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Disclaimers and Notices
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Integrated Algebra is the first mathematics course in the high
school. The algebra course set forth here is not the algebra of 30 years
ago. The focal point of this course is
the algebra content strand. Algebra
provides tools and ways of thinking that are necessary for solving problems in
a wide variety of disciplines, such as science, business, social sciences, fine
arts, and technology. This course will
assist students in developing skills and processes to be applied using a
variety of techniques to successfully solve problems in a variety of
settings. Problem situations may result
in all types of linear equations in one variable, quadratic functions with integral
coefficients and roots as well as absolute value and exponential
functions. Coordinate geometry will be
integrated into the investigation of these functions allowing students to make
connections between their analytical and geometrical representations. Problem situations resulting in systems of
equations will also be presented.
Alternative solution methods should be given equal value within the
strategies used for problem solving.
For example, a matrix solution to a system of equations is just as valid
as a graphical solution or an algebraic algorithm such as elimination. Measurement within a problem-solving context
will include calculating rates using appropriate units and converting within
measurement systems. Data analysis
including measures of central tendency and visual representations of data will
be studied. An understanding of
correlation and causation will be developed and reasonable lines of best fit
will be used to make predictions.
Students will solve problem situations requiring right triangle
trigonometry. Elementary probability theory will be used to determine the
probability of events including independent, dependent and mutually exclusive
events.
CROSSWALK
Comparison of 1999 Core Curriculum and 2005 Core Curriculum for High
School Mathematics
The following chart lists the concepts and skills in Integrated Algebra (2005 Core) and indicates where it was included in the 1999 Core.
INTEGRATED
ALGEBRA
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Number Sense and Operations Strand |
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2005 Core Curriculum |
1999 Core Curriculum |
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Performance |
Concept/Skill |
Key Idea |
Concept/Skill |
|
A.N.1 |
Identify and apply properties of real numbers |
Math A 2C Math A 3D |
Properties of real numbers Use field properties to justify mathematical procedures |
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A.N.2 |
Simplify radical terms (no variable in radicand) |
Math A 3A |
Simplification of radicals |
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A.N.3 |
Operations with radicals (using like and unlike radical terms) |
Math A 3A |
Operations with radicals |
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A.N.4 |
Scientific notation to compute products and quotients |
Use addition,
subtraction, multiplication, division, and exponentiation with real numbers
and Algebraic expressions ·
Scientific notation |
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| A.N.5 | Solving Algebraic problems involving fractions, decimals, percents (decrease/increase and discount), and proportionality/direct variation | Math 7/8 2B |
Understand and apply
ratios, proportions, and percents through a wide variety of hands-on
explorations · Find the percent of a number, calculate the percent of increases and decreases, rate, commissions, taxes, and simple interest |
| A.N.6 | Evaluating expressions involving factorial(s), absolute value(s), and exponential expression(s) |
Math A 3B Math A 5G Math A 6D Math 7/8 2A Math7/8 3A |
Use integral exponents on integers and Algebraic expressions Absolute value and the length of a line segment Factorial notation Understand the meaning of
absolute value symbol Determine the absolute value of real numbers expanded to include numerical expressions beyond a single value
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| A.N.7 | Fundamental Principle of Counting | Math A 6C | Counting principle |
| A.N.8 | Permutations | Math A 6C |
Permutations: nPn and nPr |
INTEGRATED
ALGEBRA
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Integrated Algebra Strand |
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2005 Core Curriculum |
1999 Core Curriculum |
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Performance Indicator |
Concept/Skill |
Key Idea |
Concept/Skill |
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A.A.1 |
Translate: Quantitative verbal phase into an Algebraic expression |
Math A 4A |
Represent problem situations symbolically by using Algebraic expressions |
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A.A.2 |
Write: Verbal expression for a given mathematical expression |
Math A 4A |
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A.A.3 |
Difference between an Algebraic expression and an Algebraic equation |
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Not directly addressed |
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A.A.4 |
Translate: Verbal sentences into mathematical equations or inequalities |
Math A 4A Math A 7C |
