Passport to Advanced Math

14. Use structure to isolate or identify a quantity of interest in an expression or isolate a quantity of interest in an equation. The student will rearrange an equation or formula to isolate a single variable or a quantity of interest.

sum of roots

Passport to Advanced Math

5. Solve a quadratic equation having rational coefficients. The equation can be presented in a wide range of forms to reward attending to algebraic structure and can require manipulation in order to solve.

Problem Solving and Data Analysis

2. Solve single- and multistep problems involving percentages. The student will solve a multistep problem to determine a percentage; calculate a percentage and then solve a multistep problem; or take a given percentage and solve a multistep problem.

Passport to Advanced Math

3.    Create equivalent expressions involving rational exponents and radicals, including simplifying or rewriting in other forms.

Heart of Algebra

5.    Create, solve, and interpret systems of two linear equations in two variables. The student will analyze one or more constraints that exist between two variables by creating, solving, or analyzing a system of linear equations to represent a context. The equations will have rational coefficients, and multiple steps may be required to simplify or solve the system.

Passport to Advanced Math? (compare coefficient)

5.    Solve a quadratic equation having rational coefficients. The equation can be presented in a wide range of forms to reward attending to algebraic structure and can require manipulation in order to solve.

Additional Topics in Math

6.    Use concepts and theorems about congruence and similarity to solve problems about lines, angles, and triangles. The student will use theorems about triangles and intersecting lines to determine missing lengths and angle measures of triangles. The student may also be asked to provide a missing length or angle to satisfy a given theorem.

Additional Topics in Math

4.    Convert between degrees and radians and use radians to determine arc lengths; use trigonometric functions of radian measure. The student will convert between angle measures in degrees and radians in order to calculate arc lengths by recognizing the relationship between an angle measured in radians and an arc length, evaluating trigonometric functions of angles in radians.

Heart of Algebra

7.    Algebraically solve systems of two linear equations in two variables. The equations will have rational coefficients, and the system may yield no solution, one solution, or infinitely many solutions. The student may also be asked to determine the value of a constant or coefficient of an equation in which the system has no solution, one solution, or infinitely many solutions.

Passport to Advanced Math

11.  Understand the relationship between zeros and factors of polynomials, and use that knowledge to sketch graphs. Students will use properties of factorable polynomials to solve conceptual problems relating to zeros, such as determining whether an expression is a factor of a polynomial based on other information provided.

Passport to Advanced Math

4. Create an equivalent form of an algebraic expression by using structure and fluency with operations.

Heart of Algebra

4. Create, solve, and interpret systems of linear inequalities in two variables. The student will analyze one or more constraints that exist between two variables by creating, solving, or interpreting an inequality in two variables or a system of inequalities in two variables to represent a context. Multiple steps may be required to create the inequality or system of inequalities or to determine whether a given point is in the solution set.

Passport to Advanced Math

13. Use function notation, and interpret statements using function notation. The student will use function notation to solve conceptual problems related to transformations and compositions of functions.

Passport to Advanced Math

Passport to Advanced Math

14. Use structure to isolate or identify a quantity of interest
in an expression or isolate a quantity of interest in an equation.
The student will rearrange an equation or formula to isolate a
single variable or a quantity of interest.

Problem Solving and Data Analysis

10.    Evaluate reports to make inferences, justify conclusions, and determine appropriateness of data collection methods. The reports may consist of tables, graphs, or text summaries.

Problem Solving and Data Analysis

4.    Given a scatterplot, use linear, quadratic, or exponential models to describe how the variables are related. The student will, given a scatterplot, select the equation of a line or curve of best fit; interpret the line in the context of the situation; or use the line or curve of best fit to make a prediction.

Heart of Algebra

Problem Solving and Data Analysis

7.    Use two-way tables to summarize categorical data and relative frequencies, and calculate conditional probability. The student will summarize categorical data or use categorical data to calculate conditional frequencies, conditional probabilities, association of variables, or independence of events.

Problem Solving and Data Analysis

2.    Solve single- and multistep problems involving percentages. The student will solve a multistep problem to determine a percentage; calculate a percentage and then solve a multistep problem; or take a given percentage and solve a multistep problem.

Problem Solving and Data Analysis

9.    Use statistics to investigate measures of center of data and analyze shape, center, and spread. The student will calculate measures of center and/or spread for a given set of data or use given statistics to compare two separate sets of data. The measures of center that may be calculated include mean, median, and mode, and the measures of spread that may be calculated include range. When comparing two data sets, the student may investigate mean, median, mode, range, and/or standard deviation.

Problem Solving and Data Analysis

9.    Use statistics to investigate measures of center of data and analyze shape, center, and spread. The student will calculate measures of center and/or spread for a given set of data or use given statistics to compare two separate sets of data. The measures of center that may be calculated include mean, median, and mode, and the measures of spread that may be calculated include range. When comparing two data sets, the student may investigate mean, median, mode, range, and/or standard deviation.

