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Free Grade 3 Vector Basics Lessons

Free Grade 3 lessons for Vector Basics: 12 real questions with a full answer key and worked solutions. A vector has size and direction. Add vectors component by component; multiply by a number to scale. Magnitude = √(x² + y²).

Price

Free

Difficulty

Higher

Estimated time

35 min

Total marks

24

Learning objectives

Every objective is checkable, and each one maps to an activity and an assessment.

  • RememberIdentify vector basics

    Identify vector basics accurately in a familiar context.

    Assessed by: Exit ticket of four short items

  • UnderstandExplain vector basics

    Explain vector basics accurately in a familiar context.

    Assessed by: Exit ticket of four short items

  • ApplyCalculate vector basics

    Calculate vector basics accurately in a familiar context.

    Assessed by: Exit ticket of four short items

  • AnalyseCompare vector basics

    Compare vector basics accurately in a familiar context.

    Assessed by: Exit ticket of four short items

Prerequisites

Close these gaps first — each has its own free lesson, worksheet and quiz.

Calculus

How Vector Basics works

A vector has size and direction. Add vectors component by component; multiply by a number to scale. Magnitude = √(x² + y²).

Key wordsvectormagnitudecomponentscalar

12 practice questions

Easy to hard, 24 marks in total. Try them first, then open the answers.

  1. 1.a = (1, 5), b = (-1, 5). Find a + 4b.[1]
  2. 2.a = (-4, -3), b = (-3, -1). Find a + 3b.[1]
  3. 3.a = (6, -6), b = (4, -5). Find a + 2b.[1]
  4. 4.a = (-3, -3), b = (-2, 3). Find a + 3b.[1]
  5. 5.a = (-2, -5), b = (-5, 4). Find a + 4b.[2]
  6. 6.a = (0, -1), b = (-5, -3). Find a + 4b.[2]
  7. 7.a = (-6, 0), b = (-1, 4). Find a + 4b.[2]
  8. 8.a = (-4, 1), b = (1, 2). Find a + 2b.[2]
  9. 9.Find the magnitude of (0, -1) to 2 d.p.[3]
  10. 10.Find the magnitude of (6, 5) to 2 d.p.[3]
  11. 11.Find the magnitude of (-3, -4) to 2 d.p.[3]
  12. 12.Find the magnitude of (2, -3) to 2 d.p.[3]
Show answers and working

  1. 1. (-3, 25)

    4b = (-4, 20). Add components: (1 + -4, 5 + 20).

  2. 2. (-13, -6)

    3b = (-9, -3). Add components: (-4 + -9, -3 + -3).

  3. 3. (14, -16)

    2b = (8, -10). Add components: (6 + 8, -6 + -10).

  4. 4. (-9, 6)

    3b = (-6, 9). Add components: (-3 + -6, -3 + 9).

  5. 5. (-22, 11)

    4b = (-20, 16). Add components: (-2 + -20, -5 + 16).

  6. 6. (-20, -13)

    4b = (-20, -12). Add components: (0 + -20, -1 + -12).

  7. 7. (-10, 16)

    4b = (-4, 16). Add components: (-6 + -4, 0 + 16).

  8. 8. (-2, 5)

    2b = (2, 4). Add components: (-4 + 2, 1 + 4).

  9. 9. 1

    |v| = √(x² + y²) = √(0 + 1). = 1.

  10. 10. 7.81

    |v| = √(x² + y²) = √(36 + 25). = 7.81.

  11. 11. 5

    |v| = √(x² + y²) = √(9 + 16). = 5.

  12. 12. 3.61

    |v| = √(x² + y²) = √(4 + 9). = 3.61.

Worked examples

Easy example

a = (2, 5), b = (6, 1). Find a + 3b.

  1. 3b = (18, 3).
  2. Add components: (2 + 18, 5 + 3).
  3. Answer: (20, 8)
Medium example

a = (-3, 4), b = (1, -1). Find a + 4b.

  1. 4b = (4, -4).
  2. Add components: (-3 + 4, 4 + -4).
  3. Answer: (1, 0)
Hard example

Find the magnitude of (-3, -6) to 2 d.p.

  1. |v| = √(x² + y²) = √(9 + 36).
  2. = 6.71.
  3. Answer: 6.71

Interactive practice

Free, no account required — answer on screen or print it.

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Common mistakes

What learners typically get wrong, and how to fix it.

  • Adds x of one vector to y of the other.

    Correction: Add x with x, y with y.

  • Forgets that a negative component means the opposite direction.

    Correction: Draw the vector to check.

Teacher tips

  • · Draw vectors on squared paper end to end.

Parent tips

  • · Give directions as '3 steps right, 2 steps up'.

Real-life applications

  • · Navigation, forces in physics, game movement.

Assessment objectives

How mastery is evidenced, and which standards it maps to.

AQA AQA-123.1 — Mapped statement covering Vector Basics.FBISE FBI-655.2 — Mapped statement covering Vector Basics.

Every free resource for Vector Basics

One concept, one ecosystem — all of it free.

Free Vector Basics worksheets
Free Vector Basics quizzes
Free Vector Basics flashcards
Free Vector Basics lesson plans

Goes deeper

The entities below this one, each with the same complete free resource set.

Vector Notation
Adding Vectors
Scalar Multiples
Magnitude of a Vector

Sibling concepts

Vector Geometry

Related concepts

Lateral links, including across subjects.

Vector Geometry
Algebra

Next topics

Vector Geometry
Number Sense
Algebra
Geometry

All free formats for this concept

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Frequently asked

Is this Grade 3 Vector Basics lesson really free?
Yes. Every lessons on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
What should a learner already know before this?
Start with Calculus. Each one has its own free lesson, worksheet and quiz.
How is the lesson sequenced?
Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
What comes next after Vector Basics?
Move on to Vector Geometry, Number Sense, Algebra, Geometry, which build directly on this idea.

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