Represent problem situations symbolically by using Algebraic expressions Translate among the verbal descriptions, tables, equations, and graphic forms of functions |
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A.A.5 |
Write Algebraic equations or inequalities that represent a situation |
Math A 4A Math A 7C |
Implied but not explicitly stated Translate linear functions and inequalities between representations that are verbal descriptions, tables, equations, or graphs |
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A.A.6 |
Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable |
Math A 7B |
Graphic and Algebraic solutions of linear function in the solution of problems |
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A.A.7 |
Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables |
Math A 7A Math A 7E |
Graphic solution of systems of linear equations and inequalities (problem solving implied) Solve systems of linear equations (problem solving implied) |
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A.A.8 |
Analyze and solve verbal problems that involve quadratic equations |
Math A 7B |
Graphic and Algebraic solutions of quadratic function in the solution of problems |
| A.A.9 | Analyze and solve verbal problems that involve exponential growth and decay | Math 7/8 7C | Use Algebraic expressions, equations, and inequalities to model exponential growth |
| A.A.10 | Algebraic solution of a system of two linear equations in two variables |
Math A 7A Math A 4E
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Algebraic solution of systems of linear equations by substitution method and addition-subtraction method Model real world problems with systems of equations · Systems of linear equations
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| A.A.11 | Solve a system of one linear and one quadratic equation in two variables (only factoring required and the quadratic equation should represent a parabola and the solution should be integers) | Math A 7A | Algebraic solution of a system of equations one linear and one quadratic |
| A.A.12 | Multiplication/Division of monomials expressions with a common base using the properties of exponents (integral exponents only) | Math A 3A | Products of monomials (division by monomials not specifically addressed as such) |
| A.A.13 | Add, subtract, and multiply monomials and polynomials | Math A 3A |
Addition and subtraction of polynomials: combining like terms Multiplication of polynomials: powers, products of monomials and binomials
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| A.A.14 | Divide a polynomial by a monomial or binomial (quotient has no remainder) | Math A 3A | Division of polynomials by monomials no mention of division by binomial |
| A.A.15 | Find values of a variable for which an Algebraic fraction is undefined | Not specifically addressed | |
| A.A.16 | Simplify fractions with polynomials in the numerator and denominator by factoring both (simplify answer) | Math A 3A | Simplification of fractions polynomials in numerator and denominator not mentioned |
| A.A.17 | Add/Subtract fractional expressions with monomial or like binomial denominators | Math A 3A | Addition and subtraction of fractions with like denominators no mention of binomial denominators |
| A.A.18 | Multiply/Divide Algebraic fractions and express answer in simplest form | Math A 3A | Multiplication and division of fractions |
| A.A.19 | Identify and factor the difference of two perfect squares | Math A 3A | Difference of two squares |
| A.A.20 | Complete factoring (including trinomials with a lead coefficient of one (after factoring a GCF) | Math A 3A | Factoring: common monomials, binomial factors of trinomials- no mention of complete factoring |
| A.A.21 | Verifying a value as a solution to a linear equation or inequality in one variable | Math 7/8 7E |
Verify results of substituting variables · Solve an equation and check the solution by substitution
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| A.A.22 | Solution of all types of linear equations in one variable | Math A 7E | Solve linear equations with integral, fraction, or decimal coefficients |
| A.A.23 | Solution of literal equations for a given variable | Math A 4A | Formulas and literal equations |
| A.A.24 | Solution of linear inequalities in one variable | Math A 7E | Solve linear inequalities |
| A.A.25 | Solve equations involving fractional expressions (fractional expressions result in linear equations in one variable) | Math A 7E | Solve linear equations with fractional coefficients |
| A.A.26 | Solution of Algebraic proportions in one variable which result in linear or quadratic equations | Solution of proportional not directly addressed | |
| A.A.27 | Use of multiplication property of zero to solve quadratic equations with integral coefficients and integral roots | Math A 7E | Solve factorable quadratic equations (zero property of multiplication implied) |
| A.A.28 | Relation between roots and factors of a quadratic equation | Not specifically addressed | |
| A.A.29 | Set builder notation and/or interval notation to represent the elements of a set | Not addressed | |
| A.A.30 | Complement of a set | Not addressed | |
| A.A.31 | Intersection of Sets | Not addressed | |
| A.A.32 | Slope as a rate of change | Not addressed | |
| A.A.33 | Slope of a line given the coordinates of two points on the line | Math A 5G | Relate absolute value, distance between two points, and the slope of a line to the coordinate plane |
