Standard 3 : Represent and perform operations with vectors.



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General Information

Number: MA.912.NSO.3
Title: Represent and perform operations with vectors.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Number Sense and Operations

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.NSO.3.1: Apply appropriate notation and symbols to represent vectors in the plane as directed line segments. Determine the magnitude and direction of a vector in component form.
MA.912.NSO.3.2: Represent vectors in component form, linear form or trigonometric form. Rewrite vectors from one form to another.
MA.912.NSO.3.3: Solve mathematical and real-world problems involving velocity and other quantities that can be represented by vectors.
MA.912.NSO.3.4: Solve mathematical and real-world problems involving vectors in two dimensions using the dot product and vector projections.
MA.912.NSO.3.5: Solve mathematical and real-world problems involving vectors in three dimensions using the dot product and cross product.
MA.912.NSO.3.6: Multiply a vector by a scalar algebraically or graphically.
MA.912.NSO.3.7: Compute the magnitude and direction of a vector scalar multiple.
MA.912.NSO.3.8: Add and subtract vectors algebraically or graphically.
MA.912.NSO.3.9: Given the magnitude and direction of two or more vectors, determine the magnitude and direction of their sum.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Lesson Plans

Name Description
Olympic Snowboard Design:

This MEA requires students to design a custom snowboard for five Olympic athletes, taking into consideration how their height and weight affect the design elements of a snowboard. There are several factors that go into the design of a snowboard, and the students must use reasoning skills to determine which factors are more important and why, as well as what factors to eliminate or add based on the athlete's style and preferences. After the students have designed a board for each athlete, they will report their procedure and reasons for their decisions.

Linear Motion:

In this activity students will learn the relationship between:

  • Distance and displacement
  • Velocity and speed
  • Vectors and scalars
  • Acceleration

and demonstrate their knowledge through group presentations.

Vectors: Tip to Tail:

In this lesson students will learn the characteristics and appropriate use of vectors. They will find the magnitude and direction of vectors, they will add and subtract vectors and use an interactive website (such as Geogebra, phet, etc.) to practice what they have learned.

Perspectives Video: Expert

Name Description
Vectors and Oceanography:

Don't let the motion of the ocean cause a commotion! Learn how vectors describe ocean movement patterns.

Download the CPALMS Perspectives video student note taking guide.

Perspectives Video: Professional/Enthusiasts

Name Description
Practical Applications of Vectors in Military Air Traffic Control:

Senior Airman Jennifer Tisdale explains the role of vectors in management of flight traffic for the United States Air Force.

Download the CPALMS Perspectives video student note taking guide.

The Relationship between Wing Shape and Flight Performance: <p>Ken Blackburn, an aerospace engineer for the United States Air Force, describes the relationship between wing shape and flight performance.&nbsp;</p>
Wind Vector Arithmetic for Making a Flight Plan: <p>Math is important to help you get where you want to go in life, especially if you plan to fly there!</p>
Vectors and Flight Forces:

When you watch this video, your knowledge related to flight and physics will really take off!

Download the CPALMS Perspectives video student note taking guide.

KROS Pacific Ocean Kayak Journey: Kites, Rowing, Wind, and Navigation:

What’s your vector, Victor? Understanding math and wind helps get you where you want to go.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Download the CPALMS Perspectives video student note taking guide.

Perspectives Video: Teaching Ideas

Name Description
Balancing Forces on a Segway: <p>Feeling off-balance when it comes to motion? Try this idea.</p>
Hands-on Vectors: <p>Can't tell if it's heads or tails with vectors? Try these demos.</p>
KROS Pacific Ocean Kayak Journey: Kites, Geometry, and Vectors:

Set sail with this math teacher as he explains how kites were used for lessons in the classroom.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Download the CPALMS Perspectives video student note taking guide.

Text Resource

Name Description
Maths Goes to the Movies:

This informational text resource is intended to support reading in the content area. The text shows how math is used to create the life-like computer generated images seen in movies such as Jurassic Park and Lord of the Rings.



Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Perspectives Video: Expert

Title Description
Vectors and Oceanography:

Don't let the motion of the ocean cause a commotion! Learn how vectors describe ocean movement patterns.

Download the CPALMS Perspectives video student note taking guide.

Perspectives Video: Professional/Enthusiasts

Title Description
Wind Vector Arithmetic for Making a Flight Plan: <p>Math is important to help you get where you want to go in life, especially if you plan to fly there!</p>
Vectors and Flight Forces:

When you watch this video, your knowledge related to flight and physics will really take off!

Download the CPALMS Perspectives video student note taking guide.



Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Perspectives Video: Expert

Title Description
Vectors and Oceanography:

Don't let the motion of the ocean cause a commotion! Learn how vectors describe ocean movement patterns.

Download the CPALMS Perspectives video student note taking guide.

Perspectives Video: Professional/Enthusiasts

Title Description
Wind Vector Arithmetic for Making a Flight Plan: <p>Math is important to help you get where you want to go in life, especially if you plan to fly there!</p>
Vectors and Flight Forces:

When you watch this video, your knowledge related to flight and physics will really take off!

Download the CPALMS Perspectives video student note taking guide.