Gizmos for West Virginia - Mathematics: Transition Mathematics for Seniors (College- and Career-Readiness Standards adopted 2015)

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

NQ: : Number and Quantity

NQ.A: : The Real Number System

1.1.1: : Extend the properties of exponents to rational exponents.

NQ.A.M.TMS.1: : Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

NQ.A.M.TMS.2: : Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

NQ.B: : The Complex Number System

1.2.1: : Use complex numbers in polynomial identities and equations.

NQ.B.M.TMS.3: : Solve quadratic equations with real coefficients that have complex solutions.

A: : Algebra

A.A: : Seeing Structure in Expressions

2.1.1: : Interpret the structure of expressions.

A.A.M.TMS.4: : Use the structure of an expression to identify ways to rewrite it.

2.1.2: : Write expressions in equivalent forms to solve problems.

A.A.M.TMS.5: : Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A.A.M.TMS.5.a: : Factor a quadratic expression to reveal the zeros of the function it defines.

A.A.M.TMS.5.b: : Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

2.1.3: : Understand the connections between proportional relationship, lines, and linear equations.

A.A.M.TMS.7: : Graph proportional relationships, interpreting the unit rates as the slope of the graph. Compare two different proportional relationships represented in different ways.

A.A.M.TMS.8: : Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plan; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

A.A.M.MTS.9: : Solve linear equations in one variable.

A.B: : Arithmetic with Polynomials and Rational Expressions

2.2.1: : Perform arithmetic operations on polynomials.

A.B.M.TMS.10: : Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract and multiply polynomials.

A.C: : Creating Equations

2.3.1: : Create equations that describe numbers or relationships.

A.C.M.TMS.11: : Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.

A.C.M.TMS.12: : Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.C.M.TMS.13: : Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context.

A.C.M.TMS.14: : Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A.D: : Reasoning with Equations and Inequalities

2.4.2: : Solve equations and inequalities in one variable.

A.D.M.TMS.16: : Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A.D.M.TMS.17: : Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A.D.M.TMS.18: : Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

2.4.3: : Solve systems of equations.

A.D.M.TMS.19: : Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

A.D.M.TMS.21: : Explain why the x-coordinates of the points where the graphs of the equation y = f(x) and y = g(x) intersect are the solution of the equation f(x) = g (x); find the solution approximately (e.g., using technology to graph the functions, make tables of values or find successive approximations).

2.4.4: : Represent and solve equations and inequalities graphically.

A.D.M.TMS.22: : Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

A.D.M.TMS.23: : Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality) and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

F: : Functions

F.A: : Interpreting Functions

3.1.1: : Understand the concept of a function and use function notation.

F.A.M.TMS.24: : Understand a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

3.1.2: : Interpret functions that arise in applications in terms of the context.

F.A.M.TMS.25: : Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

F.A.M.TMS.26: : Interpret the parameters in a linear or exponential function in terms of a context.

F.A.M.TMS.27: : For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F.A.M.TMS.28: : Distinguish between situations that can be modeled with linear functions and with exponential functions.

3.1.3: : Analyze functions using different representations.

F.A.M.TMS.29: : Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line, give examples of functions that are not linear.

F.A.M.TMS.30: : Describe qualitatively the functional relationship between two quantities by analyzing a graph.

F.A.M.TMS.31: : Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.

F.A.M.TMS.32: : Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.A.M.TMS.32.a: : Graph linear and quadratic functions and show intercepts, maxima, and minima.

F.A.M.TMS.32.b: : Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F.A.M.TMS.33: : Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasingly linearly, quadratically, or (more generally) as a polynomial function.

F.A.M.TMS.34: : Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

F.B: : Building Functions

3.2.1: : Build a function that models a relationship between two quantities.

F.B.M.TMS.36: : Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

F.B.M.TMS.37: : Write a function that describes a relationship between two quantities.

F.B.M.TMS.37.a: : Combine standard function types using arithmetic operations.

G: : Geometry

G.A: : Geometric Measuring and Dimension

4.1.1: : Explain volume formulas and use them to solve problems.

G.A.M.TMS.38: : Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

G.A.M.TMS.39: : Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

G.B: : Expressing Geometric Properties with Equations

4.2.1: : Use coordinates to prove simple geometric theorems algebraically.

G.B.M.TMS.40: : Use coordinates to prove simple geometric theorems algebraically.

G.B.M.TMS.41: : Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, (e.g., using the distance formula).

SP: : Statistics and Probability

SP.A: : Interpreting Categorical & Quantitative Data

5.1.1: : Summarize, represent, and interpret data on two categorical and quantitative variables.

SP.A.M.TMS.43: : Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Interpret linear models.

SP.A.M.TMS.44: : Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

SP.A.M.TMS.45: : Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

5.1.2: : Summarize, represent, and interpret data on a single count or measurement variable.

SP.A.M.TMS.47: : Represent data with plots on the real number line (dot plots, histograms, and box plots).

SP.A.M.TMS.48: : Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

SP.A.M.TMS.49: : Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

SP.A.M.TMS.50: : Compute (using technology) and interpret the correlation coefficient of a linear fit.

SP.A.M.TMS.51: : Distinguish between correlation and causation.

SP.B: : Interpreting Categorical & Quantitative Data

5.2.1: : Understand and evaluate random processes underlying statistical experiments.

SP.B.M.TMS.52: : Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Correlation last revised: 1/10/2023

West Virginia - Mathematics: Transition Mathematics for Seniors

College- and Career-Readiness Standards | Adopted: 2015

NQ: : Number and Quantity

A: : Algebra

F: : Functions

G: : Geometry

SP: : Statistics and Probability