### 1: The student will demonstrate the ability to investigate, interpret, and communicate solutions to mathematical and real-world problems using patterns, functions and algebra.

#### 1.1: The student will analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology.

1.1.1: The student will recognize, describe and/or extend patterns and functional relationships that are expressed numerically, algebraically, and/or geometrically.

1.1.1.A: The given pattern must represent a relationship of the form y = mx + b (linear), y = x² + c (simple quadratic), y = x³ + c (simple cubic), simple arithmetic progression, or simple geometric progression with all exponents being positive.

1.1.1.B: The student will not be asked to draw three-dimensional figures.

1.1.1.C: Algebraic description of patterns is in indicator 1.1.2

1.1.1.a: Given a narrative, numeric, algebraic, or geometric representation description of a pattern or functional relationship, the student will give a verbal description, or predict the next term or a specific term in a pattern or functional relationship.

1.1.1.b: Given a numerical or graphical representation of a relation, the student will identify if the relation is a function and/or describe it.

1.1.1.1: The student will define and interpret relations and functions numerically, graphically, and algebraically.

1.1.1.2: The student will use patterns of change in function tables to develop the concept of rate of change.

1.1.1.5: The student will compare, order and describe rational numbers.

1.1.1.7: The student will identify and extend an exponential pattern in a table of values.

1.1.2: The student will represent patterns and/or functional relationships in a table, as a graph, and/or by mathematical expression.

1.1.2.A: The given pattern must represent a relationship of the form mx + b (linear), x² (simple quadratic), simple arithmetic progression, or simple geometric progression with all exponents being positive.

1.1.2.1: The student will be able to graph an exponential function given as a table of values or as an equation of the form y= a(b to the x power), where a is a positive integer, b>0 and b is not equal to 1.

1.1.3: The student will apply addition, subtraction, multiplication, and/or division of algebraic expressions to mathematical and real-world problems.

1.1.3.A: The algebraic expression is a polynomial in one variable.

1.1.3.B: The polynomial is not simplified.

1.1.3.a: The student will represent a situation as a sum, difference, product, and/or quotient in one variable.

1.1.3.1: The student will locate the position of a number on the number line, know its distance from the origin is its absolute value and know that the distance between two numbers on the number line is the absolute value of their difference.

1.1.3.3: The student will add, subtract, and multiply polynomials.

1.1.3.4: The student will divide a polynomial by a monomial.

1.1.3.5: The student will factor polynomials:

1.1.3.5.a: Using greatest common factor

1.1.3.5.b: Using the form ax² + bx + c

1.1.3.5.c: Using special product patterns

1.1.3.5.c.1: Difference of squares a² + b² = (a - b)(a + b)

1.1.3.5.c.2: Perfect square trinomial a² + 2ab + b² = (a + b)²; a² - 2ab + b² = (a - b)²

1.1.3.6: The student will use the laws of exponents, including negative exponents, to simplify expressions.

1.1.3.7: The student will simplify radical expressions with or without variables.

1.1.4: The student will describe the graph of a non-linear function and discuss its appearance in terms of the basic concepts of maxima and minima, zeros (roots), rate of change, domain and range, and continuity.

1.1.4.A: A coordinate graph will be given with easily read coordinates.

1.1.4.B: ?Zeros? refers to the x-intercepts of a graph, ?roots? refers to the solution of an equation in the form p(x) = 0.

1.1.4.C: Problems will not involve a real-world context.

1.1.4.a: Given the graph of a non-linear function, the student will identify maxima/minima, zeros, rate of change over a given interval (increasing/decreasing), domain and range, or continuity.

1.1.4.1: The student will describe the graph of the quadratic, exponential, absolute value, piece-wise, and step functions.

1.1.4.2: The student will solve quadratic equations by factoring and graphing.

#### 1.2: The student will model and interpret real-world situations using the language of mathematics and appropriate technology.

