Ohio - Mathematics: High School: Number and Quantity
Learning Standards | Adopted: 2017
This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.
OH.Math.HSN.RN: : The Real Number System
OH.Math.HSN.RN.A: : Extend the properties of exponents to rational exponents.
OH.Math.HSN.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.
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OH.Math.HSN.CN.A: : Perform arithmetic operations with complex numbers.
OH.Math.HSN.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.
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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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OH.Math.HSN.CN.2: : Use the relation ??²= ?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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OH.Math.HSN.CN.3: : Find the conjugate of a complex number; use conjugates to find magnitudes 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.
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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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OH.Math.HSN.CN.B: : Represent complex numbers and their operations on the complex plane.
OH.Math.HSN.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.
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OH.Math.HSN.CN.5: : Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this 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.
5 Minute Preview
OH.Math.HSN.CN.6: : Calculate the distance between numbers in the complex plane as the magnitude 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
OH.Math.HSN.CN.C: : Use complex numbers in polynomial identities and equations.
OH.Math.HSN.CN.7: : Solve quadratic equations with real coefficients that have 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
OH.Math.HSN.VM.A: : Represent and model with vector quantities.
OH.Math.HSN.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., 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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OH.Math.HSN.VM.B: : Perform operations on vectors.
OH.Math.HSN.VM.4: : Add and subtract vectors.
OH.Math.HSN.VM.4a: : 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
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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OH.Math.HSN.VM.4b: : Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
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
OH.Math.HSN.VM.4c: : 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, and 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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OH.Math.HSN.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 (x, y) form and in matrix form.
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OH.Math.HSN.VM.5a: : Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as ?? (???, ?? subscript ??) = (?????, ???? subscript ??).
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
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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OH.Math.HSN.VM.5b: : Compute the magnitude of a scalar multiple ???? using ||???? || = |??| ??. Compute the direction of ???? knowing that when | ?? | ?? ? 0, the direction of ???? is either along ?? (for ?? > 0) or against ?? (for ??
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
OH.Math.HSN.VM.C: : Perform operations on matrices, and use matrices in applications.
OH.Math.HSN.VM.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
OH.Math.HSN.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 (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.