Problem Solving and Data Analysis

9.    Use statistics to investigate measures of center of data and analyze shape, center, and spread. The student will calculate measures of center and/or spread for a given set of data or use given statistics to compare two separate sets of data. The measures of center that may be calculated include mean, median, and mode, and the measures of spread that may be calculated include range. When comparing two data sets, the student may investigate mean, median, mode, range, and/or standard deviation.

Heart of Algebra

4.    Create, solve, and interpret systems of linear inequalities in two variables. The student will analyze one or more constraints that exist between two variables by creating, solving, or interpreting an inequality in two variables or a system of inequalities in two variables to represent a context. Multiple steps may be required to create the inequality or system of inequalities or to determine whether a given point is in the solution set.

Passport to Advanced Math

14.    Use structure to isolate or identify a quantity of interest in an expression or isolate a quantity of interest in an equation. The student will rearrange an equation or formula to isolate a single variable or a quantity of interest.

Problem Solving and Data Analysis

1.    Use ratios, rates, proportional relationships, and scale drawings to solve single- and multistep problems. The student will use a proportional relationship between two variables to solve a multistep problem to determine a ratio or rate; calculate a ratio or rate and then solve a multistep problem; or take a given ratio or rate and solve a multistep problem.

Additional Topics in Math

8.    Create or use an equation in two variables to solve a problem about a circle in the coordinate plane. The student will create an equation or use properties of an equation of a circle to demonstrate or determine a property of the circle’s graph.

Heart of Algebra

9.    Understand connections between algebraic and graphical representations. The student will select a graph described by a given linear equation, select a linear equation that describes a given graph, determine the equation of a line given a verbal description of its graph, determine key features of the graph of a linear function from its equation, or determine how a graph may be affected by a change in its equation.

Passport to Advanced Math
13.    Use function notation, and interpret statements using function notation. The student will use function notation to solve conceptual problems related to transformations and compositions of functions.

Passport to Advanced Math

12.    Understand a nonlinear relationship between two variables by making connections between their algebraic and graphical representations. The student will select a graph corresponding to a given nonlinear equation; interpret graphs in the context of solving systems of equations; select a nonlinear equation corresponding to a given graph; determine the equation of a curve given a verbal description of a graph; determine key features of the graph of a linear function from its equation; or determine the impact on a graph of a change in the defining equation.

Heart of Algebra

3.    Build a linear function that models a linear relationship between two quantities. The student will describe a linear relationship that models a context using either an equation in two variables or function notation. The equation or function will have rational coefficients, and multiple steps may be required to build and simplify the equation or function.

Heart of Algebra

6.    Algebraically solve linear equations (or inequalities) in one variable. The equation (or inequality) will have rational coefficients and may require multiple steps to solve for the variable; the equation may yield no solution, one solution, or infinitely many solutions. The student may also be asked to determine the value of a constant or coefficient for an equation with no solution or infinitely many solutions.

7.    Use the relationship between similarity, right triangles, and trigonometric ratios; use the relationship between sine and cosine of complementary angles. The student will use trigonometry and theorems about triangles and intersecting lines to determine missing lengths and angle measures of right triangles. The student may also be asked to provide a missing length or angle that would satisfy a given theorem.

Problem Solving and Data Analysis

1.    Use ratios, rates, proportional relationships, and scale drawings to solve single- and multistep problems. The student will use a proportional relationship between two variables to solve a multistep problem to determine a ratio or rate; calculate a ratio or rate and then solve a multistep problem; or take a given ratio or rate and solve a multistep problem

Heart of Algebra

Heart of Algebra

5.    Create, solve, and interpret systems of two linear equations in two variables. The student will analyze one or more constraints that exist between two variables by creating, solving, or analyzing a system of linear equations to represent a context. The equations will have rational coefficients, and multiple steps may be required to simplify or solve the system.

Heart of Algebra

5.    Create, solve, and interpret systems of two linear equations in
two variables. The student will analyze one or more constraints that
exist between two variables by creating, solving, or analyzing a system
of linear equations to represent a context. The equations will have
rational coefficients, and multiple steps may be required to simplify or
solve the system.

Heart of Algebra

3.    Build a linear function that models a linear relationship between two quantities. The student will describe a linear relationship that models a context using either an equation in two variables or function notation. The equation or function will have rational coefficients, and multiple steps may be required to build and simplify the equation or function.

Additional Topics in Math

5.    Apply theorems about circles to find arc lengths, angle measures, chord lengths, and areas of sectors. The student will use given information about circles and lines to calculate missing values for radius, diameter, chord length, angle, arc, and sector area.

Problem Solving and Data Analysis?
6.    Compare linear growth with exponential growth. The student will infer the connection between two variables given a context in order to determine what type of model fits best.

Heart of Algebra

2.    Create, solve, or interpret linear inequalities in one variable that represent a context. The inequality will have rational coefficients, and multiple steps may be required to simplify or solve for the variable.