Algebra Course KUD. Green Highlight - Incorporate notation in class, with understanding that not tested on

Transcription

1 Algebra Course KUD Yellow Highlight Need to address in Seminar Green Highlight - Incorporate notation in class, with understanding that not tested on Blue Highlight Be sure to teach in class Postive and Negative Numbers* students will know numbers can be represented as points on the real number line the definition of negative and positive relative to the position of the origin the definition of absolute value the definition of inequality and the appropriate notation for representing them opposites combine to make zero opposites have the same absolute value multiplying by -1 results in a reflection across the origin solutions to inequalities are represented by sets of numbers plot points on the real number line compare values on the real number line calculate absolute values simplify expressions with signed values represent inequalities on the real number line

2 Fractions, Decimals, and Percents* fractions, decimals and percents represent portions of whole numbers several methods for simplifying expressions involving fractions with four major operations several processes for converting between fractions, decimals and percents (long division for converting ratios to decimals) the definition of fractions, decimals, percents the definition of reciprocal fractions of the form, where is some non-zero real number can be treated like a "unit" multiplying by a number less than one causes a decrease in quantity, as does dividing by a number greater than one multiplying by a number greater than one causes an increase in quantity, as does dividing by a number less than one multiplying and dividing by one preserves the quantity the ratio of a constant to an increasingly large number has a limit of zero compare values (using a common denominator, GCF, LCM and LCD) convert values back and forth between fractions, decimals and percents (express solutions in equivalent forms) simplify expressions using fractions, decimals and percents (using reciprocals when needed) identify the limit of an expression the ratio of a constant to an increasingly small number has an undefined limit *From Pre-Algebra KUD

3 Algebraic Properties At the end of this course, students will understand students will be able to simplify expressions using appropriate order of operations (with and without variables) the order of operations the definition of like terms the properties of equality the associative, commutative, and distributive properties the properties of exponents inverses "undo" expressions variables represents a set of values use inverses and properties of equality to simplify expressions and solve equations use associative, commutative, and distributive properties to simplify expression and solve equations evaluate expressions represent equations over a given domain both numerically and graphically write equations to model and solve problems

4 Linear Relationships the concept of a constant rate of change the concept of an initial value slope-intercept form, pointslope, and standard form for representing linear equation solutions satisfy equations (if working in systems and a solution exist it satisfies each equation in the system) several methods for solving systems of linear equations and inequalities (graphically, by substitution, by elimination) the definition of independent and dependent variables linear relationships are characterized by a constant rate of change slope is the rate of change the y-intercept is the initial value the solution to a system of two non-parallel and unique linear equations is given by the x and y coordinates of the point of intersection or the ordered pair the solution to a system of two non-parallel and unique linear inequalities is given by the overlapping region and possibly the boundaries optimum solutions to systems of linear inequalities exists on boundaries and/or corner points linear relationships can be represented in various, equivalent forms (graph, equation, and table) sketch and appropriately scale the coordinate plane, and plot and identify points solve for a given variable in linear equations and proportions graph linear relationships from a table graph linear equations from three forms identify and calculate rate of change identify and calculate initial values write equations in slopeintercept form and pointslope form graph systems and estimate solutions (if they exist) provide a sketch in the xyplane of a system of two linear equations having no solution solve linear systems using methods of substitution, elimination and graphing (included shaded region of a system of linear inequalities) ~6 weeks review of Linear start of 8th grade

5 Exponential Equations concept of constant multiplier for sequences constant multiplier of a sequence is the base of the corresponding exponential equation definition of a recursive routine rules for simplifying expressions involving exponents and other operations scientific notation constant multipliers greater than one in magnitude represent growth; constant multipliers between zero and one in magnitude represent decay the difference between the rate of change of linear relationships (constant) and the rate of change of exponential relationships (variable) scientific notation gives us a means for representing very large and very large numbers the contextual meaning of negative and positive exponents identify and calculate the constant multiplier of sequence and from a table graph an exponential equation model exponential growth and decay with equations write and simplify expressions involving exponents and other operations represent quantities in scientific notation and apply exponent rules to quantities in scientific notation solve exponential equations graphically and using a table on some technological device Recursive is the name for what you are already doing. It is the natural process you use in order to find the formula. It is a strategy and essentially the building blocks you need to start somewhere.

6 Functions the definition of relation the definition of function the definition of discrete and continuous functions the definition of the absolute value function, squares and square roots the definition of piecewise function function notation the definition of an inverse of a function the definition of independent and dependent variables the definition of domain and range the roles of independent and dependent variables in functions passing the vertical line test means the relationship between the independent and dependent variables is a function inverses undo relations identify relationships as functions write equations using function notation calculate absolute values, squares, and square roots solve equations involving absolute value functions, squares, and square roots find the inverses of linear and quadratic functions

7 Quadratic Equations the general, vertex, and factored forms of quadratics equations definitions of prefixes: poly-, mono-, bi- the quadratic formula zero product property quadratic equations model projectile motion and area problems the contextual meaning of roots, vertices and the y- intercept convert vertex to general form factor polynomials in general form solve quadratic equations by: symbolical manipulation, if possible; graphing; factoring, and using the quadratic formula

8