1.2.1: The student will determine the equation for a line, solve linear equations, and/or describe the solutions using numbers, symbols, and/or graphs.

1.2.1.A: Functions are to have no more than two variables with rational coefficients.

1.2.1.B: Linear equations will be given in the form: Ax + By = C, Ax + By + C = 0, or y = mx + b.

1.2.1.C: Vertical lines are included.

1.2.1.D: The majority of these items should be in real-world context.

1.2.1.a: Given one or more of the following:

1.2.1.a.a: the graph of a line

1.2.1.a.b: written description of a situation that can be modeled by a linear function

1.2.1.a.c: two or more collinear points

1.2.1.a.d: a point and slope

1.2.1.b: the student will do one or more of the following:

1.2.1.b.a: write the equation

1.2.1.b.b: solve a one-variable equation for the unknown

1.2.1.b.c: solve a two-variable equation for one of the variables

1.2.1.b.d: graph the resulting equation

1.2.1.b.e: interpret the solution in light of the context

1.2.1.b.g: create a table of values

1.2.1.b.h: find and/or interpret the slope (rate of change) and/or intercepts in relation to the context.

1.2.1.c: Any correct form of a linear equation will be acceptable as a response.

1.2.2: The student will solve linear inequalities and describe the solutions using numbers, symbols, and/or graphs.

1.2.2.A: Inequalities will have no more than two variables with rational coefficients.

1.2.2.B: Acceptable forms of the problem or solution are the following: Ax + By < C, Ax + By is less than or equal to C, Ax + By > C, Ax + By is greater than or equal to C, Ax + By + C < 0, Ax + By + C is less than or equal to 0, Ax + By + C > 0, Ax + By + C is greater than or equal to 0, y < mx + b, y is less than or equal to mx + b, y is greater than or equal to mx + b, y > mx + b, y < b, y is less than or equal to b, y > b, y is greater than or equal to b, x < b, x is less than or equal to b, x > b, x is greater than or equal to b, a is less than or equal to x is less than or equal to b, a < x < b, a is less than or equal to x < b, a < x is less than or equal to b, a is less than or equal to x + c is less than or equal to b, a < x + c < b, a is less than or equal to x + c < b, a < x + c is less than or equal to b.

1.2.2.C: The majority of these items should be in real-world context.

1.2.2.D: Systems of linear inequalities will not be included.

1.2.2.E: Compound inequalities will be included.

1.2.2.F: Disjoint inequalities will not be included.

1.2.2.G: Absolute value inequalities will not be included.

1.2.2.a: Given a linear inequality in narrative, algebraic, or graphical form, the student will graph the inequality, write an inequality and/or solve it, or interpret an inequality in the context of the problem.

1.2.2.b: Any correct form of a linear inequality will be an acceptable response.

1.2.2.1: The student will graph systems of linear inequalities and apply their solution to real-world applications.

1.2.3: The student will solve and describe using numbers, symbols, and/or graphs if and where two straight lines intersect.

1.2.3.A: Functions will be of the form: Ax + By = C, Ax + By + C = 0, or y = mx + b.

1.2.3.B: All coefficients will be rational.

1.2.3.C: Vertical lines will be included.

1.2.3.D: Systems of linear functions will include coincident, parallel, or intersecting lines.

1.2.3.E: The majority of these items should be in real-world context.

1.2.3.a: Given one or more of the following:

1.2.3.a.a: a narrative description

1.2.3.a.b: the graph of two lines

1.2.3.a.c: equations for two lines

1.2.3.b: the student will do one or more of the following:

1.2.3.b.a: determine the system of equations and/or its solution

1.2.3.b.b: describe the relationship of the points on one line with points on the other line

1.2.3.b.c: give the meaning of the point of intersection in the context of the problem

1.2.3.b.d: graph the system, determine the solution and interpret the solution in the context of the problem

1.2.3.b.e: use slope to recognize the relationship between parallel lines.

1.2.3.c: Any correct form of a linear equation will be an acceptable response.

