Gizmos for South Dakota - Mathematics: Algebra I (Content Standards adopted 2018)

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

N.RN: : The Real Number System

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

N.RN.1: : Explain how the definition of rational exponents follows from extending the properties of integer exponents, allowing for a notation for radicals in terms of rational exponents.

A.SSE: : Seeing Structure in Expression

3.1: : Interpret the structure of expressions.

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

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

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

A.SSE.2: : Recognize and use the structure of an expression to identify ways to rewrite it.

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

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

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

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

A.SSE.3.c: : Use the properties of exponents to write equivalent expressions for exponential functions.

A.APR: : Arithmetic with Polynomials and Rational Expressions

4.1: : Perform arithmetic operations on polynomials.

A.APR.1: : Understand that polynomials form a system closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

A.CED: : Creating Equations

5.1: : Create equations that describe numbers or relationships.

A.CED.1: : Create equations and inequalities in one variable arising from situations in which linear, quadratic, and exponential functions are appropriate and use them to solve problems.

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

A.CED.3: : 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.CED.4: : Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A.REI: : Reasoning With Equations and Inequalities

6.1: : Understand solving equations as a process of reasoning.

A.REI.1: : Explain each step in solving an 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.

6.2: : Solve equations and inequalities in one variable.

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

A.REI.4: : Solve quadratic equations in one variable.

A.REI.4.a: : 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.

A.REI.4.b: : Derive the quadratic formula from this form completing the square.

A.REI.4.c: : 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.

6.3: : Solve systems of equations.

A.REI.5: : Understand the principles of the elimination method.

A.REI.6: : Solve systems of linear equations exactly and approximately by graphing, focusing on pairs of linear equations in two variables.

6.4: : Represent and solve equations and inequalities graphically.

A.REI.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).

A.REI.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, including but not limited to using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, quadratic and exponential.

A.REI.12: : Graph a linear inequality (strict or inclusive) in two variables; graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

F.IF: : Interpreting Functions

7.1: : Understand the concept of a function and use functions notation.

F.IF.1: : Understand that a function maps each element of the domain to 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 off is the graph of the equation y = f(x).

F.IF.2: : Use function notation, evaluate functions, and interpret statements that use function notation in terms of a context.

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

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

F.IF.4: : For functions, including linear, quadratic, and exponential, that model 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 or decreasing, including using interval notation; maximums and minimums; symmetries.

F.IF.5: : Relate the domain of a function to its graph and find an appropriate domain in the context of the problem.

7.3: : Analyze functions using different representations.

F.IF.7: : Graph parent functions and their transformations expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.7.a: : Graph linear, exponential, and quadratic functions and show intercepts, maxima, and minima.

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

F.IF.8.a: : Use the process of graphing, 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.IF.9: : Compare properties of two functions (linear, quadratic and exponential) each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

F.BF: : Building Functions

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

F.BF.1: : Write a function (linear, quadratic, and exponential) that describes a relationship between two quantities.

F.BF.1.a: : Determine an explicit expression, a recursive process, or steps for calculation from a context.

F.BF.1.b: : Determine an explicit expression from a graph.

F.BF.1.c: : Combine standard function types using arithmetic operations.

F.BF.2: : Write arithmetic and geometric sequences both recursively and with an explicit formula and use them to model situations.

8.2: : Build new functions from existing functions.

F.BF.3: : Identify the effect on the graph of f(x) (linear, exponential, quadratic) replaced with 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. Experiment with contrasting cases and illustrate an explanation of the effects on the graph using technology.

F.LE: : Linear, Quadratic and Exponential Models

9.1: : Construct and compare linear and exponential models and solve problems.

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

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

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

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

F.LE.2: : 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.LE.3: : Recognize, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.

9.2: : Interpret expressions for functions in terms of the situation they model.

F.LE.5: : Interpret the parameters in a linear or exponential function in terms of a context.

S.ID: : Interpreting Categorical and Quantitative Data

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

S.ID.1: : Represent data with plots on the real number line (dot plots, histograms, and box plots).

S.ID.2: : Use statistics appropriate to the shape and context of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

S.ID.3: : Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

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

S.ID.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.

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

S.ID.6.a: : Determine the function (linear, quadratic, or exponential model) that best fits a set of data and use that function fitted to data to solve problems within context.

S.ID.6.b: : Informally and using technology assess the fit of a function by plotting and analyzing residuals.

S.ID.6.c: : Fit a linear function for a scatter plot that suggests a linear association.

10.3: : Interpret linear models.

S.ID.7: : Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

S.ID.8: : Compute (using technology) and interpret the correlation coefficient of a linear fit.

S.ID.9: : Distinguish between correlation and causation.

Correlation last revised: 9/16/2020

South Dakota - Mathematics: Algebra I

Content Standards | Adopted: 2018