| A.A.34 | Write the equation of a line, given its slope and the coordinates of a point on the line | Math A 5G | Equation of a line: point-slope |
| A.A.35 | Write the equation of a line given the coordinates of two points on the line | Not addressed | |
| A.A.36 | Write the equation of a line parallel to the x- or y-axis | Not addressed | |
| A.A.37 | Determine the slope of a line given its equation in any form | Math A -5G | Equation of a line: point-slope and slope intercept form |
| A.A.38 | Determine if two lines are parallel, given their equation in any form | Math A 5G | Comparison of parallel and perpendicular lines |
| A.A.39 | Determine whether a given point is on a line , given the equation of the line | Implied in Math A 7E | |
| A.A.40 | Determine whether a given point is in the solution set of a system of linear inequalities | Implied in Math A 7E | |
| A.A.41 | Vertex and axis of symmetry of a parabola | Not specifically addressed | |
| A.A.42 | Trigonometric Ratios of an acute angle of a right triangle |
Math A 5E Math 7/8 7J |
Right triangle trigonometry Explore and develop basic concepts of right triangle trigonometry · Understand the relationships of the sides of a right triangle · Develop and apply the formulas for sine, cosine, and tangent |
| A.A.43 | Find an acute angle of a right triangle given the lengths of its sides |
Math A 5E Math 7/8- 7J
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Right triangle trigonometry Use trigonometry as a method to measure indirectly Develop and apply the formulas for sine, cosine, and tangent
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| A.A.44 | Find the length of a side of a right triangle given the measure of an acute angle and the measure of one side |
Math A 5E Math 7/8 7J |
Right triangle trigonometry Use trigonometry as a method to measure indirectly Develop and apply the formulas for sine, cosine, and tangent |
| A.A.45 | Application of Pythagorean theorem | Math 7/8 7I |
Develop and apply the
Pythagorean principle in the solution of problems · Use the Pythagorean theorem in the solution of problems
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INTEGRATED
ALGEBRA
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Geometry Strand |
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2005 Core Curriculum |
1999 Core Curriculum |
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Performance Indicator |
Concept/Skill |
Key Idea |
Concept/Skill |
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A.G.1 |
Area/Perimeter of figures composed of polygons, circles, or sectors of circles |
Math A 5A |
Perimeter of polygons and circumference of circles Areas of polygons Sectors of a circle not addressed |
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A.G.2 |
Volume and Surface Area of regular solids and cylinders |
Math A 5A |
Volume of solids |
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A.G.3 |
Determine when a relation is a function |
Math B 7A |
Determine if a relation is a function |
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A.G.4 |
Identify and graph linear, quadratic (parabola), absolute value, and exponential functions |
Math A 7A |
Graphs of linear relations: slope and intercept Graphs of conics: circle and parabola |
|
AG.5 |
How coefficient change in a function effects its graph |
Math B 6B Math B 7D Math B 4J |
Determine the effects of changing the parameters of graphs of linear, quadratic, trigonometric, exponential, and circular functions Analyze the effect of parametric changes on the graphs of functions Determine the effects of changing parameters on the graphs of functions |
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A.G.6 |
Graphing linear inequalities |
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A.G.7 |
Graph and solve systems of linear equations and inequalities (rational coefficients in two variables) |
Math A 7A |
Graphic solution of systems of linear equations and inequalities |
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A.G.8 |
Graphic solution of a quadratic (parabolic) equation (integral solutions only) |
Math A 7A |
Graphs of conics parabola |
| A.G.9 | Graphic solutions of systems of linear and quadratic equations (solutions whose coordinates are integers) | Not directly addressed | |
| A.G.10 | Determine the vertex and axis of symmetry of a parabola given its graph (ordered pair of vertex are integers and integral value for axis of symmetry) | Not directly addressed | |
INTEGRATED
ALGEBRA
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Measurement Strand |
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2005 Core Curriculum |
1999 Core Curriculum |
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Performance Indicator |
Concept/Skill |
Key Idea |
Concept/Skill |
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A.M.1 |
Calculations of rate |
Math 7/8 3G |
Determine the unit cost to compare price |
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A.M.2 |
Solution of problems involving conversions |
Math A 5B Math A 5C |
Choose and apply appropriate units and tools to measurement situations Converting to equivalent measurements within metric and English measurement systems Dimensional Analysis |
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A.M.3 |
Relative error in measuring square and cubic units when error occurs in linear measure |
Math A 5H |
