Free Grade 3 Working with Adding Vectors Essentials Flashcards
Free Grade 3 flashcards for Working with Adding Vectors Essentials: 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).
Free
Foundation
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with adding vectors essentials
Explain working with adding vectors essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with adding vectors essentials
Calculate working with adding vectors essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with adding vectors essentials
Compare working with adding vectors essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with adding vectors essentials
Justify working with adding vectors essentials 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.
How Working with Adding Vectors Essentials works
A vector has size and direction. Add vectors component by component; multiply by a number to scale. Magnitude = √(x² + y²).
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.a = (6, -2), b = (-3, -6). Find a + 2b.[1]
- 2.a = (4, -3), b = (1, 1). Find a + 4b.[1]
- 3.a = (0, -5), b = (1, 0). Find a + 2b.[1]
- 4.a = (5, 0), b = (-1, 3). Find a + 4b.[1]
- 5.a = (6, 3), b = (-5, -4). Find a + 4b.[2]
- 6.a = (-3, -6), b = (-5, -1). Find a + 3b.[2]
- 7.a = (-2, -5), b = (2, -1). Find a + 3b.[2]
- 8.a = (-3, 5), b = (-6, 4). Find a + 2b.[2]
- 9.Find the magnitude of (3, -1) to 2 d.p.[3]
- 10.Find the magnitude of (4, 6) to 2 d.p.[3]
- 11.Find the magnitude of (-6, 3) to 2 d.p.[3]
- 12.Find the magnitude of (-6, 6) to 2 d.p.[3]
Show answers and working
1. (0, -14)
2b = (-6, -12). Add components: (6 + -6, -2 + -12).
2. (8, 1)
4b = (4, 4). Add components: (4 + 4, -3 + 4).
3. (2, -5)
2b = (2, 0). Add components: (0 + 2, -5 + 0).
4. (1, 12)
4b = (-4, 12). Add components: (5 + -4, 0 + 12).
5. (-14, -13)
4b = (-20, -16). Add components: (6 + -20, 3 + -16).
6. (-18, -9)
3b = (-15, -3). Add components: (-3 + -15, -6 + -3).
7. (4, -8)
3b = (6, -3). Add components: (-2 + 6, -5 + -3).
8. (-15, 13)
2b = (-12, 8). Add components: (-3 + -12, 5 + 8).
9. 3.16
|v| = √(x² + y²) = √(9 + 1). = 3.16.
10. 7.21
|v| = √(x² + y²) = √(16 + 36). = 7.21.
11. 6.71
|v| = √(x² + y²) = √(36 + 9). = 6.71.
12. 8.49
|v| = √(x² + y²) = √(36 + 36). = 8.49.
Worked examples
a = (2, 5), b = (-4, -2). Find a + 4b.
- 4b = (-16, -8).
- Add components: (2 + -16, 5 + -8).
- Answer: (-14, -3)
a = (5, 6), b = (-5, -4). Find a + 4b.
- 4b = (-20, -16).
- Add components: (5 + -20, 6 + -16).
- Answer: (-15, -10)
Find the magnitude of (-5, -2) to 2 d.p.
- |v| = √(x² + y²) = √(25 + 4).
- = 5.39.
- Answer: 5.39
Interactive practice
Free, no account required — answer on screen or print it.
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.
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Frequently asked
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- Yes. Every flashcards 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 Introducing Adding Vectors. Each one has its own free lesson, worksheet and quiz.
- How is the flashcards 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 Working with Adding Vectors Essentials?
- Move on to Working with Adding Vectors Techniques, Working with Adding Vectors Word Problems, Working with Adding Vectors Common Errors, Introducing Adding Vectors, which build directly on this idea.
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