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Vectors: Quantities with Direction

Students explore vectors — quantities that carry both magnitude and direction — learning to break them into components, add them, and see why they are indispensable in physics, navigation, and engineering.

Grade 12Vectors50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Define a vector.
  • ✓Explain magnitude and direction.
  • ✓Break a vector into components.
  • ✓Add vectors.
Essential Question

“60 miles per hour” tells you speed — but not which way. How does adding direction turn a number into a vector, and why does that matter everywhere from flight paths to video games?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Vectors Explorer · Interactive

The Vectors Explorer

Project this and tap each idea. Have students learn what a vector is, how to break it into components, and how to add vectors.

➡️ Explore vectors — tap eachTry it

The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Speed vs. Velocity

5 min

“60 mph” vs. “60 mph north” — what’s the difference?

👩‍🏫 Teacher Moves

  • Contrast a number and a vector.
  • Ask what direction adds.
  • Set the goal: vectors.

🎒 Student Actions

  • Compare them.
  • See the difference.
  • Predict the idea.
2

I Do — Magnitude, Direction, Components

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Define magnitude and direction.
  • Break a vector into components.
  • Add two vectors.

🎒 Student Actions

  • Learn the parts.
  • Find components.
  • Add vectors.
3

We Do — Explore Together

13 min

Class uses the Vectors Explorer.

👩‍🏫 Teacher Moves

  • Tap each idea.
  • Find components of a vector.
  • Add vectors tip-to-tail.

🎒 Student Actions

  • Tap each idea.
  • Find components.
  • Add vectors.
4

You Do — On Your Own

12 min

Students work with vectors.

👩‍🏫 Teacher Moves

  • Find magnitude and components.
  • Add and subtract vectors.
  • Solve an applied problem.

🎒 Student Actions

  • Find components.
  • Add vectors.
  • Solve one.
5

Close — Close

5 min

One vector problem.

👩‍🏫 Teacher Moves

  • Give two vectors to add.
  • Find the resultant.
  • Hand out the exit ticket.

🎒 Student Actions

  • Add them.
  • Find the resultant.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics (High School: Precalculus).

CCSS
N-VM.1

Recognize vectors as quantities with magnitude and direction.

CCSS
N-VM.2

Find the components of a vector.

CCSS
N-VM.4

Add and subtract vectors.

CCSS
N-VM.3

Solve problems involving velocities and other vector quantities.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Vector arrow diagrams.
  • Sentence frame: “A vector has ___ and ___.”
  • Draw tip-to-tail addition.

Support & Access

IEP / 504
  • Focus on magnitude and direction.
  • Use arrow diagrams.
  • Add along axes first.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Add vectors using components.
  • Find the resultant’s angle.
  • Apply vectors to a force problem.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻The Vectors Explorer
  • 📐Graph paper + rulers
  • 🧮Calculators
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

vectora quantity with magnitude and directionscalara quantity with magnitude onlymagnitudethe length or size of a vectordirectionthe angle a vector pointscomponentthe x or y part of a vectorresultantthe sum of two or more vectorstip-to-taila method of adding vectorsvelocitya vector: speed with direction
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
What is the difference between a vector and a scalar?
A vector has both magnitude and direction; a scalar has magnitude only.
QUESTION 2
What are the components of a vector?
Its horizontal (x) and vertical (y) parts.
QUESTION 3
When you add two vectors, what is the result called?
The resultant.

Going deeper? Add by components.

Have students add vectors by breaking them into x- and y-components, summing each, and finding the resultant’s magnitude and direction. A printable vectors sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 VectorsFlip
Card 1
Term
Tap to flip →
Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 VectorsQuiz
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Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ VectorsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: component, direction, magnitude, resultant, scalar, tip-to-tail, vector, velocity
  1. the x or y part of a vector
  2. a quantity with magnitude only
  3. a method of adding vectors
  4. the length or size of a vector
  5. the sum of two or more vectors
  6. the angle a vector points
  7. a vector: speed with direction
  8. a quantity with magnitude and direction

Part B · Show what you learned

  1. What is the difference between a vector and a scalar?
  2. What are the components of a vector?
  3. When you add two vectors, what is the result called?
Answer key — Part A: 1) component · 2) scalar · 3) tip-to-tail · 4) magnitude · 5) resultant · 6) direction · 7) velocity · 8) vector
Part B: 1) A vector has both magnitude and direction; a scalar has magnitude only. 2) Its horizontal (x) and vertical (y) parts. 3) The resultant.