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

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

A1.A: : Algebra

A1.A-SSE: : Seeing Structure in Expressions

A1.A-SSE.A: : Interpret the structure of expressions.

A1.A-SSE.A.1: : Interpret expressions that represent a quantity in terms of its context.

A1.A-SSE.A.1a: : Interpret parts of an expression, such as terms, factors, and coefficients.

A1.A-SSE.A.1b: : Interpret expressions by viewing one or more of their parts as a single entity.

A1.A-SSE.A.2: : Use structure to identify ways to rewrite numerical and polynomial expressions. Focus on polynomial multiplication and factoring patterns.

A1.A-SSE.B: : Write expressions in equivalent forms to solve problems.

A1.A-SSE.B.3: : Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A1.A-SSE.B.3a: : Factor a quadratic expression to reveal the zeros of the function it defines.

A1.A-SSE.B.3b: : Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

A1.A-APR: : Arithmetic with Polynomials and Rational Expressions

A1.A-APR.A: : Perform arithmetic operations on polynomials.

A1.A-APR.A.1: : 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.

A1.A-APR.B: : Understand the relationship between zeros and factors of polynomials.

A1.A-APR.B.3: : Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Focus on quadratic and cubic polynomials in which linear and quadratic factors are available.

A1.A-CED: : Creating Equations

A1.A-CED.A: : Create equations that describe numbers or relationships.

A1.A-CED.A.1: : Create equations and inequalities in one variable and use them to solve problems. Include problem-solving opportunities utilizing real-world context. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).

A1.A-CED.A.2: : Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A1.A-CED.A.3: : Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

A1.A-CED.A.4: : Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A1.A-REI: : Reasoning with Equations and Inequalities

A1.A-REI.A: : Understand solving equations as a process of reasoning and explain the reasoning.

A1.A-REI.A.1: : Explain each step in solving linear and quadratic equations 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.

A1.A-REI.B: : Solve equations and inequalities in one variable.

A1.A-REI.B.3: : Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A1.A-REI.B.4: : Solve quadratic equations in one variable.

A1.A-REI.B.4a: : Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - k)² = q that has the same solutions. Derive the quadratic formula from this form.

A1.A-REI.B.4b: : Solve quadratic equations by inspection (e.g., x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Focus on solutions for quadratic equations that have real roots. Include cases that recognize when a quadratic equation has no real solutions.

A1.A-REI.C: : Solve systems of equations.

A1.A-REI.C.5: : 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.

A1.A-REI.C.6: : Solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables. Include problem solving opportunities utilizing real-world context.

A1.A-REI.D: : Represent and solve equations and inequalities graphically.

A1.A-REI.D.10: : Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve, which could be a line.

A1.A-REI.D.11: : Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately (e.g., using technology to graph the functions, make tables of values, or find successive approximations). Focus on cases where f(x) and/or g(x) are linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).

A1.A-REI.D.12: : 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.

A1.F: : Functions

A1.F-IF: : Interpreting Functions

A1.F-IF.A: : Understand the concept of a function and use function notation.

A1.F-IF.A.1: : Understand that 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).

A1.F-IF.A.2: : Evaluate a function for inputs in the domain, and interpret statements that use function notation in terms of a context.

A1.F-IF.A.3: : Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

A1.F-IF.B: : Interpret functions that arise in applications in terms of the context.

A1.F-IF.B.4: : 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. Include problem-solving opportunities utilizing real-world context. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).

A1.F-IF.B.5: : Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

A1.F-IF.B.6: : Calculate and interpret the average rate of change of a continuous function (presented symbolically or as a table) on a closed interval. Estimate the rate of change from a graph. Include problem-solving opportunities utilizing real-world context. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).

A1.F-IF.C: : Analyze functions using different representations.

A1.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. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).

A1.F-IF.C.8: : Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

A1.F-IF.C.8a: : Use the process of factoring and completing the square of a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

A1.F-IF.C.9: : Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).

A1.F-BF: : Building Functions

A1.F-BF.A: : Build a function that models a relationship between two quantities.

A1.F-BF.A.1: : Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from real-world context. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).

A1.F-BF.B: : Build new functions from existing functions.

A1.F-BF.B.3: : Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step).

A1.F-LE: : Linear, Quadratic, and Exponential Models

A1.F-LE.A: : Construct and compare linear, quadratic, and exponential models and solve problems.

A1.F-LE.A.1: : Distinguish between situations that can be modeled with linear functions and with exponential functions.

A1.F-LE.A.1a: : Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

A1.F-LE.A.1b: : Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

A1.F-LE.A.1c: : Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

A1.F-LE.A.2: : Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or input/output pairs.

A1.F-LE.A.3: : Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.

A1.F-LE.B: : Interpret expressions for functions in terms of the situation they model.

A1.F-LE.B.5: : Interpret the parameters in a linear or exponential function with integer exponents utilizing real world context.

A1.S: : Statistics and Probability

A1.S-ID: : Summarize, represent, and interpret data on a single count or measurement variable.

A1.S-ID.A: : Summarize, represent, and interpret data on a single count or measurement variable.

A1.S-ID.A.1: : Represent real-value data with plots for the purpose of comparing two or more data sets.

A1.S-ID.A.2: : 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.

A1.S-ID.A.3: : Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of outliers if present.

A1.S-ID.B: : Summarize, represent, and interpret data on two categorical and quantitative variables.

A1.S-ID.B.5: : Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data, including joint, marginal, and conditional relative frequencies. Recognize possible associations and trends in the data.

A1.S-ID.B.6: : Represent data on two quantitative variables on a scatter plot, and describe how the quantities are related.

A1.S-ID.B.6a: : Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Focus on linear models.

A1.S-ID.B.6b: : Informally assess the fit of a function by plotting and analyzing residuals.

A1.S-ID.C: : Interpret linear models.

A1.S-ID.C.7: : Interpret the slope as a rate of change and the constant term of a linear model in the context of the data.

A1.S-ID.C.8: : Compute and interpret the correlation coefficient of a linear relationship.

A1.S-ID.C.9: : Distinguish between correlation and causation.

A1.S-CP: : Conditional Probability and the Rules of Probability

A1.S-CP.A: : Understand independence and conditional probability and use them to interpret data.

A1.S-CP.A.1: : Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections, or complements of other events.

A1.S-CP.A.2: : Use the Multiplication Rule for independent events to understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

A1.MP: : Standards for Mathematical Practices

A1.MP.1: : Make sense of problems and persevere in solving them.

5.1.1: : 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.

A1.MP.2: : Reason abstractly and quantitatively.

A1.MP.3: : Construct viable arguments and critique the reasoning of others.

5.3.1: : 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.

A1.MP.4: : Model with mathematics.

A1.MP.5: : Use appropriate tools strategically.

5.5.1: : 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.

A1.MP.6: : Attend to precision.

5.6.1: : 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.

A1.MP.7: : Look for and make use of structure.

5.7.1: : 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.

A1.MP.8: : Look for and express regularity in repeated reasoning.

5.8.1: : 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: Algebra I

Academic Standards | Adopted: 2016

A1.A: : Algebra

A1.F: : Functions

A1.S: : Statistics and Probability

A1.MP: : Standards for Mathematical Practices