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- Mathematics: Mathematics I Honors

# Utah - Mathematics: Mathematics I Honors

## UT--Core Standards | Adopted: 2016

### N: : Number and Quantity

N.VM: : Vector and Matrix Quantities

(Framing Text): : Represent and model with vector 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., v, |v|, ||v||, v).

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.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

(Framing Text): : Perform operations on vectors.

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

N.VM.4.c: : 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

Vectors

N.VM.5: : Multiply a vector by a scalar.

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(vx , vy) = (cvx , cvy).

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Vectors

N.VM.5.b: : 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 vs (for c < 0).

Vectors

(Framing Text): : Perform operations on matrices and use matrices in applications.

N.VM.7: : Multiply matrices by scalars to produce new matrices, e.g., as when all of the pay-offs 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

Correlation last revised: 9/16/2020

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