Gizmos for Arizona - Mathematics: Plus Standards (Academic Standards adopted 2016)

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

P.N: : Number and Quantity

P.N-CN: : The Complex Number System

P.N-CN.A: : Perform arithmetic operations with complex numbers.

P.N-CN.A.3: : Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

P.N-CN.B: : Represent complex numbers and their operations on the complex plane.

P.N-CN.B.4: : Represent complex numbers on the complex plane in rectangular and polar form, including real and imaginary numbers, and explain why the rectangular and polar forms of a given complex number represent the same number.

P.N-CN.B.5: : Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

P.N-CN.B.6: : Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

P.N-VM: : Vector and Matrix Quantities

P.N-VM.A: : Represent and model with vector quantities.

P.N-VM.A.1: : Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.

P.N-VM.A.3: : Solve problems involving velocity and other quantities that can be represented by vectors.

P.N-VN.B: : Perform operations on vectors.

P.N-VM.B.4: : Add and subtract vectors.

P.N-VM.B.4a: : Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

P.N-VM.B.4b: : Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

P.N-VM.B.4c: : Understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

P.N-VM.B.5: : Multiply a vector by a scalar.

P.N-VM.B.5a: : Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise e.g., as ??(?? subscript ?, ?? subscript ??) = (???? subscript ?, ???? subscript ??).

P.N-VM.B.5b: : Compute the magnitude of a scalar multiple ???? using ||????|| = |??|??. Compute the direction of ???? knowing that when |??|?? ? 0, the direction of ???? is either along ?? (for ?? > 0) or against ?? (for ??

P.N-VM.C: : Perform operations on matrices and use matrices in applications.

P.N-VM.C.7: : Multiply matrices by scalars to produce new matrices.

P.N-VM.C.8: : Add, subtract, and multiply matrices of appropriate dimensions.

P.N-VM.C.12: : Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

P.A: : Algebra

P.A-APR: : Arithmetic with Polynomials and Rational Expressions

P.A-APR.C: : Use polynomial identities to solve problems.

P.A-APR.C.5: : Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.

P.A-REI: : Reasoning with Equations and Inequalities

P.A-REI.C: : Solve systems of equations.

P.A-REI.C.8: : Represent a system of linear equations as a single matrix equation in a vector variable.

P.A-REI.C.9: : Find the inverse of a matrix if it exists, and use it to solve systems of linear equations (using technology for matrices of dimension 3 x 3 or greater).

P.F: : Functions

P.F-IF: : Interpreting Functions

P.F-IF.C: : Analyze functions using different representations.

P.F-IF.C.7: : Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

P.F-BF: : Building Functions

P.F-BF.A: : Build a function that models a relationship between two quantities.

P.F-BF.A.1: : Write a function that describes a relationship between two quantities.

P.F-BF.A.1c: : Compose functions.

P.F-BF.B: : Build new functions from existing functions.

P.F-BF.B.4: : Find inverse functions.

P.F-BF.B.4b: : Verify by composition that one function is the inverse of another.

P.F-BF.B.4c: : Read values of an inverse function from a graph or a table, given that the function has an inverse.

P.F-BF.B.4d: : Produce an invertible function from a non-invertible function by restricting the domain.

P.F-BF.B.5: : Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

P.F-TF: : Trigonometric Functions

P.F-TF.A: : Extend the domain of trigonometric functions using the unit circle.

P.F-TF.A.3: : Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi - x, pi + x, and 2pi - x in terms of their values for x, where x is any real number.

P.F-TF.A.4: : Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

P.F-TF.C: : Apply trigonometric identities.

P.F-TF.C.9: : Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

P.G: : Geometry

P.G-GPE: : Expressing Geometric Properties with Equations

P.G-GPE.A: : Translate between the geometric description and the equation for a conic section.

P.G-GPE.A.2: : Derive the equation of a parabola given a focus and directrix.

P.G-GPE.A.3: : Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

P.G-GMD: : Geometric Measurement and Dimension

P.G-GMD.A: : Explain volume formulas and use them to solve problems.

P.G-GMD.A.2: : Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

P.S: : Statistics and Probability

P.S-IC: : Making Inferences and Justifying Conclusions

P.S-IC.B: : Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

P.S-IC.B.3: : Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

P.S-IC.B.4: : Use data from a random sample to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

P.S-IC.B.5: : Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

P.S-IC.B.6: : Evaluate reports based on data.

