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GSE Precalculus Honors

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U7E3: Distance and Midpoints in the Complex Plane

Mr. Montgomery

Monday, April 27

Never, ever give up.

Assessment:

Unit 7 Test: Due Friday, May 22nd

Complete in Edgenuity (Underclassmen)

Remind

2-A: @4b6k89

4-A: @7afh82

3-B: @28b3b8

4-B: @ggd32eb

For basic class information including join codes, go to my public information page and find your class from the drop-down menu in the upper right-hand corner:

http://mybackpack.apsk12.org/

http://tinyAPS.com/?mr-montgomery

Standard(s)

G.SRT.7*

GSE Pre-Calculus Honors

MGSE9-12.G.SRT.7*

Explain and use the relationship between the sine and cosine of complementary angles.

*GSE Geometry

Unpacking N.CN.6

  • How is the distance formula applied in the complex plane?

  • How is the midpoint formula applied in the complex plane?

N.VM.1

GSE Pre-Calculus Honors

MGSE9-12.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).

Unpacking N.CN.6

  • How is the distance formula applied in the complex plane?

  • How is the midpoint formula applied in the complex plane?

N.VM.2

GSE Pre-Calculus Honors

MGSE9-12.N.VM.2

Find the components of a vector by subtracting the coordinates of an initial point from the

coordinates of a terminal point.

Unpacking N.CN.6

  • How is the distance formula applied in the complex plane?

  • How is the midpoint formula applied in the complex plane?

N.VM.4a

GSE Pre-Calculus Honors

MGSE9-12.N.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.

Unpacking N.CN.6

  • How is the distance formula applied in the complex plane?

  • How is the midpoint formula applied in the complex plane?

N.VM.4b

GSE Pre-Calculus Honors

MGSE9-12.N.VM.4b

Given two vectors in magnitude and direction form, determine the magnitude and

direction of their sum.

Unpacking N.CN.6

  • How is the distance formula applied in the complex plane?

  • How is the midpoint formula applied in the complex plane?

N.VM.c

GSE Pre-Calculus Honors

MGSE9-12.N.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.

Unpacking N.CN.6

  • How is the distance formula applied in the complex plane?

  • How is the midpoint formula applied in the complex plane?

Unpacking

Standards

Unpacking the Standards

  • SRT.7 - This is a standard from GSE Geometry that we are maintaining. Triangle ABC has C=90. How does sinA relate to cosB? To sin B?
  • N.VM.1-What does it mean for a vector to have magnitude and direction?
  • N.VM.2-How does a vector relate to a right triangle?
  • N.VM.4a-Why is the magnitude of a sum not equal to the sum of magnitudes?
  • N.VM.4b-How do we add vectors in magnitude/direction form?
  • N.VM.4c-How is vector subtraction similar to integer subtraction?

Instructional Objective

Instructional Objective(s)

#1

Instructional Objective #1 (N.VM.2)

SWBAT subtract the coordinates of an initial point from the coordinates of a terminal point IOT find the components of a vector.

#2

Instructional Objective #2 (N.VM.4a)

SWBAT Use end-to-end construction, component-wise representation, and the parallelogram rule IOT add vectors.

#3

Instructional Objective #3 (N.VM.4b)

SWBAT use the magnitude and direction form of two vectors IOT determine the magnitude and direction of their sum.

#4

Instructional Objective #4 (N.VM.4c)

SWBAT use the additive inverse of a vector and vector addition IOT solve vector subtraction problems.

Connections

What is a vector?

What is a vector?

Scalar

vs.

Vector

Scalar and Vector Measurements - A simple tutorial answering: what are they?

Vectors

and

Scalars

Vectors and Scalars (Physics)

Teaching & Learning

(I Do)

Every Monday at 9:30 AM , join us on Zoom for a live video conference. You can get an overview of the current lesson in Edgenuity, ask questions about concepts or problems that you need help with or just check-in. This recurring invite has also been posted in the Google Calendar for your class. If you miss, don't worry. The video will be posted in Google Classroom immediately afterward.

Join Zoom Meeting

https://zoom.us/j/95101455457?pwd=SW1PVE5qaUdjVThjU1g1Q0NvSWJXZz09

Meeting ID: 951 0145 5457

Password: 6qEyRk

Engagement

(We Do)

Desmos: Visualizing the Imaginary

https://student.desmos.com/?prepopulateCode=ng745k

Practice (You Do)

Practice

(You Do)

Edgenuity (U7L3): Distance and Midpoints in the Complex Plane

  • Warm-up

  • Instruction

  • Summary

  • Assignment

  • Quiz
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