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New York - Mathematics: The Plus Standards
Next Generation Learning Standards | Adopted: 2017
N: : Number and Quantity
N.CN: : The Complex Number System
1.1.1: : Perform arithmetic operations with complex numbers.
N.CN.3: : Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
![Screenshot of Points in the Complex Plane](/Assets/img/blank.gif)
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
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
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
1.1.2: : Represent complex numbers and their operations on the complex plane.
N.CN.4a: : Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and convert between rectangular and polar forms of a given complex number.
![Screenshot of Points in the Complex Plane](/Assets/img/blank.gif)
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
N.CN.5: : Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.
![Screenshot of Points in the Complex Plane](/Assets/img/blank.gif)
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
N.CN.6a: : Calculate the distance between two points in the complex plane.
![Screenshot of Points in the Complex Plane](/Assets/img/blank.gif)
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
1.1.3: : Use complex numbers in polynomial identities and equations.
N.CN.8: : Extend polynomial identities to the complex numbers.
![Screenshot of Points in the Complex Plane](/Assets/img/blank.gif)
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
N.VM: : Vector and Matrix Quantities
1.2.1: : Represent and model with vector quantities.
N.VM.1: : Represent a vector analytically and geometrically.
![Screenshot of Adding Vectors](/Assets/img/blank.gif)
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
![Screenshot of Vectors](/Assets/img/blank.gif)
Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
N.VM.2: : Find the magnitude and direction of a given vector.
![Screenshot of Adding Vectors](/Assets/img/blank.gif)
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
![Screenshot of Vectors](/Assets/img/blank.gif)
Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
N.VM.3: : Solve problems using vectors analytically and geometrically.
![Screenshot of 2D Collisions](/Assets/img/blank.gif)
2D Collisions
Investigate elastic collisions in two dimensions using two frictionless pucks. The mass, velocity, and initial position of each puck can be modified to create a variety of scenarios. 5 Minute Preview
![Screenshot of Adding Vectors](/Assets/img/blank.gif)
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
![Screenshot of Golf Range](/Assets/img/blank.gif)
Golf Range
Try to get a hole in one by adjusting the velocity and launch angle of a golf ball. Explore the physics of projectile motion in a frictional or ideal setting. Horizontal and vertical velocity vectors can be displayed, as well as the path of the ball. The height of the golfer and the force of gravity are also adjustable. 5 Minute Preview
![Screenshot of Vectors](/Assets/img/blank.gif)
Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
1.2.2: : Perform operations on vectors.
N.VM.4: : Add and subtract vectors analytically and geometrically.
![Screenshot of Adding Vectors](/Assets/img/blank.gif)
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
![Screenshot of Vectors](/Assets/img/blank.gif)
Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
1.2.3: : Perform operations on matrices and use matrices in applications.
N.VM.7: : Multiply matrices by scalars.
![Screenshot of Dilations](/Assets/img/blank.gif)
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
N.VM.8: : Add, subtract, and multiply matrices.
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
N.VM.11: : Use matrices to perform linear transformations in the plane.
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
N.VM.12: : Calculate and interpret the determinant of a matrix.
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
A: : Algebra
A.APR: : Arithmetic with Polynomial and Rational Expressions
2.1.1: : Use polynomial identities to solve problems.
A.APR.5: : Use the Binomial Theorem for the expansion of (x + y)^n for a positive integer n.
![Screenshot of Binomial Probabilities](/Assets/img/blank.gif)
Binomial Probabilities
Find the probability of a number of successes or failures in a binomial experiment using a tree diagram, a bar graph, and direct calculation. 5 Minute Preview
A.REI: : Reasoning with Equations and Inequalities
2.2.1: : Solve systems of equations.
A.REI.8: : Represent a system of linear equations as a single matrix equation in a vector variable.
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
A.REI.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 × 3 or greater).
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
F: : Functions
F.IF: : Interpreting Functions
3.1.1: : Analyze functions using different representations.
F.IF.7d: : Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available.
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
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
![Screenshot of Rational Functions](/Assets/img/blank.gif)
Rational Functions
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
F.BF: : Building Functions
3.2.2: : Build new functions from existing functions.
F.BF.3c: : Determine algebraically whether or not a function is even or odd.
