This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.
PC.F: : Functions
PC.F.1: : 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.
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle.5 Minute Preview
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs.5 Minute Preview
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.5 Minute Preview
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function.5 Minute Preview
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response.5 Minute Preview
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior.5 Minute Preview
Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph.5 Minute Preview
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response.5 Minute Preview
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation.5 Minute Preview
Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation.5 Minute Preview
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle.5 Minute Preview
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle.5 Minute Preview
Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function.5 Minute Preview
PC.F.2: : Find linear models by using median fit and least squares regression methods, making use of technology. Decide which among several linear models gives a better fit. Interpret the slope and intercept in terms of the original context.
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line.5 Minute Preview
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line.5 Minute Preview
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line.5 Minute Preview
PC.F.4: : Determine if a graph or table has an inverse, and justify if the inverse is a function, relation, or neither. Identify the values of an inverse function/relation from a graph or a table, given that the function has an inverse. Derive the inverse equation from the values of the inverse.
对数函数
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the liney=xto compare the associated exponential function.5 Minute Preview
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation.5 Minute Preview
PC.F.6: : Recognize even and odd functions from their graphs and algebraic expressions.
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle.5 Minute Preview
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle.5 Minute Preview
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle.5 Minute Preview
PC.QPR: : Quadratic, Polynomial and Rational Equations and Functions
PC.QPR。1: : Use the method of completing the square to transform any quadratic equation into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.5 Minute Preview
PC.QPR。2: : Understand and use addition, subtraction, multiplication, and conjugation of complex numbers.
Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response.5 Minute Preview
PC.QPR。3:计算数据之间的距离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.
Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response.5 Minute Preview
PC.QPR。4: : Know and apply the Remainder Theorem and the Factor Theorem.
Dividing Polynomials Using Synthetic Division
Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division.5 Minute Preview
PC.QPR。5: : Understand the Fundamental Theorem of Algebra. Find a polynomial function of lowest degree with real coefficients when given its roots.
Polynomials and Linear Factors
Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function.5 Minute Preview
PC.QPR。6: : Graph rational functions with and without technology. Identify and describe features such as intercepts, domain and range, and asymptotic and end behavior.
General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response.5 Minute Preview
Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation.5 Minute Preview
PC.EL.2: : Use the laws of logarithms to simplify logarithmic expressions, approximate the value of a logarithmic expression, and solve logarithmic equations.
对数函数
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the liney=xto compare the associated exponential function.5 Minute Preview
Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph.5 Minute Preview
PC.EL.3: : Graph and solve real-world and other mathematical problems that can be modeled using exponential and logarithmic functions; interpret the solution and determine whether it is reasonable. Identify and describe features such as intercepts, domain, range, asymptotes, and end behavior.
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function.5 Minute Preview
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph.5 Minute Preview
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the liney=xto compare the associated exponential function.5 Minute Preview
Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph.5 Minute Preview
PC.SS.1: : Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
算术序列
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response.5 Minute Preview
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response.5 Minute Preview
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas.5 Minute Preview
PC.SS.2: : Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms.
算术序列
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response.5 Minute Preview
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas.5 Minute Preview
PC.SS.4: : Model and solve real-world problems involving applications of sequences and series, interpret the solutions and determine whether the solutions are reasonable.
算术序列
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response.5 Minute Preview
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response.5 Minute Preview
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas.5 Minute Preview
PC.CO。1: : Construct the equation of a parabola given a focus and directrix.
Parabolas
Explore parabolas in a conic section context. Find the relationship among the vertex, focus, and directrix of a parabola, and how that relates to its equation.5 Minute Preview
PC.CO。2::构造g的圆的方程iven center and radius. Complete the square to find the center and radius of a circle given by an equation.
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response.5 Minute Preview
PC.CO。3: : Construct the equations of ellipses and hyperbolas given at least 2 of the following: foci, vertices, length of an axis, or point on the curve.
Ellipses
Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their Pythagorean relationship, and discover the string property.5 Minute Preview
Compare the equation of a hyperbola to its graph. Vary the terms of the equation of the hyperbola. Examine how the graph of the hyperbola and its asymptotes changes in response.5 Minute Preview
PC.CO。4: : Graph conic sections. Identify and describe features like center, vertex or vertices, focus or foci, directrix, axis of symmetry, major axis, minor axis, and eccentricity.
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response.5 Minute Preview
Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their Pythagorean relationship, and discover the string property.5 Minute Preview
Compare the equation of a hyperbola to its graph. Vary the terms of the equation of the hyperbola. Examine how the graph of the hyperbola and its asymptotes changes in response.5 Minute Preview
Explore parabolas in a conic section context. Find the relationship among the vertex, focus, and directrix of a parabola, and how that relates to its equation.5 Minute Preview
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