P.S-CP: : Conditional Probability and the Rules of Probability

P.S-CP.B: : Use the rules of probability to compute probabilities of compound events in a uniform probability model.

P.S-CP.B.9: : Use permutations and combinations to compute probabilities of compound events and solve problems.

P.S-MD: : Using Probability to Make Decisions

P.S-MD.A: : Calculate expected values and use them to solve problems.

P.S-MD.A.1: : Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

P.S-MD.A.2: : Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

P.S-MD.A.3: : Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated. Find the expected value.

P.S-MD.A.4: : Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically. Find the expected value.

P.S-MD.B: : Use probability to evaluate outcomes of decisions.

P.S-MD.B.5: : Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

P.S-MD.B.5a: : Find the expected payoff for a game of chance.

P.S-MD.B.5b: : Evaluate and compare strategies on the basis of expected values.

P.S-MD.B.6: : Use randomization to make fair decisions based on probabilities.

P.S-MD.B.7: : Analyze decisions and strategies using probability concepts.

P.MP: : Standards for Mathematical Practice

P.MP.1: : Make sense of problems and persevere in solving them.

7.1.1: : Mathematically proficient students explain to themselves the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. While engaging in productive struggle to solve a problem, they continually ask themselves, “Does this make sense?' to monitor and evaluate their progress and change course if necessary. Once they have a solution, they look back at the problem to determine if the solution is reasonable and accurate. Mathematically proficient students check their solutions to problems using different methods, approaches, or representations. They also compare and understand different representations of problems and different solution pathways, both their own and those of others.

P.MP.2: : Reason abstractly and quantitatively.

P.MP.3: : Construct viable arguments and critique the reasoning of others.

7.3.1: : Mathematically proficient students construct mathematical arguments (explain the reasoning underlying a strategy, solution, or conjecture) using concrete, pictorial, or symbolic referents. Arguments may also rely on definitions, assumptions, previously established results, properties, or structures. Mathematically proficient students make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. Mathematically proficient students present their arguments in the form of representations, actions on those representations, and explanations in words (oral or written). Students critique others by affirming or questioning the reasoning of others. They can listen to or read the reasoning of others, decide whether it makes sense, ask questions to clarify or improve the reasoning, and validate or build on it. Mathematically proficient students can communicate their arguments, compare them to others, and reconsider their own arguments in response to the critiques of others.

P.MP.4: : Model with mathematics.

P.MP.5: : Use appropriate tools strategically.

7.5.1: : Mathematically proficient students consider available tools when solving a mathematical problem. They choose tools that are relevant and useful to the problem at hand. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful; recognizing both the insight to be gained and their limitations. Students deepen their understanding of mathematical concepts when using tools to visualize, explore, compare, communicate, make and test predictions, and understand the thinking of others.

P.MP.6: : Attend to precision.

7.6.1: : Mathematically proficient students clearly communicate to others using appropriate mathematical terminology, and craft explanations that convey their reasoning. When making mathematical arguments about a solution, strategy, or conjecture, they describe mathematical relationships and connect their words clearly to their representations. Mathematically proficient students understand meanings of symbols used in mathematics, calculate accurately and efficiently, label quantities appropriately, and record their work clearly and concisely.

P.MP.7: : Look for and make use of structure.

7.7.1: : Mathematically proficient students use structure and patterns to assist in making connections among mathematical ideas or concepts when making sense of mathematics. Students recognize and apply general mathematical rules to complex situations. They are able to compose and decompose mathematical ideas and notations into familiar relationships. Mathematically proficient students manage their own progress, stepping back for an overview and shifting perspective when needed.

P.MP.8: : Look for and express regularity in repeated reasoning.

7.8.1: : Mathematically proficient students look for and describe regularities as they solve multiple related problems. They formulate conjectures about what they notice and communicate observations with precision. While solving problems, students maintain oversight of the process and continually evaluate the reasonableness of their results. This informs and strengthens their understanding of the structure of mathematics which leads to fluency.

Correlation last revised: 9/16/2020

Arizona - Mathematics: Plus Standards

Academic Standards | Adopted: 2016