Explain the role of error of measurement and its consequence on subsequent calculations Error of measurement and its consequences on calculations of perimeter of polygons and circumference of circles Areas of polygons and circles Volume of solids Percent of error in measurements |
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Statistics and Probability Strand |
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2005 Core Curriculum |
1999 Core Curriculum |
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Performance Indicator |
Concept/Skill |
Key Idea |
Concept/Skill |
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A.S.1 |
Categorize data as qualitative or quantitative |
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A.S.2 |
Determine whether the data to be analyzed is univariate or bivariate |
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Not addressed |
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A.S.3 |
Determine when collected data or display of data may be biased |
Math B 5I |
Bias |
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A.S.4 |
Compare and contrast the appropriateness of different measures of central tendency for a given data set |
Math B 5I |
Choose appropriate statistical measures |
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A.S.5 |
Construct a histogram, cumulative frequency histogram, and a box-and-whisker plot, given a set of data |
Math A 5D |
Collect and organize data: histogram, cumulative frequency histogram, box-and-whisker plot |
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A.S.6 |
Understand how the five statistical summary (minimum, maximum, and the three quartiles) is used to construct a box-and-whisker plot |
Math A -5D |
Organize data using a box-and-whisker plot |
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A.S.7 |
Create a scatter plot of bivariate data |
Math A -5D |
Collect and organize data: scatter plots |
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A.S.8 |
Line of best fit for a scatter plot and its equation |
Math B 5J |
Use statistical methods,
including scatter plots and lines of best fit, to make predictions · Given data, produce scatter plots and lines of best fit |
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A.S.9 |
Analyze and interpret a frequency distribution table or histogram, a cumulative frequency distribution table or histogram, or a box-and-whisker plot |
Math A 5D |
Use statistical methods
including measures of central tendency to describe and compare data |
| A.S.10 | Evaluate published reports and graphs that are based on data by considering: experimental design, appropriateness of the data analysis, and the soundness of the conclusions | Not specifically addressed | |
| A.S.11 | Find the percentile rank of an item in a data set and identify the point values for the first, second, and third quartiles | Math A 5D |
Use statistical methods including the measures of central
tendency to describe and compare data · Percentiles |
| A.S.12 | Identify the relationship between the independent and dependent variables from a scatter plot (positive, negative, or none) |
Implied in Math B 5J Use statistical methods, including scatter plots and lines of best fit, to make predictions
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| A.S.13 | Understand the difference between correlation and causation | Not addressed | |
| A.S.14 | Identify variables that might have a correlation but not a causal relationship | Not addressed | |
| A.S.15 | Identify and describe sources of bias and its effect, drawing conclusion from data | Math B 5I |
Design a statistical experiment to study a problem and
communicate the outcome, including dispersion · Bias |
| A.S.16 | Recognize how linear transformations of one-variable data affect the datas mean, median, mode, and range | Not directly addressed | |
| A.S.17 | Use a reasonable line of best fit to make a prediction involving interpolation or extrapolation |
Math A- 6G Math B 5J |
Make predictions based on interpolations and extrapolations of data Use statistical methods, including scatter plots and lines of best fit, to make predictions |
| A.S.18 | Conditional probability | ||
| A.S.19 | Sample space and favorable events | Math A 6C |
Use the concept of random variable in computing probabilities · Sample space
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| A.S.20 | Probability of an event and its complement | Math A 6B | Probability of the complement of an event |
| A.S.21 | Determine empirical probabilities based on specific sample data | Math A 6A | Theoretical versus empirical probability |
| A.S.22 |
Determine, based on calculated probability of a set of events, if: · Some or all are equally likely to occur · One is more likely to occur than another · Whether or not an event is certain to happen or not to happen |
Not addressed as specifically as this might be implied | |
| A.S.23 |
Calculate the probability of · series of independent events · series of dependent events · two mutually exclusive events · two events that are not mutually exclusive
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Math A 6B Math A 6C
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Use experimental and theoretical probability to represent and solve problems involving uncertainty
Use the concept of random variable in computing probabilities
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