Arkansas - Mathematics: High School: Number and Quantity
Curriculum Framework | Adopted: 2016
This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.
AR.Math.Content.HSN.RN: : The Real Number System
AR.Math.Content.HSN.RN.A: : Extend the properties of exponents to rational exponents
AR.Math.Content.HSN.RN.A.1: : Explain how extending the properties of integer exponents to rational exponents provides an alternative notation for radicals.
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.
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AR.Math.Content.HSN.CN: : The Complex Number System
AR.Math.Content.HSN.CN.A: : Perform arithmetic operations with complex numbers
AR.Math.Content.HSN.CN.A.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.
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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.
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AR.Math.Content.HSN.CN.A.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.
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AR.Math.Content.HSN.CN.A.3: : Find the conjugate of a complex number. Use conjugates to find quotients of complex numbers. Use conjugates to find moduli.
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.
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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.
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AR.Math.Content.HSN.CN.B: : Represent complex numbers and their operations on the complex plane
AR.Math.Content.HSN.CN.B.4: : Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers). 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.
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AR.Math.Content.HSN.CN.B.5: : Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of geometrical representation for computation.
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.
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AR.Math.Content.HSN.CN.C: : Use complex numbers in polynomial identities and equations
AR.Math.Content.HSN.CN.C.7: : Solve quadratic equations with real coefficients that have real or complex solutions.
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
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
AR.Math.Content.HSN.VM: : Vector and Matrix Quantities
AR.Math.Content.HSN.VM.A: : Represent and model with vector quantities
AR.Math.Content.HSN.VM.A.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., v, |v|, ||v||, v).
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation.
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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.
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AR.Math.Content.HSN.VM.A.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.
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AR.Math.Content.HSN.VM.A.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.
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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.
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AR.Math.Content.HSN.VM.B: : Perform operations on vectors
AR.Math.Content.HSN.VM.B.4: : Add and subtract vectors. 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. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. Understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order. Perform vector subtraction component-wise.
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation.
5 Minute Preview
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.
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AR.Math.Content.HSN.VM.B.5: : Multiply a vector by a scalar. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; Perform scalar multiplication component-wise, e.g., as 𝘤(𝘷ₓ, 𝘷 subscript 𝘺) = (𝘤𝘷ₓ, 𝘤𝘷 subscript 𝘺). Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form and in matrix form.
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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.
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AR.Math.Content.HSN.VM.C: : Perform operations on matrices and use matrices in applications
AR.Math.Content.HSN.VM.C.7: : Multiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled).
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form and in matrix form.
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.