![Screenshot of Graphs of Polynomial Functions](/Assets/img/blank.gif)
Graphs of Polynomial Functions
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
F.BF.4c: : Given the graph or table of an invertible function, determine coordinates of its inverse.
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
Logarithmic Functions
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 line y = x to compare the associated exponential function. 5 Minute Preview
F.BF.5b: : Use inverse relationships to solve problems involving logarithms and exponents.
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
Logarithmic Functions
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 line y = x to compare the associated exponential function. 5 Minute Preview
F.TF: : Trigonometric Functions
3.3.1: : Extend the domain of trigonometric functions using the unit circle.
F.TF.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, cosines, and tangent for x, pi + x, and 2pi – x in terms of their values for x, where x is any real number.
![Screenshot of Cosine Function](/Assets/img/blank.gif)
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
![Screenshot of Sine Function](/Assets/img/blank.gif)
Sine Function
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
![Screenshot of Tangent Function](/Assets/img/blank.gif)
Tangent Function
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
3.3.3: : Prove and apply trigonometric identities.
F.TF.9: : Prove the sum and difference formulas for sine, cosine, and tangent and use them to solve problems.
![Screenshot of Sum and Difference Identities for Sine and Cosine](/Assets/img/blank.gif)
Sum and Difference Identities for Sine and Cosine
Choose the correct steps to evaluate a trigonometric expression using sum and difference identities. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
G: : Geometry
G.GPE: : Expressing Geometric Properties with Equations
4.3.1: : Translate between the geometric description and the equation for a conic section.
G.GPE.2: : Explore the relationship among the parabola, focus, and directrix and use the equation to model a real-life situation, using technology as appropriate.
![Screenshot of Parabolas](/Assets/img/blank.gif)
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
G.GPE.3a: : Derive the equations of ellipses and hyperbolas given the foci.
![Screenshot of Ellipses](/Assets/img/blank.gif)
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
![Screenshot of Hyperbolas](/Assets/img/blank.gif)
Hyperbolas
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
G.GMD: : Geometric Measurement and Dimension
4.4.1: : Explain volume formulas and use them to solve problems.
G.GMD.2: : Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
![Screenshot of Prisms and Cylinders](/Assets/img/blank.gif)
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
![Screenshot of Pyramids and Cones](/Assets/img/blank.gif)
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
S: : Statistics and Probability
S.ID: : Interpreting Categorical and Quantitative Data
5.1.1: : Summarize, represent, and interpret data on two categorical and quantitative variables.
S.ID.6b: : Informally assess the fit of a function by plotting and analyzing residuals.
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
S.CP: : Conditional Probability and the Rules of Probability
5.2.1: : Use the rules of probability to compute probabilities of compound events in a uniform probability model.
S.CP.9: : Solve problems using permutations and combinations to compute probabilities of compound events.
![Screenshot of Permutations and Combinations](/Assets/img/blank.gif)
Permutations and Combinations
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview
S.MD: : Using Probability to Make Decisions
5.3.1: : Calculate expected values and use them to solve problems.
S.MD.1a: : Define a random variable for a quantity of interest.
![Screenshot of Lucky Duck (Expected Value)](/Assets/img/blank.gif)
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
S.MD.1b: : Graph a probability distribution for a discrete random variable based on either empirical or theoretical probabilities.
![Screenshot of Lucky Duck (Expected Value)](/Assets/img/blank.gif)
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
S.MD.2: : Calculate and interpret the expected value of a random variable.
![Screenshot of Lucky Duck (Expected Value)](/Assets/img/blank.gif)
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
5.3.2: : Use probability to evaluate outcomes of decisions.
S.MD.5: : Use expected values from probability distributions to evaluate and compare the outcomes of decisions.
![Screenshot of Lucky Duck (Expected Value)](/Assets/img/blank.gif)
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
S.MD.6: : Use probabilities to make fair decisions.
![Screenshot of Lucky Duck (Expected Value)](/Assets/img/blank.gif)
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
S.MD.7: : Using probability concepts, evaluate decisions and strategies.
![Screenshot of Lucky Duck (Expected Value)](/Assets/img/blank.gif)
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
Correlation last revised: 12/9/2022
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