1.2.3.1: The student will determine if two lines in a plane are parallel, perpendicular, or neither.

1.2.4: The student will describe how the graphical model of a non-linear function represents a given problem and will estimate the solution.

1.2.4.A: The problem is to be in a real-world context.

1.2.4.D: The features of the graph may include maxima/minima, zeros (roots), rate of change over a given interval (increasing/decreasing), continuity, or domain and range.

1.2.4.E: ?Zeros? refers to the x-intercepts of a graph, ?roots? refers to the solution of an equation in the form p(x) = 0.

1.2.4.F: Functions may include step, absolute value, or piece-wise functions.

1.2.4.a: Given a graph which represents a real-world situation, the student will describe the graph and/or explain how the graph represents the problem or solution and/or estimate a solution.

1.2.4.1: The student will describe the graph of the quadratic and exponential functions.

1.2.4.2: The student will identify horizontal and vertical asymptotes given the graph of a non-linear function.

1.2.4.3: The student will solve, by factoring or graphing, real-world problems that can be modeled using a quadratic equation.

1.2.5: The student will apply formulas and/or use matrices (arrays of numbers) to solve real-world problems.

1.2.5.B: Formulas may express linear or non-linear relationships.

1.2.5.1: The student will solve literal equations for a specified variable.

### 3: The student will demonstrate the ability to apply probability and statistical methods for representing and interpreting data and communicating results, using technology when needed.

#### 3.1: The student will collect, organize, analyze, and present data.

3.1.1: The student will design and/or conduct an investigation that uses statistical methods to analyze data and communicate results.

3.1.1.B: Types of investigations may include: simple random sampling, representative sampling, and probability simulations.

3.1.1.C: Probability simulations may include the use of spinners, number cubes, or random number generators.

3.1.1.D: In simple random sampling each member of the population is equally likely to be chosen and the members of the sample are chosen independently of each other. Sample size will be given for these investigations.

3.1.1.c: The student will demonstrate an understanding of the concepts of bias, sample size, randomness, representative samples, and simple random sampling techniques.

3.1.1.1: The student will organize and display data to detect patterns and departures from patterns. One example of an appropriate method for displaying data is a spreadsheet.

3.1.1.2: The student will communicate the differences between randomized experiments and observational studies.

3.1.2: The student will use the measures of central tendency and/or variability to make informed conclusions.

3.1.2.A: Measures of central tendency include mean, median, and mode.

3.1.2.B: Measures of variability include range, interquartile range, and quartiles.

3.1.2.C: Data may be displayed in a variety of representations, which may include: frequency tables, box and whisker plots, and other displays.

3.1.2.a: The student uses measures of central tendency and variability to solve problems, make informed conclusions and/or display data.

3.1.2.b: The student will recognize and apply the effect of the distribution of the data on the measures of central tendency and variability.

3.1.2.1: The student will identify an outlier and describe its effect on a measure of central tendency.

3.1.3: The student will calculate theoretical probability or use simulations or statistical inferences from data to estimate the probability of an event.

3.1.3.A: This indicator does not include finding probabilities of dependent events.

3.1.3.a: Using given data, the student determines the experimental probability of an event.

3.1.3.b: Given a situation involving chance, the student will determine the theoretical probability of an event.

3.1.3.1: The student will determine the probability of a dependent event (conditional probability).

#### 3.2: The student will apply the basic concepts of statistics and probability to predict possible outcomes of real-world situations

3.2.1: The student will make informed decisions and predictions based upon the results of simulations and data from research.

3.2.1.a: Given data from a simulation or research, the student makes informed decisions and predictions.

3.2.3: The student will communicate the use and misuse of statistics.

3.2.3.A: Examples of ?misuse of statistics? include the following:

3.2.3.A.b: misuse of measures of central tendency and variability to represent data,

3.2.3.A.f: using data from simulations incorrectly

Correlation last revised: 3/12/2015

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.