratics 2. Absolute Value 3. Exponential functions.
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Real world problems
The learner will be able to communicate real world problems graphically, algebraically, numerically and verbally.
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| Data Interpretation and Probability |
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Inferences from scatter plots
The learner will be able to construct and use scatter plots and line of best fit to make inferences in real life situations.
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Simple matrices
The learner will be able to use simple matrices in addition, subtraction, and scalar multiplication.
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Construct matrices
The learner will be able to construct simple matrices for real life situations.
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Measures of central tendency
The learner will be able to determine the effects of changes in the data set on the measures of central tendency.
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Box-and-whisker plots
The learner will be able to use two or more graphs (i.e., box-and-whisker, histograms, scatter plots) to compare data sets.
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Cumulative frequency histogram
The learner will be able to construct and interpret a cumulative frequency histogram in real life situations.
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Recognize linear/nonlinear functions
The learner will be able to recognize linear functions and non-linear functions by using a table or a graph.
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