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- Mathematics: High School: Number and Quantity
California - Mathematics: High School: Number and Quantity
California Standards | Adopted: 2014
N-RN: : The Real Number System
N-RN.1: : Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
N-CN: : The Complex Number System
N-CN.1: : Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real.
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.2: : Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply 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
N-CN.3: : Find the conjugate of a complex number; use conjugates to find moduli and quotients 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
N-CN.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.
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.7: : Solve quadratic equations with real coefficients that have complex solutions.
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
N-VM: : Vector and Matrix Quantities
N-VM.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 (e.g., ??, |??|, ||??||, ??).
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 components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
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 involving velocity and other quantities that can be represented by vectors.
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
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
N-VM.4: : Add and subtract vectors.
N-VM.4.a: : 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.
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
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.4.b: : Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
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.5: : Multiply a vector by a scalar.
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
N-VM.5.a: : Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(???, ?? subscript y) = (c???, c?? subscript y).
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
N-VM.10: : Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
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
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
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
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
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
N-VM.12: : Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
Correlation last revised: 12/27/2023
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